Chapter 5 Definite Integral Topics Review
•Download as PPTX, PDF•
0 likes•849 views
This document discusses several topics in calculus including RAM theory for approximating functions, computing definite integrals using formulas and a TI-89 calculator, properties of definite integrals like additivity and the mean value theorem, the fundamental theorem of calculus in two parts, and the trapezoidal rule for approximating definite integrals which overestimates for increasing functions and underestimates for decreasing functions.
Report
Share
Report
Share
Recommended
Doc 20180130-wa0002
This document is a model exam paper for a data communication and networks course. It contains 5 questions testing knowledge of:
1) The OSI model layers and protocols, differences between IPv4 and IPv6.
2) Encoding techniques used in data transmission including Manchester encoding and modulation methods.
3) How data is broken into frames for transmission and the selective reject ARQ protocol.
4) Using time division multiplexing and frequency division multiplexing to transmit multiple telephone channels.
5) Differences between circuit switching and packet switching, comparing OSI layer 2 to IEEE 802 layer 2, functions of hubs and switches, transmission media for Ethernet, and Fast Ethernet specifications.
Parallel algorithms
Parallel algorithms can be specifically written to execute on computers with multiple processing units. When designing parallel algorithms, the cost of communication and number of processors must be considered. Parallel algorithms are often modeled using the parallel random-access machine (PRAM) model, which simplifies issues like synchronization and communication. Common parallel algorithms include matrix multiplication, merge sort, and shortest path algorithms like Floyd's algorithm.
Kashif lab no 3
This document discusses translating and rotating frames in 3D space in MATLAB. It defines a universal coordinate system {U} and another frame {A}. Commands like transl() and trplot() are used to translate and rotate frames and plot them in 3D. Transl() translates a frame by moving its origin to specified coordinates, while trplot() plots coordinate frames and allows setting options like axis dimensions, colors, and view parameters.
Information and network security 35 the chinese remainder theorem
In number theory, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.
facility layout paper
This document summarizes a survey paper on using intelligent techniques like expert systems, fuzzy logic, genetic algorithms, and neural networks to solve facility layout problems (FLP). FLP involves assigning facilities to locations to minimize costs associated with facility interactions. The paper discusses conventional algorithms and intelligent techniques for FLP, including optimal algorithms like branch and bound, and suboptimal algorithms like construction and improvement heuristics.
1 sollins algorithm
This document describes Sollin's algorithm, also known as Boruvka's algorithm, for finding a minimum spanning tree (MST) of a connected, edge-weighted undirected graph. Sollin's algorithm is a greedy algorithm that works by repeatedly contracting edges of minimum weight to form subgraphs until a single vertex remains, resulting in an MST. The algorithm proceeds by first highlighting the cheapest outgoing edge for each vertex, then contracting edges to form subgraphs and repeating on each subgraph until an MST is produced. An example applying the algorithm to a graph is provided.
CAD: introduction to floorplanning
This document discusses floorplanning, which is an important first step in physical design. There are two main approaches to floorplanning: simulated annealing and analytical formulation. Popular representations of geometric relationships used in floorplanning are normalized Polish expression, B*-tree, and sequence pair. The goal of floorplanning is to optimize metrics like area and wire length. Slicing floorplans can be represented by binary trees, while non-slicing floorplans use constraint graphs.
유한요소법(FEM)을 이용한 구조해석
This document discusses different numerical analysis methods for structural analysis, including finite element methods (FEM). It covers static and dynamic analysis approaches, as well as implicit and explicit solution procedures. It also summarizes characteristics of direct and iterative solvers for implicit methods, and techniques for parallelizing analysis solutions. Direct solvers require matrix factorization while iterative solvers use matrix-vector multiplications, which can be efficiently parallelized through domain decomposition and minimizing interface degrees of freedom.
Recommended
Doc 20180130-wa0002
This document is a model exam paper for a data communication and networks course. It contains 5 questions testing knowledge of:
1) The OSI model layers and protocols, differences between IPv4 and IPv6.
2) Encoding techniques used in data transmission including Manchester encoding and modulation methods.
3) How data is broken into frames for transmission and the selective reject ARQ protocol.
4) Using time division multiplexing and frequency division multiplexing to transmit multiple telephone channels.
5) Differences between circuit switching and packet switching, comparing OSI layer 2 to IEEE 802 layer 2, functions of hubs and switches, transmission media for Ethernet, and Fast Ethernet specifications.
Parallel algorithms
Parallel algorithms can be specifically written to execute on computers with multiple processing units. When designing parallel algorithms, the cost of communication and number of processors must be considered. Parallel algorithms are often modeled using the parallel random-access machine (PRAM) model, which simplifies issues like synchronization and communication. Common parallel algorithms include matrix multiplication, merge sort, and shortest path algorithms like Floyd's algorithm.
Kashif lab no 3
This document discusses translating and rotating frames in 3D space in MATLAB. It defines a universal coordinate system {U} and another frame {A}. Commands like transl() and trplot() are used to translate and rotate frames and plot them in 3D. Transl() translates a frame by moving its origin to specified coordinates, while trplot() plots coordinate frames and allows setting options like axis dimensions, colors, and view parameters.
Information and network security 35 the chinese remainder theorem
In number theory, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.
facility layout paper
This document summarizes a survey paper on using intelligent techniques like expert systems, fuzzy logic, genetic algorithms, and neural networks to solve facility layout problems (FLP). FLP involves assigning facilities to locations to minimize costs associated with facility interactions. The paper discusses conventional algorithms and intelligent techniques for FLP, including optimal algorithms like branch and bound, and suboptimal algorithms like construction and improvement heuristics.
1 sollins algorithm
This document describes Sollin's algorithm, also known as Boruvka's algorithm, for finding a minimum spanning tree (MST) of a connected, edge-weighted undirected graph. Sollin's algorithm is a greedy algorithm that works by repeatedly contracting edges of minimum weight to form subgraphs until a single vertex remains, resulting in an MST. The algorithm proceeds by first highlighting the cheapest outgoing edge for each vertex, then contracting edges to form subgraphs and repeating on each subgraph until an MST is produced. An example applying the algorithm to a graph is provided.
CAD: introduction to floorplanning
This document discusses floorplanning, which is an important first step in physical design. There are two main approaches to floorplanning: simulated annealing and analytical formulation. Popular representations of geometric relationships used in floorplanning are normalized Polish expression, B*-tree, and sequence pair. The goal of floorplanning is to optimize metrics like area and wire length. Slicing floorplans can be represented by binary trees, while non-slicing floorplans use constraint graphs.
유한요소법(FEM)을 이용한 구조해석
This document discusses different numerical analysis methods for structural analysis, including finite element methods (FEM). It covers static and dynamic analysis approaches, as well as implicit and explicit solution procedures. It also summarizes characteristics of direct and iterative solvers for implicit methods, and techniques for parallelizing analysis solutions. Direct solvers require matrix factorization while iterative solvers use matrix-vector multiplications, which can be efficiently parallelized through domain decomposition and minimizing interface degrees of freedom.
Parallel algorithm in linear algebra
This document discusses parallel algorithms for linear algebra operations. It begins by defining parallel algorithms and linear algebra. It then describes dense matrix algorithms like matrix-vector multiplication and solving systems of linear equations using Gaussian elimination. It presents the serial algorithms for these operations and discusses parallel implementations using 1D row-wise partitioning among processes. It analyzes the computation and communication costs of the parallel Gaussian elimination algorithm.
Merge Sort
Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are:
1. Divide the array into equal halves until reaching base cases of arrays with one element.
2. Recursively sort the left and right halves by repeating the divide step.
3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array.
Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory
Dynamic programming prasintation eaisy
Dynamic programming is a technique for solving complex problems by breaking them down into simpler sub-problems. It involves storing solutions to sub-problems for later use, avoiding recomputing them. Examples where it can be applied include matrix chain multiplication and calculating Fibonacci numbers. For matrix chains, dynamic programming finds the optimal order for multiplying matrices with minimum computations. For Fibonacci numbers, it calculates values in linear time by storing previous solutions rather than exponentially recomputing them through recursion.
Building Intuitions about Machine Learning and Deep Learning
This document provides an overview of machine learning and different types of data-oriented learning algorithms. It discusses how machine learning algorithms find mathematical descriptions to model data in a way that fits observations. Supervised learning techniques like linear regression, support vector machines, boosted trees, and neural networks are used to discover patterns in labeled data to define decision boundaries between classes. Neural networks can learn complex decision boundaries useful for problems that can't be solved by defining simple linear boundaries. The document explains how neural networks work by minimizing the cost or penalty between the predicted and actual classifications of data points to determine the optimal decision boundary. Evaluation metrics like accuracy, precision and recall are also important to consider depending on the learning problem.
k10790 nilesh prajapati control me 6th sem
This document discusses root locus analysis, which graphically shows how the closed-loop poles of a system change with a parameter. It outlines the general steps for drawing a root locus, which include determining open-loop poles and zeros, drawing the pole-zero plot, calculating asymptotes and breakaway points, and sketching the overall root locus. The document also briefly mentions that root locus analysis can provide insights into a system's stability and performance and be used to aid control system design.
Matrix multiplication
This document discusses parallel matrix multiplication algorithms on the Parallel Random Access Machine (PRAM) model. It describes algorithms that multiply matrices using different numbers of processors, from n3 processors down to n2 processors. The time complexity is O(log n) in all cases, while the processor and work complexities vary based on the number of processors. Block matrix multiplication is also introduced as a more efficient approach for shared memory machines by improving data locality.
Optimal Chain Matrix Multiplication Big Data Perspective
How matrix multiplication in database. Larger set matrix multiplication in map reduce based hadoop framework.
Design and analysis of algorithms - Abstract View
This document discusses the design and analysis of algorithms. It introduces algorithms and defines them as sets of rules to solve computational problems. It emphasizes the importance of both designing algorithms through techniques like divide-and-conquer as well as analyzing their performance through complexity analysis. The document provides examples of analyzing worst-case, best-case, and average-case runtime and uses an example algorithm to find the largest number in an array to demonstrate space and time analysis methods.
Algorithm analysis
This document discusses algorithm analysis and complexity. It explains that algorithm analysis aims to predict performance by analyzing time and space complexity as functions of input size. Time complexity indicates how fast an algorithm runs, while space complexity refers to memory usage. Common complexities include constant, logarithmic, linear, linearithmic, polynomial, and exponential orders of growth. The analysis framework focuses on analyzing asymptotic order of growth for running time and memory usage as input size increases.
Directed Acyclic Graph Representation of basic blocks
The document summarizes a seminar presentation on using directed acyclic graphs (DAGs) to represent and optimize basic blocks in compiler design. DAGs can be constructed from three-address code to identify common subexpressions and eliminate redundant computations. Rules for DAG construction include creating a node only if it does not already exist, representing identifiers as leaf nodes and operators as interior nodes. DAGs allow optimizations like common subexpression elimination and dead code elimination to improve performance of local optimizations on basic blocks. Examples show how DAGs identify common subexpressions and avoid recomputing the same values.
Unit 7 dynamic programming
The document introduces dynamic programming as a technique for making optimal decisions over multiple time periods. It discusses how dynamic programming breaks large problems into smaller subproblems and solves each in order, working backwards from the last period. The document provides an example of using dynamic programming to find the shortest route between two cities by breaking the problem into stages and working backwards from the final destination.
PRAM algorithms from deepika
The document summarizes a seminar presentation on parallel random access machine (PRAM) algorithms. It discusses the computational model of PRAM, algorithms like merging and sorting using odd-even merge. It also covers applications such as computing convex hulls and mentions that PRAM is a source of inspiration for parallel algorithms.
Parallel algorithms
Parallel algorithms can be specifically written to execute on computers with multiple processors. They are often modeled using parallel random-access machines (PRAM) which allow for an unlimited number of processors that can access shared memory uniformly. Common parallel algorithms include matrix multiplication, merge sort, and shortest path algorithms like Floyd's algorithm.
Dynamic programming class 16
Dynamic programming is an algorithm design technique that solves problems by breaking them down into smaller overlapping subproblems and storing the results of already solved subproblems, rather than recomputing them. It is applicable to problems exhibiting optimal substructure and overlapping subproblems. The key steps are to define the optimal substructure, recursively define the optimal solution value, compute values bottom-up, and optionally reconstruct the optimal solution. Common examples that can be solved with dynamic programming include knapsack, shortest paths, matrix chain multiplication, and longest common subsequence.
Root locus techniques
This document discusses the root locus technique for analyzing control systems. It describes the 7 step procedure for constructing a root locus plot: (1) locate poles and zeros, (2) determine the real axis path, (3) find asymptote angles, (4) identify breakaway points, (5) calculate departure and arrival angles, (6) find imaginary axis intersections, (7) sketch the root locus using test points. The root locus technique allows observing how closed-loop poles move in the s-plane as the system gain varies, helping to achieve desired performance.
Parallel searching
This document discusses four parallel searching algorithms: Alpha-Beta search, Jamboree search, Depth-First search, and PVS search. Alpha-Beta search prunes unpromising branches without missing better moves. Jamboree search parallelizes the testing of child nodes. Depth-First search recursively explores branches until reaching a dead end, then backtracks. PVS search splits the search tree across processors, backing up values in parallel at each level. However, load imbalance can occur if some branches are much larger than others.
Root locus method
This document summarizes the key rules and concepts for constructing root locus diagrams. It lists the names and student IDs of 5 group members working on a control systems engineering project. The document then explains that the root locus shows how the roots of the characteristic equation change in the s-plane as the system parameter K varies from 0 to infinity, and can be used to analyze a system's stability and transient response. It proceeds to describe 8 rules for constructing root loci, including rules about the locus originating from open-loop poles, terminating at open-loop zeros or infinity, determining breakaway points, and calculating the angle of departure.
Towards the Design of Heuristics by Means of Self-Assembly
This document proposes using self-assembly to design heuristics for combinatorial optimization problems. It describes how low-level heuristics can be modeled as Wang tiles that self-assemble into "execution threads" via local interactions. Analysis of the best execution threads reveals common combinations of heuristics. These common execution threads are shown to be more reliable than random threads on a travelling salesman problem instance. The approach could be improved by reducing stochasticity and testing on other problems.
Detection and identification of cheaters in (t, n) secret
The document outlines a system for detecting and identifying cheaters in a (t,n) secret sharing scheme. It discusses the problem definition, related work, proposed system features and architecture. The system architecture uses a Thien-Lin secret sharing scheme and includes initialization, construction, and reconstruction/verification phases. It also provides use cases, state transitions, implementation plans with a Gantt chart and cost model.
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
The document summarizes three polynomial time algorithms for scheduling directed acyclic graph (DAG) tasks on multiprocessor systems without considering communication costs between tasks. The algorithms are: 1) Scheduling in-forests/out-forests task graphs which prioritizes tasks by level, 2) Scheduling interval ordered tasks which prioritizes by number of successors, and 3) Two-processor scheduling which assigns priorities lexicographically based on successors' labels. All algorithms assign the highest priority ready task to idle processors. Examples are provided for each algorithm.
Definite Integral Review
This document provides an overview of key concepts in calculus including the definite integral, properties of definite integrals, the Mean Value Theorem for Integrals, the Average Value Theorem, the Fundamental Theorem of Calculus parts 1 and 2, and the Trapezoidal Rule for approximating definite integrals. It defines integrals, discusses how to evaluate them on a TI-84 calculator, and lists properties such as additivity, constant multiples, and order of integration. It also introduces concepts like finding the average value of a function over an interval using the integral, and relating the derivative of an integral to the original function.
Integral (area)
The document discusses using definite integrals to find the area under a curve. It provides examples of finding the area of various shaded regions bounded by curves and the x-axis using the formula: area = ∫f(x)dx from x=a to x=b. It also shows how to find the coordinates of points where two curves intersect in order to divide the region into multiple areas and calculate them separately.
More Related Content
What's hot
Parallel algorithm in linear algebra
This document discusses parallel algorithms for linear algebra operations. It begins by defining parallel algorithms and linear algebra. It then describes dense matrix algorithms like matrix-vector multiplication and solving systems of linear equations using Gaussian elimination. It presents the serial algorithms for these operations and discusses parallel implementations using 1D row-wise partitioning among processes. It analyzes the computation and communication costs of the parallel Gaussian elimination algorithm.
Merge Sort
Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are:
1. Divide the array into equal halves until reaching base cases of arrays with one element.
2. Recursively sort the left and right halves by repeating the divide step.
3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array.
Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory
Dynamic programming prasintation eaisy
Dynamic programming is a technique for solving complex problems by breaking them down into simpler sub-problems. It involves storing solutions to sub-problems for later use, avoiding recomputing them. Examples where it can be applied include matrix chain multiplication and calculating Fibonacci numbers. For matrix chains, dynamic programming finds the optimal order for multiplying matrices with minimum computations. For Fibonacci numbers, it calculates values in linear time by storing previous solutions rather than exponentially recomputing them through recursion.
Building Intuitions about Machine Learning and Deep Learning
This document provides an overview of machine learning and different types of data-oriented learning algorithms. It discusses how machine learning algorithms find mathematical descriptions to model data in a way that fits observations. Supervised learning techniques like linear regression, support vector machines, boosted trees, and neural networks are used to discover patterns in labeled data to define decision boundaries between classes. Neural networks can learn complex decision boundaries useful for problems that can't be solved by defining simple linear boundaries. The document explains how neural networks work by minimizing the cost or penalty between the predicted and actual classifications of data points to determine the optimal decision boundary. Evaluation metrics like accuracy, precision and recall are also important to consider depending on the learning problem.
k10790 nilesh prajapati control me 6th sem
This document discusses root locus analysis, which graphically shows how the closed-loop poles of a system change with a parameter. It outlines the general steps for drawing a root locus, which include determining open-loop poles and zeros, drawing the pole-zero plot, calculating asymptotes and breakaway points, and sketching the overall root locus. The document also briefly mentions that root locus analysis can provide insights into a system's stability and performance and be used to aid control system design.
Matrix multiplication
This document discusses parallel matrix multiplication algorithms on the Parallel Random Access Machine (PRAM) model. It describes algorithms that multiply matrices using different numbers of processors, from n3 processors down to n2 processors. The time complexity is O(log n) in all cases, while the processor and work complexities vary based on the number of processors. Block matrix multiplication is also introduced as a more efficient approach for shared memory machines by improving data locality.
Optimal Chain Matrix Multiplication Big Data Perspective
How matrix multiplication in database. Larger set matrix multiplication in map reduce based hadoop framework.
Design and analysis of algorithms - Abstract View
This document discusses the design and analysis of algorithms. It introduces algorithms and defines them as sets of rules to solve computational problems. It emphasizes the importance of both designing algorithms through techniques like divide-and-conquer as well as analyzing their performance through complexity analysis. The document provides examples of analyzing worst-case, best-case, and average-case runtime and uses an example algorithm to find the largest number in an array to demonstrate space and time analysis methods.
Algorithm analysis
This document discusses algorithm analysis and complexity. It explains that algorithm analysis aims to predict performance by analyzing time and space complexity as functions of input size. Time complexity indicates how fast an algorithm runs, while space complexity refers to memory usage. Common complexities include constant, logarithmic, linear, linearithmic, polynomial, and exponential orders of growth. The analysis framework focuses on analyzing asymptotic order of growth for running time and memory usage as input size increases.
Directed Acyclic Graph Representation of basic blocks
The document summarizes a seminar presentation on using directed acyclic graphs (DAGs) to represent and optimize basic blocks in compiler design. DAGs can be constructed from three-address code to identify common subexpressions and eliminate redundant computations. Rules for DAG construction include creating a node only if it does not already exist, representing identifiers as leaf nodes and operators as interior nodes. DAGs allow optimizations like common subexpression elimination and dead code elimination to improve performance of local optimizations on basic blocks. Examples show how DAGs identify common subexpressions and avoid recomputing the same values.
Unit 7 dynamic programming
The document introduces dynamic programming as a technique for making optimal decisions over multiple time periods. It discusses how dynamic programming breaks large problems into smaller subproblems and solves each in order, working backwards from the last period. The document provides an example of using dynamic programming to find the shortest route between two cities by breaking the problem into stages and working backwards from the final destination.
PRAM algorithms from deepika
The document summarizes a seminar presentation on parallel random access machine (PRAM) algorithms. It discusses the computational model of PRAM, algorithms like merging and sorting using odd-even merge. It also covers applications such as computing convex hulls and mentions that PRAM is a source of inspiration for parallel algorithms.
Parallel algorithms
Parallel algorithms can be specifically written to execute on computers with multiple processors. They are often modeled using parallel random-access machines (PRAM) which allow for an unlimited number of processors that can access shared memory uniformly. Common parallel algorithms include matrix multiplication, merge sort, and shortest path algorithms like Floyd's algorithm.
Dynamic programming class 16
Dynamic programming is an algorithm design technique that solves problems by breaking them down into smaller overlapping subproblems and storing the results of already solved subproblems, rather than recomputing them. It is applicable to problems exhibiting optimal substructure and overlapping subproblems. The key steps are to define the optimal substructure, recursively define the optimal solution value, compute values bottom-up, and optionally reconstruct the optimal solution. Common examples that can be solved with dynamic programming include knapsack, shortest paths, matrix chain multiplication, and longest common subsequence.
Root locus techniques
This document discusses the root locus technique for analyzing control systems. It describes the 7 step procedure for constructing a root locus plot: (1) locate poles and zeros, (2) determine the real axis path, (3) find asymptote angles, (4) identify breakaway points, (5) calculate departure and arrival angles, (6) find imaginary axis intersections, (7) sketch the root locus using test points. The root locus technique allows observing how closed-loop poles move in the s-plane as the system gain varies, helping to achieve desired performance.
Parallel searching
This document discusses four parallel searching algorithms: Alpha-Beta search, Jamboree search, Depth-First search, and PVS search. Alpha-Beta search prunes unpromising branches without missing better moves. Jamboree search parallelizes the testing of child nodes. Depth-First search recursively explores branches until reaching a dead end, then backtracks. PVS search splits the search tree across processors, backing up values in parallel at each level. However, load imbalance can occur if some branches are much larger than others.
Root locus method
This document summarizes the key rules and concepts for constructing root locus diagrams. It lists the names and student IDs of 5 group members working on a control systems engineering project. The document then explains that the root locus shows how the roots of the characteristic equation change in the s-plane as the system parameter K varies from 0 to infinity, and can be used to analyze a system's stability and transient response. It proceeds to describe 8 rules for constructing root loci, including rules about the locus originating from open-loop poles, terminating at open-loop zeros or infinity, determining breakaway points, and calculating the angle of departure.
Towards the Design of Heuristics by Means of Self-Assembly
This document proposes using self-assembly to design heuristics for combinatorial optimization problems. It describes how low-level heuristics can be modeled as Wang tiles that self-assemble into "execution threads" via local interactions. Analysis of the best execution threads reveals common combinations of heuristics. These common execution threads are shown to be more reliable than random threads on a travelling salesman problem instance. The approach could be improved by reducing stochasticity and testing on other problems.
Detection and identification of cheaters in (t, n) secret
The document outlines a system for detecting and identifying cheaters in a (t,n) secret sharing scheme. It discusses the problem definition, related work, proposed system features and architecture. The system architecture uses a Thien-Lin secret sharing scheme and includes initialization, construction, and reconstruction/verification phases. It also provides use cases, state transitions, implementation plans with a Gantt chart and cost model.
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
The document summarizes three polynomial time algorithms for scheduling directed acyclic graph (DAG) tasks on multiprocessor systems without considering communication costs between tasks. The algorithms are: 1) Scheduling in-forests/out-forests task graphs which prioritizes tasks by level, 2) Scheduling interval ordered tasks which prioritizes by number of successors, and 3) Two-processor scheduling which assigns priorities lexicographically based on successors' labels. All algorithms assign the highest priority ready task to idle processors. Examples are provided for each algorithm.
What's hot (20)
Building Intuitions about Machine Learning and Deep Learning
Building Intuitions about Machine Learning and Deep Learning
Optimal Chain Matrix Multiplication Big Data Perspective
Optimal Chain Matrix Multiplication Big Data Perspective
Directed Acyclic Graph Representation of basic blocks
Directed Acyclic Graph Representation of basic blocks
Towards the Design of Heuristics by Means of Self-Assembly
Towards the Design of Heuristics by Means of Self-Assembly
Detection and identification of cheaters in (t, n) secret
Detection and identification of cheaters in (t, n) secret
Viewers also liked
Definite Integral Review
This document provides an overview of key concepts in calculus including the definite integral, properties of definite integrals, the Mean Value Theorem for Integrals, the Average Value Theorem, the Fundamental Theorem of Calculus parts 1 and 2, and the Trapezoidal Rule for approximating definite integrals. It defines integrals, discusses how to evaluate them on a TI-84 calculator, and lists properties such as additivity, constant multiples, and order of integration. It also introduces concepts like finding the average value of a function over an interval using the integral, and relating the derivative of an integral to the original function.
Integral (area)
The document discusses using definite integrals to find the area under a curve. It provides examples of finding the area of various shaded regions bounded by curves and the x-axis using the formula: area = ∫f(x)dx from x=a to x=b. It also shows how to find the coordinates of points where two curves intersect in order to divide the region into multiple areas and calculate them separately.
Lesson 8 the definite integrals
The document defines definite integrals and discusses their properties. It states that a definite integral evaluates to a single number by integrating a function over a closed interval from a lower limit to an upper limit. It gives examples of using definite integrals to find areas bounded by curves. The mean value theorem for integrals is also introduced, which states that there is a rectangle between the inscribed and circumscribed rectangles with an area equal to the region under the curve. Exercises are provided on evaluating definite integrals and applying the mean value theorem.
Coordinate geometry
The document defines key concepts related to coordinate grids and ordered pairs:
- A coordinate grid uses horizontal and vertical intersecting lines to locate points via distances from the lines.
- The x-axis is horizontal and the y-axis is vertical.
- Ordered pairs use the format (x,y) to give the location of a point by listing the distance from each axis.
- Points can be plotted on a four-quadrant grid by first finding the x value and then the y value, with negative numbers indicating left/below the origin.
Coordinate geometry
This document provides information on various concepts in elementary and additional mathematics including:
- The distance, midpoint, and gradient formulas for lines
- Equations of lines
- Parallel and perpendicular lines
- Intersecting lines and finding intersection points
- Perpendicular bisectors
- Finding the area of polygons
It includes examples of applying these concepts to solve problems involving lines, midpoints, gradients, intersections, perpendiculars, and calculating areas.
Application of coordinate system and vectors in the real life
1. The document discusses the application of coordinate systems and vectors in real life contexts. It provides several examples, such as using coordinates to describe the location of objects or aircraft, map projections, latitude and longitude coordinates, their use in economics, and by the military.
2. Vectors are also discussed as applied to cannons, sports like baseball and football, wind vectors, and sailing. Calculating forces, torques, acceleration, and velocity also require the use of vectors.
3. Coordinate systems and vectors have many practical applications, from describing positions to applications in transportation, navigation, military targeting, sports, and physics concepts like motion. They underlie many areas of science, engineering, and daily life.
Viewers also liked (6)
Application of coordinate system and vectors in the real life
Application of coordinate system and vectors in the real life
Similar to Chapter 5 Definite Integral Topics Review
DSP IEEE paper
This document discusses the design of a pipelined architecture for sparse matrix-vector multiplication on an FPGA. It begins with introductions to matrices, linear algebra, and matrix multiplication. It then describes the objective of building a hardware processor to perform multiple arithmetic operations in parallel through pipelining. The document reviews literature on pipelined floating point units. It provides details on the proposed pipelined design for sparse matrix-vector multiplication, including storing vector values in on-chip memory and using multiple pipelines to complete results in parallel. Simulation results showing reduced power and execution time are presented before concluding the design can improve performance for scientific applications.
Parallel Computing 2007: Bring your own parallel application
This document discusses parallelizing several algorithms and applications including k-means clustering, frequent itemset mining, integer programming, computer chess, and support vector machines (SVM). For k-means and frequent itemset mining, the algorithms can be parallelized by partitioning the data across processors and performing partial computations locally before combining results with an allreduce operation. Computer chess can be parallelized by exploring different game tree branches simultaneously on different processors. SVM problems involve large dense matrices that are difficult to solve in parallel directly due to their size exceeding memory; alternative approaches include solving smaller subproblems independently.
FPGA based BCH Decoder
This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.
A simple framework for contrastive learning of visual representations
Link: https://machine-learning-made-simple.medium.com/learnings-from-simclr-a-framework-contrastive-learning-for-visual-representations-6c145a5d8e99
If you'd like to discuss something, text me on LinkedIn, IG, or Twitter. To support me, please use my referral link to Robinhood. It's completely free, and we both get a free stock. Not using it is literally losing out on free money.
Check out my other articles on Medium. : https://rb.gy/zn1aiu
My YouTube: https://rb.gy/88iwdd
Reach out to me on LinkedIn. Let's connect: https://rb.gy/m5ok2y
My Instagram: https://rb.gy/gmvuy9
My Twitter: https://twitter.com/Machine01776819
My Substack: https://devanshacc.substack.com/
Live conversations at twitch here: https://rb.gy/zlhk9y
Get a free stock on Robinhood: https://join.robinhood.com/fnud75
This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.
Comments: ICML'2020. Code and pretrained models at this https URL
Subjects: Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)
Cite as: arXiv:2002.05709 [cs.LG]
(or arXiv:2002.05709v3 [cs.LG] for this version)
Submission history
From: Ting Chen [view email]
[v1] Thu, 13 Feb 2020 18:50:45 UTC (5,093 KB)
[v2] Mon, 30 Mar 2020 15:32:51 UTC (5,047 KB)
[v3] Wed, 1 Jul 2020 00:09:08 UTC (5,829 KB)
Statistics and Fitting: overview and thoughts
The document provides an overview of fitting and statistical analysis techniques, including maximum likelihood estimation, chi-squared fits, and incorporating external information. It discusses key concepts like likelihood functions, parameter errors and correlations, goodness-of-fit tests, and adding penalty terms to account for systematic uncertainties or other measurements. Examples are given of maximum likelihood and chi-squared fits performed with ROOT/RooFit. Recommended references on statistical data analysis techniques are also listed.
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORM
In this paper the Delay Computation method for Common Sub expression Elimination algorithm is being implemented on Cyclotomic Fast Fourier Transform. The Common Sub Expression Elimination algorithm is combined with the delay computing method and is known as Gate Level Delay Computation with Common Sub expression Elimination Algorithm. Common sub expression elimination is effective
optimization method used to reduce adders in cyclotomic Fourier transform. The delay computing method is based on delay matrix and suitable for implementation with computers. The Gate level delay computation method is used to find critical path delay and it is analyzed on various finite field elements. The presented algorithm is established through a case study in Cyclotomic Fast Fourier Transform over finite field. If Cyclotomic Fast Fourier Transform is implemented directly then the system will have high additive complexities. So by using GLDC-CSE algorithm on cyclotomic fast Fourier transform, the additive
complexities will be reduced and also the area and area delay product will be reduced.
Machine Learning Algorithms (Part 1)
This document provides an overview of various machine learning algorithms and concepts, including supervised learning techniques like linear regression, logistic regression, decision trees, random forests, and support vector machines. It also discusses unsupervised learning methods like principal component analysis and kernel-based PCA. Key aspects of linear regression, logistic regression, and random forests are summarized, such as cost functions, gradient descent, sigmoid functions, and bagging. Kernel methods are also introduced, explaining how the kernel trick can allow solving non-linear problems by mapping data to a higher-dimensional feature space.
Fuzzy c-Means Clustering Algorithms
This document summarizes recent convergence results for the fuzzy c-means clustering algorithm (FCM). It discusses both numerical convergence, referring to how well the algorithm attains the minima of an objective function, and stochastic convergence, referring to how accurately the minima represent the actual cluster structure in data. For numerical convergence, the document outlines global and local convergence theorems, showing FCM converges to minima or saddle points globally and linearly to local minima. For stochastic convergence, it discusses a consistency result showing the minima accurately represent cluster structure under certain statistical assumptions.
Shor's discrete logarithm quantum algorithm for elliptic curves
This document summarizes John Proos and Christof Zalka's research on implementing Shor's quantum algorithm for solving the discrete logarithm problem over elliptic curves. It shows that for elliptic curve cryptography, a quantum computer could solve problems beyond the capabilities of classical computers using fewer qubits than for integer factorization. Specifically, a 160-bit elliptic curve key could be broken using around 1000 qubits, compared to 2000 qubits needed to factor a 1024-bit RSA modulus. The main technical challenge is implementing the extended Euclidean algorithm to compute multiplicative inverses modulo a prime p.
An Introduction to Model Order Reduction
This document provides an introduction to model order reduction techniques. It discusses how model order reduction works by projecting large dynamical systems onto dominant subspaces to obtain reduced order models. It covers motivation for model order reduction due to rising complexity in mathematical models. It also describes moment matching and Krylov subspace methods, which are different approaches for finding projection matrices. Krylov subspace methods allow for implicit moment matching through Arnoldi iteration and have advantages in terms of computational cost and memory requirements over other methods.
Network Security CS3-4
Random numo Galois Field
Polynomial Arithmetic
Example of Polynomial Arithmetic
bers, its types and usage.
TRNG, PRNG, CHPRNG
Review of BBS
Stream Ciphering
RC4 algorithm
Basic Number Theory
Extended Euclidean Algorithm
Relevance of Extended Euclidean Algorithm
Firefly exact MCMC for Big Data
MCMC exact solutions for Big Data
Firefly is a novel algorithm proposed to work directly with a big data set
Bisection method in maths 4
In this PPT I am talking about the bisection method(midpoint method for equation).
Hope you like it!
ADAPTIVE FUZZY KERNEL CLUSTERING ALGORITHM
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional feature space using gaussian kernel and clustering in the feature space. The Matlab simulation results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results.
ADAPTIVE FUZZY KERNEL CLUSTERING ALGORITHM
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results
Full parameterization process
Although fuzzy systems demonstrate their ability to
solve different kinds of problems in various applications, there is an increasing interest on developing solid mathematical implementations suitable for control applications such as that used in fuzzy logic controllers (FLC). It is well known that, wide range of parameters is needed to be specified before the construction of a fuzzy system. To simplify in a systematic way the design and construction of a general fuzzy system, and without loss for generality a full parameterization process for a singleton type FLC is proposed in this paper. The resented methodology is very helpful in developing a universal computing algorithm for a standard fuzzy like PID controllers. An illustrative example shows the simplicity of applying the new paradigm.
VCE Unit 01 (2).pptx
The document discusses algorithms, data abstraction, asymptotic analysis, arrays, polynomials, and sparse matrices. It defines algorithms and discusses their advantages and disadvantages. It explains how to design an algorithm and describes iterative and recursive algorithms. It defines data abstraction and gives an example using smartphones. It discusses time and space complexity analysis and different asymptotic notations like Big O, Omega, and Theta. It describes what arrays are, different types of arrays, and applications of arrays. It explains how to represent and add polynomials using linked lists. Finally, it defines sparse matrices and two methods to represent them using arrays and linked lists.
Matrix transposition
1) The document presents various algorithms for efficiently transposing matrices while minimizing memory accesses and cache misses.
2) It analyzes the algorithms under different memory models: RAM, I/O, cache, and cache-oblivious. The block transpose, half/full copying, and Morton layout algorithms improve performance by reusing data blocks.
3) Experimental results on a 300MHz system show the Morton layout and half copying algorithms have the fastest runtimes due to minimizing data references, L1 misses, and TLB misses. The relative performance of algorithms depends on cache miss latency.
VCE Unit 01 (1).pptx
The document discusses data types, data structures, algorithms, recursion, and asymptotic analysis. It provides definitions and examples of key concepts like abstract data types, data abstraction, algorithms, iterative vs recursive algorithms, complexity analysis using Big-O, Big-Omega and Big-Theta notations. Examples of recursively implementing algorithms to find sum of natural numbers, factorial, GCD, Fibonacci series are presented.
Section5 Rbf
The document summarizes radial basis function (RBF) networks. Key points:
- RBF networks use radial basis functions as activation functions and can universally approximate continuous functions.
- They are local approximators compared to multilayer perceptrons which are global approximators.
- Learning involves determining the centers, widths, and weights. Centers can be randomly selected or via clustering. Widths are usually different for each basis function. Weights are typically learned via least squares or gradient descent methods.
Similar to Chapter 5 Definite Integral Topics Review (20)
Parallel Computing 2007: Bring your own parallel application
Parallel Computing 2007: Bring your own parallel application
A simple framework for contrastive learning of visual representations
A simple framework for contrastive learning of visual representations
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORM
DESIGN OF DELAY COMPUTATION METHOD FOR CYCLOTOMIC FAST FOURIER TRANSFORM
Shor's discrete logarithm quantum algorithm for elliptic curves
Shor's discrete logarithm quantum algorithm for elliptic curves
More from Sharon Henry
6.1 Law of Sines Ambiguous Case
This document discusses the ambiguous case of the Law of Sines when given an acute angle (A) and sides a and c of a triangle, where a < c. It explains that:
1) When a < h, where h is the altitude of the triangle, no triangle can be formed.
2) When a = h, one right triangle is formed.
3) When a > h, two triangles are formed - one acute triangle and one obtuse triangle.
So in summary, given the measurements A, a and c where a < c, there will be 0 triangles formed if a < h, 1 triangle if a = h, and 2 triangles if a > h.
6.2 law of cosines
This document provides instruction on using the Law of Cosines to solve triangles. It begins by explaining that the Law of Sines cannot be used to solve triangles when the side-side-side (SSS) or side-angle-side (SAS) configurations are given. The Law of Cosines formulas are then introduced. Examples are worked through demonstrating how to use the Law of Cosines to solve triangles in SSS and SAS formations. Key steps like verifying a triangle can be formed from given SSS measurements and properly applying order of operations are emphasized. Students are assigned homework problems applying these concepts.
Second Derivative Information
The second derivative of a function f(x) provides information about the concavity and points of inflection of f(x). It indicates the intervals where f(x) is concave up or down. A curve is concave up where the second derivative is positive and concave down where the second derivative is negative. Points of inflection are where the concavity changes from up to down or vice versa, and occur where the second derivative is zero or undefined.
4.4 Fundamental Theorem of Calculus
This document discusses the mean value theorem and how it can be used to find the average value of a function over an interval. It states that for a continuous function, there exists some value c within the interval where the area under the curve between the bounds is equal to the value of the function at c multiplied by the width of the interval. It then works through an example of finding the average value of the function f(x)=3x^2-2x over the interval [1,4].
4.3 The Definite Integral
The document discusses notation and properties for definite integrals. It defines the definite integral from a to b of f(x) dx as the area under the curve of f(x) between the x-axis and the limits of a and b. It lists five properties of definite integrals: 1) the order of integration does not matter, 2) the integral from a to a of any function f(x) is equal to zero, 3) a constant can be pulled out of the integral, 4) integrals can be added or subtracted, and 5) a definite integral over an interval can be broken into a sum of integrals over subintervals.
Lesson 3.3 First Derivative Information
The first derivative of a function f(x) indicates where the function is increasing, decreasing, or constant. If f'(x) is positive, f(x) is increasing, and if f'(x) is negative, f(x) is decreasing. If f'(x) is 0, f(x) is constant. To determine where a function is increasing or decreasing, identify the critical numbers and determine the sign of f'(x) in intervals between them. The first derivative test also allows identification of relative extrema - if f'(x) changes from negative to positive at a critical number c, then f(c) is a relative minimum, and if it changes from positive to negative, f(c
Lesson 3.2 Rolle and Mean Value Theorems
Rolle's Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), with f(a) = f(b), then there exists at least one value c in the open interval where the derivative f'(c) is equal to 0. The Mean Value Theorem similarly guarantees the existence of at least one value c where the derivative is equal to the average rate of change of the function over the interval, (f(b)-f(a))/(b-a).
Lesson 3.3 3.4 - 1 st and 2nd Derivative Information
1) The document discusses tests for determining whether a function is increasing, decreasing, or constant based on the sign of the first derivative on an interval.
2) It also describes how to use the first and second derivative tests to determine if a critical point is a relative maximum or minimum. The tests analyze how the sign of the first or second derivative changes at the critical point.
3) Finally, the document outlines the test for concavity and points of inflection based on the sign of the second derivative on an interval. A change in the sign of the second derivative indicates an inflection point.
3.5 3.6 exp-log models 13-14
1. This document discusses several common mathematical models involving exponential and logarithmic functions, including exponential growth/decay models, logistic growth models, Gaussian models, logarithmic models, and Newton's Law of Cooling.
2. Examples are provided to illustrate how to set up and solve problems using each type of model. For instance, an example uses an exponential growth model to predict when the world's population will reach 7.1 billion people.
3. Guidance is also given on using graphing utilities and calculators to analyze exponential and logarithmic relationships. Instructions for performing exponential regression on a TI-84 calculator are provided.
3.1 Extreme Values of Functions
This document defines and discusses absolute and local extreme values of functions. It states that absolute extrema (global maximum and minimum values) can occur at endpoints or interior points of an interval, but a function is not guaranteed to have an absolute max or min on every interval. The Extreme Value Theorem says that if a function is continuous on a closed interval, it will have both an absolute maximum and minimum value. Local extrema are defined as maximum or minimum values within an open neighborhood of a point, and the theorem is presented that if a function has a local extremum at an interior point where the derivative exists, the derivative must be zero at that point. Critical points are defined as points where the derivative is zero or undefined. Methods
2.6 Related Rates
This document defines and provides examples of related rate problems. Related rate problems involve calculating the rates of change of two or more related variables with respect to time. The document outlines the steps to solve related rate problems: 1) identify changing quantities, 2) write an equation relating the quantities, 3) differentiate both sides with respect to time, 4) solve for the required quantity and substitute known values. Examples include calculating the rate of change of a dog's circular puddle area, a melting snowball's radius, the top of a slipping ladder, and the height of a conical sand pile.
3.5 EXP-LOG MODELS
The document discusses various mathematical models involving exponential and logarithmic functions, including exponential growth and decay models, logistic growth models, Gaussian models, and logarithmic models. It provides examples of how each type of model can be used, such as modeling world population growth with an exponential function, modeling the spread of a virus on a college campus with a logistic function, and modeling cooling of a heated object using Newton's Law of Cooling. The document also discusses how to graph and solve problems involving these different mathematical models.
Larson 4.4
This document discusses evaluating trigonometric functions of any angle by using reference angles. It defines trigonometric functions for any real value of the angle θ. For angles greater than 90° or less than 0°, the values can be determined from the acute reference angle. Examples show how to find the reference angle and then use it to evaluate trigonometric functions in different quadrants, including for nonacute angles.
Larson 4.3
This document discusses trigonometric functions and their applications. It defines the six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - using ratios of sides of a right triangle. Examples are provided to evaluate the trig functions of given angles and to use identities to relate functions. The document also discusses applications of solving right triangles by using trig functions when given angle and side length information.
Larson 4.2
The unit circle relates real numbers to points on a circle of radius 1 centered at the origin. Each real number t corresponds to a point (x, y) on the circle, allowing the definition of the six trigonometric functions in terms of x and y. The trigonometric functions sine and cosine are periodic with period 2π, meaning their values repeat every 2π units. Their domains are all real numbers and their ranges are between -1 and 1.
Larson 4.1
The document describes angles and their measurement in radians and degrees. It defines an angle, measures angles in radians using central angles of a circle, and defines the relationship between radians and degrees. Examples show converting between radians and degrees, finding coterminal angles, complementary and supplementary angles, and calculating arc length and linear speed using angular measurements.
Derivative rules ch2
This document provides the basic derivative rules from Chapter 2. It lists various expressions and their derivatives on subsequent slides, including the derivatives of sums, products, quotients, composite functions, powers, trigonometric functions like sine, cosine, tangent, cotangent, secant and cosecant, and constants. The derivatives covered are: du/dv, df(g(x))/dx, dn/dx, d/dx cot(u), d/dx cu, d/dx tan(u), d/dx (u*v), d/dx c, d/dx cos(u), d/dx sec(u), dx/dx, and d/dx csc(
1.4 Continuity
The document discusses continuity of functions at a point c. It defines continuity as a function being defined at c, the limit existing at c, and the function value at c equaling the limit value. Five examples are given and categorized as continuous, discontinuous with removable discontinuities, or discontinuous with nonremovable discontinuities. Removable discontinuities can be resolved by redefining the function value at c, while nonremovable discontinuities cannot be resolved.
Lesson 4.3 First and Second Derivative Theory
1) To determine if a function is increasing or decreasing, examine the sign of the first derivative f'(x) at points around any critical points. A change from positive to negative indicates a relative maximum, and a change from negative to positive indicates a relative minimum.
2) A curve is concave up if the second derivative f''(x) is positive, and concave down if f''(x) is negative. To determine concavity, examine the sign of f''(x) around any points where it is zero or undefined. A change in sign indicates an inflection point where the concavity changes.
Lesson 4.1 Extreme Values
1) A function has an absolute maximum value on its domain if its value is greater than or equal to its value at all other points in its domain, and an absolute minimum value if its value is less than or equal to its value at all other points.
2) By the Extreme Value Theorem, if a function is continuous on a closed interval, it will have both an absolute maximum and minimum value within that interval. These extreme values can occur at interior points or endpoints.
3) A local extreme value of a function is a maximum or minimum value within a neighborhood of some interior point, where the function's derivative is equal to 0 or undefined at that point, according to the Local Extreme Value Theorem.
More from Sharon Henry (20)
Lesson 3.3 3.4 - 1 st and 2nd Derivative Information
Lesson 3.3 3.4 - 1 st and 2nd Derivative Information
Recently uploaded
The Enigmatic Portrait, In the heart of a sleepy town
In the heart of a sleepy town nestled between rolling hills and whispering pines …
created with AI assistance…
Leonardo DiCaprio Super Bowl: Hollywood Meets America’s Favorite Game
Introduction
Leonardo DiCaprio is synonymous with Hollywood stardom and acclaimed performances. has a unique connection with one of America's most beloved sports events—the Super Bowl. The "Leonardo DiCaprio Super Bowl" phenomenon combines the worlds of cinema and sports. drawing attention from fans of both domains. This article delves into the multifaceted relationship between DiCaprio and the Super Bowl. exploring his appearances at the event, His involvement in Super Bowl advertisements. and his cultural impact that bridges the gap between these two massive entertainment industries.
Follow us on: Pinterest
Leonardo DiCaprio: The Hollywood Icon
Early Life and Career Beginnings
Leonardo Wilhelm DiCaprio was born in Los Angeles, California, on November 11, 1974. His journey to stardom began at a young age with roles in television commercials and educational programs. DiCaprio's breakthrough came with his portrayal of Luke Brower in the sitcom "Growing Pains" and later as Tobias Wolff in "This Boy's Life" (1993). where he starred alongside Robert De Niro.
Rise to Stardom
DiCaprio's career skyrocketed with his performance in "What's Eating Gilbert Grape" (1993). earning him his first Academy Award nomination. He continued to gain acclaim with roles in "Romeo + Juliet" (1996) and "Titanic" (1997). the latter of which cemented his status as a global superstar. Over the years, DiCaprio has showcased his versatility in films like "The Aviator" (2004). "Start" (2010), and "The Revenant" (2015), for which he finally won an Academy Award for Best Actor.
Environmental Activism
Beyond his film career, DiCaprio is also renowned for his environmental activism. He established the Leonardo DiCaprio Foundation in 1998, focusing on global conservation efforts. His commitment to ecological issues often intersects with his public appearances. including those related to the Super Bowl.
The Super Bowl: An American Institution
History and Significance
The Super Bowl is the National Football League (NFL) championship game. is one of the most-watched sporting events in the world. First played in 1967, the Super Bowl has evolved into a cultural phenomenon. featuring high-profile halftime shows, memorable advertisements, and significant media coverage. The event attracts a diverse audience, from avid sports fans to casual viewers. making it a prime platform for celebrities to appear.
Entertainment and Advertisements
The Super Bowl is not only about football but also about entertainment. The halftime show features performances by some of the biggest names in the music industry. while the commercials are often as anticipated as the game itself. Companies invest millions in Super Bowl ads. creating iconic and sometimes controversial commercials that capture public attention.
Leonardo DiCaprio's Super Bowl Appearances
A Celebrity Among the Fans
Leonardo DiCaprio's presence at the Super Bowl has noted several times. As a high-profile celebrity. DiCaprio attracts
From Teacher to OnlyFans: Brianna Coppage's Story at 28
At 28, Brianna Coppage left her teaching career to become an OnlyFans content creator. This bold move into digital entrepreneurship allowed her to harness her creativity and build a new identity. Brianna's experience highlights the intersection of technology and personal branding in today's economy.
Leonardo DiCaprio House: A Journey Through His Extravagant Real Estate Portfolio
Introduction
Leonardo DiCaprio, A name synonymous with Hollywood excellence. is not only known for his stellar acting career but also for his impressive real estate investments. The "Leonardo DiCaprio house" is a topic that piques the interest of many. as the Oscar-winning actor has amassed a diverse portfolio of luxurious properties. DiCaprio's homes reflect his varied tastes and commitment to sustainability. from retreats to historic mansions. This article will delve into the fascinating world of Leonardo DiCaprio's real estate. Exploring the details of his most notable residences. and the unique aspects that make them stand out.
Follow us on: Pinterest
Leonardo DiCaprio House: Malibu Beachfront Retreat
A Prime Location
His Malibu beachfront house is one of the most famous properties in Leonardo DiCaprio's real estate portfolio. Situated in the exclusive Carbon Beach. also known as "Billionaire's Beach," this property boasts stunning ocean views and private beach access. The "Leonardo DiCaprio house" in Malibu is a testament to the actor's love for the sea and his penchant for luxurious living.
Architectural Highlights
The Malibu house features a modern design with clean lines, large windows. and open spaces blending indoor and outdoor living. The expansive deck and patio areas provide ample space for entertaining guests or enjoying a quiet sunset. The house has state-of-the-art amenities. including a gourmet kitchen, a home theatre, and many guest suites.
Sustainable Features
Leonardo DiCaprio is a well-known environmental activist. whose Malibu house reflects his commitment to sustainability. The property incorporates solar panels, energy-efficient appliances, and sustainable building materials. The landscaping around the house is also designed to be water-efficient. featuring drought-resistant plants and intelligent irrigation systems.
Leonardo DiCaprio House: Hollywood Hills Hideaway
Privacy and Seclusion
Another remarkable property in Leonardo DiCaprio's collection is his Hollywood Hills house. This secluded retreat offers privacy and tranquility. making it an ideal escape from the hustle and bustle of Los Angeles. The "Leonardo DiCaprio house" in Hollywood Hills nestled among lush greenery. and offers panoramic views of the city and surrounding landscapes.
Design and Amenities
The Hollywood Hills house is a mid-century modern gem characterized by its sleek design and floor-to-ceiling windows. The open-concept living space is perfect for entertaining. while the cozy bedrooms provide a comfortable retreat. The property also features a swimming pool, and outdoor dining area. and a spacious deck that overlooks the cityscape.
Environmental Initiatives
The Hollywood Hills house incorporates several green features that are in line with DiCaprio's environmental values. The home has solar panels, energy-efficient lighting, and a rainwater harvesting system. Additionally, the landscaping designed to support local wildlife and promote
Odia New Web Series at your fingerprint.
Stay ahead of the curve with the latest in Odia entertainment! Our Odia new web series promise an exciting blend of fresh narratives, talented performances, and engaging plots. Immerse yourself in the evolving world of Odia storytelling with our curated selection of cutting-edge web content. for more visit: https://aaonxt.com/series
定制(mu毕业证书)美国迈阿密大学牛津分校毕业证学历证书原版一模一样
原版定制【微信:bwp0011】《(mu毕业证书)美国迈阿密大学牛津分校毕业证学历证书》【微信:bwp0011】成绩单 、雅思、外壳、留信学历认证永久存档查询，采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信bwp0011】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信bwp0011】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
The Enigma of the Midnight Canvas, In the heart of Paris
In the heart of Paris, where the Seine River flowed languidly beneath the city's graceful bridges …
created with AI assistance…
Abraham Laboriel Records ‘The Bass Walk’ at Evergreen Stage
A legendary musician records an intricate song designed to show off his expert bass guitar chops at a historical Los Angeles studio.
The Future of Independent Filmmaking Trends and Job Opportunities
The landscape of independent filmmaking is evolving at an unprecedented pace. Technological advancements, changing consumer preferences, and new distribution models are reshaping the industry, creating new opportunities and challenges for filmmakers and film industry jobs. This article explores the future of independent filmmaking, highlighting key trends and emerging job opportunities.
Anasuya Sengupta Cannes 2024 Award Winner
Anasuya Sengupta, an Indian actress and designer, won the Best Actress Award at the Cannes Film Festival for the Bulgarian film 'The Shameless'.
原版制作(MUN毕业证书)纽芬兰纪念大学毕业证PDF成绩单一模一样
学校原件一模一样【微信：741003700 】《(MUN毕业证书)纽芬兰纪念大学毕业证》【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
The Unbelievable Tale of Dwayne Johnson Kidnapping: A Riveting Saga
Introduction
The notion of Dwayne Johnson kidnapping seems straight out of a Hollywood thriller. Dwayne "The Rock" Johnson, known for his larger-than-life persona, immense popularity. and action-packed filmography, is the last person anyone would envision being a victim of kidnapping. Yet, the bizarre and riveting tale of such an incident, filled with twists and turns. has captured the imagination of many. In this article, we delve into the intricate details of this astonishing event. exploring every aspect, from the dramatic rescue operation to the aftermath and the lessons learned.
Follow us on: Pinterest
The Origins of the Dwayne Johnson Kidnapping Saga
Dwayne Johnson: A Brief Background
Before discussing the specifics of the kidnapping. it is crucial to understand who Dwayne Johnson is and why his kidnapping would be so significant. Born May 2, 1972, Dwayne Douglas Johnson is an American actor, producer, businessman. and former professional wrestler. Known by his ring name, "The Rock," he gained fame in the World Wrestling Federation (WWF, now WWE) before transitioning to a successful career in Hollywood.
Johnson's filmography includes blockbuster hits such as "The Fast and the Furious" series, "Jumanji," "Moana," and "San Andreas." His charismatic personality, impressive physique. and action-star status have made him a beloved figure worldwide. Thus, the news of his kidnapping would send shockwaves across the globe.
Setting the Scene: The Day of the Kidnapping
The incident of Dwayne Johnson's kidnapping began on an ordinary day. Johnson was filming his latest high-octane action film set to break box office records. The location was a remote yet scenic area. chosen for its rugged terrain and breathtaking vistas. perfect for the film's climactic scenes.
But, beneath the veneer of normalcy, a sinister plot was unfolding. Unbeknownst to Johnson and his team, a group of criminals had planned his abduction. hoping to leverage his celebrity status for a hefty ransom. The stage was set for an event that would soon dominate worldwide headlines and social media feeds.
The Abduction: Unfolding the Dwayne Johnson Kidnapping
The Moment of Capture
On the day of the kidnapping, everything seemed to be proceeding as usual on set. Johnson and his co-stars and crew were engrossed in shooting a particularly demanding scene. As the day wore on, the production team took a short break. providing the kidnappers with the perfect opportunity to strike.
The abduction was executed with military precision. A group of masked men, armed and organized, infiltrated the set. They created chaos, taking advantage of the confusion to isolate Johnson. Johnson was outnumbered and caught off guard despite his formidable strength and fighting skills. The kidnappers overpowered him, bundled him into a waiting vehicle. and sped away, leaving everyone on set in a state of shock and disbelief.
The Immediate Aftermath
The immediate aftermath of the Dwayne Johnson kidnappin
The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...
Leonardo DiCaprio, a name synonymous with Hollywood stardom and acting excellence. has captivated audiences for decades with his talent and charisma. But, the Leonardo DiCaprio haircut is one aspect of his public persona that has garnered attention. From his early days as a teenage heartthrob to his current status as a seasoned actor and environmental activist. DiCaprio's hairstyles have evolved. reflecting both his personal growth and the changing trends in fashion. This article delves into the many phases of the Leonardo DiCaprio haircut. exploring its significance and impact on pop culture.
University of Western Sydney degree offer diploma Transcript
澳洲UWS毕业证书制作西悉尼大学假文凭定制Q微168899991做UWS留信网教留服认证海牙认证改UWS成绩单GPA做UWS假学位证假文凭高仿毕业证申请西悉尼大学University of Western Sydney degree offer diploma Transcript
The Gallery of Shadows, In the heart of a bustling city
In the heart of a bustling city, hidden away from the modern chaos …
created with AI assistance…
From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx
Know about the five famous artists who have transitioned to Big Band Music from Swing Music. Here is a glimpse of their work and contributions.
Sara Saffari: Turning Underweight into Fitness Success at 23
Uncover the remarkable journey of Sara Saffari, whose transformation from underweight struggles to being recognized as a fitness icon at 23 underscores the importance of perseverance, discipline, and embracing a healthy lifestyle.
一比一原版(AUT毕业证)奥克兰理工大学毕业证如何办理
AUT毕业证假文凭【微信95270640】购买（奥克兰理工大学毕业证成绩单硕士学历）Q微信95270640代办AUT学历认证留信网伪造奥克兰理工大学学位证书精仿奥克兰理工大学本科/硕士文凭证书补办奥克兰理工大学 diplomaoffer,Transcript购买奥克兰理工大学毕业证成绩单购买AUT假毕业证学位证书购买伪造奥克兰理工大学文凭证书学位证书,专业办理雅思、托福成绩单，学生ID卡，在读证明，海外各大学offer录取通知书，毕业证书，成绩单，文凭等材料:1:1完美还原毕业证、offer录取通知书、学生卡等各种在读或毕业材料的防伪工艺（包括 烫金、烫银、钢印、底纹、凹凸版、水印、防伪光标、热敏防伪、文字图案浮雕，激光镭射，紫外荧光，温感光标）学校原版上有的工艺我们一样不会少，不论是老版本还是最新版本，都能保证最高程度还原，力争完美以求让所有同学都能享受到完美的品质服务。
办国外奥克兰理工大学奥克兰理工大学毕业证文凭证书教育部学历学位认证留信认证大使馆认证留学回国人员证明修改成绩单信封申请学校offer录取通知书在读证明offer letter。
快速办理高仿国外毕业证成绩单：
1奥克兰理工大学毕业证+成绩单+留学回国人员证明+教育部学历认证（全套留学回国必备证明材料给父母及亲朋好友一份完美交代）;
2雅思成绩单托福成绩单OFFER在读证明等留学相关材料（申请学校转学甚至是申请工签都可以用到）。
3.毕业证 #成绩单等全套材料从防伪到印刷从水印到钢印烫金高精仿度跟学校原版100%相同。
专业服务请勿犹豫联系我！联系人微信号：95270640诚招代理：本公司诚聘当地代理人员如果你有业余时间有兴趣就请联系我们。
国外奥克兰理工大学奥克兰理工大学毕业证文凭证书办理过程：
1客户提供办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）。蜿蜒小溪一直都是山娃和小伙伴们盛夏的天然泳场水不深碎石底石缝里总有摸不尽的鱼虾活蹦乱跳的还有乌龟和王八贼头贼脑的倒也逗人喜爱日上三竿时山娃总爱窜进自家瓜棚里跟小伙伴们坐着聊天聊着聊着便忍不住往瓜田里逡巡一番抱起一只硕大的西瓜用石刀劈开抑或用拳头砸开每人抱起一大块就啃啃得满嘴满脸猴屁股般的红艳大家一个劲地指着对方吃吃地笑瓜裂得古怪奇形怪状却丝毫不影响瓜味甜丝丝的满嘴生津遍地都是瓜横七竖八的活像掷满这
一比一原版(UCSF毕业证)旧金山分校毕业证如何办理
原件一模一样【微信：95270640】【旧金山分校毕业证UCSF学位证成绩单】【微信：95270640】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：95270640】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：95270640】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份【微信：95270640】
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
办理旧金山分校毕业证毕业证offerUCSF学位证【微信：95270640 】外观非常精致，由特殊纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理旧金山分校毕业证UCSF学位证毕业证offer【微信：95270640 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理旧金山分校毕业证毕业证offerUCSF学位证【微信：95270640 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理旧金山分校毕业证毕业证offerUCSF学位证【微信：95270640 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
Recently uploaded (20)
The Enigmatic Portrait, In the heart of a sleepy town
The Enigmatic Portrait, In the heart of a sleepy town
Leonardo DiCaprio Super Bowl: Hollywood Meets America’s Favorite Game
Leonardo DiCaprio Super Bowl: Hollywood Meets America’s Favorite Game
From Teacher to OnlyFans: Brianna Coppage's Story at 28
From Teacher to OnlyFans: Brianna Coppage's Story at 28
Leonardo DiCaprio House: A Journey Through His Extravagant Real Estate Portfolio
Leonardo DiCaprio House: A Journey Through His Extravagant Real Estate Portfolio
The Enigma of the Midnight Canvas, In the heart of Paris
The Enigma of the Midnight Canvas, In the heart of Paris
Abraham Laboriel Records ‘The Bass Walk’ at Evergreen Stage
Abraham Laboriel Records ‘The Bass Walk’ at Evergreen Stage
The Future of Independent Filmmaking Trends and Job Opportunities
The Future of Independent Filmmaking Trends and Job Opportunities
The Unbelievable Tale of Dwayne Johnson Kidnapping: A Riveting Saga
The Unbelievable Tale of Dwayne Johnson Kidnapping: A Riveting Saga
The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...
The Evolution of the Leonardo DiCaprio Haircut: A Journey Through Style and C...
University of Western Sydney degree offer diploma Transcript
University of Western Sydney degree offer diploma Transcript
The Gallery of Shadows, In the heart of a bustling city
The Gallery of Shadows, In the heart of a bustling city
From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx
From Swing Music to Big Band Fame_ 5 Iconic Artists.pptx
Sara Saffari: Turning Underweight into Fitness Success at 23
Sara Saffari: Turning Underweight into Fitness Success at 23
Chapter 5 Definite Integral Topics Review
- 2. 5.1 Do you know RAM theory? Which over- and under-approximates increasing and decreasing functions? How to compute given an equation? How to compute given data?
- 3. 5.2 The Definite Integral Net Area:
- 4. Integrals on the TI-89 Syntax: To evaluate … 2nd 7 (f(x),x,a,b)
- 5. 1. Order of Integration 2. Zero 3. Constant Multiple 4. Sum and Difference 5. Additivity 5.3 Properties of Definite Integrals:
- 6. 5.3 MVT for Integrals… Somewhere between an inscribed and circumscribed rectangle is a rectangle whose area is exactly the area of the region under the curve.
- 7. 5.3 Average Value Theorem The value f(c) from the MVT is the average value of f on [a,b]…
- 8. 5.4 Fund. Thm of Calc: Part I
- 9. 5.4 Fund Thm of Calc: Part 2
- 10. 5.5 Trapezoidal Rule where n is the number of subintervals. The trapezoidal rule overapproximates CCU functions and underapproximates CCD functions.