Domain & Range (from graph) - Mohd Noor
•Download as PPSX, PDF•
0 likes•385 views
This slide demonstrates how you can obtain the domain and range of a particular function based on its graph.
Report
Share
Report
Share
Recommended
Math AB Chapter 8 Polynomials
1. The document reviews multiplying polynomials including binomials and trinomials using the FOIL method. It provides examples of multiplying binomial expressions.
2. It then has students practice simplifying the addition and subtraction of polynomials and multiplying binomial expressions using FOIL.
3. The document concludes with examples of using polynomials to represent and calculate the area of a rectangle.
Ejercicios resueltos
1. The document provides examples of solving logarithm exercises. It shows calculations of logarithms with different bases and operations like addition, subtraction, and change of base.
2. Several examples involve taking the logarithm of quotients or products and using logarithm properties to simplify the calculations.
3. The last part introduces variables a, b, and c to represent logarithms of specific numbers and derives additional logarithm expressions in terms of these variables.
Cryptology Caesar Cipher
From this slide you will learn about Cryptology's Caesar Cipher method where you will learn how to encrypt or decry-pt a message.
Sum and difference of two squares
This document discusses multiplying polynomials. It defines polynomials as expressions of variables and constants combined using addition, subtraction, multiplication, and division. It provides examples of monomials, binomials, and trinomials. It then demonstrates multiplying polynomials using the distributive property and explains that when multiplying binomials, one should square the first term and subtract the square of the second term. Finally, it provides examples of multiplying binomial expressions.
Matematicas
This document contains several functions with their domains and ranges expressed in both words and symbols:
1) It defines various functions including linear, square root, absolute value, logarithmic and exponential functions.
2) For each function, it provides the domain of x-values and the corresponding range of y-values.
3) The domains and ranges are expressed using both numeric intervals and symbolic notation.
Assignment 1 DUM 3272 Mathematics 3
This document contains 5 math assignment questions: 1) Find the equation of a parabola with a given focus and directrix. 2) Find the center, vertices, and foci of a hyperbola with a given equation. 3) Take the derivative of a polynomial function. 4) Find the derivative of an implicit function. 5) Find the equations of the tangent and normal lines to an ellipse at a given point.
Unit 3 Math Test
This document appears to be a math test containing 25 multiple choice questions covering order of operations, evaluating expressions, properties of operations, solving equations, and simplifying algebraic expressions. The questions progress from basic order of operations to more advanced topics involving variables, properties, and multi-step simplifications. The final bonus question asks students to write an expression for the perimeter of a polygon shown.
Factoring the difference of two squares
The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.
Recommended
Math AB Chapter 8 Polynomials
1. The document reviews multiplying polynomials including binomials and trinomials using the FOIL method. It provides examples of multiplying binomial expressions.
2. It then has students practice simplifying the addition and subtraction of polynomials and multiplying binomial expressions using FOIL.
3. The document concludes with examples of using polynomials to represent and calculate the area of a rectangle.
Ejercicios resueltos
1. The document provides examples of solving logarithm exercises. It shows calculations of logarithms with different bases and operations like addition, subtraction, and change of base.
2. Several examples involve taking the logarithm of quotients or products and using logarithm properties to simplify the calculations.
3. The last part introduces variables a, b, and c to represent logarithms of specific numbers and derives additional logarithm expressions in terms of these variables.
Cryptology Caesar Cipher
From this slide you will learn about Cryptology's Caesar Cipher method where you will learn how to encrypt or decry-pt a message.
Sum and difference of two squares
This document discusses multiplying polynomials. It defines polynomials as expressions of variables and constants combined using addition, subtraction, multiplication, and division. It provides examples of monomials, binomials, and trinomials. It then demonstrates multiplying polynomials using the distributive property and explains that when multiplying binomials, one should square the first term and subtract the square of the second term. Finally, it provides examples of multiplying binomial expressions.
Matematicas
This document contains several functions with their domains and ranges expressed in both words and symbols:
1) It defines various functions including linear, square root, absolute value, logarithmic and exponential functions.
2) For each function, it provides the domain of x-values and the corresponding range of y-values.
3) The domains and ranges are expressed using both numeric intervals and symbolic notation.
Assignment 1 DUM 3272 Mathematics 3
This document contains 5 math assignment questions: 1) Find the equation of a parabola with a given focus and directrix. 2) Find the center, vertices, and foci of a hyperbola with a given equation. 3) Take the derivative of a polynomial function. 4) Find the derivative of an implicit function. 5) Find the equations of the tangent and normal lines to an ellipse at a given point.
Unit 3 Math Test
This document appears to be a math test containing 25 multiple choice questions covering order of operations, evaluating expressions, properties of operations, solving equations, and simplifying algebraic expressions. The questions progress from basic order of operations to more advanced topics involving variables, properties, and multi-step simplifications. The final bonus question asks students to write an expression for the perimeter of a polygon shown.
Factoring the difference of two squares
The document discusses factoring the difference of two squares through examples such as (x+5)(x-5)=x^2 - 25. It explains that to factor a difference of two squares, we write the expression as the difference of two terms squared, then group the terms with the same bases and opposite signs inside parentheses. Several practice problems are provided to reinforce this technique for factoring completely the difference of two squares.
Squaring binomials
This document discusses squaring binomial expressions. It provides three examples of squaring binomials of the form (x + a), showing that (x + a)2 = x2 + 2a*x + a2. Specifically, it squares (x + 3), (b - 5), and (m - 15) to get x2 + 6x + 9, b2 - 10b + 25, and m2 - 60m + 225 respectively.
2.7 more parabolas a& hyperbolas (optional) t
The document provides examples of how to graph and identify properties of hyperbolas and parabolas. It includes:
1) An example of a hyperbola with center (3, -1), x-radius of 4, y-radius of 2, and vertices of (7, -1) and (-1, -1).
2) Steps for completing the square to put a quadratic equation into standard form for a hyperbola, including an example starting with 4y^2 - 9x^2 - 18x - 16y = 29.
3) An example of graphing a parabola given by the equation x = -y^2 + 2y + 15, identifying
MATH: ORDER OF OPERATIONS
1. Student X was first in line, Student Z was second, Student Y was third, and Student L was last.
2. The order of operations is: multiply, subtract, square, multiply.
3. Order of operations dictates that exponents, multiplication/division from left to right, then addition/subtraction from left to right must be followed when evaluating expressions.
Mcqs
The document contains a multiple choice quiz with 35 questions testing mathematical concepts. The questions cover topics like sets, operations, ratios, proportions, factors, primes and more. For each question there are 4 possible answer choices to choose from.
3.4 a linear programming
The document discusses using linear programming to find the maximum and minimum values of an objective function given certain constraints. It provides an example of finding the minimum and maximum values of the function f(x,y)=3x-2y when constrained by y≥2, 1≤x≤5, and y≤x+3. The values are found by graphing the inequalities to determine the vertices and substituting the vertices into the objective function.
Add,sub,mult polynomials
1) To add or subtract polynomials, combine like terms by adding or subtracting their coefficients.
2) To multiply polynomials, use FOIL or the distributive property to multiply each term of one factor with each term of the other.
3) Important patterns for multiplying binomials include the sum and difference pattern, square of a binomial, and cube of a binomial.
2.5 conic sections circles-t
The document provides examples of writing the equation of a circle given its center and radius or vice versa. It demonstrates:
1) Writing the equation (x-h)2 + (y-k)2 = r2 given the center (h,k) and radius r.
2) Finding the center and radius from an equation by completing the square and rewriting it in standard form.
3) Identifying the center, radius, and extreme points to graph the circle.
10 mathfinal2011review
The document contains 25 math problems involving simplifying expressions, evaluating expressions for given values, writing expressions in algebraic form, combining like terms, expanding, factoring, solving equations, working with polygons, and trigonometric functions. The problems cover a wide range of algebra and geometry topics tested on standardized exams.
Algebra review
This document provides 20 algebra problems involving simplifying expressions, solving equations, graphing lines, writing equations in slope-intercept form, determining if lines are parallel or perpendicular, and operations with scientific notation. Students are instructed to show all work.
3.4 linear programming
The document discusses linear programming problems. It provides two examples of finding the minimum and maximum values of objective functions subject to certain constraints. In the first example, the objective is to minimize or maximize the function f(x,y)=3x-2y within the constraints 1≤x≤5, y≥2, and y≤x+3. In the second example, the objective is to minimize or maximize the function f(x,y)=4x+3y within the constraints y≥-x+2, y≤(1/4)x+2, and y≥2x-5. Both examples solve the problems by finding the vertices of the constrained regions and calculating the objective
Quadratic equations 7
The document discusses solving the equation Log9 (x – 3) = Log3 (x – 7) for the number of real values of x. It is shown that the equation can be rewritten as x2 – 15x + 52 = 0, which has a discriminant of 17, indicating two possible solutions. However, one solution is less than 7, and the log function is only defined for positive terms greater than 7. Therefore, there is only one real solution for x. The number of real values for x is 1.
Writing quadratic equation
The document provides 5 examples of writing quadratic equations in the standard form of ax^2 + bx + c = 0. Each example expresses a given equation in terms of x and then identifies the coefficients a, b, and c. For example 1, the equation x^2 = 5 - 2x is written as x^2 + 2x - 5 = 0, with a = 1, b = 2, c = -5. The examples demonstrate how to rearrange various equations involving x terms and constants into the standard quadratic form.
Adición y sustracción de fracciones
1. The document discusses adding and subtracting fractions with both equal and unequal denominators. It provides examples of finding a common denominator and then adding or subtracting the numerators.
2. It also provides examples of factoring expressions before combining like terms, as well as canceling terms before simplifying fractions.
3. The document concludes by solving two multi-step word problems involving fractions.
Matrices 44.4
The document discusses matrix operations including addition, subtraction, and scalar multiplication of matrices. It provides examples of adding and subtracting matrices according to the rules of matrix arithmetic. The document also discusses solving matrix equations by setting matrix expressions equal to each other and solving the resulting systems of equations for the unknown values.
Composite function bingo
This document contains 16 problems involving composition of functions. For each problem, two functions f(x) and g(x) are defined, and an expression involving composition of those functions is given to evaluate or determine.
Difference of squares
This document discusses factoring perfect-square trinomials, which are expressions of the form a^2x^2 ± 2abx + b^2. It provides examples of factoring different trinomials like x^2 - 49, 9a^2 - 25b^2, and 16x^4 - 64y^2. Readers are instructed to practice factoring additional examples like x^2 - 49, c^2 - 81, 4x^2 - 25, a^2b^2 - 64c^2, and 25x^2 - 121y^2.
Module of integer exponents
The document defines and provides examples of absolute value, operations on real numbers including addition, subtraction, multiplication and division of signed numbers, powers and roots. Absolute value of a number is its distance from the origin on a number line. Rules for addition and subtraction of signed numbers include adding/subtracting absolute values and determining the sign based on unlike or like signs. Multiplication and division of signed numbers involves multiplying/dividing absolute values and determining the sign based on the numbers having the same or different signs.
Chapter 1 test corrections (algebra)
This document contains corrections to problems on a chapter 1 test. It provides the work and solutions to problems involving fractions, solving equations, simplifying algebraic expressions, identifying counterexamples, and writing verbal expressions algebraically and vice versa.
5.1 5.3 Review Power Point
The document contains 7 math word problems involving concepts like:
1) Identifying if a set of ordered pairs represents a function.
2) Solving for a missing value in an ordered pair to satisfy an equation.
3) Identifying the slope between two points as negative.
4) Calculating the slope between two points by using the rise over run formula.
5) Finding the slope when the rise and run are given.
6) Calculating the slope between two points.
7) Writing an equation to represent a direct variation relationship when given the constant of variation.
6 3 Add,Sub,Mult Polynomials
The document provides examples and explanations of adding, subtracting, multiplying polynomials and binomials. It discusses key concepts like like terms, the FOIL method, and patterns in binomial products. Examples are provided to demonstrate multiplying polynomials vertically and horizontally, using the distributive property, and finding the cube of a binomial.
Chapter 5 case study
This document provides definitions and key features of case study research. It defines a case study as an in-depth investigation of a contemporary phenomenon in its real-life context. Case studies look closely at one or a small number of organizations, events, or individuals, usually over time. The goal is to develop a comprehensive understanding of the specific case. Case studies are appropriate when researchers are asking "how" and "why" questions about contemporary events over which they have little control.
Chapter 4 common features of qualitative data analysis
This document provides guidance on qualitative data analysis methods, including:
- The process of immersion in qualitative data through repeated reading/listening to become familiar with the content.
- Coding qualitative data by applying abstract representations or labels to segments of data that are relevant to the research question.
- Developing codes that are data-derived (based on the explicit content) or researcher-derived (conceptual interpretations).
- Using analytical memos and diaries to document the analysis process, including emerging codes, themes, and interpretations.
- Identifying themes by examining codes for patterns and relationships that answer the research question. Themes capture broader meanings than codes.
More Related Content
What's hot
Squaring binomials
This document discusses squaring binomial expressions. It provides three examples of squaring binomials of the form (x + a), showing that (x + a)2 = x2 + 2a*x + a2. Specifically, it squares (x + 3), (b - 5), and (m - 15) to get x2 + 6x + 9, b2 - 10b + 25, and m2 - 60m + 225 respectively.
2.7 more parabolas a& hyperbolas (optional) t
The document provides examples of how to graph and identify properties of hyperbolas and parabolas. It includes:
1) An example of a hyperbola with center (3, -1), x-radius of 4, y-radius of 2, and vertices of (7, -1) and (-1, -1).
2) Steps for completing the square to put a quadratic equation into standard form for a hyperbola, including an example starting with 4y^2 - 9x^2 - 18x - 16y = 29.
3) An example of graphing a parabola given by the equation x = -y^2 + 2y + 15, identifying
MATH: ORDER OF OPERATIONS
1. Student X was first in line, Student Z was second, Student Y was third, and Student L was last.
2. The order of operations is: multiply, subtract, square, multiply.
3. Order of operations dictates that exponents, multiplication/division from left to right, then addition/subtraction from left to right must be followed when evaluating expressions.
Mcqs
The document contains a multiple choice quiz with 35 questions testing mathematical concepts. The questions cover topics like sets, operations, ratios, proportions, factors, primes and more. For each question there are 4 possible answer choices to choose from.
3.4 a linear programming
The document discusses using linear programming to find the maximum and minimum values of an objective function given certain constraints. It provides an example of finding the minimum and maximum values of the function f(x,y)=3x-2y when constrained by y≥2, 1≤x≤5, and y≤x+3. The values are found by graphing the inequalities to determine the vertices and substituting the vertices into the objective function.
Add,sub,mult polynomials
1) To add or subtract polynomials, combine like terms by adding or subtracting their coefficients.
2) To multiply polynomials, use FOIL or the distributive property to multiply each term of one factor with each term of the other.
3) Important patterns for multiplying binomials include the sum and difference pattern, square of a binomial, and cube of a binomial.
2.5 conic sections circles-t
The document provides examples of writing the equation of a circle given its center and radius or vice versa. It demonstrates:
1) Writing the equation (x-h)2 + (y-k)2 = r2 given the center (h,k) and radius r.
2) Finding the center and radius from an equation by completing the square and rewriting it in standard form.
3) Identifying the center, radius, and extreme points to graph the circle.
10 mathfinal2011review
The document contains 25 math problems involving simplifying expressions, evaluating expressions for given values, writing expressions in algebraic form, combining like terms, expanding, factoring, solving equations, working with polygons, and trigonometric functions. The problems cover a wide range of algebra and geometry topics tested on standardized exams.
Algebra review
This document provides 20 algebra problems involving simplifying expressions, solving equations, graphing lines, writing equations in slope-intercept form, determining if lines are parallel or perpendicular, and operations with scientific notation. Students are instructed to show all work.
3.4 linear programming
The document discusses linear programming problems. It provides two examples of finding the minimum and maximum values of objective functions subject to certain constraints. In the first example, the objective is to minimize or maximize the function f(x,y)=3x-2y within the constraints 1≤x≤5, y≥2, and y≤x+3. In the second example, the objective is to minimize or maximize the function f(x,y)=4x+3y within the constraints y≥-x+2, y≤(1/4)x+2, and y≥2x-5. Both examples solve the problems by finding the vertices of the constrained regions and calculating the objective
Quadratic equations 7
The document discusses solving the equation Log9 (x – 3) = Log3 (x – 7) for the number of real values of x. It is shown that the equation can be rewritten as x2 – 15x + 52 = 0, which has a discriminant of 17, indicating two possible solutions. However, one solution is less than 7, and the log function is only defined for positive terms greater than 7. Therefore, there is only one real solution for x. The number of real values for x is 1.
Writing quadratic equation
The document provides 5 examples of writing quadratic equations in the standard form of ax^2 + bx + c = 0. Each example expresses a given equation in terms of x and then identifies the coefficients a, b, and c. For example 1, the equation x^2 = 5 - 2x is written as x^2 + 2x - 5 = 0, with a = 1, b = 2, c = -5. The examples demonstrate how to rearrange various equations involving x terms and constants into the standard quadratic form.
Adición y sustracción de fracciones
1. The document discusses adding and subtracting fractions with both equal and unequal denominators. It provides examples of finding a common denominator and then adding or subtracting the numerators.
2. It also provides examples of factoring expressions before combining like terms, as well as canceling terms before simplifying fractions.
3. The document concludes by solving two multi-step word problems involving fractions.
Matrices 44.4
The document discusses matrix operations including addition, subtraction, and scalar multiplication of matrices. It provides examples of adding and subtracting matrices according to the rules of matrix arithmetic. The document also discusses solving matrix equations by setting matrix expressions equal to each other and solving the resulting systems of equations for the unknown values.
Composite function bingo
This document contains 16 problems involving composition of functions. For each problem, two functions f(x) and g(x) are defined, and an expression involving composition of those functions is given to evaluate or determine.
Difference of squares
This document discusses factoring perfect-square trinomials, which are expressions of the form a^2x^2 ± 2abx + b^2. It provides examples of factoring different trinomials like x^2 - 49, 9a^2 - 25b^2, and 16x^4 - 64y^2. Readers are instructed to practice factoring additional examples like x^2 - 49, c^2 - 81, 4x^2 - 25, a^2b^2 - 64c^2, and 25x^2 - 121y^2.
Module of integer exponents
The document defines and provides examples of absolute value, operations on real numbers including addition, subtraction, multiplication and division of signed numbers, powers and roots. Absolute value of a number is its distance from the origin on a number line. Rules for addition and subtraction of signed numbers include adding/subtracting absolute values and determining the sign based on unlike or like signs. Multiplication and division of signed numbers involves multiplying/dividing absolute values and determining the sign based on the numbers having the same or different signs.
Chapter 1 test corrections (algebra)
This document contains corrections to problems on a chapter 1 test. It provides the work and solutions to problems involving fractions, solving equations, simplifying algebraic expressions, identifying counterexamples, and writing verbal expressions algebraically and vice versa.
5.1 5.3 Review Power Point
The document contains 7 math word problems involving concepts like:
1) Identifying if a set of ordered pairs represents a function.
2) Solving for a missing value in an ordered pair to satisfy an equation.
3) Identifying the slope between two points as negative.
4) Calculating the slope between two points by using the rise over run formula.
5) Finding the slope when the rise and run are given.
6) Calculating the slope between two points.
7) Writing an equation to represent a direct variation relationship when given the constant of variation.
6 3 Add,Sub,Mult Polynomials
The document provides examples and explanations of adding, subtracting, multiplying polynomials and binomials. It discusses key concepts like like terms, the FOIL method, and patterns in binomial products. Examples are provided to demonstrate multiplying polynomials vertically and horizontally, using the distributive property, and finding the cube of a binomial.
What's hot (20)
More from Mohd. Noor Abdul Hamid
Chapter 5 case study
This document provides definitions and key features of case study research. It defines a case study as an in-depth investigation of a contemporary phenomenon in its real-life context. Case studies look closely at one or a small number of organizations, events, or individuals, usually over time. The goal is to develop a comprehensive understanding of the specific case. Case studies are appropriate when researchers are asking "how" and "why" questions about contemporary events over which they have little control.
Chapter 4 common features of qualitative data analysis
This document provides guidance on qualitative data analysis methods, including:
- The process of immersion in qualitative data through repeated reading/listening to become familiar with the content.
- Coding qualitative data by applying abstract representations or labels to segments of data that are relevant to the research question.
- Developing codes that are data-derived (based on the explicit content) or researcher-derived (conceptual interpretations).
- Using analytical memos and diaries to document the analysis process, including emerging codes, themes, and interpretations.
- Identifying themes by examining codes for patterns and relationships that answer the research question. Themes capture broader meanings than codes.
Chapter 2 incorporating theory and conducting literature search and review
This document discusses qualitative research methods and literature reviews. It provides information on:
1) The key aspects of qualitative research including a focus on meaning rather than just occurrences, searching for concepts and theories rather than just data, and avoiding stereotypes that do not include concepts or theories.
2) Different approaches to qualitative research including inductive bottom-up approaches and deductive top-down approaches.
3) Steps for conducting a systematic literature review including planning, identification of research, selection and assessment of studies, data extraction, synthesis, and reporting. The goal is to be comprehensive and objective.
System and Information Quality
This document discusses information systems and decision support systems. It defines an information system as a system whose purpose is to store, process, and communicate information. A decision support system is defined as an information system that uses one or more databases to provide information to support decision making, does not update the databases it uses, and communicates with the decision maker. The document also discusses information quality and factors that impact quality such as relevance, correctness, accuracy, and timeliness.
The process of making a decision
This document discusses decision making methods and factors that influence decision making. It describes the Kepner-Tregoe decision making method which involves defining the problem, generating alternatives, establishing objectives, evaluating alternatives against objectives, and making a final choice. It also discusses how psychological types, culture, and decision structure (structured, semi-structured, unstructured) can impact decision making.
Introduction to DSS
This document provides an overview of decision support systems (DSS), including their history, evolution, definitions, components, users, and categories. It discusses how DSS have developed from early computers used for calculations during World War II to today's data-driven systems. A DSS is defined as an information system that provides knowledge workers with information to make informed decisions. Key components of a DSS include a database, model base, knowledge base, and user interface. DSS support but do not replace human decision makers such as executives and managers. Common categories of DSS are data-driven versus model-driven and individual versus group-oriented systems.
Classification Using Decision tree
The document provides an introduction to classification techniques in machine learning. It defines classification as assigning objects to predefined categories based on their attributes. The goal is to build a model from a training set that can accurately classify previously unseen records. Decision trees are discussed as a popular classification technique that recursively splits data into more homogeneous subgroups based on attribute tests. The document outlines the process of building decision trees, including selecting splitting attributes, stopping criteria, and evaluating performance on a test set. Examples are provided to illustrate classification tasks and building a decision tree model.
Decision tree Using c4.5 Algorithm
The document describes the C4.5 algorithm for building decision trees. It begins with an overview of decision trees and the goals of minimizing tree levels and nodes. It then outlines the steps of the C4.5 algorithm: 1) Choose the attribute that best differentiates training instances, 2) Create a tree node for that attribute and child nodes for each value, 3) Recursively create subordinate nodes until reaching criteria or no remaining attributes. An example applies these steps to build a decision tree to predict customers' responses to a life insurance promotion using attributes like age, income and insurance status.
Types of functions and their domain & range - mohd noor
This document defines and provides examples of constant and linear functions. A constant function has values that do not vary, with examples given by y=5 and x=50. A linear function is a first degree polynomial of one variable in the form of y=mx+c, where m is the slope and c is the y-intercept. Linear functions are represented by straight lines that can be skewed left if m<0 or right if m>0. Examples of linear functions and their domains and ranges are given.
Limit - Mohd Noor
This document discusses how to calculate limits of functions as the input value approaches a given number. It explains how to build left and right tables to determine one-sided limits and check if the left and right limits are equal to determine if the overall limit exists. It also discusses special cases for calculating limits of rational functions and limits as the input approaches infinity. The key steps are to identify the terms with the highest powers, eliminate lesser terms, simplify, and substitute the given input value.
Lagrange Multiplier - Mohd Moor
This document discusses maximizing production levels for t-shirts and pants given constraints. It introduces Mohd Noor Abdul Hamid and provides his contact information. The level of production is defined by an equation using variables x for t-shirts and y for pants. The objective is to maximize production and the constraint is that 1.5x + 2y must equal 250 meters of fabric.
Introduction to Function, Domain and Range - Mohd Noor
This slide introduce the concept of mathematical function as well as the concepts of domain and range.
Introduction to Exponential Function - Mohd noor
To cut a pizza into 8 equal pieces with 3 cuts:
1) Cut the pizza in half, making 2 pieces.
2) Stack the 2 pieces and cut again, making 4 pieces.
3) Stack the 4 pieces and cut again, making the final 8 pieces.
The number of pieces grows exponentially based on the number of cuts, following the formula N = 2c, where N is the number of pieces and c is the number of cuts.
Differentiation using First Principle - By Mohd Noor Abdul Hamid
1. The document discusses the concept of the derivative and differentiation using the first principle. It explains how to calculate the slope of a tangent line to a curve at a point using limits, which gives the derivative of the function at that point.
2. Rules for differentiating common functions like polynomials, exponentials, and logarithms are covered. Higher-order derivatives and applications of derivatives to business and economics are also mentioned.
3. The goals of the class are to explain the concept of the derivative, differentiate functions using the first principle (limits), and understand various differentiation rules.
More from Mohd. Noor Abdul Hamid (14)
Chapter 4 common features of qualitative data analysis
Chapter 4 common features of qualitative data analysis
Chapter 2 incorporating theory and conducting literature search and review
Chapter 2 incorporating theory and conducting literature search and review
Types of functions and their domain & range - mohd noor
Types of functions and their domain & range - mohd noor
Introduction to Function, Domain and Range - Mohd Noor
Introduction to Function, Domain and Range - Mohd Noor
Differentiation using First Principle - By Mohd Noor Abdul Hamid
Differentiation using First Principle - By Mohd Noor Abdul Hamid
Recently uploaded
Hindi varnamala | hindi alphabet PPT.pdf
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaAdvanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Recently uploaded (20)
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Domain & Range (from graph) - Mohd Noor
- 1. F R O M G R A P H Mohd Noor Abdul Hamid, Ph.D
- 2. a) g(-3) = 2
- 3. b) g(3) = Not define
- 4. c)g(∞) ∞ = 6 d) g(-∞) = ??
- 5. DOMAIN = -∞ -3 3 +∞ { any number from -∞ to +∞ except 3} = { x Є R, x ≠ 3 }
- 6. RANGE = -∞ -2 0 4 6 { y <-2, 0 ≤ y < 4 and y =6 }