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Application of Derivative Class 12th Best Project by Shubham prasad

Application of Derivative Class 12th Best Project by Shubham prasad, Student of Nalanda English Medium School Kurud Bhilai Durg Chhattisgarh.
Art Integrated Learning on Mathematics branch Application of Derivatives Class 12th Ncert

Applications of Derivatives

This document discusses the definition, notation, history, and applications of derivatives. It begins by defining a derivative as the instantaneous rate of change of a quantity with respect to another. It then discusses differentiation, derivative notation, and the history of derivatives developed by Newton and Leibniz. Real-life applications described include using derivatives in automobiles, radar guns, and analyzing graphs. Derivatives are also applied in physics to calculate velocity and acceleration, and in mathematics to find extreme values and use the Mean Value Theorem.

Derivatives and it’s simple applications

The document provides an introduction to derivatives and their applications. It defines the derivative as the rate of change of a function near an input value and discusses how it relates geometrically to the slope of the tangent line. It then gives examples of finding the derivatives of common functions like constants, polynomials, and exponentials. The document also covers basic derivative rules like the constant multiple rule, sum and difference rules, product rule, and quotient rule. Finally, it discusses applications of derivatives in topics like physics, such as calculating velocity and acceleration from a position function.

Applications of derivative

The document defines the derivative as the exact rate at which one quantity changes with respect to another. It discusses the history of differentiation, credited to Isaac Newton and Gottfried Leibniz in the 17th century. Real-life applications of derivatives include using them to calculate speed from a car's odometer and distance traveled or to determine speed from a police radar gun. Derivatives also have various applications in science, business, physics, chemistry, and mathematics.

Application of derivative

Additional Applications of the Derivative related to engineering maths
this presentation is only for the knowledge...............

Integral calculus

1) The document discusses basic rules and concepts of integration, including that integration is the inverse process of differentiation and that the indefinite integral of a function f(x) is notated as ∫f(x) dx = F(x) + c, where F(x) is the primitive function and c is the constant of integration.
2) Methods of integration discussed include the substitution method, where a function is substituted for the variable, and integration by parts, which uses the product rule in reverse to solve integrals involving products.
3) Finding the constant of integration c requires knowing the value of the primitive function F(x) at a specific point, which eliminates the family of functions and isolates a

Calculus

This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

derivatives math

This document is a presentation submitted by a group of 6 mechanical engineering students to their professor. It contains an introduction, definitions of derivatives, a brief history of derivatives attributed to Newton and Leibniz, and applications of derivatives in various fields such as automobiles, radar guns, business, physics, biology, chemistry, and mathematics. It also provides rules and examples of calculating derivatives using power, multiplication by constant, sum, difference, product, quotient and chain rules.

Application of Derivative Class 12th Best Project by Shubham prasad

Application of Derivative Class 12th Best Project by Shubham prasad, Student of Nalanda English Medium School Kurud Bhilai Durg Chhattisgarh.
Art Integrated Learning on Mathematics branch Application of Derivatives Class 12th Ncert

Applications of Derivatives

This document discusses the definition, notation, history, and applications of derivatives. It begins by defining a derivative as the instantaneous rate of change of a quantity with respect to another. It then discusses differentiation, derivative notation, and the history of derivatives developed by Newton and Leibniz. Real-life applications described include using derivatives in automobiles, radar guns, and analyzing graphs. Derivatives are also applied in physics to calculate velocity and acceleration, and in mathematics to find extreme values and use the Mean Value Theorem.

Derivatives and it’s simple applications

The document provides an introduction to derivatives and their applications. It defines the derivative as the rate of change of a function near an input value and discusses how it relates geometrically to the slope of the tangent line. It then gives examples of finding the derivatives of common functions like constants, polynomials, and exponentials. The document also covers basic derivative rules like the constant multiple rule, sum and difference rules, product rule, and quotient rule. Finally, it discusses applications of derivatives in topics like physics, such as calculating velocity and acceleration from a position function.

Applications of derivative

The document defines the derivative as the exact rate at which one quantity changes with respect to another. It discusses the history of differentiation, credited to Isaac Newton and Gottfried Leibniz in the 17th century. Real-life applications of derivatives include using them to calculate speed from a car's odometer and distance traveled or to determine speed from a police radar gun. Derivatives also have various applications in science, business, physics, chemistry, and mathematics.

Application of derivative

Additional Applications of the Derivative related to engineering maths
this presentation is only for the knowledge...............

Integral calculus

1) The document discusses basic rules and concepts of integration, including that integration is the inverse process of differentiation and that the indefinite integral of a function f(x) is notated as ∫f(x) dx = F(x) + c, where F(x) is the primitive function and c is the constant of integration.
2) Methods of integration discussed include the substitution method, where a function is substituted for the variable, and integration by parts, which uses the product rule in reverse to solve integrals involving products.
3) Finding the constant of integration c requires knowing the value of the primitive function F(x) at a specific point, which eliminates the family of functions and isolates a

Calculus

This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

derivatives math

This document is a presentation submitted by a group of 6 mechanical engineering students to their professor. It contains an introduction, definitions of derivatives, a brief history of derivatives attributed to Newton and Leibniz, and applications of derivatives in various fields such as automobiles, radar guns, business, physics, biology, chemistry, and mathematics. It also provides rules and examples of calculating derivatives using power, multiplication by constant, sum, difference, product, quotient and chain rules.

A presentation on differencial calculus

This presentation provides an introduction to differential calculus. It defines calculus and differentiation, and classifies calculus into differential calculus and integral calculus. Differential calculus deals with finding rates of change of functions with respect to variables using derivatives, while integral calculus involves determining lengths, areas, volumes, and solving differential equations using integrals. The presentation explains key calculus concepts like derivatives, differentiation, and differential curves. It concludes by presenting some common formulas for differentiation.

Applications of Integrations

The document discusses various applications of the definite integral, including finding the area under a curve, the area between two curves, and the volume of solids of revolution. It provides examples of calculating each of these, such as finding the area between the curves y=x and y=x5 from x=-1 to x=0. It also explains how to set up definite integrals to calculate volumes when rotating an area about the x- or y-axis. In conclusion, it states that integrals can represent areas or generalized areas and are fundamental objects in calculus, along with derivatives.

Continuity and differentiability

The document discusses key concepts in calculus including continuity, differentiation, integration, and their applications. It defines continuity as being able to draw a function's graph without lifting the pen, and differentiation as computing the rate of change of a dependent variable with respect to changes in the independent variable. The document also covers differentiation rules and techniques for implicit, inverse, exponential, logarithmic, and parametric functions.

Derivatives and their Applications

Derivatives & their Applications, rules of derivatives, derivatives formulas, Derivative Notations, reverse of differentiation

Application of derivatives

The document discusses applications of differentiation, including:
- How derivatives help locate maximum and minimum values of functions by determining if a function is increasing or decreasing over an interval.
- Examples of optimization problems involving finding maximum/minimum values, such as the optimal shape of a can.
- Key terms related to maximum/minimum values including local/global extrema, critical points, and how the first and second derivatives relate to concavity.
- An example problem involving finding the maximum area of a rectangular temple room given a perimeter constraint.

Differential calculus

Differential calculus is the study of rates of change of functions using limits and derivatives. The derivative of a function represents the rate of change of the output variable with respect to the input variable or slope at a point. A function is continuous if it has no holes or jumps at any point in its domain. The tangent line approximates the curve at a point, while the normal line is perpendicular to the tangent line. Maxima and minima refer to local extremes where the function reaches a maximum or minimum value. Derivatives can also be used to determine rates of change for a variety of applications.

Maxima and minima

This document discusses maxima and minima in the context of calculus. It provides examples of functions having maximum or minimum values at interior points or endpoints of an interval. It also discusses the first and second derivative tests for identifying maxima and minima. Examples are provided for finding the maximum area of a rectangular field given a perimeter, and finding the maximum volume of a cylinder given a surface area. Finally, some uses of maxima and minima concepts in fields like marketing and manufacturing are outlined.

Integrals and its applications

This document discusses integrals and their applications. It introduces integral calculus and its use in joining small pieces together to find amounts. It lists several types of integrals and mathematicians influential in integral calculus development like Euclid, Archimedes, Newton, and Riemann. The document also discusses applications of integration in business processes, automation tools for integrating disparate applications, and applications of very large scale integration circuit design.

The Application of Derivatives

This document discusses several topics related to calculus including:
1) Derivatives of position, velocity, and acceleration and how they relate to each other.
2) An example problem calculating velocity from a position function.
3) The Mean Value Theorem and how to apply it to find critical points of a function.
4) How the first and second derivatives of a function relate to critical points, maxima, minima, and points of inflection or concavity.
5) Related rates problems and how to set them up using derivatives and relationships between variables.

Integration

This document discusses integration in mathematics. It defines integration as the process opposite to differentiation, where integration finds the direct relationship between two variables given their rate of change. Several techniques for integration are described, including integration by parts and substitution. The document outlines the history of integration and its applications in fields like engineering, business, and its use in estimating important values.

Real Life Application of Vector

This presentation is related to real life application of vector. Where vector is used in our life e.g projectile,in gaming,avoiding crosswind,aviation,designing roller coaster etc.

Real life application of Function.

The document discusses the many uses of functions and calculus across various fields. It notes that functions were initially developed for better navigation systems and are now used in fields like engineering, robotics, computer hardware, vehicle safety, ecosystem modeling, medicine, economics, business, and astronomy. Functions allow modeling relationships between variables and are essential mathematical tools for describing physical systems and solving optimization problems.

Differentiation

The document discusses differentiation and its applications. It provides a brief history of differentiation and introduces concepts such as the derivative and reverse process of integration. Some key applications of differentiation discussed include using it to determine maximum/minimum values, in subjects like physics, chemistry, and economics, and in devices like odometers, speedometers, and radar guns. Two surveys were conducted on the awareness and uses of differentiation. In conclusion, differentiation can help improve devices and make tomorrow better by finding how one variable changes with respect to another.

Application of derivatives 2 maxima and minima

This document discusses key concepts related to derivatives and their applications:
- It defines increasing and decreasing functions and explains how to determine if a function is increasing or decreasing based on the sign of the derivative.
- It introduces the use of derivatives to find maximum and minimum values, extreme points, and critical points of functions.
- Theorems 1 and 2 provide rules for determining if a critical point represents a maximum or minimum.
- Examples are provided to demonstrate finding the intervals where a function is increasing/decreasing, identifying extrema, and determining the greatest and least function values over an interval.

Benginning Calculus Lecture notes 2 - limits and continuity

This document discusses limits and continuity in calculus. It begins by defining limits and providing examples of computing limits of functions. It then covers one-sided limits, properties of limits, and using direct substitution to evaluate limits. The document also discusses limits of trigonometric functions and infinite limits. The overall goal is to determine the existence of limits, compute limits, understand continuity of functions, and connect the ideas of limits and continuity.

Rules of derivative

This document discusses differentiation and derivatives. It defines differentiation as finding the average rate of change of one variable with respect to another. It then discusses various methods of finding derivatives, including the direct method using derivative rules, as well as discussing specific rules like the power rule, product rule, quotient rule, chain rule, and rules for derivatives of trigonometric, exponential, and logarithmic functions.

MEAN VALUE THEOREM

The document discusses the Mean Value Theorem, which states that if a function f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists some value c in (a,b) such that:
f(b) - f(a) = f'(c)(b - a)
In other words, there is at least one point where the slope of the tangent line equals the slope of the secant line between points a and b. The document provides examples and illustrations to demonstrate how to apply the Mean Value Theorem.

Basic Calculus 11 - Derivatives and Differentiation Rules

It is a powerpoint presentation that discusses about the lesson or topic of Derivatives and Differentiation Rules. It also encompasses some formulas, definitions and examples regarding the said topic.

Laplace Transformation & Its Application

This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.

Complex Numbers

iTutor provides information on complex numbers. Complex numbers consist of real and imaginary parts and can be written as a + bi, where a is the real part and b is the imaginary part. The imaginary unit i = √-1. Properties of complex numbers include: the square of i is -1; complex conjugates are obtained by changing the sign of the imaginary part; and the basic arithmetic operations of addition, subtraction, and multiplication follow predictable rules when applied to complex numbers. Complex numbers allow representing solutions, like the square root of a negative number, that are not possible with real numbers alone.

differentiation (1).pptx

This document provides an overview of differentiation and derivatives. It defines the derivative as the instantaneous rate of change of a quantity with respect to another. The process of finding derivatives is called differentiation. Isaac Newton and Gottfried Leibniz developed the fundamental theorem of calculus in the 17th century. Derivatives have many applications across various sciences such as physics, biology, economics, and chemistry. They are used to calculate velocity, acceleration, population growth rates, marginal costs/revenues, reaction rates, and more.

Mathematician inretgrals.pdf

This document outlines a group project on derivatives. It includes definitions of derivatives, a brief history of their development, and examples of applications in various fields such as automobiles, business, and mathematics. Rules for finding derivatives of sums, quotients, logarithmic, trigonometric, and exponential functions are also presented, along with examples of applying the rules to calculate derivatives.

A presentation on differencial calculus

This presentation provides an introduction to differential calculus. It defines calculus and differentiation, and classifies calculus into differential calculus and integral calculus. Differential calculus deals with finding rates of change of functions with respect to variables using derivatives, while integral calculus involves determining lengths, areas, volumes, and solving differential equations using integrals. The presentation explains key calculus concepts like derivatives, differentiation, and differential curves. It concludes by presenting some common formulas for differentiation.

Applications of Integrations

The document discusses various applications of the definite integral, including finding the area under a curve, the area between two curves, and the volume of solids of revolution. It provides examples of calculating each of these, such as finding the area between the curves y=x and y=x5 from x=-1 to x=0. It also explains how to set up definite integrals to calculate volumes when rotating an area about the x- or y-axis. In conclusion, it states that integrals can represent areas or generalized areas and are fundamental objects in calculus, along with derivatives.

Continuity and differentiability

The document discusses key concepts in calculus including continuity, differentiation, integration, and their applications. It defines continuity as being able to draw a function's graph without lifting the pen, and differentiation as computing the rate of change of a dependent variable with respect to changes in the independent variable. The document also covers differentiation rules and techniques for implicit, inverse, exponential, logarithmic, and parametric functions.

Derivatives and their Applications

Derivatives & their Applications, rules of derivatives, derivatives formulas, Derivative Notations, reverse of differentiation

Application of derivatives

The document discusses applications of differentiation, including:
- How derivatives help locate maximum and minimum values of functions by determining if a function is increasing or decreasing over an interval.
- Examples of optimization problems involving finding maximum/minimum values, such as the optimal shape of a can.
- Key terms related to maximum/minimum values including local/global extrema, critical points, and how the first and second derivatives relate to concavity.
- An example problem involving finding the maximum area of a rectangular temple room given a perimeter constraint.

Differential calculus

Differential calculus is the study of rates of change of functions using limits and derivatives. The derivative of a function represents the rate of change of the output variable with respect to the input variable or slope at a point. A function is continuous if it has no holes or jumps at any point in its domain. The tangent line approximates the curve at a point, while the normal line is perpendicular to the tangent line. Maxima and minima refer to local extremes where the function reaches a maximum or minimum value. Derivatives can also be used to determine rates of change for a variety of applications.

Maxima and minima

This document discusses maxima and minima in the context of calculus. It provides examples of functions having maximum or minimum values at interior points or endpoints of an interval. It also discusses the first and second derivative tests for identifying maxima and minima. Examples are provided for finding the maximum area of a rectangular field given a perimeter, and finding the maximum volume of a cylinder given a surface area. Finally, some uses of maxima and minima concepts in fields like marketing and manufacturing are outlined.

Integrals and its applications

This document discusses integrals and their applications. It introduces integral calculus and its use in joining small pieces together to find amounts. It lists several types of integrals and mathematicians influential in integral calculus development like Euclid, Archimedes, Newton, and Riemann. The document also discusses applications of integration in business processes, automation tools for integrating disparate applications, and applications of very large scale integration circuit design.

The Application of Derivatives

This document discusses several topics related to calculus including:
1) Derivatives of position, velocity, and acceleration and how they relate to each other.
2) An example problem calculating velocity from a position function.
3) The Mean Value Theorem and how to apply it to find critical points of a function.
4) How the first and second derivatives of a function relate to critical points, maxima, minima, and points of inflection or concavity.
5) Related rates problems and how to set them up using derivatives and relationships between variables.

Integration

This document discusses integration in mathematics. It defines integration as the process opposite to differentiation, where integration finds the direct relationship between two variables given their rate of change. Several techniques for integration are described, including integration by parts and substitution. The document outlines the history of integration and its applications in fields like engineering, business, and its use in estimating important values.

Real Life Application of Vector

This presentation is related to real life application of vector. Where vector is used in our life e.g projectile,in gaming,avoiding crosswind,aviation,designing roller coaster etc.

Real life application of Function.

The document discusses the many uses of functions and calculus across various fields. It notes that functions were initially developed for better navigation systems and are now used in fields like engineering, robotics, computer hardware, vehicle safety, ecosystem modeling, medicine, economics, business, and astronomy. Functions allow modeling relationships between variables and are essential mathematical tools for describing physical systems and solving optimization problems.

Differentiation

The document discusses differentiation and its applications. It provides a brief history of differentiation and introduces concepts such as the derivative and reverse process of integration. Some key applications of differentiation discussed include using it to determine maximum/minimum values, in subjects like physics, chemistry, and economics, and in devices like odometers, speedometers, and radar guns. Two surveys were conducted on the awareness and uses of differentiation. In conclusion, differentiation can help improve devices and make tomorrow better by finding how one variable changes with respect to another.

Application of derivatives 2 maxima and minima

This document discusses key concepts related to derivatives and their applications:
- It defines increasing and decreasing functions and explains how to determine if a function is increasing or decreasing based on the sign of the derivative.
- It introduces the use of derivatives to find maximum and minimum values, extreme points, and critical points of functions.
- Theorems 1 and 2 provide rules for determining if a critical point represents a maximum or minimum.
- Examples are provided to demonstrate finding the intervals where a function is increasing/decreasing, identifying extrema, and determining the greatest and least function values over an interval.

Benginning Calculus Lecture notes 2 - limits and continuity

This document discusses limits and continuity in calculus. It begins by defining limits and providing examples of computing limits of functions. It then covers one-sided limits, properties of limits, and using direct substitution to evaluate limits. The document also discusses limits of trigonometric functions and infinite limits. The overall goal is to determine the existence of limits, compute limits, understand continuity of functions, and connect the ideas of limits and continuity.

Rules of derivative

This document discusses differentiation and derivatives. It defines differentiation as finding the average rate of change of one variable with respect to another. It then discusses various methods of finding derivatives, including the direct method using derivative rules, as well as discussing specific rules like the power rule, product rule, quotient rule, chain rule, and rules for derivatives of trigonometric, exponential, and logarithmic functions.

MEAN VALUE THEOREM

The document discusses the Mean Value Theorem, which states that if a function f(x) is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists some value c in (a,b) such that:
f(b) - f(a) = f'(c)(b - a)
In other words, there is at least one point where the slope of the tangent line equals the slope of the secant line between points a and b. The document provides examples and illustrations to demonstrate how to apply the Mean Value Theorem.

Basic Calculus 11 - Derivatives and Differentiation Rules

It is a powerpoint presentation that discusses about the lesson or topic of Derivatives and Differentiation Rules. It also encompasses some formulas, definitions and examples regarding the said topic.

Laplace Transformation & Its Application

This document presents an overview of the Laplace transform and its applications. It begins with an introduction to Laplace transforms as a mathematical tool to convert differential equations into algebraic expressions. It then provides definitions and properties of both the Laplace transform and its inverse. Examples are given of how Laplace transforms can be used to solve ordinary and partial differential equations, as well as applications in electrical circuits and other fields. The document concludes by noting some limitations of the Laplace transform method and references additional resources.

Complex Numbers

iTutor provides information on complex numbers. Complex numbers consist of real and imaginary parts and can be written as a + bi, where a is the real part and b is the imaginary part. The imaginary unit i = √-1. Properties of complex numbers include: the square of i is -1; complex conjugates are obtained by changing the sign of the imaginary part; and the basic arithmetic operations of addition, subtraction, and multiplication follow predictable rules when applied to complex numbers. Complex numbers allow representing solutions, like the square root of a negative number, that are not possible with real numbers alone.

A presentation on differencial calculus

A presentation on differencial calculus

Applications of Integrations

Applications of Integrations

Continuity and differentiability

Continuity and differentiability

Derivatives and their Applications

Derivatives and their Applications

Application of derivatives

Application of derivatives

Differential calculus

Differential calculus

Maxima and minima

Maxima and minima

Integrals and its applications

Integrals and its applications

The Application of Derivatives

The Application of Derivatives

Integration

Integration

Real Life Application of Vector

Real Life Application of Vector

Real life application of Function.

Real life application of Function.

Differentiation

Differentiation

Application of derivatives 2 maxima and minima

Application of derivatives 2 maxima and minima

Benginning Calculus Lecture notes 2 - limits and continuity

Benginning Calculus Lecture notes 2 - limits and continuity

Rules of derivative

Rules of derivative

MEAN VALUE THEOREM

MEAN VALUE THEOREM

Basic Calculus 11 - Derivatives and Differentiation Rules

Basic Calculus 11 - Derivatives and Differentiation Rules

Laplace Transformation & Its Application

Laplace Transformation & Its Application

Complex Numbers

Complex Numbers

differentiation (1).pptx

This document provides an overview of differentiation and derivatives. It defines the derivative as the instantaneous rate of change of a quantity with respect to another. The process of finding derivatives is called differentiation. Isaac Newton and Gottfried Leibniz developed the fundamental theorem of calculus in the 17th century. Derivatives have many applications across various sciences such as physics, biology, economics, and chemistry. They are used to calculate velocity, acceleration, population growth rates, marginal costs/revenues, reaction rates, and more.

Mathematician inretgrals.pdf

This document outlines a group project on derivatives. It includes definitions of derivatives, a brief history of their development, and examples of applications in various fields such as automobiles, business, and mathematics. Rules for finding derivatives of sums, quotients, logarithmic, trigonometric, and exponential functions are also presented, along with examples of applying the rules to calculate derivatives.

Applications Of Math In Real Life And Business

The document provides an overview of topics in business mathematics including linear equations, cost-output functions, matrices, logarithmic and exponential functions, and their applications in business and real life. Examples of applications given include using linear equations to model costs, revenues, and profits; break-even analysis; modeling population growth with exponential functions; and using derivatives and integrals to solve problems in physics, engineering, and economics. The document aims to demonstrate how mathematics is relevant across many domains including business, science, and daily life.

Maths Investigatory Project Class 12 on Differentiation

This document provides an overview of differentiation and its applications. It defines differentiation as finding the slope of the tangent line to a function's graph at a given point, which provides the instantaneous rate of change. The document then lists the group members working on the topic, outlines the contents to be covered, and gives a brief history of differentiation. It provides definitions and graphical understandings of derivatives, discusses some basic differentiation formulas and their applications in mathematics, sciences, business, physics, chemistry and more. It concludes that derivatives are constantly used to measure rates of change in various everyday and professional contexts.

Finding the Extreme Values with some Application of Derivatives

There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint

Emm3104 chapter 1 part2

1. This document provides information about the Dynamics course EMM 3104 taught by Dr. Azizan As'arry in semester 1 of 2016-2017. It outlines the instructor details, textbook, course rules, objectives, evaluation, and introduction topics.
2. The course objectives are to relate concepts of rigid body motion, forces, moments, velocity and acceleration and solve problems involving rigid body motion.
3. The course is evaluated through two tests, assignments, and a final exam which make up 20%, 20%, 20%, and 40% of the final grade respectively.

Intro diffcall3b

This document provides an introduction to differential calculus. It begins by motivating the concept of instantaneous velocity and derivative using the example of calculating speed from position over time. It then discusses how the derivative can be used to calculate rates of change in various contexts from mechanics to economics. The document proceeds to define the gradient of tangents and secants to a graph, and introduces methods for calculating derivatives, such as the definition of the derivative and differentiation rules. It concludes by discussing the history of calculus and links to further topics.

At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins,.docx

At a Halloween pumpkin sale, Sara buys two sphere-shaped pumpkins, one with radius 3 inches and the other with radius 10 inches. Compute the surface area and the volume for each pumpkin. Then find the surface-area-to-volume ratio for both pumpkins. Which pumpkin has the larger ratio? (Do not round until the final answer. Then round to nearest tenth as needed.)
Find the angular size of a circular object with a 2-inch diameter viewed from a distance of 5 yards. (Do not round until the final answer. Then round to nearest tenth as needed.)
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of 64 squares of a chess board. On the second square the King would place two grains of wheat on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed in square 15? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.)
The initial population of a town is 3400, and it grows with a doubling time of 10 years. What will the population be in 12 years? (Round to the nearest whole number as needed.)
An economic indicator is increasing at the rate of 7% per year. What is its doubling time? By what factor will the indicator increase in 2 years? (Type an integer or decimal rounded to the nearest tenth as needed.)
The half-life of the radioactive element unobtanium-41 is 10 seconds. If 48 grams of unobtanium-41 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?
Urban encroachment is causing the area of a forest to decline at the rate of 9% per year. What is the half-life of the forest? What fraction of the forest will remain in 20 years? (Type an integer of decimal rounded to the nearest hundredth as needed.)
Use a growth rate of 0.6% to predict the population in 2038 of a country that in the year 2006 has a population of 400 million. Use the approximate doubling time formula. (Round the final answer to the nearest whole number as needed. Round the doubling time to the nearest year as needed.)
How many times greater is the intensityof sound from a concert speaker at a distant of 1 meter than the intensity at a distance of 14 meters?
The intensity of sound is times as strong at 1 m as at 14 m. (Simplify your answer.)
The concentration of hydroen ions in a liquid laboratory sample is 0.001 moles/liter. Find the pH of the sample. ph= (Simplify your answer.)
You drive along the highway at a constant speed of 60 miles per hour. How far do you travel in 4.7 hours? in 6.5 hours? (Type a integer or decimal.)
The price of a particular model car is $60,000 today and rises with time at a constant rate of $1,700 per year. How much will a new car cost in 5 years? Identify the independent and dependent varia ...

Caculus

Calculus involves the study of limits, derivatives, and integrals to understand changes in quantities. It was developed by Newton and Leibniz and is divided into differential and integral calculus. Differential calculus examines rates of change, while integral calculus concerns quantities given rates of change. Calculus is applied in fields like science, technology, physics, and engineering to model real-world systems and problems.

Caculus.pptx

Calculus is the major part of Mathematis. This theoretical presentation covered all relevant definations and systematic review points about calculus. It also brings and promote you towards in advance mathematics.

Calculus

This document is a report submitted by seven students to Sajal Chakroborty on the topic of calculus. It defines calculus and discusses its origins and inventors. It explains that calculus is used in physics, engineering, economics, and other fields. The document then covers topics within calculus including differentiation, integration, maxima and minima, and applications such as modeling tumor growth. It concludes that calculus has many real-world applications and has been crucial to advances in fields like engineering, science, and technology.

Mathematical modelling and its application in weather forecasting

what is mathematical modelling. how it is useful to us. future prediction with the help of mathematical modelling

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- 1. Derivatives
- 2. Submitted To: Ma’m Sapna Makhdoom Submitted By: •Irum GulBahar 02 •Hajrah Majeed 14 •Humera Yousaf 19 •Amna Ayub 21 Topic: Derivatives Session: 2013-17 Department: Mathematics Mirpur University Of Science & Technology (MUST)
- 4. • Dedication: We dedicate this project named “ Derivatives” to our parents and Family members.
- 5. • Abstract In this project we have discussed about Derivatives such as Definition , History, Real life applications, and Application of derivatives in different sciences.
- 6. • Acknowledgement First of all we would like to thank Allah almighty for making this project possible for us. Then special thanks to Ma’m Sapna Makhdoom for helping us in completing this project
- 7. Contents: 1. Definition of Derivative 2. History 3. Real life Applications 4. Applications in Sciences
- 8. Definition of Derivative: 1. The Derivative is the exact rate at which one quantity changes with respect to another. 2. Geometrically, the derivative is the slope of curve at the point on the curve. 3. The derivative is often called the “instantaneous “ rate of change. 4. The derivative of a function represents an infinitely small change the function with respect to one of its variables. • The Process of finding the derivative is called “differentiation.”
- 9. History: • Modern differentiation and derivatives are usually cradited to “Isaac Newton” and “Gottfried Leibniz”. • They developed the fundamental theorem of calculus in the 17th century. This related differentiation and integration in ways which revolutionized the methods for computing areas and volumes. • However , Newton’s work would not have been possible without the efforts of Isaac Borrow who began early development of the derivative in the 16th century.
- 10. Real life Applications of Derivatives
- 11. Automobiles • In an automobile there is always an odometer and a speedometer. These two gauges work in tandem and allow the driver to determine his speed and his distance that he has traveled. Electronic versions of these gauges simply use derivatives to transform the data sent to the electronic motherboard from the tires to miles per Hour(MPH) and distance(KM).
- 12. Radar Guns • Keeping with the automobile theme from the previous slide , all police officers who use radar guns are actually taking advantage of the easy use of derivatives. When a radar gun is pointed and fired at your care on the highway. The gun is able to determine the time and distance at which the radar was able to hit a certain section of your vehicle. With the use of derivative it is able to calculate the speed at which the car was going and also report the distance that the car was from the radar gun.
- 13. Business • In the business world there are many applications for derivatives. One of the most important application is when the data has been charted on graph or data table such as excel. Once it has been input, the data can be graphed and with the applications of derivatives you can estimate the profit and loss point for certain ventures.
- 14. Graphs: • The most common application of derivative is to analyze graphs of data that can be calculated from many different fields. Using derivative one is able to calculate the gradient at any point of a graph.
- 15. Applications of Derivatives in Various fields/Sciences: Such as in: –Physics –Biology –Economics –Chemistry –Mathematics –Others(Psychology, sociology & geology)
- 16. Derivatives in Physics • In physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity W.R.T time is acceleration. • Newton’s second law of motion states that the derivative of the momentum of a body equals the force applied to the body.
- 17. Derivatives in Biology • Population growth is another instance of the derivative used in the sciences. • Suppose n=f(t) is the number of individuals in some animal or plant population at time t. the change in the population size between time t1 and t2 ∆n=f(t2)-f(t1). • The average rate of growth is then is: Average rate of growth is = (∆n/ ∆t)=(f(t2)-f(t1))/(t2-t1) • The instantaneous rate of growth is the derivative of the function n with respect to t, i.e. growth rate=lim(∆t→0) (∆n/ ∆t)=(dn/dt)
- 18. Derivatives in Biology: • The instantaneous rate of change does not make exact sense in the previous example because the change in population is not exactly a continuous process. However, for large population we can approximate the population function by a smooth(continuous) curve. – Example: Suppose that a population of bacteria doubles its population , n, every hour. Denote by n0 the initial population i.e. n(0)=n0. In general then, n(t)=2t no – Thus the rate of growth of the population at time t is (dn/dt)=no2tln2
- 19. Derivatives in Economics: • Use of derivatives in Economics is as follows: • Let x represent the number of units of a certain commodity produced by some company. Denote by C(x) the cost the company incurs in producing x units. Then the derivative of C(x) is what’s called the marginal cost: Marginal cost =(dC/dx) • Furthermore, suppose the company knows that if it produces x units, they can expect the revenue to be R(x),i.e. the revenue is a function of the number of units produced. Then the derivative of R(x) is what’s called the marginal revenue. Marginal revenue= (dR/dx) • If x units are sold, then total profit is given by the formula: P(x)=R(x)-C(x) • The derivative of profit function is the marginal profit: Marginal profit=(dP/dx)= (dR/dx)-(dC/dx).
- 20. Derivatives in Chemistry • One use of derivatives in chemistry is when you want to find the concentration of an element in a product. • Derivative is used to calculate rate of reaction and compressibility in chemistry.
- 21. Derivatives in Mathematics: The most common use of the derivatives in Mathematics is to study functions such as: • Extreme values of function • The Mean Value theorem • Monotonic functions • Concavity & curve sketching • Newton’s Method etc.
- 23. Some other Applications of Derivatives • Derivatives are also use to calculate: 1. Rate of heat flow in Geology. 2. Rate of improvement of performance in psychology 3. Rate of the spread of a rumor in sociology.
- 24. Conclusion: • Derivatives are constantly used in everyday life to help measure how much something is changing. They're used by the government in population censuses, various types of sciences, and even in economics. Knowing how to use derivatives, when to use them, and how to apply them in everyday life can be a crucial part of any profession, so learning early is always a good thing.