5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Question

Chapter 4.5, Problem 2C

To determine

To find: A function f for which the fundamental theorem of calculus does not apply on [0,10] .

To determine

To find: three functions f that we do not yet know how to anti differentiate.

To determine

To find: A non constant function f for which ∫04f(x)dx=0 .

Expert Solution & Answer

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Chapter 4.5, Problem 1C

Chapter 4.5, Problem 3C

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Chapter 4 Solutions

Calculus

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A function f for which the fundamental theorem of calculus does not apply on [ 0 , 10 ] .

Solution Summary: The author explains that the fundamental theorem of calculus does not apply on left[0,10right].

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To find: A function f for which the fundamental theorem of calculus does not apply on [0,10] .

To find: three functions f that we do not yet know how to anti differentiate.

To find: A non constant function f for which ∫04f(x)dx=0 .

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Chapter 4 Solutions