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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.9, Problem 45E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 79E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find f.

f″(x) = ex − 2 sin x, f(0) = 3, f(π/2) = 0

To determine

To find: The general antiderivative for the function f″(x)=ex−2sinx,   f(0)=3,   f(π2)=0 .

Explanation

Given Data:

Write the given function as follows.

f″(x)=ex−2sinx,   f(0)=3,   f(π2)=0

Formula used:

The antiderivative function for the function ex is ex+C .

Here, C is the constant.

The antiderivative function for the function sinx is −cosx+C .

The antiderivative function for the function cosx is sinx+C .

Calculation of f′(x) :

Rewrite the function f″(x)=ex−2sinx as follows.

f″(x)=ex−2sinx (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows.

f′(x)=ex−2(−cosx)+C=ex+2cosx+C

Calculation of f(x) :

Rewrite the function f′(x)=ex+2cosx+C as follows.

f′(x)=ex+2cosx+Cx0 (2)

From the antiderivative function formula, the antiderivative for the function in equation (2) is written as follows.

f(x)=ex+2(sinx)+C(x0+10+1)+D

f(x)=ex+2sinx+Cx+D (3)

As f(0)=3 , substitute 0 for x in equation (3),

f(0)=e0+2sin(0)+C(0)+D=1+0+0+D=1+D

Rewrite the expression as follows

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Chapter 4.9,
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Problem 46E
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Mathematical Applications for the Management, Life, and Social Sciences

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In Exercises 9 to 12, find the complement of the set given that U = {x | x 1 and –3 x 7}. (–2, 0, 2, 4, ...

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Suppose that circles of equal diameter are packed tightly in n rows inside an equilateral triangle. (The figure...

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Contemporary Mathematics for Business & Consumers

Suppose the probability of erroneously transmitting a single digit is . Compute the probability of transmitting...

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The questions are available for instructors to help assess if you have successfully met the learning objectives...

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Orthogonal Functions The inner product of two functions f and g on [a, b] is given by f,g=abf(x)g(x)dx. Two dis...

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Using Trigonometric Substitution In Exercises 2934, use trigonometric substitution to find or evaluate the inte...

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In one type of regular polygon, the measure of each interior angle (I=(n2)180n) is equal to the measure of each...

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The graph of y = f(3x) is obtained from the graph of y = f(x) by: stretching vertically by a factor of 3. compr...

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If yc(x) is the general solution to ay″ + by′ + cy = 0 and yp(x) is a particular solution to ay″ + by′ + cy = G...

Study Guide for Stewart's Multivariable Calculus, 8th

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Evaluating a Second Derivative In Exercises 89-92, evaluate the second derivative of the function at the given ...

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Explain how replacing the single observation before and after treatment with a series of observations converts ...

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The graphs accompanying this exercise are based on data from an experiment to assess the effects of logging on ...

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Consider the following two sets of rankings for six items. Note that in the first case the rankings are identic...

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Under what circumstances would you use a multiple-baseline design instead of an ABAB (reversal) design?

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