Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3, Problem 83RE

To determine

To draw: A graph of f in the window [−2π,2π] by [−2,2].

Expert Solution

Answer to Problem 83RE

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3, Problem 83RE , additional homework tip 1

Explanation of Solution

Given information: Let f(x)=(cos(x))/(cos(x)−2) for −2π≤x≤2π.

Calculation:

To sketch a graph, make an xy table to find points on the curve.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3, Problem 83RE , additional homework tip 2

Draw the graph by using table.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3, Problem 83RE , additional homework tip 3

To determine

To find: f'(x).

Expert Solution

Answer to Problem 83RE

f'(x)=2sinx/(cosx−2)2.

Explanation of Solution

Given information: : Let f(x)=(cos(x))/(cos(x)−2) for −2π≤x≤2π.

Calculation:

f(x)=cosx/(cosx−2). f'(x)=((cosx−2)(−sinx)−(cosx)(−sinx))/ (cosx−2) 2 f'(x)=(−cosxsinx+2sinx+cosxsinx)/ (cosx−2) 2 f'(x)=2sinx/ (cosx−2) 2

To determine

To find: All values in the domain of f for which f'(x)=0.

Expert Solution

Answer to Problem 83RE

x=0,±π,±2π.

Explanation of Solution

Given information: Let f(x)=(cos(x))/(cos(x)−2) for −2π≤x≤2π.

Calculation:

f'(x)=2sinx/ (cosx−2) 2 . 0=2sinx/ (cosx−2) 2 .2sinx=0.x=−2π,−π,0,π,2π.x=0,±π,±2π.

To determine

To use: Information obtained from parts(a) and part (c) to find the range of f.

Expert Solution

Answer to Problem 83RE

Range of f is [−1,1/3].

Explanation of Solution

Given information: : Let f(x)=(cos(x))/(cos(x)−2) for −2π≤x≤2π.

Calculation :

From part (d) ,

f'(x)=0 at x=0,±π,±2π.f(0)=f(2π)=f(−2π) since 0 and ±2π are coterminal angle.Similarly f(-π)=f(π)since -π and π are coterminal angles.f(0)=cos0/(cos0−2)=1/(1−2)=−1.f(π)=cosπ/(cosπ−2)=−1/(−1−2)=1/3.

The smallest value of f(x) is then -1 and largest is 1/3 so the range is [−1,1/3].

Chapter 3, Problem 82RE

Chapter 4.1, Problem 1QR

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.2 - Prob. 1QR Ch. 3.2 - Prob. 2QR Ch. 3.2 - Prob. 3QR Ch. 3.2 - Prob. 4QR Ch. 3.2 - Prob. 5QR Ch. 3.2 - Prob. 6QR Ch. 3.2 - Prob. 7QR Ch. 3.2 - Prob. 8QR Ch. 3.2 - Prob. 9QR Ch. 3.2 - Prob. 10QR Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - Prob. 47E Ch. 3.2 - Prob. 48E Ch. 3.3 - Prob. 1QR Ch. 3.3 - Prob. 2QR Ch. 3.3 - Prob. 3QR Ch. 3.3 - Prob. 4QR Ch. 3.3 - Prob. 5QR Ch. 3.3 - Prob. 6QR Ch. 3.3 - Prob. 7QR Ch. 3.3 - Prob. 8QR Ch. 3.3 - Prob. 9QR Ch. 3.3 - Prob. 10QR Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - 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Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.5 - Prob. 1QR Ch. 3.5 - Prob. 2QR Ch. 3.5 - Prob. 3QR Ch. 3.5 - Prob. 4QR Ch. 3.5 - Prob. 5QR Ch. 3.5 - Prob. 6QR Ch. 3.5 - Prob. 7QR Ch. 3.5 - Prob. 8QR Ch. 3.5 - Prob. 9QR Ch. 3.5 - Prob. 10QR Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Prob. 8E Ch. 3.5 - 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Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE

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