EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Question
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Chapter 5.1, Problem 66E
To determine

To write:To write the given expression f'(x)=secxtanx−sinx in the simplified form

Expert Solution & Answer
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Answer to Problem 66E

The simplified form of rate of change expressionis f'(x)=sinxtan2x

Explanation of Solution

Given information:Given that the rate of change of f(x)=secx+cosx is secxtanx−sinx

Given that f'(x)=secxtanx−sinx

Using the quotient and reciprocal identity of trigonometry

We have

  f'(x)=secxtanx−sinx=1cosx×sinxcosx−sinx=sinxcos2x−sinx=sinx(1cos2x−1)=sinx(sec2x−1)=sinxtan2x

Therefore, the rate of change expression can also be written as f'(x)=sinxtan2x

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Chapter 5.1, Problem 65E
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Chapter 5.1, Problem 67E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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