Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.1 Derivatives and Rates of Change - 2.1 Exercises - Page 115: 41


$f(x)$ = $cos(x)$ $a = \pi$

Work Step by Step

The form of the equation given resembles the form $\lim\limits_{h \to 0}$ $\frac{f(h+a) - f(a)}{h}$ Since $\pi$ is being added to $x$, $a = \pi$. We also see that $f(a + h) $ = $cos(\pi + h)$, so our function $f(x)$ must be $cos(x)$. We can check our answer by looking at the right term in the numerator, which would be $f(a)$ = $f(\pi)$ = $cos(\pi)$ = -1. Since the right term is subtracted, we would be left with -(-1) or 1. Thus, $f(x)$ = $cos(x)$ and $a = \pi$
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