Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.1 Tangent Lines And Rates Of Change - Exercises Set 2.1: 19

Answer

True.

Work Step by Step

It is given that, if $\lim\limits_{x \to 1} \frac{f(x)-f(1)}{x-1}=3$. Step-1: Let $x=h+1 \implies h=x-1$. Thus, $x \to 1$, $h \to 0$. Step-2: Therefore, our limit becomes $$\lim\limits_{h \to 0} \frac{f(h+1)-f(1)}{h}=3$$
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