Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 162: 13


The given limit is $f'(1)$ where $f(x)=\sqrt x$.

Work Step by Step

By definition, the derivative at a point $a$ is $f'(a)=\lim\limits_{h \to 0}\frac{f(a+h)-f(a)}{h}=\lim\limits_{h \to 0}\frac{\sqrt {1+h}-1}{h}$ $\implies f(a+h)=\sqrt {1+h}$ and $f(a)=1$ $\implies a=1$ and $f(x)=\sqrt x$ The given limit is $f'(1)$ where $f(x)=\sqrt x$
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