Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 17



Work Step by Step

We know that $ \lim\limits_{x \to a}\frac{x^{n}-a^{n}}{x-a}=na^{n-1}$ Then, $\lim\limits_{x \to 1}\frac{\sqrt x-1}{x-1}=\lim\limits_{x \to 1}\frac{x^{1/2}-1^{1/2}}{x-1}=\frac{1}{2}×1^{\frac{1}{2}-1}$ =$\frac{1}{2}×\frac{1}{\sqrt 1}= \frac{1}{2}$
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