Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 74: 12


$$\lim _{x \rightarrow1^{+}} \sqrt{\frac{x-1}{x+2}}=0$$

Work Step by Step

Given $$\lim _{x \rightarrow1^{+}} \sqrt{\frac{x-1}{x+2}}$$ The function is defined when coming from the right of $1$ (it is actually defined on and around 1 on both sides), so the limit is just the function value. So, we get $$\begin{aligned}L&=\lim _{x \rightarrow 1^{+}} \sqrt{\frac{x-1}{x+2}}\\ &=\sqrt{\frac{1-1}{1+2}}\\ &=\sqrt{\frac{0}{3}}=0 \end{aligned}$$
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