Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 73: 35



Work Step by Step

From the figure, we get: $$\lim _{x \rightarrow 4} \frac{x-4}{\sqrt{x}-\sqrt{8-x}}=2$$ and algebraically, we get: \begin{aligned} \lim _{x \rightarrow 4} \frac{\sqrt{5-x}-1}{2-\sqrt{x}} &=\lim _{x \rightarrow 4} \frac{2+\sqrt{x}}{\sqrt{5-x}+1} \\ &=\frac{2+\sqrt{4}}{\sqrt{5-4}+1} \\ &=\frac{2+2}{\sqrt{1}+1}\\ &=2 \end{aligned}
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