Calculus, 10th Edition (Anton)

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

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2 - Page 70: 37



Work Step by Step

Given $$\lim_{x\to 0}\frac{\sqrt{x+4}-2}{x}$$ Then \begin{align*} \lim_{x\to 0}\frac{\sqrt{x+4}-2}{x}&=\lim_{x\to 0}\frac{\sqrt{x+4}-2}{x}\frac{\sqrt{x+4}+2}{\sqrt{x+4}+2}\\ &=\lim_{x\to 0}\frac{x+4-2}{x\sqrt{x+4}+2} \\ &=\lim_{x\to 0}\frac{1}{ \sqrt{x+4}+2}\\ &=\frac{1}{4} \end{align*}
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