## Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning

# Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises: 6

#### Answer

$\lim\limits_{u \to -2}(\sqrt{u^4+3u+6})=4$

#### Work Step by Step

$\lim\limits_{u \to -2}(\sqrt{u^4+3u+6})$ $=\sqrt{\lim\limits_{u \to -2}(u^4+3u+6)}$ (root law) (we assume that $\lim\limits_{u \to -2}(u^4+3u+6)\geq0$) $=\sqrt{\lim\limits_{u \to -2}u^4+\lim\limits_{u \to -2}3u+\lim\limits_{u \to -2}6}$ (addition law) $=\sqrt{\lim\limits_{u \to -2}u^4+3\lim\limits_{u \to -2}u+\lim\limits_{u \to -2}6}$ (constant multiple law) $=\sqrt{(-2)^4+3\times(-2)+6}$ $=4$

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