Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 6

Answer

4

Work Step by Step

$\displaystyle \lim_{u\rightarrow-2}\sqrt{u^{4}+3u+6}$ ...Law 11: $\displaystyle \lim_{x\rightarrow a}\sqrt[n]{f(x)}=\sqrt[n]{\lim_{x\rightarrow a}f(x)}$ $=\sqrt{\lim_{u\rightarrow-2}(u^{4}+3u+6)}$ ...Laws 1 (sum), 2 (difference), and 3 (constant multiple) $=\sqrt{\lim_{u\rightarrow-2}u^{4}+3\lim_{u\rightarrow-2}u+\lim_{u\rightarrow-2}6}$ Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$) $=\sqrt{(-2)^{4}+3(-2)+6}$ $=\sqrt{16-6+6}$ $=\sqrt{16}$ $=4$
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