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: 9

Answer

$\displaystyle \frac{3}{2}$

Work Step by Step

$\displaystyle \lim_{x\rightarrow 2}\sqrt{2x^{2}+13x-2}=$ ... Law 11, $\displaystyle \lim_{x\rightarrow a}\sqrt[n]{f(x)}=\sqrt[n]{\lim_{x\rightarrow a}f(x)}$ = $\sqrt{\lim_{x\rightarrow 2}\dfrac{2x^{2}+1}{3x-2}}$ ... Law 5, quotient $=\sqrt{\dfrac{\lim_{x\rightarrow 2}(2x^{2}+1)}{\lim_{x\rightarrow 2}(3x-2)}}$ ...Laws 1 (sum), 2 (difference), and 3 (constant multiple) $=\sqrt{\dfrac{\lim_{x\rightarrow 2}2x^{2}+\lim_{x\rightarrow 2}1}{\lim_{x\rightarrow 2}3x-\lim_{x\rightarrow 2}2}}$ ... Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$) $=\sqrt{2(2)^{2}+13(2)-2}$ $=\sqrt{\dfrac{9}{4}}$ $=\displaystyle \frac{3}{2}$
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