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: 5

Answer

$\displaystyle \frac{7}{8}$

Work Step by Step

$\displaystyle \lim_{t\rightarrow-2}\frac{t^{4}-2}{2t^{2}-3t+2}$ ...Limit Law 5, limit of a quotient $=\displaystyle \frac{\lim_{t\rightarrow-2}(t^{4}-2)}{\lim_{t\rightarrow-2}(2t^{2}-3t+2)}$ ...1 (sum), 2 (difference), and 3 (constant multiple) $=\displaystyle \frac{\lim_{t\rightarrow-2}t^{4}-\lim_{t\rightarrow-2}2}{2\lim_{t\rightarrow-2}t^{2}-3\lim_{t\rightarrow-2}t+\lim_{t\rightarrow-2}2} =$ Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$) $=\displaystyle \frac{16-2}{2(4)-3(-2)+2}$ $=\displaystyle \frac{14}{16}$ $=\displaystyle \frac{7}{8}$
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