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: 4

Answer

$-4$

Work Step by Step

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