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: 57

Answer

please see step-by-step

Work Step by Step

$p(x)=a_{0}+a_{1}x+a_{2}x^{2}+\cdots+a_{n}x^{n}$ $\displaystyle \lim_{x\rightarrow a}p(x)=\lim_{x\rightarrow a}(a_{0}+a_{1}x+a_{2}x^{2}+\cdots+a_{n}x^{n})=$ ... Law 1, The limit of a sum... =$\displaystyle \lim_{x\rightarrow a}a_{0}+\lim_{x\rightarrow a}a_{1}x+\lim_{x\rightarrow a}a_{2}x^{2}+\cdots+\lim_{x\rightarrow a}a_{n}x^{n}$ ... Law 3, The limit of a constant times a function... =$\displaystyle \lim_{x\rightarrow a}a_{0}+a_{1}\lim_{x\rightarrow a}x+a_{2}\lim_{x\rightarrow a}x^{2}+\cdots+a_{n}\lim_{x\rightarrow a}x^{n}$ ... Law 7. $\displaystyle \lim_{x\rightarrow a}c=c$, ...Law 9. $\displaystyle \lim_{x\rightarrow a}x^{n}=a^{n}$, $=a_{0}+a_{1}a+a_{2}a^{2}+\cdots+a_{n}a^{n}=p(a)$ So, $\displaystyle \lim_{x\rightarrow a}p(x)=p(a)$
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