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Answers without the blur. Sign up and see all textbooks for free! Q. 44

Expert-verified Found in: Page 107 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # For each limit statement in Exercises $41-44$, use algebra to find $\delta$ or $N$ in terms of $\epsilon$ or $M$, according to the appropriate formal limit definition.$\underset{x\to \infty }{\mathrm{lim}}\left({x}^{2}+2\right)=\infty$,find $N$ in terms of $M$.

For $\underset{x\to \infty }{\mathrm{lim}}\left({x}^{2}+2\right)=\infty$, $N=\sqrt{M-2}$.

See the step by step solution

## Step 1. Given information

$\underset{x\to \infty }{\mathrm{lim}}\left({x}^{2}+2\right)=\infty$.

## Step 2. From the limit expression,

$f\left(x\right)={x}^{2}+2\phantom{\rule{0ex}{0ex}}c=\infty \phantom{\rule{0ex}{0ex}}L=\infty$

Now for $\delta >0$.

$\left|x\right|

Therefore,

${N}^{2}+2=M\phantom{\rule{0ex}{0ex}}{N}^{2}=M-2\phantom{\rule{0ex}{0ex}}N=\sqrt{M-2}$ ### Want to see more solutions like these? 