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Q. 33

Expert-verified
Found in: Page 120

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.$\underset{x\to -1}{\mathrm{lim}}6.$

The limit exists and it is equal to 6.

See the step by step solution

## Step 1. Given Information.

$Given:\phantom{\rule{0ex}{0ex}}\underset{x\to -1}{\mathrm{lim}}6.$

## Step 2. Theorem 1.16

$Cons\mathrm{tan}t,identity,andlinearfunctionsarecontinuouseverywhere.\phantom{\rule{0ex}{0ex}}Intermsoflimits,foreveryk,c,m,andbinRwehave\phantom{\rule{0ex}{0ex}}\underset{x\to c}{\mathrm{lim}}k=k,\underset{x\to c}{\mathrm{lim}}x=cand\underset{x\to c}{\mathrm{lim}}\left(mx+b\right)=\left(mc+b\right).$

## Step 3. Finding limit of given function.

$U\mathrm{sin}gtheabovetheorem\text{'}s1stcaseweget,\phantom{\rule{0ex}{0ex}}c=-1andk=6.\phantom{\rule{0ex}{0ex}}Puttingthesevaluesweget,\phantom{\rule{0ex}{0ex}}\underset{x\to -1}{\mathrm{lim}}6=6.$