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Answers without the blur. Sign up and see all textbooks for free! Q. 36

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.$\underset{x\to 3}{\mathrm{lim}}{x}^{4}.$

The limit exists and it is equal to 81.

See the step by step solution

## Step 1. Given Information.

$Given:\phantom{\rule{0ex}{0ex}}\underset{x\to 3}{\mathrm{lim}}{x}^{4}$

## Step 2. Theorem 1.16

$Powerfunctionsarecontinuousontheirdomains.\phantom{\rule{0ex}{0ex}}Intermsoflimits,ifAisrealandkisrational,\phantom{\rule{0ex}{0ex}}thenforallvaluesx=catwhich{x}^{k}isdefinedwehave\phantom{\rule{0ex}{0ex}}\underset{x\to c}{\mathrm{lim}}A{x}^{k}=A{c}^{k}.$

## Step 3. Finding limit of given function.

$U\mathrm{sin}gtheabovetheorem,\phantom{\rule{0ex}{0ex}}A=1,c=3andk=4.\phantom{\rule{0ex}{0ex}}So,puttingthesevalueswegetourlimitas:\phantom{\rule{0ex}{0ex}}\underset{x\to 3}{\mathrm{lim}}{x}^{4}={3}^{4}=81.$ ### Want to see more solutions like these? 