Question
Asked Nov 23, 2019
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Estimate the one-sided limits for the function below.

 f(x)=(11−x)/(x−8)^2

 

lim f(x)=

x-->8+

 

limf(x)=

x-->8-

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Expert Answer

Step 1

Given function is 

11-x
f(x)
(x-8)
help_outline

Image Transcriptionclose

11-x f(x) (x-8)

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Step 2

To find right hand limit , we substitute x=8+h, where h is positive

11-(8+h)
-h
- lim
1
lim
h0 h
lim f(x) lim
h0
|(8+h-8) 0 h
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11-(8+h) -h - lim 1 lim h0 h lim f(x) lim h0 |(8+h-8) 0 h

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Step 3

To find left hand limit , we substitu...

11-(8-h)
-0(8-h-8)
h
= lim
h0 h2
1
lim
lim f(x) lim
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11-(8-h) -0(8-h-8) h = lim h0 h2 1 lim lim f(x) lim

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