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Q. 36

Found in: Page 107


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

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Short Answer

For each limit statement , use algebra to find δ > 0 in terms of ε > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.



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Step by Step Solution

Step1. Given information. 

We have been given a limit statement as limx0(x3+1)=1.

We have to find δ in terms of ε.

Step 2. Use algebra.

From the given limit statement, we can identify

f(x)=x3+1c=0L=1For ε>0x3+11<εx3+11<εx3<ε|x|3<ε|x|<ε13For 0<|xc|<δ, we get |x|<ε13.Therefore, δ=ε13

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