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Q. 43

Found in: Page 97


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

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Short Answer

For each limit limxcf(x)=Lin Exercises 43–54, use graphs and algebra to approximate the largest value of δsuch that if x(c-δ,c)(c,c+δ) then f(x)(L-ε,L+ε) .

role="math" localid="1648027918805" limx2x3=8, ε=0.5

The largest value of δ0.0408.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

The given expression is limx2x3=8, ε=0.5.

Step 2. Explanation.

From the given expression, we have, c=2, L=8.

The limit expression can be written as a formal statement as below,

For all epsilon positive, there exists a delta positive such that if

localid="1648188825671" x(2-δ,2)(2,2+δ) Then x3(8-ε,8+ε)

Now, the largest value of delta is given by,




Step 3. Conclusion.

The largest value of δ0.0408.

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