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Chapter 1: Q. 4 (page 107)

Suppose you show that |(1-2x)-(-5)|<0.05 for all x with 0<|x-3|<0.025Explain why this does not prove thatrole="math" localid="1648055981096" limx鈫�3(1-2x)=-5

Short Answer

Expert verified

As-蔚2<|x-3|<未thus we cannot say thatlimx鈫�3(1-2x)=-5

Step by step solution

01

Step 1. Given Information

The given limit expression is limx鈫�3(1-2x)=-5

02

Step 2. Explanation

From the given limit expression, we have,

f(x)=1-2x,c=3,L=-5

Hence, delta-epsilon statement will be as follows,

For all epsilon positive there exists a delta positive if 0<|x-3|<未

Then,

|(1-2x)-(-5)|<蔚|1-2x+5|<蔚|6-2x|<蔚-2|x-3|<蔚|x-3|>-蔚2

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