Solution: In Exercises 1–6, sketch the interval (a, b) on

Chapter 2, Problem 3E

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QUESTION:

In Exercises 1–6, sketch the interval \((a, b)\) on the \(x\)-axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a<x<b\).

\(a=-7 / 2\),           \(b=-1 / 2\),                \(c = -3\)

Equation Transcription:

Text Transcription:

(a,b)

x

c

delta > 0

x, 0 < |x - c| < delta right arrow  a < x < b

a = -7/2

b = -1/2

c = -3

Questions & Answers

QUESTION:

In Exercises 1–6, sketch the interval \((a, b)\) on the \(x\)-axis with the point \(c\) inside. Then find a value of \(\delta>0\) such that for all \(x, 0<|x-c|<\delta \Rightarrow a<x<b\).

\(a=-7 / 2\),           \(b=-1 / 2\),                \(c = -3\)

Equation Transcription:

Text Transcription:

(a,b)

x

c

delta > 0

x, 0 < |x - c| < delta right arrow  a < x < b

a = -7/2

b = -1/2

c = -3

ANSWER:

Solution:-

Step 1 of 3

Given that

We have to draw the interval (a, b) on the x-axis with the point c inside. Then we have to find a value of δ > 0 such that for all x, 0 < |x – c| < δ  a < x < b.

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