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Solved: In Exercises 1–6, sketch the interval (a, b) on
Chapter 2, Problem 2E(choose chapter or problem)
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 \(x, 0<|x-c|<\delta \Rightarrow a<x<b\).
\(a = 1\), \(b = 7\), \(c = 2\)
Equation Transcription:
Text Transcription:
(a,b)
x
c
delta > 0
x, 0 < |x - c| < delta right arrow a < x < b.
a = 1
b = 7
c = 2
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 \(x, 0<|x-c|<\delta \Rightarrow a<x<b\).
\(a = 1\), \(b = 7\), \(c = 2\)
Equation Transcription:
Text Transcription:
(a,b)
x
c
delta > 0
x, 0 < |x - c| < delta right arrow a < x < b.
a = 1
b = 7
c = 2
ANSWER:
Solution:
Step 1 of 3:
In this problem, we need to sketch the interval on the x-axis with the point c inside, and then we need to find a value of
such that for all x,
.