Suppose that f(x) is a function such that for any given > 0, the condition 0 <

Chapter 1, Problem 2

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QUESTION:

Suppose that \(f(x)\) is a function such that for any given \(\epsilon>0\), the condition \(0<|x-1|<\epsilon / 2\) guarantees that \(|f(x)-5|<\epsilon\). What limit results from this property?

Equation Transcription:

Text Transcription

f(x)

epsilon > 0

0 < |x-1| < epsilon/2

|f(x)-5| < epsilon

Questions & Answers

QUESTION:

Suppose that \(f(x)\) is a function such that for any given \(\epsilon>0\), the condition \(0<|x-1|<\epsilon / 2\) guarantees that \(|f(x)-5|<\epsilon\). What limit results from this property?

Equation Transcription:

Text Transcription

f(x)

epsilon > 0

0 < |x-1| < epsilon/2

|f(x)-5| < epsilon

ANSWER:

Step 1 of 3

Let  is a function. For any given number  there is a number  such that :

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