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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use Definition 8 to prove that lim x 1 x = 0.

Definition 8

Chapter 2.6, Problem 77E, Use Definition 8 to prove that limx1x=0. Definition 8

To determine

To prove: The limit function of limx1x=0.

Explanation

Definition:

“Let f be a function defined on some interval (,a). Then limxf(x)=L means that for every ε>0 there is a corresponding number N such that if x<N then |f(x)L|<ε

Proof:

Consider the function f(x)=1x

By definition,

Given ε>0, to find N such that,

If x<N, then |1x0|<ε

Assume x

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