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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) How large do we have to take x so that 1 x < 0.0001 ?

(b) Taking r = 1 2 in Theorem 5, we have the statement

lim x 1 x = 0

Prove this directly using Definition 7.

Definition 7

Chapter 2.6, Problem 76E, (a) How large do we have to take x so that 1x0.0001? (b) Taking r = 12 in Theorem 5, we have the

(a)

To determine

To find: The large values of x when 1x<0.0001.

Explanation

Calculation:

Consider the inequality 1x<0.0001.

1x<0.00011x<110000

Take the reciprocal on both sides resulting by change in sign.

x>10000

Squaring on both sides

(b)

To determine

To prove: The limit function limx1x=0.

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