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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

Suppose that | f(x) | ≤ g(x) for all x, where lim x a g ( x ) = 0. Find lim x a f ( x ) .

To determine

To find: The limxaf(x).

Explanation

Given:

The inequality is |f(x)|g(x) for all x

limxag(x)=0.

Calculation:

Consider the inequality |f(x)|g(x).

Recall that |x|y means yxy

So, |f(x)|g(x) implies g(x)f(x)g(x).

Take limits on the expression g(x)f(x)g(x).

limxa{g(x)}limxaf(x)limxag(x)

which implies that limxag(x)limxaf(x)limxag(x)

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