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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

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

lim x 3 x 2 9 x 3 = lim x 3 ( x + 3 )

To determine

Whether the statement, limx3x29x3=limx3(x+3) is true or false.

Explanation

Fact 1: “If f(x)=g(x) when xa, then limxaf(x)=limxag(x), provided the limits exist”.

Calculation:

Let the function f(x)=x29x3 and g(x)=x+3.

Here, the function f(x) is undefined at x=3, but g(x) is defined.

That is, x29x3=x+3 is true whenever x3.

Apply fact 1 to check the limit exist are not.

limx3x29x3=limx3x232x<

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