10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary.

lim x → 1 x a − 1 x b − 1 , where a , b ≠ 0

To determine

To calculate: The value of limit limx→1xa−1xb−1 by the use of L’Hopital’s Rule if necessary.

The provided limit is limx→1xa−1xb−1.

Formula used:

L’Hopital’s Rule:

If the limit of f(x)/g(x) when x approaches c from right produces indeterminate form 0/0, then:

limx→cf(x)g(x)=limx→cf′(x)g′(x)

Calculation:

Consider the function xa−1xb−1.

Apply the limit x→1 to the function as;

limx→1xa−1xb−1=1a−11b−1=1−11−1=00

As the direct substitution of limit produces indeterminate form 0/0, so L’Hopital’s Rule can be applied.

Recall the L’Hopital’s Rule, limx→cf(x)g(x)=limx→cf′(x)g′(x)

Apply the L’Hopital’s Rule,

Check out a sample textbook solution.

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Calculus

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary. lim x → 1 x a − 1 x b − 1 , where a , b ≠ 0

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Calculus Calculus 10th Edition

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary.

lim x → 1 x a − 1 x b − 1 , where a , b ≠ 0