   Chapter 4.4, Problem 39E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x → 1 x a − 1 x b − 1 ,     b ≠ 0

To determine

To evaluate: The value of limx1xa1xb1 .

Explanation

Obtain the value of the function as x approaches 1 .

As x approaches 1 , the numerator value becomes,

xa1=(1)a1=11=0

And the denominator value becomes,

xb1=(1)b1=11=0

Thus, limx1xa1xb1=00 is in an indeterminate form.

Therefore, apply L’Hospital’s Rule and obtain the limit as shown below

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 