   Chapter 4.4, Problem 56E ### 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 +   [ ln ( x 7 − 1 ) − ln ( x 5 − 1 ) ]

To determine

To evaluate: The value of limx1+[ln(x71)ln(x51)] .

Explanation

Express given function as below.

limx1+[ln(x71)ln(x51)]=limx1+[ln(x71x51)]=ln[limx1+(x71x51)]

Obtain the value of the function as x approaches 1+ .

As x approaches 1+ , the numerator x71=171 approaches to 0 and denominator x51=151 also approaches to 0 .

Thus, limx1+[ln(x71)ln(x51)]=00 is in an indeterminate form.

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

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