   Chapter 4.4, Problem 32E ### 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 → ∞ ( ln x ) 2 x

To determine

To evaluate: The value of limx(lnx)2x .

Explanation

Obtain the value of the function as x approaches .

As x approaches , the numerator (lnx)2 approaches to and denominator x also approaches to .

Thus, limx(lnx)2x= is in an indeterminate form.

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

limx(lnx)2x=limx2(lnx)(1x)1=limx2(

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