   Chapter 4.4, Problem 48E ### 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 → ∞ x 3 / 2 sin ( 1 / x )

To determine

To evaluate: The value of limxx32sin(1x) .

Explanation

Express given function as below, limxx32sin(1x)=limxsin(1x)(1x)32

Obtain the value of the function as x approaches .

As x approaches , the numerator sin(1x) approaches to 0 and denominator (1x)32 also approaches to 0 .

Thus, limxx32sin(1x)=00 is in an indeterminate form.

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

limxx32sin(1x)=limxsin(1x)

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