   Chapter 4.4, Problem 47E ### 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 e − x 2

To determine

To evaluate: The value of limxx3ex2 .

Explanation

Express the given function as, limxx3ex2=limxx3ex2 .

Obtain the value of the function as x approaches .

As x approaches , the numerator is,

x3=3=

As x approaches , the denominator is,

ex2=e2=

Thus, limxx3ex2= is in an indeterminate form.

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

limxx3ex2=limxx3ex2=limx

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