Chapter 5.6, Problem 71E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Comparing Functions In Exercises 69-74, use L' Hospital’s Rule to determine the comparative rates of increase of the functions f ( x ) = x m ,   g ( x ) = e n x ,   and   h ( x ) = ( ln   x ) n where n > 0 ,   m > 0 ,   and   x → ∞ . lim x → ∞ ( ln   x ) 3 x

To determine

To calculate: The comparative rates of increase of the function limx(lnx)3x use to L’Hospital’s rule.

Explanation

Given:

The function,

limxâ†’âˆž(lnx)3x

Formula used:

Differentiate numerator and denominator by Lâ€™Hospitalâ€™s rule.

limxâ†’af(x)=f(a)

Calculation:

The function,

limxâ†’âˆž(lnx)3x

Substitute direct limit in the indeterminate form âˆžâˆž, then apply Lâ€™ Hospitalâ€™s rule to obtain

limxâ†’âˆž(lnx)3x=limxâ†’âˆž3(lnx)2Ã—1x1=limxâ†’âˆž3(ln

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