Explanation Given: The given problem is lim x → ∞ x 3 e 2 x where f ( x ) = x 3 , g ( x ) = e 2 x . Formula used: Applying L’HospitaL’s Rule in this problem, we get the solution. The rule is: Let f ( x ) and g ( x ) be functions that are differentiable on an open interval ( a , b ) containing c , except possibly at c itself. Assume that g ′ ( x ) ≠ 0 for all x in ( a , b ) , except possibly at c itself. If the limit of f ( x ) / g ( x ) , as x approaches c , produces the indeterminate form 0 / 0 , then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) Provided the limit on right exists (or is infinite)

Calculus: Early Transcendental Functions

6th Edition

ISBN: 9781305005303

Author: Ron Larson, Bruce Edwards

Publisher: CENGAGE C

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Question

Chapter 8.7, Problem 70E

To determine

To calculate: The comparative rate of increase of the function f(x)=x3,g(x)=e2x by L’HospitaL’s Rule and x→∞.

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Chapter 8.7, Problem 69E

Chapter 8.7, Problem 71E

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Chapter 8 Solutions

Calculus: Early Transcendental Functions

Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 14, select...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, selectthe...

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The comparative rate of increase of the function f ( x ) = x 3 , g ( x ) = e 2 x by L’HospitaL’s Rule and x → ∞ .

Solution Summary: The author explains how L'HospitaL's Rule calculates the comparative rate of increase of the function x3,g(x)=e2x

To calculate: The comparative rate of increase of the function f(x)=x3,g(x)=e2x by L’HospitaL’s Rule and x→∞.

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Chapter 8 Solutions