Explanation Given: lim x → ∞ x 101 + 500 e x Concept Used: 1. L'Hopital's Rule: If f and g are differentiable functions and g ( x ) is nonzero, and if lim x → c f ( x ) g ( x ) is of the indeterminate form, then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) 2. Exponential growth function e k x always dominates power function x r ; that is, lim x → ∞ e k x > lim x → ∞ x r Calculation: To evaluate the limit lim x → ∞ x 101 + 500 e x By using the quotient rule of limits lim x → ∞ x 101 + 500 e x = lim x → ∞ ( x 101 + 500 ) lim x → ∞ ( e x ) Using the concept that exponential growth function dominates power function i

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.6, Problem 75S

To determine

To find the limit (if it exists)

limx→∞x101+500ex

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Chapter 3.6, Problem 74S

Chapter 3.6, Problem 76S

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