Explanation Given information : exponential growth function and power function are e x and x n , n ∈ Z respectively. Formula used : If lim x → ∞ f ( x ) g ( x ) = ∞ then f ( x ) dominates g ( x ) . Proof : Case 1: if n is a positive real number. lim x → ∞ e x x n ( ∵ ∞ ∞ f o r m ) Applying L'Hopital's rule = lim x → ∞ e x n x n − 1 ( ∵ ∞ ∞ f o r m ) Again applying L'Hopital's rule = lim x → ∞ e x n x n − 1

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Differential Equations

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Chapter 3.6, Problem 93P

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Toprove : that every exponential growth ex dominates the power function xn n∈Z.

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Chapter 3.6, Problem 92P

Chapter 3.6, Problem 94P

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Chapter 3 Solutions

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Toprove : that every exponential growth e x dominates the power function x n n ∈ Z .

Solution Summary: The author demonstrates that every exponential growth ex dominates the power function.

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Toprove : that every exponential growth ex dominates the power function xn n∈Z.

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Chapter 3 Solutions