Explanation Given: u ( x ) = 0.001 x 2 − 100 x , and v ( x ) = 100 log 3 x Concept Used: The function f dominates function g as x → ∞ if f ( x ) is very much lager than g ( x ) for very large value of x ; that is if: lim x → ∞ g ( x ) f ( x ) = 0 d d x log a x = 1 x log a 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 ) Calculation: To determine whether u ( x ) dominates v ( x ) , or v ( x ) dominates or neither u ( x ) , where u ( x ) = 0.001 x 2 − 100 x , and v ( x ) = 100 log 3 x First check if lim x → ∞ u ( x ) v ( x ) = 0 or lim x → ∞ v ( x ) u ( x ) = 0

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.6, Problem 74S

To determine

To find whether u(x) dominates v(x) , or v(x) dominates or neither u(x) , where

u(x)=0.001x2−100x, and v(x)=100log3x

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Chapter 3.6, Problem 73S

Chapter 3.6, Problem 75S

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To find whether u ( x ) dominates v ( x ) , or v ( x ) dominates or neither u ( x ) , where u ( x ) = 0.001 x 2 − 100 x , and v ( x ) = 100 log 3 x

Solution Summary: The author analyzes how u(x) dominates function g, if f is very much lager than a function of the indeterminate form.

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To find whether u(x) dominates v(x) , or v(x) dominates or neither u(x) , where

u(x)=0.001x2−100x, and v(x)=100log3x

Want to see the full answer?

Chapter 3 Solutions

To find whether u ( x ) dominates v ( x ) , or v ( x ) dominates or neither u ( x ) , where u ( x ) = 0.001 x 2 − 100 x , and v ( x ) = 100 log 3 x

Solution Summary: The author analyzes how u(x) dominates function g, if f is very much lager than a function of the indeterminate form.

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To find whether u(x) dominates v(x) , or v(x) dominates or neither u(x) , where u(x)=0.001x2−100x, and v(x)=100log3x

Want to see the full answer?

Chapter 3 Solutions

To find whether u(x) dominates v(x) , or v(x) dominates or neither u(x) , where

u(x)=0.001x2−100x, and v(x)=100log3x