Explanation Given: 1) f ( x ) = ∫ 2 x d t ln t . 2) g ( x ) = x ln x . 3) Need to calculate L = lim x → ∞ f ( x ) g ( x ) Formula used: 1) L’Hopital’s Rule states that if lim x → c f ( x ) = lim x → c g ( x ) = 0 or ± ∞ , g ′ ( x ) ≠ 0 for all x in I with x ≠ c and lim x → c f ′ ( x ) g ′ ( x ) exists then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) 2) ∫ d t ln t = ln | ln ( t ) | + ln ( t ) + ∑ k = 2 ∞ | ln ( t ) | k k . k ! . s3) ln ( ∞ ) = ∞ Calculation: Calculating value of f ( x ) f ( x ) = ∫ 2 x d t ln t [ Given ] = [ ln | ln ( t ) | + ln ( t ) + ∑ k = 2 ∞ | ln ( t ) | k k . k ! ] 2 x [usingformula ∫ d t ln t = ln | ln ( t ) | + ln ( t ) + ∑ k = 2 ∞ | ln ( t ) | k k ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8.7, Problem 97E

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To Calculate: $L$ for a given functions $f (x)$ and $g (x)$ using L’Hopital’s Rule.

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Chapter 8.7, Problem 96E

Chapter 8.7, Problem 98E

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L for a given functions f ( x ) and g ( x ) using L’Hopital’s Rule.

Solution Summary: The author explains how to calculate L for a given function f (x) and g ( x ) using L’Hopital’s Rule.

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To Calculate: $L$ for a given functions $f (x)$ and $g (x)$ using L’Hopital’s Rule.

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Chapter 8 Solutions

L for a given functions f ( x ) and g ( x ) using L’Hopital’s Rule.

Solution Summary: The author explains how to calculate L for a given function f (x) and g ( x ) using L’Hopital’s Rule.

Concept explainers

Videos

To Calculate: Lfor a given functions f(x) and g(x)using L’Hopital’s Rule.

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Chapter 8 Solutions

To Calculate: $L$ for a given functions $f (x)$ and $g (x)$ using L’Hopital’s Rule.