Explanation Given : The function is f ( x ) = ( 1 − cos x ) x . Calculation: Apply right hand limit of the function as follows: lim x → 0 f ( x ) = lim x → 0 ( 1 − cos x ) x Apply log on the function as follows: lim x → 0 ln f ( x ) = lim x → 0 ln ( ( 1 − cos x ) x ) = lim x → 0 ( x ) ln ( 1 − cos x ) = lim x → 0 ln ( 1 − cos x ) ( x ) − 1 Thus, this will give ∞ ∞ condition. Apply L’Hopital’s Rule as follows: lim x → 0 ln f ( x ) = lim x → 0 ln ( 1 − cos x ) ( x ) − 1 = lim x → 0 sin x 1 − cos x ( − 1 ) ( x ) − 2 = lim x

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 3.6, Problem 64S

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To find: the limit of function f(x)=(1−cosx)x .

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Chapter 3.6, Problem 63S

Chapter 3.6, Problem 65S

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Chapter 3 Solutions

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the limit of function f ( x ) = ( 1 − cos x ) x .

Solution Summary: The author explains how to find the function's limit, which is 1.

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To find: the limit of function f(x)=(1−cosx)x .

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Chapter 3 Solutions