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

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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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, Problem 32SC

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To find: the limit of function f(x)=x1−cosx .

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Chapter 3, Problem 31SC

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

Solution Summary: The author calculates the right hand limit of the function as follows: cundersetx

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To find: the limit of function f(x)=x1−cosx .

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