Explanation Given : The function is lim x → 0 ( tan − 1 x 1 − cos x ) . Calculation: Apply the limit of the function as follows: lim x → 0 ( tan − 1 x 1 − cos x ) = 0 0 The function is of indeterminate form. Apply L’Hopital’s rule in the limit from the left as follows: lim x → 0 − ( tan − 1 x 1 − cos x ) = lim x → 0 − ( d d x ( tan − 1 x ) d d x ( 1 − cos x ) ) = lim x → 0 − ( 1 1 + x 2 sin x ) = lim x → 0 − ( 1 ( 1

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

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, Problem 30SC

To determine

To find: The limit of function limx→0( tan −1x1−cosx) .

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Chapter 3, Problem 29SC

Chapter 3, Problem 31SC

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Chapter 3 Solutions

Calculus

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The limit of function lim x → 0 ( tan − 1 x 1 − cos x ) .

Solution Summary: The author calculates the limit of the function undersetxto 0mathrmlimleft. The function is of indeterminate form.

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To find: The limit of function limx→0( tan −1x1−cosx) .

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Chapter 3 Solutions