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

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 47S

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

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Chapter 3.6, Problem 46S

Chapter 3.6, Problem 48S

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4 Consider f(x) periodic function with period 2, coinciding with (x) = -x on the interval [,0) and being the null function on the interval [0,7). The Fourier series of f: (A) does not converge in quadratic norm to f(x) on [−π,π] (B) is pointwise convergent to f(x) for every x = R П (C) is in the form - 4 ∞ +Σ ak cos(kx) + bk sin(kx), ak ‡0, bk ‡0 k=1 (D) is in the form ak cos(kx) + bk sin(kx), ak 0, bk 0 k=1

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Chapter 3 Solutions

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

Solution Summary: The author calculates the limit of the function undersetxto 0mathrmlim(

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

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Chapter 3 Solutions