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Q. 23

Expert-verified

Calculus

Found in: Page 692

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

In Exercises 23–32 we ask you to give Lagrange’s form for the corresponding remainder, $R_{4} (x)$
$\cos x$

The required answer is $R_{4} (x) = - \frac{\sin c}{120} x^{5}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given function is $f (x) = \cos x$

Step 2. Explanation

Using the Lagrange form of remainder, we have,

$R_{n} (x) = \frac{f^{n + 1} (c)}{(n + 1)!} x^{n + 1} R_{4} (x) = \frac{f^{5} (c)}{5!} x^{5}$

Now, we will find fifth derivative of the function.

$f^{1} (x) = - \sin x f^{2} (x) = - \cos x f^{3} (x) = \sin x f^{4} (x) = \cos x f^{5} (x) = - \sin x$

Thus, we get,

$R_{4} (x) = - \frac{\sin c}{120} x^{5}$

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