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Q. 24

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, $R_{4} (x)$
$e^{x}$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given function is $f (x) = e^{x}$

Step 2. Explanation

The lagrange form for the remainder $R_{4} (x) is R_{4} (x) = \frac{f^{5} (c)}{5!} x^{5}$

Now, we will evaluate the fifth derivative of the function $f (x) = e^{x} which is e^{x}$

Thus, we get,

$R_{4} (x) = \frac{e^{c}}{5!} x^{5} R_{4} (x) = \frac{e^{c}}{120} x^{5}$

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