Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.10 - Linear Approximations and Differentials. - 3.10 Exercises: 27

Answer

$e^{0.1} \approx 1.1$

Work Step by Step

$f(a) = e^a$ $f(0) = e^0$ $f(0) = 1$ $f'(x) = e^a$ $f'(0) = e^0$ $f'(0) = 1$ $L(x) = f(a) + f'(a)(x-a)$ $L(x) = 1 + 1(x-0)$ $L(x) = 1 + x - 0$ $L(x) = 1 + x$ $L(0.1) = 1 + 0.1$ $L(0.1) = 1.1$ $e^{0.1} \approx 1.1$
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