Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 63


$$x+1,\ \ 0.9$$

Work Step by Step

Given $$ f(x)= e^x,\ \ \ \ a=0$$ Since $f(0)=1$ and \begin{align*} f'(x)&= e^x\\ f'(0)&=1 \end{align*} Then the linearization is given by \begin{align*} L(x)&=f^{\prime}(a)(x-a)+f(a)\\ &=(x-0)+1\\ &=x+1 \end{align*} Hence \begin{align*} e^{-0.1}&= -0.1+1\\ &= 0.9 \end{align*}
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