Answer
$L(x)=-x+1$
Work Step by Step
$f(x)=e^{-x}$,
$L(x)=f(a)+f'(a)(x-a)$
$f'(x)=-e^{-x}$
$x_{0}=0$
$f(0)={e^0}=1$
$f'(0)=-e^{-0}=-1$
then $L(x)=1-1(x-0)=-x+1$
$L(x)=-x+1$
Thus, the final answer is: $L(x)=-x+1$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 198: 13
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
