Answer
$L(x)=2$
Work Step by Step
Given: $f(x)=x+\frac{1}{x}$,
$L(x)=f(a)+f'(a)(x-a)$
$f'(x)=1-\frac{1}{x^2}$
a=1
$f(1)=1+\frac{1}{1}=2$
$f'(1)=1-1=0$
then $L(x)=2+0(x-1)$
$L(x)=2$
Thus, the final answer is: $L(x)=2$
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: 3
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.
