Answer
See explanations.
Work Step by Step
Step 1. $f(x)=(1+x)^k$, $f'(x)=k(1+x)^{k-1}$,
Step 2. At $x=0$, $f(0)=1$, $f'(0)=k$,
Step 3. The linearization at $x=0$ is $L(x)=f(0)+f'(0)(x-0)=1+k(x)=1+kx$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 174: 13
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