Answer
a. $1.01$
b. $1.003$,
Work Step by Step
Use the linear approximation $(1+x)^k=1+kx$
a. $(1.0002)^{50}=(1+0.0002)^{50}=1+50(0.0002)=1.01$,
b. $\sqrt[3] {1.009}=(1.009)^{1/3}=(1+0.009)^{1/3}=1+\frac{1}{3}(0.009)=1.003$,
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: 15
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