Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.9 Local Linear Approximation; Differentials - Exercises Set 2.9 - Page 181: 24

Answer

$6.0025$

Work Step by Step

The expression for $y$ can be written as: $y=x^{0.5}$ Now, $\dfrac{dy}{dx}=0.5x^{-0.5}$ $dy=0.5x^{-0.5} dx$ Next, we have: $dy=0.5 \times (36)^{-0.5}(0.03)=0.0025$ So, the new $y$ value is equal to $0.0025+(36)^{0.5}=6.0025$
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