Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 13 - Section 13.3 - Tangent Lines and Derivatives - 13.3 Exercises - Page 922: 40

Answer

$16\pi$

Work Step by Step

Given $S(r)=4\pi r^2S$, the rate of change of the surface area with respect to the radius at $r=2$ is given by: $$S'=\lim_{h\to 0}\frac{S(2+h)-S(2)}{h}=\lim_{h\to 0}\frac{4\pi(2+h)^2-4\pi2^2}{h}=\lim_{h\to 0}\frac{4\pi(4h+h^2)}{h}=\lim_{h\to 0}4\pi(4+h)=16\pi$$
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