Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Review Exercises - Page 1180: 59


$100 \pi $ cubic inches per inch

Work Step by Step

a) Now, $ f′(x)=\lim_\limits{ h\to 0} \dfrac{f(x+h)-f(x)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\dfrac{4 \pi}{3}(x+h)^3-\dfrac{4 \pi}{3}x^3}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\dfrac{4 \pi}{3}(x^3+3x^2h+3xh^2+h^3)-\dfrac{4 \pi}{3}x^3}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{(4 \pi x^2+4\pi xh+(4/3) \pi h^2}{h}$ or, $=4 \pi x^2$ and $ f(5)=4 \pi (5)^2=100 \pi $
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