Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 118: 62

Answer

y = (x+h)^{3}/h gets closer to y = 3x^{2} as h gets smaller and smaller.

Work Step by Step

The graphs are shown below for h = 2,1,0.5. The function y = 3x^{2} is the derivative of the function y = x^{3} so that 3x^{2} = \lim\limits_{h \to 0}(x+h)^{3}/h
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