Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 94: 50

Answer

See solution and answer

Work Step by Step

a) $h(1)=\frac{\tan(1)-1}{1^3}=0.557$ $h(0.5)=0.370$ $h(0.1)=0.335$ $h(0.05)=0.3337$ $h(0.01)=0.333347$ $h(0.005)=0.333337$ b) $\lim\limits_{x \to 0}\frac{\tan x-x}{x^3}=\frac{1}{3}$ c) $h(10^{-5})=0.333$ $h(10^{-6})=0.3$ $h(10^{-7})=0$ For very small values of x, tanx=0, so the value of h(0) became 0 d) At first glance, it looks like the limit is $\frac{1}{3}$, however, zooming in will allow you to see the distortions.
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