Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 197: 58

Answer

Jump discontinuity

Work Step by Step

a) At $x=0$, the numerator is equal to 0 and the denominator is equal to 0. This could be a jump discontinuity where the function has different left and right limits. b) $f(-0.1)=-0.708287$ $f(-0.01)=-0.707119$ $f(-0.0001)=-0.707107$ $\lim\limits_{x \to 0^-}=-0.707107$ $f(0.1)=0.708287$ $f(0.01)=0.707119$ $f(0.0001)=0.707107$ $\lim\limits_{x \to 0^-}=0.707107$ These values confirm our answer to part (a)
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