University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises - Page 152: 65

Answer

The curves of the centered difference quotient do converge faster than the ones used in the previous two exercises.
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Work Step by Step

a) The graphs are shown on the left side. b) The graphs are shown on the right side. On both cases, we see that at the same scale of zooming in as the one used in Exercise 63 and 64, and we only test $h$ as small as $0.3$, the curves of the centered difference quotient already converge into both $y=\cos x$ and $y=-\sin$ faster than the ones used in the previous two exercises.
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