Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - Review Exercises - Page 124: 20


$\sqrt {2}$

Work Step by Step

$\lim _{\theta \rightarrow \dfrac {\pi }{4}}\dfrac {\sin ^{2}\theta -\cos ^{2}\theta }{\sin \theta -\cos \theta }=\lim _{\theta \rightarrow \dfrac {\pi }{4}} \dfrac {\left( \sin \theta -\cos \theta \right) \left( \sin \theta +\cos \theta \right) }{\sin \theta -\cos \theta }=\lim _{\theta \rightarrow \dfrac {\pi }{4}}\left( \sin \theta +\cos \theta \right) =\sin \dfrac {\pi }{4}+\cos \dfrac {\pi }{4}=\dfrac {\sqrt {2}}{2}+\dfrac {\sqrt {2}}{2}=\sqrt {2}$
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