Thomas' Calculus 13th Edition

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

Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 57: 44

Answer

$\dfrac{1}{2}$

Work Step by Step

Note that, $\lim\limits_{x \to a}\sin x=\sin a$ for all real numbers $a$. Using this along with our limit laws, we get $\lim\limits_{x \to \frac{\pi}{4}}\sin^2 x=\left(\sin\left(\frac{\pi}{4}\right)\right)^2=\left(\dfrac{1}{\sqrt{2}}\right)^2=\dfrac{1}{2}.$
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