Calculus: Early Transcendentals (2nd Edition)

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

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises: 55

Answer

$\lim_{x\to\pi/4}3\csc2x\cot2x=0$

Work Step by Step

$\lim_{x\to\pi/4}3\csc2x\cot2x$ Evaluate this limit applying direct substitution: $\lim_{x\to\pi/4}3\csc2x\cot2x=3\csc\Big[2\Big(\dfrac{\pi}{4}\Big)\Big]\cot\Big[2\Big(\dfrac{\pi}{4}\Big)\Big]=...$ $...=3\csc\dfrac{\pi}{2}\cot\dfrac{\pi}{2}=3(1)(0)=0$
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