University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Practice Exercises - Page 277: 69



Work Step by Step

Consider $f(x)=\lim\limits_{x \to 0} \csc x-\cot x=\lim\limits_{x \to 0} \dfrac{1}{\sin x}-\lim\limits_{x \to 0} \dfrac{\cos x}{\sin x}$ This can be further simplified as: $\lim\limits_{x \to 0} \dfrac{1}{\sin x}-\lim\limits_{x \to 0} \dfrac{\cos x}{\sin x}=\lim\limits_{x \to 0} \dfrac{(1-\cos x )\sin x}{(1-cos x)(1+\cos x)}$ Then $\lim\limits_{x \to 0}\dfrac{\sin x}{1+\cos x}=0$
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