Calculus: Early Transcendentals (2nd Edition)

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

Chapter 2 - Limits - 2.4 Infinite Limits - 2.4 Exercises - Page 87: 37

Answer

$\lim\limits_{x \to 0^+}(-10\cot x)=\lim\limits_{x \to 0^+}\frac{-10\cos x}{\sin x}=-\infty \\ (as\,x\,approach\,0\,from\,right\,\,\,\cos x\,approach\,1\,so\,the\,numerator\,approach\,\,-10\,\\and\,\sin x\,is\,positive\,and\,approach\,0 \,\\so\,the\,denominator\,is\,positive\,and\,approach\,\,\,0)\\ $

Work Step by Step

$\lim\limits_{x \to 0^+}(-10\cot x)=\lim\limits_{x \to 0^+}\frac{-10\cos x}{\sin x}=-\infty \\ (as\,x\,approach\,0\,from\,right\,\,\,\cos x\,approach\,1\,so\,the\,numerator\,approach\,\,-10\,\\and\,\sin x\,is\,positive\,and\,approach\,0 \,\\so\,the\,denominator\,is\,positive\,and\,approach\,\,\,0)\\ $
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