Thomas' Calculus 13th Edition

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

Chapter 3: Derivatives - Practice Exercises - Page 180: 101

Answer

$1$

Work Step by Step

$\lim_{x\to0}\frac{x\cdot sin(x)}{2-2cos(x)}=\lim_{x\to0}\frac{2x\cdot sin(x/2)cos(x/2)}{2(1-cos(x))}=\lim_{x\to0}\frac{x\cdot sin(x/2)cos(x/2)}{2sin^2(x/2)}=\lim_{x\to0}\frac{x/2}{sin(x/2)}\frac{cos(x/2)}{1}=(1)(1)=1$
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