Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises: 73

Answer

$\lim\limits_{t\to0}\dfrac{\sin{3t}}{2}=\dfrac{3}{2}.$

Work Step by Step

$\lim\limits_{t\to0}\dfrac{\sin{3t}}{2t}=\frac{3}{2}\lim\limits_{t\to0}\dfrac{3\sin{3t}}{3t}=\frac{3}{2}\lim\limits_{t\to0}\dfrac{\sin{3t}}{3t}.$ Let $y=3t.$ Notice that as $t\to0$; $y\to0$ $\frac{3}{2}\lim\limits_{y\to0}\dfrac{\sin{y}}{y}=(\frac{3}{2})(1)=\dfrac{3}{2}.$
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