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: 68

Answer

$\lim\limits_{x\to 0}\dfrac{\tan^2{x}}{x}=0.$

Work Step by Step

Using Theorem $1.9:$ $\lim\limits_{x\to 0}\dfrac{\tan^2{x}}{x}=\lim\limits_{x\to 0}\dfrac{\tan{x}}{x}\times\lim\limits_{x\to 0}\tan{x}=\lim\limits_{x\to 0}\dfrac{\dfrac{\sin{x}}{\cos{x}}}{x}\times\lim\limits_{x\to 0}\tan{x}$ $=\lim\limits_{x\to 0}\dfrac{\sin{x}}{x}\times\lim\limits_{x\to 0}\dfrac{1}{\cos{x}}\times\lim\limits_{x\to 0}\tan{x}=(1)(1)(0)=0.$
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