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 - 1.5 Exercises: 47


$\lim\limits_{x\to\frac{1}{2}^-}(x\sec{(\pi x)})=+\infty.$

Work Step by Step

$\lim\limits_{x\to\frac{1}{2}^-}(x\sec{(\pi x)})\to$ $\lim\limits_{x\to\frac{1}{2}^-}(x)=\dfrac{1}{2}^-=\dfrac{1}{2}.$ $\lim\limits_{x\to\frac{1}{2}^-}\sec{(\pi x)}=\sec{\frac{1}{2}^-(\pi)}=+\infty.$ By Theorem $1.15:$ $\lim\limits_{x\to\frac{1}{2}^-}(x\sec{(\pi x)})=+\infty.$
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