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: 48


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

Work Step by Step

$\lim\limits_{x\to\frac{1}{2}^+}(x^2\tan{(\pi x)})\to$ $\lim\limits_{x\to\frac{1}{2}^+}x^2=(\frac{1}{2}^+)^2=\dfrac{1}{4}.$ $\lim\limits_{x\to\frac{1}{2}^+}\tan{(\pi x)}=\tan{(\pi(\frac{1}{2}^+))}=-\infty.$ By Theorem $1.15:$ $\lim\limits_{x\to\frac{1}{2}^+}(x^2\tan{(\pi x)})=-\infty.$
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