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: 45

Answer

$\lim\limits_{x\to\pi^+}\dfrac{\sqrt{x}}{\csc{x}}=0.$

Work Step by Step

$\lim\limits_{x\to\pi^+}\dfrac{\sqrt{x}}{\csc{x}}\to$ $\lim\limits_{x\to\pi^+}\sqrt{x}=\sqrt{\pi^+}=\sqrt{\pi}$ $\lim\limits_{x\to\pi^+}\csc{x}=\csc{\pi^+}=-\infty.$ By Theorem $1.15:$ $\lim\limits_{x\to\pi^+}\dfrac{\sqrt{x}}{\csc{x}}=-\dfrac{\sqrt{\pi}}{\infty}=0.$
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