Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.5 - Continuity - Exercises 2.5 - Page 84: 20

Answer

$ y $ is continuous on $$...\cup(-\frac{3\pi}{2},-\frac{\pi}{2})\cup (-\frac{\pi}{2},\frac{\pi}{2})\cup(\frac{\pi}{2},\frac{3\pi}{2}) \cup(\frac{3\pi}{2},\frac{5\pi}{2})\cup(\frac{5\pi}{2},\frac{7\pi}{2})\cup...$$

Work Step by Step

Given $$ y=\frac{x+2}{\cos x} $$ Since the of the denominator is zero at $\cos x=0 \Rightarrow x=\frac{\pi}{2}+k \pi, \ \ k \in Z $ So, $ y $ is continuous on $$...\cup(-\frac{3\pi}{2},-\frac{\pi}{2})\cup (-\frac{\pi}{2},\frac{\pi}{2})\cup(\frac{\pi}{2},\frac{3\pi}{2}) \cup(\frac{3\pi}{2},\frac{5\pi}{2})\cup(\frac{5\pi}{2},\frac{7\pi}{2})\cup...$$
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