Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.3 One-sided Limits; Continuous Functions - 13.3 Assess Your Understanding - Page 910: 67

Answer

Continuous for all real numbers except $\dfrac{\pi (2n+1)}{2}$, where $n$ represents an integer.

Work Step by Step

We know that the tangent function is undefined for $\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2}$. That is, for $\dfrac{\pi (2n+1)}{2}$, where $n$ represents an integer. Therefore, it is continuous everywhere, except for $\dfrac{(2n+1)}{2}\pi$, where $n$ represents an integer.
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