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 909: 53


not continuous

Work Step by Step

Based on the given piece-wise function, we can find that $\lim_{x\to0}\frac{x^3+3x}{x^2-3x}=\lim_{x\to0}\frac{x^2+3}{x-3}=\frac{0^2+3}{0-3}=-1$, thus it is not continuous at $x=0$.
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