Answer
continuous
Work Step by Step
Based on the given piece-wise function, we can find that
$\lim_{x\to0}\frac{x^2-6x}{x^2+6x}=\lim_{x\to0}\frac{x-6}{x+6}=\frac{0-6}{0+6}=-1$, thus
it is continuous at $x=0$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
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: 56
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