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: 72

Answer

$f(x)=\dfrac{\ln x}{x-3}$ is continuous for every positive number, except at $x=3$.

Work Step by Step

Given: $f(x)=\dfrac{\ln x}{x-3}$ As we can see that the $x$ in the denominator must be greater than zero and $x \ne 3$ . The fraction function is continuous for every positive number, except for where it is undefined. So, $f(x)=\dfrac{\ln x}{x-3}$ is continuous for every positive number, except at $x=3$.
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