Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.3 - Limits and Continuity - Exercise Set - Page 1160: 7


No, the function $ f\left( x \right)=\frac{x+5}{x-5}$ is not continuous at $5$.

Work Step by Step

Consider the function $ f\left( x \right)=\frac{x+5}{x-5}$, First check whether the function is defined at the point $ a $ or not. Find the value of $ f\left( x \right)$ at $ a=5$, $ f\left( 5 \right)=\frac{5+5}{5-5}$ The function is not defined at the point $5$. Thus, the function do not satisfy the first property of being continuous. Hence, the function $ f\left( x \right)=\frac{x+5}{x-5}$ is not continuous at $5$.
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