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: 12


No, the function $ f\left( x \right)=\frac{{{x}^{2}}+8x}{{{x}^{2}}-8x}$ is not continuous at $0$.

Work Step by Step

Consider the function $ f\left( x \right)=\frac{{{x}^{2}}+8x}{{{x}^{2}}-8x}$, First check whether the function is defined at the point $ a $ or not. Find the value of $ f\left( x \right)$ at $ a=0$, $ f\left( 0 \right)=\frac{{{\left( 0 \right)}^{2}}+8\left( 0 \right)}{{{\left( 0 \right)}^{2}}-8\left( 0 \right)}$ The function is not defined at the point $0$. Thus, the function does not satisfy the first property of being continuous. Hence, the function $ f\left( x \right)=\frac{{{x}^{2}}+8x}{{{x}^{2}}-8x}$ is not continuous at $0$.
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