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 1161: 23

Answer

The function $ f\left( x \right)=\frac{\sin x}{x}$ is discontinuous at the point $0$.

Work Step by Step

Consider the rational function $ f\left( x \right)=\frac{\sin x}{x}$, Here, $ p\left( x \right)=\sin x\text{ and }q\left( x \right)=x $ Find the zeros of the function $ q\left( x \right)=x $ by $ q\left( x \right)=0$, $ x=0$ The zero of the function $ q\left( x \right)=x $ is $0$. Thus, the function $ f\left( x \right)=\frac{\sin x}{x}$ is discontinuous at the point $0$.
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