Chapter 11 - Section 11.3 - Limits and Continuity - Exercise Set - Page 1161: 24

The function $f\left( x \right)=\frac{1-\cos x}{x}$ is discontinuous at the point $0$.

Work Step by Step

Consider the rational function $f\left( x \right)=\frac{1-\cos x}{x}$, Here, $p\left( x \right)=1-\cos x\text{ and }q\left( x \right)=x$ 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 $f\left( x \right)=\frac{1-\cos x}{x}$ is discontinuous at the point $0$.

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