Question

For the function $f\left(x\right)=\frac{\sin x}{x},x\ne 0$ which of the following statement is TRUE

• A. $f\left(x\right)$ has missing point discontinuity
• B. $f\left(x\right)$ has isolated point discontinuity
• C. $f\left(x\right)$ has finite type discontinuity
• D. $f\left(x\right)$ has infinite type discontinuity

Answer 1

The correct option is A $f\left(x\right)$ has missing point discontinuity

$f\left(x\right)=\frac{\sin x}{x},x\ne 0$
$f\left(0\right)$ is not defined, but limit exists at $x=0$
$\because \underset{x\to 0}{lim}\frac{\sin x}{x}=1$.
Hence, $f\left(x\right)$ has missing point discontinuity at $x=0$.