Is the Discontinuity in $\frac{\sin x}{x}$ at $x=0$ a Jump Type?

[Dustinsfl]

$f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$.We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity.
Is this correct reasoning?

 

[Sudharaka]

$f(x) = \frac{\sin x}{x}$ if $x\neq 0$, $f(0) = 0$.We know that the $\lim\limits_{n\to 0}f(x) = 1$. Since $f(0) = 0$, we will have a jump discontinuity.
Is this correct reasoning?

No this is a removable discontinuity. :)