Mathematics - Limits Question with Solution | TestHub

$f$ is continuous

$f$ has removable discontinuity (i.e., ${\mathrm{Lt}}_{x\to 1}f(x)$ exists, but this limit is different from f(1) )

$f$ has finite (jump) discontinuity (i.e., $f(1+)$ and $f(1-)$ both exist finitely, but they are different)

$f$ has infinite or oscillatory discontinuity (for eg like $\sin \frac{1}{x}$ at $x=0$ and $\tan x$ at $x=\frac{\pi }{2}$ )