Question

For the function $f\left(x\right)=2^{\tan x}$ at $x=\frac{\pi }{2}$ which of the following statement is TRUE

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

Answer 1

The correct option is C $f\left(x\right)$ has infinite type discontinuity

Here ,
At $x=\frac{\pi }{2}$ limit doesn't exists as
$R.H.L.=f\left({\frac{\pi }{2}}^{+}\right)=0$
$L.H.L.=f\left({\frac{\pi }{2}}^{-}\right)=\infty$
$\therefore$ It has Infinite type discontinuity.