Question

$f\left(x\right)=\{\begin{array}{c}\tan xx\ne \frac{\pi }{4}\\ 1x=\frac{\pi }{4}\end{array}$ discuss continuity at $x=\frac{\pi }{4}$

Answer 1

${lim}_{x\to \pi /4^{+}}\tan x=1$

${lim}_{x\to \pi /4^{-}}\tan x=1$

$f\left(\pi /4\right)=1$

${lim}_{x\to a^{+}}f\left(x\right)=lim-x\to x^{-}f\left(x\right)=f\left(x\right)$

So Function is continuos at $x=\frac{\pi }{4}$