Question

${lim}_{x\to \frac{\pi }{2}}\tan x$

Answer 1

${lim}_{x\to {\frac{\pi }{2}}^{-}}\tan x\tan \frac{\pi }{2}=\infty$

${lim}_{x\to {\frac{\pi }{2}}^{+}}\tan x\tan \frac{\pi }{2}=-\infty$

Since the right and left hand limits are not equal

The limit doesnt exist.