F(x)=tan(x)
find the limit as x approaches pi/2 from the negative and positive sides then find the limit as x approaches 0.

F(x) = tan(x)= sin(x)/cos(x)
lim tan (x) =sin (Pi/2) / cos (Pi/2)= 1/0 = infinite
x  to Pi/2
so lim tan (x) =1/0 - = - infinite (neg)   and  lim tan (x) =1/0 + = + infinite (pos) 
x  to (Pi/2)-                                                   x  to (Pi/2)+
and when x approaches 0, it is very simple
lim tan (x) =sin (0) / cos (0)= 0/1 = 0, because sin (0)=0 and cos (0)=1
x  to 0