Question

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.

Answer 1

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