Calculus
posted by NYCalc on .
Find the limit
lim as x approaches (pi/2) e^(tanx)
I have the answer to be zero:
t = tanx
lim as t approaches negative infi e^t
= 0
Why is tan (pi/2) approaching negative infinity is my question?

tan x = sin x / cos x
as x>pi/2
sin x > +1 and cos x>0
cos goes to +0 from the first quadrant and cos goes to 0 from the second quadrant as x>pi/2
so depending on if you approach pi/2 from right or from left, tan x >__+oo or oo