posted by NY-Calc .
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
Why is tan (pi/2) approaching negative infinity is my question?
tan x = sin x / cos x
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