Calculus

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?

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  1. 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

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