What is lim_(xrarrpi/2) e^(-tan^2x ?

1 Answer
Feb 4, 2018

lim_(x->pi/2)e^(-tan^2x)=0

Explanation:

Since

lim_(x->pi/2)tanx=+oo

we get

lim_(x->pi/2)tan^2x=+oo

lim_(x->pi/2)-tan^2x=-oo

lim_(x->pi/2)e^(-tan^2x)=e^-oo=1/e^(+oo)=1/oo=0