Question

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

Answer 1

`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`