Question

What's the limit of `1/(x-1)arctan(2/(x-1)-pi/2)` as x approaches positive 1 ? Thanks!

Answer 1

`oo`

Explanation:

`lim_(x->1)arctan(a/(x-1)+b)` with `a > 0` is `pi/2` so

`lim_(x->1)1/(x-1)arctan(2/(x-1)-pi/2) = lim_(x->1)1/(x-1)lim_(x->1)arctan(2/(x-1)-pi/2) = oo xx pi/2= oo`