Question

what is the limit as x goes to 1- of
(arcsin(x) - pi/2 ) / sqrt(1-x) ?
I tried using L'Hopital's and it doesn't work.

Answer 1

It looks to me like the numerator remains finite (although oscillating) while the denominator approaches infinity. That should give you a clue

Answer 2

Squeeze law? then the limit is 0 right?
-pi/sqrt(1-x) <= f(x) <= 0