Got any leads on calculating:
:
Sorry for the bad latex, but I am trying you know.
Lim(X-->pi/2)[cotX / (2x -pi)]
= cot(pi/2) / 2*pi/2 -pi
= 0/0
Indeterminate.
Use the L'Hopital's Rule: Lim(x->a)[f(x)/g(x)] = Lim(x->a)[f'(x)/g'(x)].
= Lim(X->pi/2)[-csc^2(X) / 2
= -csc^2(pi/2) / 2
= -[1/sin(pi/2)]^2 /2
= -[1/1]^2 / 2
= -1/2 ------------answer.