Question

With the added challenge of not using l'hopital's rule, what is the limit as x approaches pi/2 of (cos x)/(2x-pi)

Answer 1

lim_(x->pi/2) (cos(x))/(2 x-pi) = -1/2

See: http://www.wolframalpha.com/input/?i=+limit+as+x+approaches+pi%2F2+of%5B+%28cos+x%29%5D%2F%5B%282x-pi%29%5D

Answer 2

Yeah, I use it pretty heavily myself, but I can't get it to come to an answer WITHOUT using l'hopital's rule...I'm trying to figure out how to manipulate the algebra without using derivatives, as I need the fundamentals.