I've been reading over the l'Hopital's rule proof here: http://www.math.uga.edu/~pete/2400diffmisc.pdf [Broken] For the first case of the proof, how does f(x)/g(x) <α imply the limit as x -> a is also A? I understand that α is an arbitrary number greater than A, which means that the limit is less than or equal to A. But I'm not sure why equals A. Does it have something to do with t? Thank you!