lim x->0 (x cos x - sin x) / (x - sin x)
lim x->0 (-x sin x) / (1 - cos x)
lim x->0 (- sin x - x cos x) / (sin x)
lim x->0 (-2cos x + x sin x) / (cos x)
= -2
This is what's written in my book (Numerical Analysis). It has a few review questions on limits but it doesn't go in to detail so I'm not sure how to go from step 1 to step 2.