Problem: Find the following limits if they exist. a) lim x->Infinity (x-sin(x))/x Work done so far: g(x) = x which goes to infinty as x goes to infinity, thus applying L'Hospitals Rule the limit must equal: 1-cos(x) / 1 = 1-cos(x) as x approaches infinity. Obviously... cos(x) oscillates from 1 to -1... not giving us a real limit. Alternative: (x-sin(x))/x = 1 - sin(x)/x = 1 - (1/x)sin(x) as X approachs infinity this limit becomes 1 - 0 = 1. My problem is that the back of the book tells me the answer is 0... I have no clue how they got this and I was wondering if anyone could give me a push in the right direction.