1. The problem statement, all variables and given/known data evaluate the following limit. limx→∞ cos3x-cos4x/x^2 , include theorems 2. Relevant equations Im guessing its a sandwhich theorem limit and that cos3x-cos4x as an upper bound of 3 and lower of -3. But was wondering if anyone can help explain to me why this is so and should I show a proof or working for this assumption. 3. The attempt at a solution -3 ≤ cos 3x - cos 4x ≤ 3 , divide through by x^2 to get original equation -3/x^2 ≤ ( cos 3x - cos 4x ) / x2≤ 4/x2 Now limx→∞ -3/x2 = 0 and limx→∞ 3/x2 = 0. So the limx→∞ ( cos 3x - cos 4x ) / x2 = 0 by the squeeze theorem. I'm not sure as to what rules I would have to put in this working out. Except maybe something about -1≤ cos ≤ 1 and how cos(3x) = cos(2x + x) = 3cos3-cos x and cos(4x) = 2 cos2(2x) - 1 = 2(2 cos2(x) - 1)2 - 1 = 8 cos4(x) - 8 cos2(x) + 1 but i don't see how this would help.