Lim x→0 (cos 3x-cos x)/(2x^2)

[latex]= lim frac{(4 cos^3x - 3cos x) - cos x }{2x^2} = lim frac{4 (cos^3x-cosx)}{2x^2} = [/latex][latex]=lim frac{2 cosx(cos^2x-1)}{x^2} = lim frac{2 cosx sin^2x}{x^2} = 2*1 *lim frac{sin^2x}{x^2} = 2* 1 = 2 [/latex]