=lim[f(sin^2x+cosx)/x^2]（等价无穷小的替换）因f'(1)存在则f(1+x)-f(1)=f'(1)x+o(x)即f[1+(sin^2x+cosx-1)]=f'(1)(sin^2x+cosx-1)+o(sin^2x+cosx-1)=f'(1)(sin^2x+cosx-1)+o(x^2)从而lim[f(sin^2x+cosx)/x^2]=lim{...