l当x趋向于零时极限 (sin(ux)+xf(x))/x^3等于零,求当X趋向于零时,(u+f(x))/x^2

问题描述:

l当x趋向于零时极限 (sin(ux)+xf(x))/x^3等于零,求当X趋向于零时,(u+f(x))/x^2

lim [sin(ux) + xf(x)] / x³
= lim [ucos(ux) +f(x) + xf'(x)] / (3x²)
= 1/3 lim [ u+f(x) ] / x²
= 0
故 lim [ u+f(x) ] / x² = 0