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

题目详情

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

▼优质解答

答案和解析

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

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