求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值

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求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值求极限(X趋向于0)lim(1/x-1/(x^2)*in

求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值
求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值

求极限(X趋向于0)lim(1/x-1/(x^2)*in(1+x))的值
原式= lim(x->0) [x - ln(1+x)] / x² 洛必达法则
= lim(x->0) [1 - 1/(1+x) ] / (2x)
= lim(x->0) (1/2) * 1/(1+x)
= 1/2