lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,

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lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2))求极限,lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2))求极限,lim(x趋向于0)((tanx-sin

lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,
lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,

lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) 求极限,
lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2)) =lim(x趋向于0)[(sinx/cosx-sinx)]/x(sinx)^2
=lim(x趋向于0)[1-cosx)/x(sinx)=lim(x趋向于0)2(sinx/2)^2/x2sinx/2cosx/2
=1/2lim(x趋向于0)[sinx/2/x/2)(1/cosx/2=lim(x趋向于0)1/cosx/2=1/2
两个重要极限 lim(x趋向于0)sinx/x=1

用泰勒公式和高阶无穷小：
因为：tanx=x+x^3/3+o(x^3)，sinx=x-x^3/3+0(x^3)，tanx-sinx=x^3/3+x^3/3!+0(x^3）
（sinx)^2与x^2是等价无穷小
所以：lim(x趋向于0)((tanx-sinx)/(x*(sinx)^2))
=lim(x趋向于0)(x^3/3+x^3/3!+o(x^3))/x^3=1/2

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