求极限： lim(x→0)(tanx-sinx)/x 求极限lim(x→0)(tanx-x)/(x²-s...

lim(x\u21920) tanx-sinx/x3\u65b9

lim(x\u21920) (tanx-sinx)/x³
=lim(x\u21920) (sinx/cosx-sinx)/x³
=lim(x\u21920) (sinx-sinxcosx)/(x³cosx)
=lim(x\u21920) sinx(1-cosx)/(x³cosx)
=lim(x\u21920) sinx(1-cosx)/(x³cosx)*sin²x/sin²x
=lim(x\u21920) sin³x/x³*(1-cosx)/(sin²xcosx)
=lim(x\u21920) (sinx/x)³*(1-cosx)/[(1-cos²x)cosx]
=lim(x\u21920) (sinx/x)³*(1-cosx)/[(1+cosx)(1-cosx)cosx]
=lim(x\u21920) (sinx/x)³*1/[(1+cosx)cosx]
=(1)³*1/[(1+1)*1],\u5b9a\u7406lim(x\u21920) (sinx/x)^n=1^n=1
=1/2

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