lim tanx-sinx/x(x趋于0) lim tanx-x/x-sinx x→0
lim(x\u21920) tanx-sinx/x3\u65b9lim(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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=lim(x→0)sinx(1/cosx-1)/x
=lim(x→0)(sinx/x)*(1/cosx-1)
=1*(1/1-1)
=0
lim(x->0) (tanx-sinx)/x =0
是不是这样
lim(x->0) (tanx-sinx)/x^3
x->0
tanx ~ x +(1/3)x^3
sinx ~ x -(1/6)x^3
tanx -sinx ~ (1/2)x^3
lim(x->0) (tanx-sinx)/x^3
=lim(x->0) (1/2)x^3/x^3
=1/2
扩展阅读：sin α π ... sin x+y ... sin 2π x ... 极限tanx-sinx ... limtanxsinxx3 x趋近于0 ... sin π a ... sin π x ... sin 兀 a ... lnx 1 ...
