求极限LIM(X趋向0）tanx-sinx/x3次方，求过程解 求极限x趋向于0，limtanx-sinx/x^3 为什么这...
Lim (tanx-sinx)/X3\u6b21\u65b9 \u7b49\u4e8e\u591a\u5c11\u5462\uff1f x~0\u663e\u7136
tanx -sinx=tanx*(1-cosx)
\u5728x\u8d8b\u4e8e0\u7684\u65f6\u5019\uff0c
tanx \u7b49\u4ef7\u4e8ex\uff0c\u800c1-cosx\u7b49\u4ef7\u4e8e0.5x^2
\u4e8e\u662f\u5f97\u5230
\u539f\u6781\u9650
=lim(x->0) x * 0.5x^2 / x^3
=0.5
\u6545\u6781\u9650\u503c\u4e3a0.5
\u8fd9\u662f0/0\u578b\uff0c\u4e0d\u80fd\u76f4\u63a5\u62c6\u5f00\u3002\u53ef\u4ee5\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\u3001\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u6216\u8005\u6cf0\u52d2\u5c55\u5f00\u6c42\u89e3\u3002\u7ed9\u4f60\u63d0\u4f9b\u6700\u57fa\u672c\u7684\u7b49\u4ef7\u65e0\u7a77\u5c0f\u65b9\u6cd5\u5427\uff1a
\u4ee5\u4e0a\uff0c\u8bf7\u91c7\u7eb3\u3002
=limsinx(1-cosx)/(x³cosx)
x趋于0
则sinx~x
1-cosx~x²/2
且cos0=1
所以原式=limx*(x²/2)/(x³cosx)
=1/2
LIM(X趋向0）tanx-sinx/x3次方
=lim(x->0)tanx(1-cosx)/x³
=lim(x->0)(x·x²/2)/x³
=1/2
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