X->0 (sinx)^2/(1-cosx+xsinx) 的极限

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X->0(sinx)^2/(1-cosx+xsinx)的极限X->0(sinx)^2/(1-cosx+xsinx)的极限X->0(sinx)^2/(1-cosx+xsinx)的极限分子分母倒一下lim

X->0 (sinx)^2/(1-cosx+xsinx) 的极限
X->0 (sinx)^2/(1-cosx+xsinx) 的极限

X->0 (sinx)^2/(1-cosx+xsinx) 的极限
分子分母倒一下
lim[x→0] (1-cosx+xsinx)/sin²x
=lim[x→0] (1-cosx+xsinx)/x²
=lim[x→0] (1-cosx)/x²+lim[x→0] xsinx/x²
=lim[x→0] (1/2)x²/x²+lim[x→0] x²/x²
=3/2
因此原题极限为:2/3