lim x趋于1 [3/(1-x^3)]/[2/(1+(x^2)]

lim x趋于1 [3/(1-x^3)]-[2/(1+(x^2)]搭错了~~

解：lim(x->1)[3/(1-x³)-2/(1-x²)]=lim(x->1){3/[(1-x)(1+x+x²)]-2/[(1-x)(1+x)]} (分母分解因式)
=lim(x->1){[3(1+x)-2(1+x+x²)]/[(1-x)(1+x)(1+x+x²)]} (通分)
=lim(x->1){(1+x-2x²)/[(1-x)(1+x)(1+x+x²)]} (分子化简)
=lim(x->1){[(1-x)(1+2x)]/[(1-x)(1+x)(1+x+x²)]} (分子分解因式)
=lim(x->1){(1+2x)/[(1+x)(1+x+x²)]} (分子分母同除(1-x))
=(1+2*1)/[(1+1)(1+1+1²)]
=1/2。

1.lim x→1 [(1/(1-x)-2/(1-x^2)] 解：原式=lim x→1 [(1+x)/(1-x^2)-2/(1-x^2)] =lim x→1[(x-1)/(1-x^2)] = lim x→1[-1/(1+x)] =-1/2 2.lim n→无限 n-[(n^2-2n+7)/n+1] 解：原式=lim n→无限 (n^2+n/n+1)-[(n^2-2n+7)/n+1] =lim n→无限(3n-7)/(n+1) =lim n→无限 (3-7/n)/(1+1/n) =3

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