1/(x+1)-3/(x^3+1)=(x^2-x-2)/(x+1)(x^2-x+1)=(x-2)(x+1)/(x+1)(x^2-x+1)=(x-2)/(x^2-x+1)所以上式在x趋于-1时的极限为-3/4
设f(x)=1/(x+1)-3/(x³+1)=(x²-x-2)/(x³+1)则对f(x)分子分母分别求导,得:(2x-1)/(3x²),则:原来的极限=分子分母分别求导后的极限==>>>以x=-1代入==-1