渐近线的求法高等数学

1)∵lim(x->-1-)f(x)=-∞lim(x->-1+)f(x)=+∞

∴x=-1是函数f(x)的垂直渐近线2)∵x->-∞时，f(x)=x^2/(1+x)->-∞此时只有斜渐近线，设渐近线方程为y=kx+b，则k=lim(x->-∞)(f(x)/x)=lim(x->-∞)(x/(x+1))=lim(x->-∞)((1/(1+1/x))=1b=lim(x->-∞)(f(x)-kx)=lim(x->-∞)(x^2/(1+x)-x)=lim(x->-∞)(-x/(x+1))=lim(x->-∞)((-1/(1+1/x))=-1∴此时斜渐近线方程为y=x-13)∵x->+∞时，f(x)=x^2/(1+x)->+∞此时只有斜渐近线，设渐近线方程为y=k1x+b1，则k1=lim(x->+∞)(f(x)/x)=lim(x->+∞)(x/(x+1))=lim(x->+∞)((1/(1+1/x))=1b1=lim(x->+∞)(f(x)-kx)=lim(x->+∞)(x^2/(1+x)-x)=lim(x->+∞)(-x/(x+1))=lim(x->-∞)((-1/(1+1/x))=-1

∴此时斜渐近线方程仍为y=x-1