求lim(3x^3+2x^2+1)/(x^3-x+2),x→正无穷的极限

问题描述:

求lim(3x^3+2x^2+1)/(x^3-x+2),x→正无穷的极限

分子分母同时除以x^3
lim (3x^3+2x^2+1)/(x^3-x+2)
=lim (3+2/x+1/x^3)/(1-1/x^2+2//x^3)
=3
(∵lim(1/x^n>=0,n=1,2,3,...)