求lim（3x^3+2x^2+1）/（x^3-x+2）,x→正无穷的极限

Question

求lim（3x^3+2x^2+1）/（x^3-x+2）,x→正无穷的极限

Answer 1

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,...)