lim√[(3n^2)+1]/(7n+1)=?

问题描述:

lim√[(3n^2)+1]/(7n+1)=?

lim√[(3n^2)+1]/(7n+1)=
=√3 / 7

分子分母同除以n:
lim√[(3n^2)+1]/(7n+1)
=lim√(3+1/n^2)/(7+1/n)
=lim√3/7

lim √(3n²+1)/(7n+1) as x->∞= lim [√(3n²+1)/n]/[(7n+1)/n],上下除以n= lim √[(3n²+1)/n²]/[(7n+1)/n]= lim √(3+1/n²)/(7+1/n)= √(3+0)/(7+0)= √3/7