ln(1+2x^2)/ln(1+3x^3) lim趋向于正无穷,用洛必达法则求它的极限
问题描述：
ln(1+2x^2)/ln(1+3x^3) lim趋向于正无穷,用洛必达法则求它的极限
答
答：
lim(x→+∞) ln(1+2x^2) / ln(1+3x^2)
=lim(x→+∞) [4x /(1+2x^2)] / [ 6x/(1+3x^2) ]
=lim(x→+∞) (2/3)*(1+3x^2) / (1+2x^2)
=(2/3)*(3/2)
=1是ln（1+3x^3)答：lim(x→+∞)ln(1+2x^2) / ln(1+3x^3)=lim(x→+∞) [4x /(1+2x^2)] / [ 9x^2/(1+3x^3) ]=lim(x→+∞) (4/9)*(1+3x^3) / [x(1+2x^2)]=(4/9) lim(x→+∞) (9x^2) / (1+6x^2)=(4/9)*(9/6)=2/3