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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/08 16:58:44

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
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

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:
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