lim(x-0)(x+1)ln(1+x)/x^2+3x

题目

lim(x-0)(x+1)ln(1+x)/x^2+3x
利用等价无穷小替换，

答案

当x-->0,ln(x + 1) x
lim(x-->0) (x + 1)ln(x + 1)/(x² + 3x)
= lim(x-->0) [(x + 1)x]/[(x + 3)x]
= lim(x-->0) (x + 1)/(x + 3)
= (0 + 1)/(0 + 3)
= 1/3