Question

求 lim (Inx)^2*(1/x) x趋于0+

Answer 1

说明：因为无穷乘无穷=无穷,所以无穷乘无穷的题目就等于无穷.原题能做出来.

原式=lim(x->0+)[(lnx)²/(1/x)]

=lim(x->0+)[(2lnx/x)/(-1/x²)] (0/0型极限,应用罗比达法则)

=lim(x->0+)[(2lnx)/(-1/x)]

=lim(x->0+)[(2/x)/(1/x²)] (0/0型极限,应用罗比达法则)

=lim(x->0+)(2x)

=2*0

=0.