Question

极限题化简不会？

画圈的那一步看不懂，求指教!

Answer 1

lim(x->0+) sin(x/2).lnx
=lim(x->0+) lnx/csc(x/2)
洛必达
=lim(x->0+) (1/x)/[-(1/2)csc(x/2).cot(x/2)]
=lim(x->0+) (1/x).sin(x/2)/[-(1/2)cot(x/2)]
x->0, sin(x/2) 等价于 x/2
=lim(x->0+) (1/x).(x/2)/[-(1/2)cot(x/2)]
=lim(x->0+) -1/cot(x/2)
=0