lim x→0 (ln(x^2+1))/xsin2x=lim(ln(1+x^2)/2x^2)/(sin2x/2x)ln(1+x)~xln(1+x^2)~x^2lim(ln(1+x^2)/2x^2)/(sin2x/2x)=(1/2)/1=1/2.即lim x→0 (ln(x^2+1))/xsin2x=1/2.