罗比达法则
原式=lim[(ln3*3^x)/(1+3^x)]/[(ln2*2^x)/(1+2^x)]
=lim[ln3*3^x(1+2^x)]/[ln2*2^x(1+3^x)]
=lim(ln3*3^x+ln3*6^x)/(ln2*2^x+ln2*6^x)
=(ln3/ln2)lim[(1/2)^x+1]/(1/3)^x+1]
=ln3/ln2=log(2)3
罗比达法则
原式=lim[(ln3*3^x)/(1+3^x)]/[(ln2*2^x)/(1+2^x)]
=lim[ln3*3^x(1+2^x)]/[ln2*2^x(1+3^x)]
=lim(ln3*3^x+ln3*6^x)/(ln2*2^x+ln2*6^x)
=(ln3/ln2)lim[(1/2)^x+1]/(1/3)^x+1]
=ln3/ln2=log(2)3