x→+∞lim (3x+e^x)^(2/x)=lim e^ln (3x+e^x)^(2/x)=e^lim ln (3x+e^x)^(2/x)考虑lim ln (3x+e^x)^(2/x)=lim 2ln(3x+e^x) / x该极限为∞/∞型,利用L'Hospital法则=2*lim [ln(3x+e^x)]' / [x]'=2lim (3+e^x)/(3x+e^x)...