limx→∞(3^x+1)^(1/x)=limx→∞ e^ln(3^x+1)^(1/x)=e^limx→∞ln(3^x+1)/x=e^limx→∞3^x*ln3/(3^x+1)=e^limx→∞ln3/(1+1/3^x)=e^ln3=3,原式=limx→∞[(3^x)*(3^x+1)]^(1/x)=3*limx→∞(3^x+1)^(1/x)=3*3=9....