lim (3^x+9^x)^(1/x) as x->∞
=e^lim ln(3^x+9^x)/x
=e^lim (3^x*ln3+9^x*ln9)/(3^x+9^x),洛必达法则
=e^lim (ln3+3^x*2ln3)/(1+3^x),上下除以3^x
=e^ln3*lim (1+2*3^x)/(1+3^x),提取ln3
=3^lim (1/3^x+2)/(1/3^x+1),上下除以3^x
=3^(0+2)/(0+1)
=3²
=9
求lim(x→∞)(3^x +9^x ）^（1/X）的极限
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