limx趋于无穷大[(2^x+3^x)/(2^(x+1)+3^(x+1))],
问题描述:
limx趋于无穷大[(2^x+3^x)/(2^(x+1)+3^(x+1))],
答
x趋于无穷大 lim[(2^x+3^x)/(2^(x+1)+3^(x+1))]
分子分母同时除以3^(x+1)
极限 = lim [(1/3)*(2/3)^x +(1/3)]/[(2/3)^(x+1)+1]
= (0 + 1/3)/(0 +1)
=1/3