lim(x→∞)(1+2∧n+3∧n)∧(1 /n)=?
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lim(x→∞)(1+2∧n+3∧n)∧(1 /n)=?
首先求函数(1+2^x+3^x)^(1/x)当x趋于正无穷大时的极限(先取对数,再用洛比达法则) lim(x→+∞)ln(1+2^x+3^x)/x=lim(x→+∞)(2^xln2+3^xln3)/(2^x+3^x)=lim(x→+∞)((2/3)^xln2+ln3)/((2/3)^x+1)=ln3 所以lim(x→+∞)(1+2^x+3^x)^(1/x)=3,故lim(n→∞)((1+2^n+3^n))^(1/n)=3
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