Question

lim (x+1/x)^x=e,求证明?

Answer 1

证明：
lim (1+x)^(1/x)
= lim e^[ln(1+x)^(1/x)]
= lim e^[ln(1+x)/x]
= e^{lim[ln(1+x)/x]}
＝〉洛必塔法则
= e^{lim[1/(x+1)]}
= e^1
= 1
如果满意请点击右上角评价点【满意】即可~