lim_{x趋于正无穷}(1+1/x)^x = e
lim_{x趋于正无穷}{x[ln(x+1)-lnx]}=lim_{x趋于正无穷}{xln[(x+1)/x]}
=lim_{x趋于正无穷}ln{[(x+1)/x]^x}
=lim_{x趋于正无穷}ln[(1+1/x)^x]
=ln(e)
=1lim_{x趋于正无穷}{xln[(x+1)/x]}=lim_{x趋于正无穷}ln{[(x+1)/x]^x}x为什么明明是xlny会变成lny^x？？？？ln[a^b] = b*ln(a), 这是对数函数的性质吧.ln[a*b] = ln(a)+ln(b), 对数的和=乘积的对数.ln[a^2]=ln[a*a] = ln(a)+ln(a)=2ln(a),...ln[a^n]=n*ln(a)哦，谢谢