设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f'(t)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/07/05 21:06:40
设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f''(t)设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f''(t)设f(t)=lim(x→∞)t(1+2/x)^(x-t),求
设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f'(t)
设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f'(t)
设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f'(t)
设f(t)=lim(x→∞)t(1+2/x)^(x-t),求f'(t)
解;∵t(1+2/x)^(x-t)=t[(1+2/x)^(x/2)]²[(1+2/x)^(-t)]
∴f(t)=x→∞limt(1+2/x)^(x-t)=x→∞limt[(1+2/x)^(x/2)]²[(1+2/x)^(-t)]=e²t
故f′(t)=e².