设f(x-1)=lim(n趋近于正无穷)((n+x)/n)^n,则f(x)=

Question

设f(x-1)=lim(n趋近于正无穷)((n+x)/n)^n,则f(x)=_______

Answer 1

f(x-1)
=lim(n→+∞)((n+x)/n)^n
=lim(n→+∞)(1+x/n)^n
=lim(n→+∞)(1+x/n)^(n/x·x)
=[lim(n→+∞)(1+x/n)^(n/x)]^x
=e^x
令t=x-1,则x=t+1
所以,f(t)=e^(t+1)
所以,f(x)=e^(x+1)