Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0...

Should i use the formula e= lim as x->0 (1+x)^(1/x)

or

e= lim as x->infinity (1+1/n)^n

Am i able to substitute in x/n for x? and then say that

e lim x ->0 (1+x/n)^(1/(x/n))

and then raise it to the xth power

ie. e^x and lim x -> (1+x/n)^(n)

Thanks for any help.. just tell me if is correct please or if i am on the right track

also,, how do i say that this is for all x>0?