Use lim n->inf (1+1/n) = e or its variation and logarithm to prove lim n->inf (1+x/n) = e^x for all x.
Again I got confused when you put an exponent on the (1+X/n) side.
It was assumed that your post had erroneously omitted the exponent, since of course the expression will not lead to the natural exponential without said exponent. For further information, kindly consult resources such as this
. If your text or your instructor is not using the standard expression (as displayed at the link), then kindly please reply with documentation of whatever non-standard methodology is being required of you. Thank you.