lim(1+1/x)^x²/x+y(x→∞,y→a),求极限

Question

lim(1+1/x)^x²/x+y (x→∞,y→a),求极限

Answer 1

显然在x趋于∞的时候,
(1+1/x)^x趋于e,
而y趋于常数a,
所以x/(x+y)趋于1,
于是
原极限
=lim(x→∞,y→a) [(1+1/x)^x] ^x/(x+y)
= e