求极限lim(1+2/x)^2x+3

题目

求极限lim(1+2/x)^2x+3
x→正无穷

答案

lim(x→∞) (1+2/x)^(2x+3)
=lim(x→∞) (1+2/x)^[(x/2)*4+3)]
=lim(x→∞) [(1+2/x)^(x/2)]^4*lim(x→∞) (1+2/x)^3
=e^4