Question

请教一道高数求极限的题目

如图，为什么这里不能用重要极限。

Answer 1

y->0

( 1+y)^(1/y^2)

=e^[ln(1+y) /y^2]

=e^{ [ y- (1/2)y^2 +o(y^2)]/y^2 }

=e^[1/y - 1/2 +o(y^0) ]

lim(x->+∞) e^x/( 1+1/x)^x^2

y=1/x

=lim(y->0) e^(1/y)/( 1+y)^(1/y^2)

=lim(y->0) e^(1/y)/e^[1/y - 1/2) ] 

=e^(1/2)