Question

求极限limx→∞(1-3／x)^x

Answer 1

为了解题看起来方便,设 y = - 3/x,则 x = -3/y.当 x →∞时,y →0

那么,

lim(1 - 3/x)^x

= lim (1 + y)^(-3/y)

= lim [(1 + y)^(1/y)]^(-3)

=[lim (1 + y)^(1/y)]^(-3)

=e^(-3)

=1/e^3