求极限limx趋近于∞时的极限。

Question

如题所述

Answer 1

lim(x->0) (x-sin2x)/(x+sin2x) =lim(x->0) (x-2x)/(x+2x) = -1/3
lim(n->∞) (1+1/n)^(n+3)=lim(n->∞) (1+1/n)^n = e
/
let
1/y = 1/(2+x)
lim(x->∞) [(3+x)/(2+x)]^(2x)
=lim(x->∞) [1 + 1/(2+x)]^(2x)
=lim(y->∞) [1 + 1/y]^[2(y-2)]
=lim(y->∞) [1 + 1/y]^(2y)
=e^2