Question

limx→∞(+x+2/+x+3)2x+5

Answer 1

(x+2)/(x+3) = 1- 1/(x+3)
let
1/y =1/(x+3)
lim(x→∞) [(x+2)/(x+3)]^(2x+5)
=lim(x→∞) [1- 1/(x+3)]^(2x+5)
=lim(y→∞) (1- 1/y)^(2(y-3)+5)
=lim(y→∞) (1- 1/y)^(2y-1)
=lim(y→∞) (1- 1/y)^(2y)
=e^(-2)