$lim_(x->infty)((x+2)/x)^((x^2-x)/(3x+2))$

A cura di: Antonio Bernardo

$lim_(x->infty)((x+2)/x)^((x^2-x)/(3x+2))$

$lim_(x->infty)(1+2/x)^(x(x-1)/(3x+2))$

$lim_(x->infty)(1+2/x)^((x/2)(2*(x-1)/(3x+2)))=e^(2/3)$

infatti

$lim_(x->infty)((1+2/x)^(x/2))=e$

$lim_(x->infty)(2*(x-1)/(3x+2))=2/3$