lim(x->∞) [(x+3)/(x+2)]^x= lim(x->∞) [((x+2)+1)/(x+2)]^x= lim(x->∞) [1 + 1/(x+2)]^x= lim(x->∞) [1 + 1/(x+2)]^[(x+2) * x/(x+2)]= e^lim(x->∞) x/(x+2)= e^lim(x->∞) 1/(1+2/x)= e^[1/(1+0)]= e