求极值x→∞ lim(3+x)/(x+2)^ 2x
问题描述：
求极值x→∞ lim(3+x)/(x+2)^ 2x
答
lim(x→∞)[(3+x)/(x+2)]^ 2x= lim(x→∞)[1 + 1/(x+2)]^ 2x= lim(x→∞){[1 + 1/(x+2)]^ (x+2)}^ [2x/(x+2)]= lim(x→∞)e^ [2x/(x+2)]= lim(x→∞)e^ [2 - 4/(x+2)]= lim(x→∞)e^2= e^2