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