计算下列极限：
(1)lim_x→0(tan5x/x)；(2)limlim_x→0(sin2x/3x)；
(3)lim_x→0xcotx；(4)lim_x→0[(1-cos2x)/xsinx]；
(5)lim_n→∞2ⁿsin(x/2ⁿ)；(6)lim_x→0(1+2x)^1/x
(7)lim_x→0(1-3x)^1/x；(8)lim_x→∞(1+1/x)^3x；
(9)lim_x→∞(1-1/2x)^x；(10)lim_n→∞[(2n+3)/(2n+1)]ⁿ⁺¹