如图
(1) 分子分母同乘以 [√(2x)+2] [x^(2/3)+(2x)^(1/3)+2^(2/3)], 得 原式 = lim 2(x-2)[x^(2/3)+(2x)^(1/3)+2^(2/3)] / {(x-2)[√(2x)+2]} = lim 2[x^(2/3)+(2x)^(1/3)+2^(2/3)] / [√(2x)+2] = 2*3*2^(2/3) / 4 = (3/2)2^(2/3) = (3/2)4^(1/3), 选 C。(2) lim 2xsin(1/x) = lim2sin(1/x)/(1/x) = 2, 选 B。(3) 分子分母同乘以(1/x^2), 得 原式 = lim (1+1/x-1/x^2)/(x^2-3+1/x^2) = 0。(4) 等价无穷小代换， 原式 = lim x^3/x^3 = 1
