(1)lim x*sin(1/x) =0 (x->0)
∵ | x*sin(1/x)|≤|x|->0(x->0),∴lim x*sin(1/x) =0;
(2)lim x[√(x^2-4)-x ]=-2(x->+∞)
lim x[√(x^2-4)-x ]=lim -4x/[√(x^2-4)+x ]=lim -4/[√(1-4/x^2)+1 ]=-2.