lim x->0 x^+2x/2-√x+4

=lim [(x^2 + 2x) (2 + √x + 4)] / [(2 - √x + 4) (2 + √x + 4)]
=lim (x^2 + 2x) (2 + √x + 4) / 4 - x - 4
=lim x(x + 2) (2 + √x+4) / x
=lim (x+2) (2 + √x+4)
=(0 + 2) (2 + √0 + 4)
=2(2 + √4)
=8