(4)
lim(x->a+) [√x-√a +√(x-a) ]/√(x-a^2)
=[√a-√a +√(a-a) ]/√(a-a^2)
=0
(5)
lim(x->7) [ 3- (x+20)^(1/3)]/(x-7) (0/0)
=lim(x->7) -(1/3)(x+20)^(-2/3)
= -(1/3)(27)^(-2/3)
=1/27
(6)
lim(x->8) [√(9+2x) - 5 ]/[ x^(1/3) -2 ] (0/0)
=lim(x->8) [1/√(9+2x)]/[ (1/3)x^(-2/3) ]
=lim(x->8) 3x^(2/3)/√(9+2x)
=3(4)/5
=12/5