корень потерял...

=lim arctg(3(x+2)-6)/(1+sin(П(x+2))-1)^1/2 при x->0
=lim arctg(3x+6-6)/(1+sin(2П+Пx)-1)^1/2= lim arctg(3x)/(1+sinПx-1)^(1/2) при x->0

тогда lim (arctg(3x)*(1-(sinПx-1))^1/2)/(1-(1-2sinПx+(sinПx)^2))^1/2=

lim (arctg(3x)*(2-sinПx)^1/2)/(sinПx(2-sinПx))^1/2

ЭБМ

=lim (3x*(2-x)^1/2)/(x(2-x))^1/2=lim (((9x^2*(2-x))/(x(2-x)))^1/2=lim (9x)^1/2 при x->0

=0