Вычислить: lim (x->-4) (scrt(x+12)-sqrt(4-x))/(x^2+2x-8)

Question

Вычислить: lim (x->-4) (scrt(x+12)-sqrt(4-x))/(x^2+2x-8)

Answer 1

Lim (x->-4) (scrt(x+12)-sqrt(4-x))/(x^2+2x-8)=lim (x->-4) (x+12-4+x)/((scrt(x+12)+sqrt(4-x))(x^2+2x-8))=lim (x->-4) (2x+8)/((scrt(x+12)+sqrt(4-x))(x+4)(x-2))=lim (x->-4) (2(x+4))/((scrt(x+12)+sqrt(4-x))((x+4)(x-2))=lim (x->-4) (2)/((scrt(x+12)+sqrt(4-x))(х-2))=2/((scrt(8)+sqrt(8))(-6))=2/((-24scrt(2))=-1/12scrt(2)=-scrt(2)/24