2.а)y=1/(x²-1)=1/(x+1)(x-1);⇒
x≠-1;x≠1;
x∈(-∞;-1);(-1;+1);(1;+∞)
б)y=(x-2)/(x²-x-12);⇒
x²-x-12≠0;
x²-x-12=0⇒x₁,₂=1/2⁺₋√(1/4+12)=1/2⁺₋√49/4=1/2⁺₋7/2;
x₁=1/2+7/2=4;x₂=1/2-7/2=-3;⇒
x≠4;x≠-3;
x∈(-∞;-3);(-3;4);(4;+∞)
в)y=√(x+12)/(x-1);⇒
x+12≥0;x≥-12;
x-1≠0;x≠1;⇒
x∈[-12;1);(1;+∞)
г)y=5x/√(x-2)⇒
x-2≥0;x≥2;⇒
x∈[2;+∞)
3.а)limₓ→₁(x³-x²)/(2x²-x-1)=0/0;
limₓ→₁x²(x-1)/2·(x-1)(x+1/2)=limₓ→₁x²/2(x+1/2)=1/2·1.5=/3;
б)limₓ→₂(x²-4x+4)/(x³-8)=0/0;
limₓ→₂(x-2)²/(x-2)(x²+2x+4)=limₓ→₂(x-2)/(x²+2x+4)=0/12=0;
в)limₓ→₃(x²-6x+9)/(x-3)=0/0;
limₓ→₃(x-3)²/(x-3)=limₓ→₃(x-3)/1=0/1=0;
г)limₓ→₁(⁴√x-1)/(√x-1)=0/0;
limₓ→₁(⁴√x-1)/(⁴√x+1)(⁴√x-1)=limₓ→₁1/(⁴√x+1)=1/(1+1)=1/2;