Question

вычислить предел lim при x0=2 3x^2-x-10 / 7x-x^2-10

Answer 1

$displaystyle lim_{x to 2} frac{3x^2-x-10}{7x-x^2-10}=bigg[frac{0}0bigg]\\\3x^2-x-10\\D=1+4cdot3cdot10=1+120=121=11^2\\x_{12}=frac{1pm11}{6}=2,,, -frac{5}3\\3x^2-x-10 quad rightarrow quad (x-2)(3x+5)\\\7x-x^2-10=-x^2+7x-10=-(x^2-7x+10)\\D=49-40=9=3^2\\x_{12}=frac{7pm3}{2}=5,,,2\\-(x^2-7x+10)quad rightarrow quad -(x-2)(x-5)\\\lim_{x to 2} frac{3x^2-x-10}{7x-x^2-10}=lim_{x to 2} frac{(x-2)(3x+5)}{-(x-2)(x-5)}=-lim_{x to 2} frac{3x+5}{x-5}=$

$=displaystyle -frac{3cdot 2+5}{2-5}=-frac{6+5}{-3}=boxed{frac{11}3}$