Question

Нужна помощь!
lim x^2-6x-7/3x^2+x-2,
x->a
1)a=-2
2)a=-1
3)a=бесконечность

Answer 1

1)
$lim_{x to -2} frac{x^2-6x-7}{3x^2+x-2} =frac{(-2)^2-6*(-2)-7}{3*(-2)^2-2-2} = frac{4+12-7}{12-4} = frac{9}{8} =1.125$

2)
$lim_{x to -1} frac{x^2-6x-7}{3x^2+x-2} =lim_{x to -1} frac{(x+1)(x-7)}{(3x-2)(x+1)} =lim_{x to -1} frac{x-7}{3x-2} = frac{-8}{-5} =1.6$

3)
$lim_{x to infty} frac{x^2-6x-7}{3x^2+x-2} =lim_{x to infty} frac{(x+1)(x-7)}{(3x-2)(x+1)} =lim_{x to infty} frac{x-7}{3x-2} =$
$=lim_{x to infty} frac{ frac{x}{x} - frac{7}{x} }{ frac{3x}{x} - frac{2}{x} } = frac{1}{3}$