Question

Раскройте, пожалуйста, предел неопределённостей
$lim_{x to3} frac{ x^{2} -2x-3}{ x^{2}-9}$

Answer 1

1 способ
lim x->3 (x^2 - 2x - 3)/(x^2 - 9) = [ 0/0] = 
= lim x->3 (x - 3)*(x + 1)/(x - 3)*(x + 3) = 
= lim x->3 (x + 1)/(x + 3) = (3 + 1)/(3 + 3) = 4/6 = 2/3

2 способ
lim x->3 (x^2 - 2x - 3)/(x^2 - 9) = [ 0/0] = 
= lim x->3 (2x - 2)/2x = (6 - 2)/6 = 4/6 = 2/3