Question

Помогите пожалуйста, найти предел

Answer 1

преобразуем выражение

1/(x - 7) - 14/(x² - 49) = (x + 7)/(x - 7)(x + 7) - 14/(x - 7)(x+7) = (x + 7 - 14)/(x - 7)(x + 7) = 1/(x + 7)

lim(x->7) ( 1/(x - 7) - 14/(x² - 49) ) = lim(x->7) 1/(x + 7) = 1/(7 + 7) = 1/14

Answer 2

$\lim\limits _{x \to 7}\Big(\dfrac{1}{x-7}-\dfrac{14}{x^2-49}\Big)=\lim\limits _{x \to 7}\dfrac{x+7-14}{(x-7)(x+7)}=\lim\limits _{x \to 7}\dfrac{x-7}{(x-7)(x+7)}=\\\\\\=\lim\limits _{x \to 7}\dfrac{1}{x+7}=\dfrac{1}{7+7}=\dfrac{1}{14}$