Question

Найдите пределы функции:

Answer 1

4)

$\displaystyle \lim_{x \to \ 5} \frac{(x-5)^2}{(x-5)(x+5)}= \lim_{x \to \ 5} \frac{x-5}{x+5}= \frac{5-5}{5+5}=0$

5)

$\displaystyle \lim_{x \to \ 3} (\frac{6}{(x-3)(x+3)}-\frac{1}{x-3})= \lim_{x \to \ 3} \frac{6-(x+3)}{(x-3)(x+3)}= \lim_{x \to \ 3} \frac{3-x}{(x-3)(x+3)}=\\\\= \lim_{x \to \ 3} \frac{-1}{x+3}= \frac{-1}{6}$

6)

$\displaystyle \lim_{x \to \ 8} \frac{16-(x+8)}{x^2-64}= \lim_{x \to \ 8} \frac{8-x}{x^2-64}= \lim_{x \to \ 8} \frac{-1}{x+8}=-\frac{1}{16}$