Решебник по алгебре 11 класс Никольский Параграф 5. Применение производной Задание 111

\[\boxed{\mathbf{111}\mathbf{.}}\]

\[\textbf{а)}\ y = \frac{- 2x + 12}{x - 4} =\]

\[= \frac{- 2(x - 4) - 8 + 12}{x - 4} =\]

\[= - \frac{2(x - 4)}{x - 4} + \frac{4}{x - 4} =\]

\[= \frac{4}{x - 4} - 2;\]

\[Асимптоты:\]

\[y = - 2;\ \ x = 4.\]

\[\textbf{б)}\ y = \left| \frac{- 2x + 12}{x - 4} \right|\]

\[\frac{- 2x + 12}{x - 4} =\]

\[= \frac{- 2(x - 4) - 8 + 12}{x - 4} =\]

\[= - \frac{2(x - 4)}{x - 4} + \frac{4}{x - 4} =\]

\[= \frac{4}{x - 4} - 2;\]

\[Асимптоты:\]

\[y = - 2;\ \ x = 4.\]

\[\textbf{в)}\ = \frac{- 2|x| + 12}{|x| - 4}\]

\[\frac{- 2x + 12}{x - 4} =\]

\[= \frac{- 2(x - 4) - 8 + 12}{x - 4} =\]

\[= - \frac{2(x - 4)}{x - 4} + \frac{4}{x - 4} =\]

\[= \frac{4}{x - 4} - 2;\]

\[Асимптоты:\]

\[y = - 2;\ \ x = 4.\]

\[\textbf{г)}\ y = \left| \frac{- 2|x| + 12}{|x| - 4} \right|\]

\[\frac{- 2x + 12}{x - 4} =\]

\[= \frac{- 2(x - 4) - 8 + 12}{x - 4} =\]

\[= - \frac{2(x - 4)}{x - 4} + \frac{4}{x - 4} =\]

\[= \frac{4}{x - 4} - 2;\]

\[Асимптоты:\]

\[y = - 2;\ \ x = 4.\]