Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 4

\[1)\ f(x) = \frac{\cos{2x}}{\sin x}\ \]

\[x_{1} = \frac{\pi}{4};\ \ \ x_{2} = \frac{7\pi}{2};\]

\[\sin x \neq 0\]

\[x \neq \pi\text{n.}\]

\[f\left( \frac{\pi}{4} \right) = \frac{\cos\frac{\pi}{2}}{\sin\frac{\pi}{4}} = 0\ :\frac{\sqrt{2}}{2} = 0;\]

\[f\left( \frac{7\pi}{2} \right) = \frac{\cos{7\pi}}{\sin\frac{7\pi}{2}} = \frac{\cos\pi}{\sin\frac{3\pi}{2}} =\]

\[= \frac{- 1}{- 1} = 1.\]

\[2)\ f(x) = \frac{x}{\cos{\pi x}}\]

\[x_{1} = 0;\ \ \ x_{2} = - 1;\ \ \ x_{3} = 100;\]

\[\cos{\pi x} \neq 0\]

\[\pi x \neq \frac{\pi}{2} + \pi n\]

\[x \neq \frac{1}{2} + n.\]

\[f(0) = \frac{0}{\cos 0} = \frac{0}{1} = 0;\]

\[f( - 1) = \frac{- 1}{\cos( - \pi)} = - \frac{1}{\cos\pi} =\]

\[= - \frac{1}{- 1} = 1;\]

\[f(100) = \frac{100}{\cos{100\pi}} = \frac{100}{\cos 0} = 100.\]