Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 741

\[\boxed{\mathbf{741}\mathbf{.}}\]

\[\lbrack 0;\ 3\pi\rbrack.\]

\[1)\ tg\ x \geq 3\]

\[arctg\ 3 + \pi n \leq x < \frac{\pi}{2} + \pi n\]

\[arctg\ 3 \leq x_{1} < \frac{\pi}{2};\]

\[arctg\ 3 + \pi \leq x_{2} < \frac{3\pi}{2};\]

\[arctg\ 3 + 2\pi \leq x < \frac{5\pi}{2}.\]

\[2)\ tg\ x < 4\]

\[- \frac{\pi}{2} + \pi n < x < arctg\ 4 + \pi n\]

\[0 \leq x_{1} < arctg\ 4;\]

\[\frac{\pi}{2} < x_{2} < arctg\ 4 + \pi;\]

\[\frac{3\pi}{2} < x_{3} < arctg\ 4 + 2\pi;\]

\[\frac{5\pi}{2} < x_{4} < arctg\ 4 + 3\pi.\]

\[3)\ tg\ x \leq - 4\]

\[- \frac{\pi}{2} + \pi n < x \leq arctg( - 4) + \pi n\]

\[- \frac{\pi}{2} + \pi n < x \leq - arctg\ 4 + \pi n\]

\[\frac{\pi}{2} < x_{1} \leq - arctg\ 4 + \pi;\]

\[\frac{3\pi}{2} < x_{2} \leq - arctg\ 4 + 2\pi;\]

\[\frac{5\pi}{2} < x_{3} \leq - arctg\ 4 + 3\pi.\]

\[4)\ tg\ x > - 3\]

\[\text{arctg}( - 3) + \pi n < x < \frac{\pi}{2} + \pi n\]

\[- arctg\ 3 + \pi n < x < \frac{\pi}{2} + \pi n\]

\[0 \leq x < \frac{\pi}{2};\]

\[- arctg\ 3 + \pi < x < \frac{3\pi}{2};\]

\[- arctg\ 3 + 2\pi < x < \frac{5\pi}{2};\]

\[- arctg\ 3 + 3\pi < x \leq 3\pi.\]