Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 1017

\[1)\ y = 2^{5x - 1}\]

\[y(x) = y(x + T)\]

\[2^{5x - 1} = 2^{5(x + T) - 1}\]

\[5x - 1 = 5(x + T) - 1\]

\[5x = 5(x + T)\]

\[x = x + T\]

\[T = 0.\]

\[Ответ:\ \ нет.\]

\[2)\ y = 2^{\sqrt{\cos^{2}x - 1}}\]

\[y(x) = y(x + T)\]

\[2^{\sqrt{\cos^{2}x - 1}} = 2^{\sqrt{\cos^{2}(x + T) - 1}}\]

\[\sqrt{\cos^{2}x - 1} = \sqrt{\cos^{2}(x + T) - 1}\]

\[\cos^{2}x - 1 = \cos^{2}(x + T) - 1\]

\[\cos^{2}x = \cos^{2}(x + T)\]

\[\frac{1 + \cos{2x}}{2} = \frac{1 + \cos{2(x + T)}}{2}\]

\[1 + \cos{2x} = 1 + \cos(2x + 2T)\]

\[\cos{2x} = \cos(2x + 2T)\]

\[2T = 2\pi\]

\[T = \pi.\]

\[Ответ:\ \ да.\]