Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 485

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\[1)\ 2^{- 2}\ \ и\ \ 1;\]

\[\frac{1}{4} < 1.\]

\[2)\ (0,013)^{- 1}\text{\ \ }и\ \ 1;\]

\[- 1 < 0;\]

\[(0,013)^{- 1} > (0,013)^{0};\]

\[(0,013)^{- 1} > 1.\]

\[3)\ \left( \frac{2}{7} \right)^{5}\text{\ \ }и\ \ 1;\]

\[5 > 0;\]

\[\left( \frac{2}{7} \right)^{5} < \left( \frac{2}{7} \right)^{0};\]

\[\left( \frac{2}{7} \right)^{5} < 1.\]

\[4)\ 27^{1,5}\ \ и\ \ 1;\]

\[1,5 > 0;\]

\[27^{1,5} > 27^{0};\]

\[27^{1,5} > 1.\]

\[5)\ 2^{- \sqrt{5}}\text{\ \ }и\ \ 1;\]

\[- \sqrt{5} < 0;\]

\[2^{- \sqrt{5}} < 2^{0};\]

\[2^{- \sqrt{5}} < 1.\]

\[6)\ \left( \frac{1}{2} \right)^{\sqrt{3}}\text{\ \ }и\ \ 1;\]

\[\sqrt{3} > 0;\]

\[\left( \frac{1}{2} \right)^{\sqrt{3}} < \left( \frac{1}{2} \right)^{0};\]

\[\left( \frac{1}{2} \right)^{\sqrt{3}} < 1.\]

\[7)\ \left( \frac{\pi}{4} \right)^{\sqrt{5} - 2}\text{\ \ }и\ \ 1;\]

\[\pi \approx 3,14 < 4,\ значит\ \frac{\pi}{4} < 1;\]

\[5 > 4;\]

\[\sqrt{5} > 2;\]

\[\sqrt{5} - 2 > 0;\]

\[\left( \frac{\pi}{4} \right)^{\sqrt{5} - 2} < \left( \frac{\pi}{4} \right)^{0};\]

\[\left( \frac{\pi}{4} \right)^{\sqrt{5} - 2} < 1.\]

\[8)\ \left( \frac{1}{3} \right)^{\sqrt{8} - 3}\text{\ \ }и\ \ 1;\]

\[8 < 9;\]

\[\sqrt{8} < 3;\]

\[\sqrt{8} - 3 < 0;\]

\[\left( \frac{1}{3} \right)^{\sqrt{8} - 3} > \left( \frac{1}{3} \right)^{0};\]

\[\left( \frac{1}{3} \right)^{\sqrt{8} - 3} > 1.\]