Страница 296 номер 992, ГДЗ по алгебре за 10-11 класс Алимов - ответы и решение

1) \(f(x) = 2x + 3\), \(M(1;\ 2)\)
\(F(x) = x^{2} + 3x + C,\)
\(F(1) = 2, 2 = 1 + 3 + C, C = - 2,\)
\(F(x) = x^{2} + 3x - 2;\)

2) \(f(x) = 4x - 1\), \(M(-1;\ 3)\)
\(F(x) = 2x^{2} - x + C,\)
\(F(-1) = 3, 3 = 2 + 1 + C, C = 0,\)
\(F(x) = 2x^{2} - x;\)

3) \(f(x) = \sin{2x}\), \(M\left( \frac{\pi}{2};\ 5 \right)\)
\(F(x) = - \dfrac{1}{2}\cos{2x} + C,\)
\(F\left( \dfrac{\pi}{2} \right) = 5, 5 = - \dfrac{1}{2}\cos\pi + C, C = \dfrac{9}{2},\)
\(F(x) = \dfrac{9}{2} - \dfrac{1}{2}\cos{2x};\)

4) \(f(x) = \cos{3x}\), \(M(0;\ 0)\)
\(F(x) = \dfrac{1}{3}\sin{3x} + C,\)
\(F(0) = 0, 0 = \dfrac{1}{3}\sin 0 + C, C = 0,\)
\(F(x) = \dfrac{1}{3}\sin{3x}.\)