Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 1033

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\[1)\ f(x) = \cos x;\]

\[F(x) = \sin x + C.\]

\[M(0;\ - 2):\]

\[- 2 = \sin 0 + C\]

\[- 2 = 0 + C\]

\[C = - 2.\]

\[Ответ:\ \ F(x) = \sin x - 2.\]

\[2)\ f(x) = \sin x;\]

\[F(x) = - \cos x + C.\]

\[M( - \pi;\ 0):\]

\[0 = - \cos( - \pi) + C\]

\[0 = - \cos\pi + C\]

\[0 = 1 + C\ \]

\[C = - 1.\]

\[Ответ:\ \ F(x) = - \cos x - 1.\]

\[3)\ f(x) = \frac{1}{\sqrt{x}} = x^{- \frac{1}{2}}\]

\[F(x) = x^{\frac{1}{2}}\ :\frac{1}{2} = 2\sqrt{x} + C.\]

\[M(4;\ 5):\]

\[5 = 2\sqrt{4} + C\]

\[5 = 2 \bullet 2 + C\]

\[5 = 4 + C\ \]

\[C = 1.\]

\[Ответ:\ \ F(x) = 2\sqrt{x} + 1.\]

\[4)\ f(x) = e^{x};\]

\[F(x) = e^{x} + C.\]

\[M(0;\ 2):\]

\[2 = e^{0} + C\]

\[2 = 1 + C\ \]

\[C = 1.\]

\[Ответ:\ \ F(x) = e^{x} + 1.\]

\[5)\ f(x) = 3x^{2} + 1;\]

\[F(x) = 3 \bullet \frac{x^{3}}{3} + 1 \bullet \frac{x^{1}}{1} =\]

\[= x^{3} + x + C.\]

\[M(1;\ - 2):\]

\[- 2 = 1^{3} + 1 + C\]

\[- 2 = 2 + C\]

\[C = - 4.\]

\[Ответ:\ \ F(x) = x^{3} + x - 4.\]

\[6)\ f(x) = 2 - 2x;\]

\[F(x) = 2 \bullet \frac{x^{1}}{1} - 2 \bullet \frac{x^{2}}{2} =\]

\[= 2x - x^{2} + C.\]

\[M(2;\ 3):\]

\[3 = 2 \bullet 2 - 2^{2} + C\]

\[3 = 4 - 4 + C\ \]

\[C = 3.\]

\[Ответ:\ \ F(x) = 2x - x^{2} + 3.\]