Question

с первым номером все буквы

Answer 1

а)

$y = 3 {x}^{3} - 1$

$F(x) = 3 \times \frac{ {x}^{4} }{4} - x = \frac{3 {x}^{4} }{4} - x$

б)

$y = 4 \cos(x) - 3 {e}^{x}$

$F(x) = 4 \sin(x) - 3 {e}^{x}$

в)

$y = \sin(3x + 4)$

$F(x) = - \frac{1}{3} \times \cos(3x + 4)$

2.

$f(x) = \sin(2x) \\ F(x) = - \frac{1}{2} \times \cos(2x) + c$

M (π/2;5)

$- \frac{1}{2} \times \cos(2 \times \frac{\pi}{2} ) + c = 5 \\ - \frac{1}{2} \times \cos(\pi) + c = 5 \\ - \frac{1}{2} \times ( - 1) + c = 5 \\ \frac{1}{2} + c = 5 \\ c = 5 - 0.5 \\ c = 4.5$

$F(x) = - \frac{1}{2} \times \cos(2x) + 4.5$