Question

Решите графически систему неравенств {(y+2>2x(y-x^3+2<0

Answer 1

В системе координат построим графики функций у=2х-2  - это прямая.   Неравенству  y>2x-2 удовлетворяют все  точки,  лежащие над прямой.
Построим кривую у=$x^{3}-2$,  все точки,  лежащие под кривой,  удовлетворяют неравенству y<$x^{3} -2$
Общее решение в приложении

Answer 2

Solving the System of Inequalities Graphically

To solve the system of inequalities graphically, we need to find the regions where the inequalities are satisfied and then shade those regions on the coordinate plane.

The given system of inequalities is: y + 2 > 2x y - x^3 + 2 < 0

Let's solve each inequality separately and then combine the results to find the solution to the system.

1. Solving y + 2 > 2x: - This inequality represents a line in the coordinate plane. To graph it, we can rewrite it as y > 2x - 2. - The line y = 2x - 2 has a slope of 2 and a y-intercept of -2. We can plot this line and then shade the region above it to represent the inequality.

2. Solving y - x^3 + 2 < 0: - This inequality represents a curve in the coordinate plane. To graph it, we can rewrite it as y < x^3 - 2. - The curve y = x^3 - 2 is a cubic function. We can plot this curve and then shade the region below it to represent the inequality.

By combining the shaded regions from both inequalities, we can find the solution to the system of inequalities.

Let's proceed with graphing these inequalities and finding the solution.