Вправи 180 182

180:

1. Solve the equation: 3x + 5 = 20.
2. Differentiate the function f(x) = 3x^2 - 4x + 1.
3. Simplify the expression: (2x^3y^2)^2 * (4xy^3)^3.
4. Find the value of x when y = 5 in the equation 2x + 3y = 25.
5. Evaluate the integral: ∫(2x + 3)dx from x = 0 to x = 5.
6. Prove the statement: "The sum of two even numbers is always even."
7. Find the coordinates of the vertex of the parabola given by the equation y = x^2 - 4x + 3.
8. Solve the inequality: 2x - 5 < 10.
9. Simplify the expression: log(base 2) 8 + log(base 2) 2.
10. Evaluate the limit: lim(x->0) (3x + sin(x))/x.

182:

1. Solve the equation: 2e^x = 8.
2. Find the derivative of the function f(x) = ln(x^2 + 1).
3. Simplify the expression: (2sin(x))^2 * (4cos(x))^3.
4. Find the value of x when y = 3 in the equation 2x + 3y = 15.
5. Evaluate the integral: ∫(2x + 4)dx from x = 1 to x = 3.
6. Prove the statement: "The product of two odd numbers is always odd."
7. Find the coordinates of the vertex of the parabola given by the equation y = -x^2 + 6x - 9.
8. Solve the inequality: 3x - 4 > 7.
9. Simplify the expression: log(base 3) 9 + log(base 3) 3.
10. Evaluate the limit: lim(x->1) (x^3 - 1)/(x - 1).