Assessments

Attempt these 10 questions:

1. Calculate the limit of (3x^2 - 2x + 1)/(2x^2 + 5x - 3) as x approaches 1.

2. Solve the integral of sin(x)cos(x) dx.

3. Find the derivative of f(x) = x^2 ln(x).

4. Solve the differential equation dy/dx = 2x + 3.

5. Calculate the determinant of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]].

6. Find the roots of the quadratic equation x^2 - 5x + 6 = 0.

7. Determine the equation of the tangent line to the curve y = x^3 - 3x^2 + 2x - 1 at the point (1, -1).

8. Evaluate the sum of the series 1/2 + 1/4 + 1/8 + 1/16 + ...

9. Find the area of the region bounded by the curves y = x^2 and y = 2x - x^2.

10. Solve the trigonometric equation 2sin(x)cos(x) = sin(x).