calculus problem

1. Write the equation below in its equivalent exponential form.

2. Write the first four terms of the sequence whose general term is given below:

            a_n­ = 4(3n – 1)

3. Use the addition method to solve the system below:

                        4x + 27y = 27

                        8x – 3y = -3

4. In the right triangle ABC below, C is the right angle, and two sides are given. Find sin θ of the given angle.

            The sin of an angle in a right triangle is equal to the ratio of the opposite side to     the hypotenuse.

5. Find the reference angle for

6. Find the area of a triangle with these measurements: C = 100º, a = 1 yard, and b = 8 yards. Round your answer to the nearest square unit.

7. Solve the right triangle in the figure below in which A = 51.9º and c = 51.2. Round lengths to one decimal place, and express angles to the nearest tenth of a degree.

8. Plot the complex number -3 + 6i.

9. Write the expression below as the cosine of an angle, knowing that the expression is the right side of the formula for  with particular values for α and β.

10. Solve the equation below on the interval  .

11. Find the exact value of the expression

12. Find the rectangular coordinates of the point whose polar coordinates are (3, -270º)

13. Complete the identity below:

14. Using the vectors given below, find

15. If the sequence below is a geometric sequence, find the common ratio.

16. Graph the solution set of the system of inequalities below.

17. Find the maximum and minimum values of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points.

            Objective function: z = 5x + 8y

18. Use Gauss-Jordan elimination to solve the system x – y + 3z = 0, 2x + 2y – z = 9, and –x + 5y – 10z = 4

19. Find the product of the matrices  and  .

20. Compute the determinant

21. Write an equation for the ellipse with vertices (2, 2), (4, 2), (3, -1) and (3, 5).

22. Find the foci of the hyperbola

23. What is the standard form equation of a parabola with directrixx = -2 and focus (2, 0)?

24. Eliminate the parameter from the parametric equations  and

25. Determine what kind of conic is represented by the equation

26. Estimate the following limit using a table:

27. Use properties of limits to compute the following limit exactly.

28. Use the limit definition to compute f’(x) if f(x) = 6x² – 9.