MATH 222  Test 2                                          Name____________________

Instructions: Answer all the questions on the paper provided and show all your work.  You may use a calculator on all questions.

1.  Plot the points given in polar coordinates in the graphical region below:   (6)

A (2,p/4),  B (-2, 7p/6), C (2, 11p/4)

2.  Find the area of the region enclosed by the curve r = cos(3q).                       (10)

3.  Find the equation of the line tangent to the parametric curve at the point corresponding to t = 3 when the curve is given by x(t) = 2t2, y(t) = t3-2.                            (8)

4.  Find three different sets of polar coordinates for the point given in x-y coordinates by .  One of the sets of polar coordinates should have a negative value for r.   (6)

5.  Transform the equation  into a standard form for a conic section. Identify the curve and find all its relevant parts (foci etc.)                     (14)

6.   Expand  in partial fractions but do not evaluate the resulting integral.  Find all necessary coefficients.                                                                                   (12)

7.  Evaluate  including all necessary limits.                                            (16)

8.  Expand  into a partial fraction expansion, but do not find the value of the coefficients.                                                                                                (8)

9.  Find the equation in standard form of the parabola with its focus at (-1,4) and its directrix given by x = -5.                                                                             (10)

10.  Find the length of the curve given by .  (8)