MATH 222 Test 3 Fall 2001 Name_______________

1. The point (4,p/6) is given in polar coordinates. What is its expression in x-y coordinates? (5)

2. The point (-2,-2) is given in x-y coordinates. Give three different expressions for this point in polar coordinates, one of which has a negative first coordinate. (12)

3. Give the equation in standard form of a parabola with its vertex at (3,-2) and its focus at (-3,-2). (8)

4. Apply the integral test to the series to determine if it converges or diverges.

(10)

5. Find the first five terms of the sequence defined by for all n greater than 2. (7)

6. Find the radius and interval of convergence of the following power series:

(15)

7. Determine whether the following infinite series converge or diverge. Clearly state which test you are using and include all required limits. (40)

a)

b)

c)

d)