MATH 222 Review Questions for Test 2

1. Let define a parametric curve.

a) What are the x-y coordinates of the point corresponding to t = 2?

b) Sketch the graph of the curve.

c) Find the points on the curve at which the tangent lines are vertical.

d) Find the points on the curve at which the tangents are horizontal.

e) Find the area enclosed by the loop in the curve.

2. Find three different sets of polar coordinates for the point represented by (3,-3) in x-y coordinates.

3. Find the area enclosed by the curve r = cos(q).

4. Evaluate and show all your substitutions.

5. Let x(t) = 3cos(t) and y(t) = 4sin(t) for .

Eliminate the parameter t and identify the curve that results.

6. Put the equation given below into standard form, identify the curve, and find all the relevant parts (foci etc.):

7. Evaluate the following, showing all necessary limits: