Test 7 Summary
Parametric Equations & Polar Coordinates

----Parametric----
1. given x(t), y(t)
 a. find x' y' dy/dx
 b. find location and dir. for time t = c
 c. find all locations of vert. tangency
 d. self intersection at (x1,y1) give both tangent lines

2. given x(t), y(t)
 a. find dy/dx
 b. find d2y/dx2
 c. find all points of inflection in graph

3. find the exact length of a param. curve (numeric/calculator)

4. 2d motion given x(t), dy/dt(t)
 a. exact dist. traveled (t1 to t2)
 b. displacement from (t1 to t2)
 c. speed at t3
	
----Polar----
5. find 2 polar coords. for (x1,y1) [0,2pi)

6. given r = f(t), find all horiz. tangent lines. & locaitons

7. find an eqn. of tangent line at t1 for r = f(t)

8. r1 = f(t),  r2 = g(t)

  a. sketch both, shade the common interior area
  b. find in one coord. pair for each intersection
  c. setup area integral(s) -> numeric approx. / calculator