MATH 230 Final: Final spring 2009
15 Feb 2019
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Make sure that your - nal answer is clearly indicated. 17 pages, 14 problems, and one bonus question. Please make sure that all pages are included. Question 3. (10 points) fill in the table, and then sketch the graph of the polar equation r = 6 cos( ), 0 . r = 6 cos( ) Question 4. (12 points) describe and sketch the parametric curve given by: x = cos t y = 4t z = sin t. Clearly indicate the direction in which the curve is being traced out, and mark the points corresponding to t = 0, t = . 2 , t = , t = 3 . Question 5. (12 points) let s be the surface given by: x2 y2. Sketch and label the traces of s in the coordinate planes, and then sketch the surface itself. Trace in yz-plane z x y x y z x.
