MATH 230 Final: Final spring 2008
15 Feb 2019
School
Department
Course
Professor
Document Summary
Make sure that your - nal answer is clearly indicated. This exam has 17 pages, and 14 problems. Please make sure that all pages are included. Question 2. (10 points) find the distance between the origin and the plane: P : 3x + y 4z = 2. Question 3. (12 points) let s be the surface given by: x2 y2 + z2 = 1. Sketch and label the traces of s in the coordinate planes, and then sketch the surface itself. y z z x y x y z x. Question 4. (10 points) describe and sketch the parametric surface given by: x = 2u cos v y = 2u sin v z = 8u. Hint: find an equation relating x, y, and z. Question 5. (18 points: sketch the following surfaces given in spherical coordinates, Question 5 continued: sketch the following surfaces given in cylindrical coordinates, z = 4 r2, r2 = 4.
