MATH 230 Final: Final spring 2011

13 views21 pages

Document Summary

June 7, 2011 (2 points) put a check mark next to your instructor"s name and section: Instructions: read each problem carefully, write legibly, show all your work on these sheets. Feel free to use the opposite side: this exam has 21 pages, and 14 problems. Please make sure that all pages are included: you may not use books, notes or calculators, you have two hours to complete this nal exami- nation. Question 2. (6 points) consider the following three planes. (i) 3x + 4y z = 6 (ii) 2x + 2y + 2z = 4 (iii) x y z = 2. Circle the correct statements. (a) planes i and ii are. Question 3. (10 points) find parametric equations for the line where the planes x 2y z = 6 and x + y + z = 0 intersect. Question 4. (15 points) (a) (12 points) sketch the following traces of the equation appropriate planes below. x2.