# Final Winter 2014 - Northwestern University NetID Math 230...

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Northwestern University NetID: Math 230 Final Exam Winter Quarter 2014 March 17, 2014 Instructions: Read each problem carefully. Write legibly. Show all your work on these sheets. Make sure that your final answer is clearly indicated. If two answers are presented, the average of the points for each answer will be given. This exam has 15 pages and 9 problems. Before starting the exam, please check that your copy contains all of them and obtain a new copy of the exam immediately if it does not. You may not use books, notes, or calculators. Good luck! (2 points) Mark your section and write your NetID in the upper right corner of this page. Do NOT write your name on this exam. Sec. # Time Instructor 21 8:00 Zhu 31 9:00 Zhu 41 10:00 Broderick 51 11:00 Xia 61 12:00 Chau 63 12:00 Yang 71 1:00 Yang 81 2:00 Kahouadji Prob. Points Score possible 0 2 1 36 2 15 3 15 4 12 5 27 6 15 7 18 8 35 9 25 TOTAL 200
Math 230 Final Exam Winter Quarter 2014 Page 2 of 15 Question 1 (36 points, 3 points each) . PART A True or False? Circle the correct answer. (a) The line x = 3 + 2 t, y = 4 - t, z = 1 + 3 t intersects the y -axis. True False (b) The function f ( x, y ) = p x 2 + y 2 is continuous on the entire xy -plane. True False (c) Let g ( x, y, z ) be a continuous function of three variables. The level surface g = 1 must not intersect the level surface g = 2 . True False (d) If z = h ( x + y ) for some differentiable function h ( u ) , then ∂z ∂x and ∂z ∂y must be equal for all values of x and y .