Northwestern UniversityNetID:Math 230 Final ExamWinter Quarter 2014March 17, 2014Instructions:•Read each problem carefully.•Write legibly.•Show all your work on these sheets.•Make sure that your final answer isclearlyindicated.If two answers arepresented, the average of the points for each answer will be given.•This exam has 15 pages and 9 problems.Before starting the exam, pleasecheck that your copy contains all of them and obtain a new copy of the examimmediately if it does not.•You may not use books, notes, or calculators.Good luck!(2 points)Mark your sectionand write yourNetIDinthe upper right corner of this page.DoNOTwrite your name on this exam.Sec. #TimeInstructor218:00Zhu319:00Zhu4110:00Broderick5111:00Xia6112:00Chau6312:00Yang711:00Yang812:00KahouadjiProb.PointsScorepossible02136215315412527615718835925TOTAL200
Math 230 Final ExamWinter Quarter 2014Page 2 of 15Question 1(36 points, 3 points each).PART ATrue or False? Circle the correct answer.(a) The linex= 3 + 2t, y= 4-t, z= 1 + 3tintersects they-axis.TrueFalse(b) The functionf(x, y) =px2+y2is continuous on the entirexy-plane.TrueFalse(c) Letg(x, y, z)be a continuous function of three variables.The levelsurfaceg= 1must not intersect the level surfaceg= 2.TrueFalse(d) Ifz=h(x+y)for some differentiable functionh(u), then∂z∂xand∂z∂ymust be equal for all values ofxandy.