Test 2 Winter 2014 Solutions - Northwestern University...

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Northwestern UniversityNetID:Solutions to Math 230 Test 2Winter Quarter 2014March 3, 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 then the average of the points for each answer will be given!This exam has 10 pages, and 8 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)Put a check mark next to your section number,and write your NetID in the upper right cornerof this page!Do not write your name on thisexam!Sec. #TimeInstructor218:00Zhu319:00Zhu4110:00Broderick5111:00Xia6112:00Chau6312:00Yang711:00Yang812:00KahouadjiProb.PointsScorepossible02112210310412518612712812TOTAL100
Solutions to Math 230 Test 2Winter Quarter 2014Page 2 of 10Question 1(12 points, 2 points each).True or False? Circle the correct answer.(a) If a functionf(x, y)is differentiable at(a, b), then the function is continuous at(a, b).
(b) If a particle moves at constant speed, then the acceleration is zero.
(c) If all directional derivatives of a functionf(x, y)at(0,0)are the same, then thegradient vector at(0,0)is zero.
(d) The directional derivative of a functionf(x, y)in the direction ofh1,1iisfx(x, y)+fy(x, y).
(e) Two curves which are tangent to each other at a point (i.e., share a commontangent line) must have the same curvature at that point.
(f) Ifu(t)andv(t)are vector-valued functions, then(u(t)×v(t))0=u0(t)×v0(t).
Solutions to Math 230 Test 2Winter Quarter 2014Page 3 of 10

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