Test 2 solutions - Northwestern University NetID ID Math...

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Northwestern UniversityNetID:ID#:Math 230 Test#2Solutions!!!!Winter Quarter 2013Monday, March 4, 2013Complete the front page!!!! [2 points!]Instructions:ShowALLof your work on the pages provided! Explain your reasoning usingcomplete sentences and correct grammar, spelling, and punctuation. All numerical answersMUSTbe exact; e.g., you should writeπinstead of 3.14...,2 instead of 1.414..., and13instead of 0.3333...Make sure that your final answer isclearlyindicated. This test hasninepages. Check to make sureyou have pages 1 -??. Calculators, course notes, textbooks, etc. areNOTallowed.Do not write your name on this exam!Write your NetID and your Student ID Number in the spaces provided atthe top of this page.Mark your section!!XSec. #TimeInstructor218:00Yang319:00Lior¨^4110:00TiM5111:00Broderick6112:00Garton6312:00Lior711:00Goldstein812:00BroderickQuestionPossible PointsScoreFront Page219210316412512614713812Total100
Math 230 Test 2Solutions!Winter Quarter 2013Page 2 of??Question 1.Suppose thatT(x, y) =101 +x2+ 4y2describes the temperature at the point (x, y) on ahot metal plate in thexy-plane.(a)(6 points) On the set of axes below sketch the two level curvesT(x, y) =kfork= 1 andk= 5.Label the curves and the points of intersection on the positive axes.
(b)(3 points) Determine which of the following surfaces is the graph ofT(x, y).Circleyour answer!I.II.III.IV.
Math 230 Test 2Solutions!Winter Quarter 2013Page 3 of??Question 2(5 points each).For each of the following, calculate the limit or explain why the limitdoes not exist.(a)lim(x,y)(0,0)x2y-4 cosy4-9x4y2+ 3x24-9x4y2+ 3x2exists if and only iflim(x,y)(0,0)y4-9x4

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