Solutions to old Exam 2 problemsHi students!I am putting this old version of my review for the secondmidterm review, place and time to be announced. Check forupdates on the web site as to which sections of the book willactually be covered.Enjoy!!Best,Bill MeeksPS. There are probably errors in some of the solutionspresented here and for a few problems you need to completethem or simplify the answers; some questions are left to youthe student. Also you might need to add more detailedexplanations or justifications on the actual similar problems onyour exam. I will keep updating these solutions with bettercorrected/improved versions. The first 5 slides are from Exam1 practice problems but the material might fall on our Exam 2.
Problem 26(a) - Exam 1 - Fall 2006Letg(x,y) =yex. Estimateg(0.1,1.9) using thelinearapproximationL(x,y) ofg(x,y) at (x,y) = (0,2).
Problem 36 - Exam 1Find an equation for thetangent planeto the graph off(x,y) =ylnxat (1,4,0).
Problem 40 - Exam 1Explain why thelimitoff(x,y) = (3x2y2)/(2x4+y4) doesnot exist as (x,y) approaches (0,0).
Problem 42(a) - Exam 1Find all of the first order and second orderpartial derivativesof the functionf(x,y) =x3-xy2+y.
Problem 43 - Exam 1Find thelinear approximationL(x,y) of the functionf(x,y) =xyexat (x,y) = (1,1), and use it to estimatef(1.1,0.9).