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exam2sol - GRADING NAME e-mail address Please mark the box...

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NAME e-mail address Please mark the box next to your recitation instructor’s name, and circle your recitation time. Recitation: square Youngmi Hur (2 pm, 3 pm) square Junecue Suh (12 pm, 1 pm) square Sunny Jung (1 pm, 2 pm) square Yuuji Tanaka (12 pm, 1 pm) square Kobi Kremnizer (2 pm, 3 pm) square Craig Van Coevering (2 pm, 3 pm) square Karl Mahlburg (10 am, 11 am) square erˆ ome Waldisp¨uhl (2 pm, 3 pm) square Pedro Reis (10 am, 11 am) GRADING 1. 2. 3. 4. 5. 6. TOTAL 18.02 Exam 2 Tuesday, Oct 16, 2007 1:05 - 1:55 Directions: Do all the work on these pages; use reverse side if needed. Answers without accompanying reasoning may only receive partial credit. No books, notes, or calculators. Please stop when asked to and don’t talk until your paper is handed in. Problem 1. (25) Let f ( x,y ) = ( x 1)( y x ). a) (10) Draw the level curve f = 0. Indicate the sign of f in the regions delimited by the level curve. a45 a54 y x b) (5) Use your sketch to determine the type of the critical point at (1,1).
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