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Quiz-2_Fall-2008-2009_Tamer_Tlas - Math 201 Exam 2(Fall 08...

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Math 201 - Exam 2 (Fall 08) T. Tlas ================================================ Please answer questions 1, 2 and 4 on the same sheet of paper on which it is written (after the line following the question). Any part of your answer written on the wrong page will not be graded. Question 3 has an extra sheet of paper on which you can write your answer. When finished leave your work on your desk for it to be collected by the proctors. There are 4 problems in total. All questions have several parts to them. Make sure that you attempt them all. ================================================ Name : ID # : Section Number : ================================================ Q 1 Q 2 Q 3 Q 4 TOTAL
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Problem 1 At a point P a function of two variables f ( x,y ) increases most rapidly in the direction of vector i + vector j . i- (5 points) If ∂f ∂x ( P ) = 1 find vector f ( P ) ii- (5 points) Find the equation of the line tangent to the level curve of f passing through P . iii- (15 points) Find the rates of change of f in the directions of vector i + 2 vector j and vector i vector j .
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