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Spring '06 Exam 2

# Spring '06 Exam 2 - Math 13 Tfts University Depa.rtmentof...

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Math 13 Tùfts University Depa.rtment of Mathematics Exam 2 (100 points) March 13, 2006 noon 1:20 p.m. This exarn consists of 9 problems. Except ir the true-fâlse questioDs, show all yoru work. Sirnplify yoru qJrswers.No calculs,tors, notes, or books are allowed. You are required to sign your bluebook. With your signatrue you a"re pledgiag tbat you have neither given nor received âssistaûce on the exam. Students found violating this pledge will receive an F in the course. 1. (6 points) Tlue or False? Write your answers on the inside front cover of the bluebook. No explênation is necessary. (a) Il f(2, 9) satisfies V11o, O; : d, ttt"o thu point (o, ô) is a local maximum or a local minimum. (b) The following integral represents the area of the disk of radius 1, centered at the oriPin: I I av 41. (c) the function /(o,g) whose contour map is given below hâs a sâddle point ât (- 1, 0). 4. (10 points) Find all the critica.l points of the function /(a, g) = a-n(t2 - y2).

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