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Unformatted text preview: Name: PID: TA: Sec. No: Sec. Time: Math 20C. Midterm Exam 2 May 23, 2007 Turn off and put away your cell phone. You may use one page of notes, but no calculators, books or other assistance. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 14 2 16 3 8 4 10 Σ 48 1. Consider the function f ( x, y ) = xe x 2 + y 2 . a. (4 points) Find the partial derivatives f x ( x, y ) and f y ( x, y ). Solution: f x ( x, y ) = e x 2 + y 2 + 2 x 2 e x 2 + y 2 and f y ( x, y ) = 2 xye x 2 + y 2 . b. (4 points) Find the directional derivative of f in the direction of the vector i + 2 j at the point (1 , 0). Solution: The unit vector u in the direction of i + 2 j is 1 √ 5 i + 2 √ 5 j . So D u f (1 , 0) = ∇ f (1 , 0) · u = parenleftbigg 3 e i + 0 j parenrightbigg · parenleftbigg 1 √ 5 i +...
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 Spring '08
 Helton
 Math, Critical Point, #, 0 j

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