SolnstoPractice2

SolnstoPractice2 - Math 212 1. 1 e 2 . 1 Solutions to...

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Math 212 Solutions to Practice exam 2 Spring 2008 1. 1 - e - 1 2 . 2. a). Φ : D IR 3 given by Φ( u,v ) = ( u,v, 1 3 u 3 + v 2 + 3). b). 2 3 (8 - 3 3). 3. a). positive b). negative c). 0 d). positive e). 0 4. a). RR S ∇ × F.d S = R ∂S F.d s b). 3 π 2 . 5. a). 4 π 15 b). Using the divergence theorem RR ∂W F.d S = RRR W div FdV . It is then easy to see (using part a) the answer is - 4 π 5 . 6. π . 7. 1 6 (5 5 - 1). 0.5 1.0 1.5 2.0 2.5 3.0 - 1.0 - 0.5 0.5
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This note was uploaded on 10/04/2010 for the course MATH 166 taught by Professor Hotlz during the Spring '08 term at HCCS.

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