20EPracticeMTSolns2!!

20EPracticeMTSolns2!! - N wne: PID: _ _ TA: Sec. No: Sec. T...

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Nwne: PID: ____________ _ TA: Sec. No: Sec. Time: __ _ Math 20E~ Midterm Exwn 2 August 28, 2008 Thm off and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page of notes, but no books or other assistance on this exam. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification . .1. (6 points) The vector field F(x,y,z) = (2 xyz 2, X 2 Z 2 , 2x 2 yz) is the gradient of the function !(x, y, z) = x 2 yz2. Let c be the path between (0,0,0) and (2,5, I) defined for 0:5 t:5 1 by c(t} = (2 tan (it) I 5 sin (~t) I t cos (~t) + t 2 ). Evaluate F . ds. 1 s \nut, ~ ~ ~wA ~ t C ~lo.\) ~ ~.~s. '= .\ (c.~ l \1\1 tA- t L \\-::: ~\o.,", ~) S" s;"Qf) I CQ'5clD -I- \) - (2,5,\) L lo) :: l2. ~'C\\o) '\ S'5~ \ o} l 0 ') I # II Points I Score 1 2 ~ °/ °,0) 3 4 5 6 6 6 6 6 I E II 30 Sc f .. ~'S = -\-l'L,S,\,) -f lO,O,o) 2- 2 ' 5. ( - 0 .20
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2. (6 points) Evaluate the iterated integral
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20EPracticeMTSolns2!! - N wne: PID: _ _ TA: Sec. No: Sec. T...

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