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Unformatted text preview: 1) Given the ﬁeld F = ( x2 + y2 , eX ~ cos(y) ) and the curve
A) Calculate the divField ' 50% ‘
l (7%? (WW 7L Fidéix'CM/m ‘ Qx ”L “(9) B) Determine the flow across for the region drawn. 9+? C) The net ﬂow is in /(circle one). D) The point (2, n) is ‘/ drain (circle one).
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A) LetF=(12x2+6xy,ey+cos(y)+3x2). IsFagradientﬁeld? Howdo youknow? L) i  ’Z , A , M
B) Let G = (1, l). G is a gradient ﬁeld for the function g(x, y) = x + y. Below are several
drawings of paths. Write if the flow of G along the paths must be the same in each
drawing. (Hint: what do you know about gradient ﬁelds and ﬂow along for closed paths?) ttst. mink/2t It
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4) If the density of an object is times the distance to the origin what is its mass if it ﬁlls
the space described as ,
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5) Draw an image of the area being integrated and change the order of integration:
l3! 2* d I” I“ + d d
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wants to ﬁnd the ﬂow along the curvex=3co y= Bonus 2) Calculus Cal want to calculate the ﬂow alon_ a circle of radius 3. He
parameterizes his variables afor O S t S 27:. He calculates
I02“ Field . (x’, y’) dt = 12.5 Was a mistake made? Which way does the ﬁeld ﬂow on average? Explain. \ we; a i9 Ao mistake) sang marl Gnarlj lac maxim/‘6 \Cffl 6/ it’s no‘l a clef“i ””63 0’7‘7
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 Spring '10
 Appuhn

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