# Calculus 3 - 1 Given the ﬁeld F = x2 y2 eX ~ cos(y and...

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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). 5/0th JEV \$5M (Dill) : 12(2) am) e L +0 “DO 6w C 2) Find the area between the planes: 6% by / o x+y+z=0 Mtxl‘jf‘z 09 L192 : :33” V. X We a 232:?“ wz él 02:] Z 2W 9&7 x z v—w Was 3 t u— (mutt/J : uvv \/ : (D l ’ l +1 4 ? A sz ) I ~) O 7; ——-l “AIW:S lﬂi‘ JV 4d W o o 1 "‘ ' ‘9 : mm 1 )2 3) . 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 HQ, '36 60 H) ”‘n E75 Gr 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 , o x2+y2+22§16 2 05: d) éTT/Z 2 2 o x+yz+zzl 9 ﬁ/[email protected](:ﬂ\/ ° yEO Z 0 X<O C. l: 0 220 , ( “(N X “c VCj—o ’ F SH“? 622 +1 x I v Q ,r-ﬂ§,n<l> Jr M A0 W Tt/Z W2 0 ( ﬂ 3 L c1 11‘ Q 7: I I '1 glass ar ”2, we 5g 7 mm 17/ 0 TI/ '0 ”i w W "3—2?3 2 17-6995 A Ti/z 2 :36) : L1 5) Draw an image of the area being integrated and change the order of integration: l3! 2* d I” I“ + d d o m (5x+y) ydx-wwx y reins I Z 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 a-for 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 9®€S % M47 Wet/ﬁg, ...
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