FM5002-HW5-2.22.12

Sin x y sin x sin x cos z u x y v x y let u

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Unformatted text preview: z y3 4 y 3 3 y z 8 2 x y z 3 dx dy x z y3 y7 x z 4 x y z 8 2 x y z 3 dx dz 7 4 3 4 3yz y x z x y z 4 y 3 dy dz 3 y 4 y 3 x z 24 y z 4 x y z 6 xy2 z 4 dx dy x y3 y10 x2 z 8 xy z x y7 z 8 z 4 2 x2 y2 z 4 2 x y z 7 dx dz 4 xy2 z 3 y8 z 3 z 4 4 y z 4 dy dz. 0042 17. Write x y2 z 3 dx x3 y2 z dy in the form f x, y, z dx dy dz. dx dz y2 2 x y z dy dz z 4 x2 y2 z 2 dy 2 y dx 5z 2 xy dz x4 y4 z 4 5 z 2 xy dx dy dz 4 x2 y2 z 2 dx dz dy y2 2 xy z z 2 y dy dz dx 444 222 x y z 5 z 2 x y dx dy dz 4 x y z dx y dz y2 2 x y z z 2 y dx dy dz 2 y3 y2 z 4 x y2 z 2 x y z 2 4 x2 y2 z 2 2 x5 y 5 z 4 5 x4 y4 z 5 dx dy dz. 0042 18. Compute d x2 d x3 sec y z x x2 yz yz , the exterior derivative of x2 dx y x2 yz dy z x2 yz yz with respect to x, y, z. dz 2 yz yz 2 x dx yz 2 x z dy x y dz. 0042 19. Compute d y 5 dx 2 x y z dy 4 x z dz , the exterior derivative of y 5 dx 2 x y z dy 4 x z dz with respect to x, y, z. d y 5 dx 2 5 y y dy 5 y4 xy z z 2 dy 4 x z dz y 5 dz dx 2 xy z y z dx dy x xy z 2 dx xy z z xy z dz xy dy dz dy xz 4 x xz dx y xz dy dz z dx dz. 0043 1. Amis designed plan imeter has its wheel at 45 degrees to the secon d leg, rather than perpendicular n ote that the legs have len gth 5 . Recompute the form Ω that des...
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