265Lesson24Problems(1)

265Lesson24Problems(1) - I S (2 z- + x- +- k ) d- s . (5)...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 24 PROBLEMS Problems are worth 20 points each. (1) Compute the curl of the vector field -→ F ( x,y,x ) = x y -→ ı + y z -→ + z x -→ k . (2) Compute the curl of the vector field -→ F ( x,y,z ) = e y + z -→ ı . (3) Use Stokes’ Theorem to evaluate I C -→ F · d -→ s where -→ F ( x,y,z ) = e y + z -→ ı , and C is the square with vertices at (1 , 0 , 1) , (1 , 1 , 1) , (0 , 1 , 1), and (0 , 0 , 1) orientated with an upward pointing normal. (4) Let S be the part of the plane z = f ( x,y ) = 4 x - 8 y + 5 above the region ( x - 1) 2 + ( y - 3) 2 9 oriented with an upward pointing normal. Use Stokes’ Theorem to evaluate
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Unformatted text preview: I S (2 z- + x- +- k ) d- s . (5) Use Stokes Theorem to evaluate ZZ T curl ( xz- ) d- S where T is the cylinder x 2 + y 2 = 9 with 0 z 2, orientated with an outward pointing normal. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Compute the curl of- F ( x,y,z ) = e x 1 + x 2 1 + sin 4 x- + (1 + y 2 cos y ) 27 1 + (arctan 2 y )- + z 7 + z 6 + 2 ln(1 + z 2 ) z 8 + 2- k . 1...
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