265Lesson24Problems(1)

265Lesson24Problems(1) - I ∂S(2 z-→ ı x-→-→ k ...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: I ∂S (2 z-→ ı + 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-→ ı + (1 + y 2 cos y ) 27 1 + (arctan 2 y )-→ + z 7 + z 6 + 2 ln(1 + z 2 ) z 8 + 2-→ k . 1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern