{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

prac4asol - MIT OpenCourseWare http/ocw.mit.edu 18.02...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus Fall 200 7 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
18.02 Practice Exam 4A - Solutions lb) We begin with fz = e5yz fy = exz + 2yz f, = e5y + y2 + 1 Integrating f, we get f = e"yz + g(y, z). Differentiating and comparing with the above equations we get Integrating g, we get g = y2z + h(z). Then g , = y2 + hl(z) so comparing with the second equation above we get hl(z) = 1. Hence h = z+C. Putting everything together we get lc) N, = 0 and P, = 1 hence the field is not conservative 2a) Consider the figure n' = $(x, y, z) hence z = 2 cos r+6 and dS = 2' sin r+6 d4 dB hence we get 6" 4 sin 4 d4 dB = 1671 cos2 4 sin r$d4 = - 1 6 ~ 2b) n' = *(x, y,O) hence 2. n' = 0. So the flux is 0. 2c) [email protected] = 1 hence ,(R) = /L 1 d v = /K d i u ~ d v
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the 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