samplefinal_001

# samplefinal_001 - MAC 2313 Final Exam(counts for 40 of...

This preview shows pages 1–2. Sign up to view the full content.

MAC 2313 Final Exam (counts for 40% of course grade) Time: Two hours. The best five solutions will count. Please show all working. Only a fraction of the total points on each problem are for the final answer itself. Read through the problems before you begin to write. They are not in order of topics or difficulty. At the bottom of the exam there is attached a list of theorems/formulae, without explanations of the symbols, which may be helpful for certain questions. 1. Find the center of mass of the lamina bounded by the graph of y = 9 - x 2 and y = 0, if the density is given by ρ ( x, y ) = ky 2 . 2. Use Green’s theorem to evaluate the work done in moving around the circle x 2 + y 2 = 4 through the force field given by F ( x, y ) = ( xy, x + y ) . 3. Use the divergence theorem to calculate the flux integral of the vector field F ( x, y, z ) = ( xe z + y 7 , ( y + x 5 ) e z , e z ) through the surface of the solid bounded by z = 4 - y , z = 0, x = 0, x = 6 and y = 0. 4. Sketch the curve C with parametric equations x = a cos t, y = b sin t, 0 t 2 π.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern