F03_Second_Midterm-M.Hutchings

F03_Second_Midterm-M.Hutchings - 11:53 FAX 510 642 9454.001...

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

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

Unformatted text preview: 03/05/2004 11:53 FAX 510 642 9454 .001 Math 53 Midterm #2, 11/13/03, 8:10 AM — 9:30 AM Hu'l'clnilzjs No calculators or notes are permitted. Each of the 6 questions is worth 10 points. Please write your solution to each of the 6 questions on a separate sheet of paper with your name and your TA’s name on it. Please put a box around the final answer. To maximize credit, please show your work, and use extra time to double check that you got the correct answer and didn’t misunderstand the question. Good luck! General hint: if something is hard to calculate, try using something you’ve learned in order to calculate it in a different and easier way. 1. Find the minimum and maximum values of the function f=(zv—1)2+(y—1)2 on the unit disc 2:2 + 3/2 S 1. 1 1 f j :1: cos (y4)dy dm. 0 932/3 1 M f / ($2 + y2)2003dfl? dy- 0 O 4. Find the area of the region enclosed by the curve 2. Calculate 3. Calculate 9:2 + my + y2 = 1. Hint: use the substitution ac=u+m/§, y=u—v\/§. 5. Let C' be a plane curve starting at (0,0) and ending at (1,1). Let F = <$Z+y,y2+x>. (a) Show that f0 F - dr has the same value for every C as above. (b) Compute f0 F - dr for a curve C as above. 6. Calculate f0 F-dr, where C is the unit circle oriented counterclockwise, and F is the following vector field in the plane: F = (—y3 + sin(sin cc), 1:3 + sin(sin (9)). ...
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