MWF Midterm 2 (Fall 2009)

# MWF Midterm 2 (Fall 2009) - the integrand as much as...

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

MAT 296 Hour Test 2 (MWF sections) November 5, 2009 Do all the following problems. To receive full credit for an answer or to have it considered for partial credit, you must show your work . This test has 9 problems on 9 pages. Make sure your test is complete! 1. (11 points) Find the partial fraction decomposition of f ( x ) = 5 x 2 + 4 x 4 + 4 x 2 . 2. (10 Points) Find the following indefinite integral Z x + 1 x 2 - 4 x + 5 dx . 3. (24 points) Do the following integrals converge? Why or why not? (a) Z 0 xe - x 2 dx . (b) Z π/ 2 0 sec x dx . 4. (10 points) A curve C has equation y = x 2 8 - ln x Set up an integral for finding the length of C between x = 1 and x = 2. You must simplify the integrand as much as possible, but You do not need to evaluate the integral. You only need to set it up. 5. (10 points) The curve y = x + 2 for 0 x 4 is rotated around the x -axis. Set up an integral for finding the area of the surface it generates. You must simplify
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the integrand as much as possible, but you do not need to evaluate the integral. You only need to set it up. 6. (6 points) The gure below shows the graph of r as a function of in Cartesian coordinates. Sketch the corresponding polar curve. 7. (12 points) A curve C in polar form has equation r = 4 + 8 cos . (a) Sketch the curve C . (b) Set up an integral for nding the area of the inner loop of C . You do not need to evaluate the integral. You only need to set it up. 8. (6 points) A curve C has polar equation r = 3 cos . (a) Rewrite the equation in Cartesian coordinates. (b) Identify the curve. 9. (10 points) Let { a n } be the sequence with a n = 2 r n n 2-n + 1 . (a) Find a 1 and a 2 . (b) Find lim n a n ....
View Full 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