MWF Midterm 2 (Fall 2009)

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

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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
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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 ....
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