M151groupfinalS07

# M151groupfinalS07 - Last Name First Name Instructor Math...

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Last Name: First Name: Instructor: Math 151 Group Final (Spring 2007) You are not allowed to use notes, books, calculators, personal stereos or cell phones. You have exactly two hours. Write clearly so that you can avoid mistakes and count on partial credits. Carry out the obvious simpli f cations so that you can display your answers in an easily readable manner. The following list is for the recording of the points only. Do not write your answersonth ispage . Points 1 /5 2/ 5 3/ 5 4/ 5 5/ 5 6 /10 7/ 10 8/ 10 9/ 10 10 / 5 11 / 10 12 / 10 13 / 5 14 / 5 Total: /100 1

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1 (5 pts.) Determine Z x cosh (5 x ) dx 2
2 (5 pts.) Determine Z x +26 x 2 2 x 8 dx 3

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3 (5 pts.) Determine Z cos 2 μ 3 x 4 dx. 4
4 (5 pts.) Determine whether the improper integral Z 0 1 16 + 4 x 2 dx converge or diverges, and its value in case it converges. 5

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5 (5 pts.) Use a comparison test to determine whether the improper integral Z 1 e x 2 x 4 dx converges or diverges. You need not determine the value of the improper integral in case of convergence. 6
6 (10 pts.) Determine the area of the surface that is obtained by revolving the graph of f ( x )= x 3 and the interval [0 , 2] about the x -axis.

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M151groupfinalS07 - Last Name First Name Instructor Math...

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