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166E2-S2010 - MA 166 Exam 2 Spring 2010 Page 1/4 NAME...

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Unformatted text preview: MA 166 Exam 2 Spring 2010 Page 1/4 NAME 10—DIGIT PUID REOITATION INSTRUCTOR RECITATION TIME _ DIRECTIONS 1. Write your name, 10»digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators, or any electronic devices may be used on this test. (9) 1. [tan2rsec493 dm 1 (12) 2. j W day [Hint: Use trigonometric substitution]. MA 166 Exam 2 Spring 2010 Name __—’___.w_______ Page 2/4 (8) 3. / mg) dzc. x2 (12) 4. Write out the form of the partial fraction decomposition of the following functions. - Do not determine the numerical values of the coefficients. $3 (a) x2+4x+3: 2x+ 1 0’) (Museum-4? = MA 166 Exam 2 Spring 2010 Name ________________.._e Page 3/4 (18) 6. Determine Whether each integral is convergent 0r divergent and find its value if it is convergent. Important: You must use the definition of improper integrals in terms of limits. 3 1 b d. ( ) 2 3—11? In 0 (c) 6“” dm ~00 (10) 7. Find the length of the curve y = 111(cos :13), 0 S w s [Hint: fsec wda: =1n|seca2 + tanfil + C]. MA 166 Exam 2 Spring 2010 Name Page 4/4 (13) 8. Consider the triangular lamina with vertices at (0, 0), (3,0) and (3, 5), and with density p z 1. Find the following: (a) The mass m of the lamina. (b) The moment My of the lamina about the y—axis. (c) The moment Mm of the lamina about the x—axis. (d) The center of mass (.753?) of the lamina. (8) 9. Determine whether each sequence below coriverges or diverges and if it converges find its limit. (You need not show work for this problem). 3n+2 (a) an : 5n ...
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