06spex01 - Math 222 Spring 2006 C. Gmez o February 15, 2006...

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Unformatted text preview: Math 222 Spring 2006 C. Gmez o February 15, 2006 Exam 1 Name: Please circle your TA's name: Problem 1 2 3 4 5 6 7 8 Total Score Garrett Alston Sharon Garthwaite James Hegeman Alec (Evan) Johnson Keya Zhu Absolutely no calculators, notes, or books are allowed. You must show all your work, and explain your reasoning to receive credit for your answers. There are 8 problems and 10 pages. The last page of the exam contains formulas that may or may not come in handy on some problems. If you want to tear off that page, please do so carefully. You don't need to simplify unless asked to do so explicitly. Be sure to check your answers whenever possible. Good luck! Math 222 Exam 1 ex cos x dx . 2 1. [15 points] Evaluate Math 222 Exam 1 cos5 d. 3 2. [15 points] Evaluate Math 222 Exam 1 1 4 1 dx or show that it diverges. Simplify your answer 1 - x2 3. [15 points] Evaluate if it converges. 0 Math 222 Exam 1 3 5 5 x dx or show that it diverges. Simplify your 9 - 25x2 4. [15 points] Evaluate answer if it converges. 0 Math 222 Exam 1 6 ex dx or show that it diverges. Simplify your answer 1 + e2x 5. [15 points ] Evaluate - if it converges. Math 222 Exam 1 7 6. [8 points ] Suppose the sequence {bn } does not converge. Can we say anything about the convergence or divergence of the series k=1 bk ? Why or why not? Math 222 Exam 1 8 7. [8 points ] Suppose that the geometric series k=1 (1 - x)k-1 converges to 3. What is x? Math 222 Exam 1 9 1 i2 - 1 8. [9 points] Determine whether the series i=2 converges or diverges. If it converges, find the sum. Math 222 Exam 1 10 Some (Possibly) Useful Trigonometric Formulas Double-Angle & Half-Angle Formulas sin 2u = 2 sin u cos u cos 2u = cos2 u - sin2 u = 1 - 2 sin2 u = 2 cos2 u - 1 sin2 u = 1-cos 2u 2 cos2 u = 1+cos 2u 2 Product-to-Sum Formulas 1 sin mx cos nx = 2 [sin(m + n)x + sin(m - n)x] 1 sin mx sin nx = - 2 [cos(m + n)x - cos(m - n)x] 1 cos mx cos nx = 2 [cos(m + n)x + cos(m - n)x] ...
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at Wisconsin.

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06spex01 - Math 222 Spring 2006 C. Gmez o February 15, 2006...

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