166E2-S03

# 166E2-S03 - MA 166 EXAM 2 Spring 2003 Page 1/4 NAME STUDENT...

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Unformatted text preview: MA 166 EXAM 2 Spring 2003 Page 1/4 NAME STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, student ID number, 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. 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 or calculators may be used on this test. Find the integrals in problems 1—6. (6) 1. /sec4xdx 1r (6) 2. /05 sin2(2:z:)d:1: HI 1 (6) 3. / xv 1132 + 1 d3: (Hint: trigonometric substitution is not necessary). 0 O U MA 166 Exam 2 (12 1 4. ———d ) /x2\/25—x2 1; Spring 2003 Name Page 2/4 MA 166 Exam 2 Spring 2003 Name __________________ Page 3/4 (12) 7. Determine whether each integral is convergent or divergent. Find its value if it is convergent. Important: You must show clearly how limits are involved. (a) AwVLEda: (b) o E dz: (10) 8. Find the length ofthe curve 3/ = f(x), 0 S :c S %, given that f’(:1:) = 2x/coscc + cos2 x. (6) 9. Write Out the form of the partial fraction decomposition of the function below. Do not determine the numerical values of the coefﬁcients. :I:+3 (\$2 — 5:1: + 4)(:c2 + 6)2 MA 166 Exam 2 Spring 2003 Name _________._____ / Page 4/4 (12) 10. Consider the lamina bounded by the curves y = ﬂ, y = 0, :1: = 1 and with density p = 1. Find the following: (a) The mass m of the lamina m = (b) The moment My of the lamina about the y—axis My = (c) The moment My; of the lamina about the (Ii—axis Mm = (d) The center of mass (:2, 37) of the lamina (E, 27) = (10) 11. Determine whether the sequence converges or diverges. If it converges, ﬁnd the limit. (You need not show work for this problem). (a) uni; :3 (b) an= (£2)! . C: (c) an gﬂ; :: {<-1>nsm<;:->} C: ...
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166E2-S03 - MA 166 EXAM 2 Spring 2003 Page 1/4 NAME STUDENT...

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