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162E2-F2002

162E2-F2002 - MA 162 Exam 2 Fall 2002 NAME STUDENT ID REC...

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Unformatted text preview: MA 162 Exam 2 Fall 2002 NAME STUDENT ID REC. INSTR. —____ REC. TIME. INSTRUCTOR INSTRUCTIONS: 1. Make sure that you have all 6 test pages. 2. Fill in your name, your student ID number, and your instructor’s name above. 3. There are 12 problems. 4. No books or notes or calculators may be used. Midpoint Rule Mn— b_ﬂa[f(i1)+ ﬂasg) +- -+ f(a:,.)] where 5.3-: \$08141 + 3;). Trapezoidaln Rule Tn: ” given) + 2f(n=1) +- -+ 2m..-) + mun Simpson’s 2Rule Sn 2 53—“ 2) + 4f(:cn_1) + f(zn)] where n. is even. Let R be the region between the graphs of f and g on [a,b]. Then the moments of R about I and y axes are M. — [3 are? —g(w)2)d:c M... = f we) —g(a:))dx. MA 162 EXAM 2 FALL 2002 (10 pts) 1. Evaluate / coat5 msin‘1 :rdx. (A) Ewi—l) (B) 2(«5—1) (0) NE (D) 3w (E) 4(ﬁ— 1) 3+3 m2+3z+2 (12 pts) 3. f1 2 4 (1011113) 4. [mm—sods: 3 (A) (B) (C) (D) (E) (A) (B) (C) (D) (E) woo Dali- I-‘ calm cum: 17 (4 pta) 5. The Simpson’s rule approximation to f Isin mix. with n = 6, is O 1r 1r {3: 2V3 5 E(0+ E + FF+2W+ TW‘I‘E‘iT-I-O) (A) True (B) False 2 :r 5 (4 pts) 6. The Midpoint rule approximation to f do, with n = 4, is —. a I "I" 1 6 (A) True (B) False (10 pts) 7. Evaluate / Izeﬂﬁdx o 1 (A) a (B) 1 (C) the integral diverges 1 (D) 5 1 (E) E 2:2 111.1: (10 pts) 8. The curve y = —4- — T, 1 g :1; 5 4 is rotated about the m—axis. The area of the surface so generated is given by the integral: 4 2 2 :1: lnm x 1 A ___ ____ (”Tr/IL: 2) 4 4.2-2“ (10 pts) 9. Find the :1: coordinate of the centroid of the region bounded by the curves, 3; = e”, y=0,x=0,z=1. (A) i=e—1 1 (B) 5;: 1 (C) 5:: l (D) i=1 (E) 5:; 10. Evaluate the following limits. Provide justiﬁcation for how you arrive at your answer. . V3112 +n (5 P155) (3) “Ego TH en (5 NS) (‘3) "Ego 2”“ OO 30+1 11. (6 pts) Evaluate "21 5“ 3 (A) E 3 (B) 5 9 (C) 5 6 (D) 3 5 (E) 5 CK) (4 pts) 12. If “lagoon = 0, then “Zia“ converges (A) True (B) False ...
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