Quiz-1_Fall-2003-2004_Lyzzaik - "‘.—o-p N H.3u.a...

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Unformatted text preview: -'-"‘ -- .—o-.-..-p N H.3u- .a\ f\7\'f£h5fi I.l[?.;-1RY U," FT‘JHUr MATHEMATICS 201 FALL SEMESTER, 2003—04 QLHZI Time: 60 hriinutes. Date: November 8. 2003‘ Name: ID Number: Section Numbenm——- Instructor: Prof A. Lyzzaik QBELQE; PART I. PART II. PART 11. PART IV. Total: 1. Investigate the convergence or divergence of the following series: 72552 —_———,——. 10 I t l 71”“? f 50123.2 + 100 { pom s) (U !- 1 (2] (V7: +1? film/2. (10 points) '1 (3) nzsi11(1/n)ln(1+1,/n). (10 points) 1 2 1% (5) N1 n! 1.3.5. - - . (2n — 1)‘ 1 n(lnn)rr’“ (10 points) (10 points) 11. Find the interval of convergence of the power series, and determine the values of :3 for which the series converges absolutely or condition— ally: i(_1n11{.‘1; Lg 1)“ n=1 1 “fill- (15 points) 111. Find an estimate with an error not exceeding 10—5 for the inte- gral: dzr. [075 1 — cos a"? . o 1‘4 (15 points) 1V. Circle the correct answer in the following n'iultiple-choice ques- tions: (5 points each) 1. The sum of the series 0° 2" 271-1-1 Elem—l ‘n=1 712(7'1 +1) (e) None of the above. 2. The Fourier series an ~2— T 10,, cos m: + 1).” sin 71:17] i T!— C113 of the function 111:5) which is zero if —7r < 3: < 0 and 2 if 0 S :r S 77 satisfies: 1E1.) a.h = 0 i177 is even and (1,, : 2/(717‘T) if n is odd. 1)) b.“ — O 1171 is odd and b.-,, — 2/1n7r ) ifn is exen. C) b”— “ 0 if n is even and bn— — 2/(nfi) )if n is odd. )T he mine 01 the bourier series at 0 is zero. ) e 1\one oi the shore 1 1C 1d 1 3. The Maciaurin‘s series of the indefinite integral '1' 11111 e t) _f(:r) 2‘ : f cit (e) None of the above. he Mada-min series of the (1 + E2)113 is a) 1+ 172/3 e 1:4/9 + 516,181 w 10358/243 + - ~ 1 b)1+ 12/3 +‘ 334/9 + 516,181+ 1033831243 -1— ‘ --. c d 4. )1+IM/’3 I4/975161.81-F104T8/243-L-'~i j1+I213—I4/9-1—5I6/27—10338181+>~ e) hone oi the above is TRUE. T 1 1 1 1 1 ...
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