MATH 201 Exam 1, Fall 2003

-—~ rd Ista aN ONIWERSE LUE GARY OF FONCT Se anes, MATHEMATICS 201 FALL SEMESTER, 2003-04 QUIZ I Time: 60 Minutes Date: November 8, 2003. Name: ID Number: Section Number:—---— Instructor: Prof. A. Lyzzaik GRADE: PART I. PART II. PART II. PART Iv. Total: I. Investigate the convergence or divergence of the following series: nol? ni/2 50n3/? + 100° (Jat1—VJnjr’?. (10 points) (10 points) n? sin(1/n)In(1 + 1/n) (10 points) nl (2n — 1) 5 — a (8) n(inn}r/e- (10 points) n=l (10 points) I. Find the interval of convergence of the power series, and determine the values of x for which the series converges absolutely or condition- ally: 1" & on (2 RCV TT (15 points) QI. Find an estimate with an error not exceeding 107° for the inte- gral: L 5 1 — cos 2? q ——,— dr. Jo x4 (15 points) IV. Circle the correct answer in the following multiple-choice ques- tions (5 points each) 1. The sum of the series << f2" 2n+1 y { i wer} n=) None of the above 2. The Fourier series 9e ag i . — +) la, cosnz + b, sin nz] 3 \ of the function f(z) which is zero if-t<2<Oand2ifO0<r<n7 satisfies: (a) a, = 0 ifn is even and a,, = 2/(nz) if n is odd. (b) 6, = 0 if nm is odd and b, = 2/(nz) if n is even. (c) b, = O if n is even and b, = 2/(n7) if n is odd. (d) The value of the Fourier series at 0 is zero. (e) None of the above. n=l 3. The Maclaurin’s series of the indefinite integral , *In(l—t y- Pm) a JO t (e} None of the above. 4. The Maclaurin series of the (1 + 27)?/9 is: (a) 1427/3 — 24/9 + 57° /8] — 10r*/243 + b) 14 22/3 + 24/9 + 528/81 + 1078/2434... . c) l-2?/34+ 24/9 — 579/81 + 1028/2434... d) 1+ 2?/3 — 24/9 + 529/27 — 1Oz*/814---. e) None of the above is TRUE. ( ( ( {