162E3-S2005 - MA 162 Exam 3 Spring 2005 Name Student ID...

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Unformatted text preview: MA 162 Exam 3 Spring 2005 Name: Student ID: Lecturer: Recitation Instructor: Recitation Time: Instructions: 1. This package contains 11 problems worth 9 points each. 2. Please supply a_ll information requested above. You get 1 point for supplying all information correctly. 3. Work only in the space provided, or on the backside of the pages. Circle your choice for each problem in this booklet. 4. No books, notes, or calculator, please. ln(1 +117) = Z x”, m < 1 n=1 n 00 (—1)” 2n+1 smxzz (2n+1)' (E MA 162 Exam 3 Spring 2005 TL °° (—1)" °° (—1) 1. Consider the series 2 n ,2 n2 . n=:1 n=l Both series are conditionally convergent. Both series are absolutely convergent. A. B. C. The first is conditionally convergent, the second is absolutely convergent. D. The first is absolutely convergent, the second is conditionally convergent. E. The first is divergent, the second is absolutely convergent. 2' Z 2k2.2k ls _ _ °° 3k k=1 A. convergent by comparison With 2 -2—k 19:1 00 3k divergent by comparison with ICE—:1 if divergent by ratio test convergent by ratio test 315.0 P0 the ratio test, applied to the series, is inconclusive 3. What is the radius of convergence of the power series 2 2 (4 A. —1 B. 0 C. 1 D. 2 wk 00 4. Given that the series 2 19—2—1; has radius of convergence 2, what is its interval of 19:1 convergence? A. B. C. D. E. None of the above. 5. The function is represented by the power series 1+2cc 71:0 B. Z 7123:" 71:1 00 C. Z(—l)"2n2xn n=1 °° 1 D. Z (—§)n$2n n=0 °° 1 E. Z n(—~§)”:I:2" n20 0° 2n+1 % 6. Iff( )=Z :3 + ,then f(:c)da:= 00 (my. n 0 “.1 A. :4; 2n+1 °° 1 B. ————-——————————— :4; (271+ 1)(2n+2)22”+2 °° 1 0' Z (nz+n)22"+1 00 D. Z 1n(2n+ 1)a:2"+l E. The integral is divergent " oo 7. If ew is expanded as a power series of the form 2 cn(ac — 1)”, then C4 = n=0 1 A. a 4 6 B. 8 C- 217 —1 D. V—1 e E- ‘4? 8. 331111052): °° _ H mm? _A' g( 1) (2n+1)! 0° x2n+2 . ——1" B 25 ) W 00 n $4n+2 C 1;)?“ (2n+1)! 0° $4n+2 . —-1” D Z? ) (w 0° 4n+3 n (L' E TQM) (2n+1)! 9. Find the first three terms of the Maclaurin series of f 2 v4 + 172. A. 1+Z$+—61—4x2 B 2+:x—61—4x2 C 1+iwz+glim4 D 2+ix2—61—4x4 E 2+ix2+élzx4 10. How many terms of the Maclaurin series for 1n(1 + as) do you need to use to estimate 1n(1.2) to within 0001? magma?» mangoes; 11. Find a Cartesian equation of the curve with parametric equations as = 2(c030 — 1), y=sin9+1. A B C D. E. (m+2)2+2(y—1) =4 . ($+2)2+4(y—1)2=4 . ($+2)2+2(y-1)2=1 .(a:+2)+(y—1)2=1 (a:+2)+2(y-—1)2=2 ...
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