test-3-plus-solns - ‘ M4039 (+) Spring 2010 Test3 Name...

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Unformatted text preview: ‘ M4039 (+) Spring 2010 Test3 Name SOL-“TM”: 1. Test the given series for convergence or divergence using the limit comparison test: so Z n2+4n+l : 2 an n7“ I ml) of: l 2 : ‘2 ; 5—? an- nz+9h+1 N m )7 wish M5, “2:; ,, Mb '7 V\ +1 h ‘ ' ">1. m ‘ CDhUt’u‘ ext by Hié 'p—ffl/‘Ia’J 75¢ (f -5 \ Eh IS 3 S ’l‘t m K; . an ’ i p “ film ’5: A game" W7 +1, 1 y 1 I’m—.900 I + d ‘ Z‘ ”Z(’+"/n+ 14%”; =xm “‘4 142] “1 mm W9 iii/W7 yx 00 (>0 ML 6 m CI‘ACC “AZ/by) CWWeSJ “Zea” can (ft/S (y [Am/tit,“ CMpa/szim T667? 4 1 36+):2 , l 1 \Césc‘i’ ' ( '3'1'“ \ 11. Find a power series representation of f (x) = and determine its Interval of Convergence. ‘ 3’6 °° 2 In x '4 2 ___I__ C¢I§ 3 36 A 5a V‘ 'Tkis S'BVMS i5 GEOmETVZlC balm +~ ~><2~ Cam mm m to r _. .32— ~?;[41 <3) §<1é=> x2434 ik/Aé é> —é 4x49 W i 7744 30.6.15 (-4.54) Page 2 (+) 111. Recall that e" = 2 ix" is the MacLaurin Series for f(x) = e* . xsgt x = -z W mamer correct to three (3) decimal places. Er n or E s If [MM-he QWF ‘ Approximate e ‘1 (1) Show all your calculations for best chances for partial credit, and (2) show in your Work how we can tell that your approximation approximates e " correct to three decimal places. Solution: e‘1 = a; - ,J, , l , l , 0, “ bm’h! . 54-4,-5'20’0Jr0134A 0006. _, I _ L0,é00§c I 57’W—ggqo 2b. 006’43 - h ‘ fiaf‘. Sngfhm [Erin/4.5444"! ‘ Ezra/L 5’57"”? ’ By 114 [ill-lyr’m‘fka {fr/r: V’l-qpl— mil—+1. 10,35 Vary“- Sé céo'éfiéa‘634'laH’éfléa: 1 a 9 2‘! 12¢? '7‘" $76 7-0363 row—,le 4:, 3&6CIM pleas, Al °° l H °‘° n e 2: Z [—1) 1—, SHJ LM 1410 “:0 m «0 (k) " l< ' 1 IV. Let f(x) = 2x5+14. "T‘ (K) s (ally-1g; W a ‘5 M 14:0 ll .’ ' .. 3 A. Determine the 3’d-degree Taylor Polynomial centered at a = 1 for f (x) = 2x5 + 14 . 1 I /-—-'; Note: f’(x) = 10x4, f"(x) = 40x3, f(3)(x) = 120x2, and f(“)(x) = 240x -. '5 /5 10/0): )0 , P1302401 {finfl}: 110. T(:/6 0 I0 4a_2_’32__3' 3X) J'A'i‘fiflt’lfi‘f“ 2-?“(X131L3KZX/J, not) = /é + [0 (w: 1+ 201x437"; 20 (WI) B. Use Taylor's Inequality to estimate the accuracy of the approximation 73(x) z f (x) when x lies in the interval 0.9 _<_ x s 1.1. W3 lw—IIéOJ ¢>szl "7 1. v! y ' Page 3 (+) 90 ~ n n [1 °° —1 — .. .. V. Considerthe following power series: 2 an 2 Z M . - E. 6‘4 [7C a) 5.8 "=‘ H‘l 14:! 4:2 (1) This power series is a power series centered at a = g . ‘j . . . an+l (2) Determine the expressron in simplified form : a n+1 an l'x—Zl 4&1)! 2?. fig? (4) Determine the Interval of Convergence of this series. 1 9 Tugcvfts CMWL365' aésAufi‘t-fg 92' “3‘2, .’ -94y—249—=§-—24’X<é2 J4 - I“, in am: we mm“ with 4:» cmwimg “6:19; 1:”) J— ):pw X's-2" Z (‘0 (‘E—23 g 2 6‘” r. z :5 M 'Zavg/L‘ h, VN 4} V‘“ m 9'” “<1 ht! * ' + we who“ Mg 53 P -Se'flmngfil IHAiZMO/UIC Page 4 ,(+) Zn ’X n! z (>0 M 0° 0‘ ) J— (xz) : VI Recall“ e’ = 2 ix" . g0 8 3 h! i ' "=0 n! J V‘ f 0 i n: D Z: 00 Determine a power series representation for the given indefinite integral and give the Radius of Convergence : Z r r (a X __ V1 @Finf‘l'w"!+€ x e » 2’ch n+1 Wet @w Wm : (saw we VII. Let z = f (x, y) : 3:2 ye” be given as a function of 2 variables. .. 2 “st A on, mm)" CM, \ r (9! a e I, an A. Determine g and g ‘ ‘F a ) 5‘ I I ax ay m 1%» mm M: (um/3"» uvwv' ...
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This note was uploaded on 07/25/2011 for the course CC 306 taught by Professor Doig during the Spring '06 term at University of Texas at Austin.

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test-3-plus-solns - ‘ M4039 (+) Spring 2010 Test3 Name...

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