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Old Test 1 from Fall'07 Chapter 12

Old Test 1 from Fall'07 Chapter 12 - 408 D(Test 1 ‘...

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Unformatted text preview: ; 408 D (Test 1) . ‘ Fall'07 (Version B) Erma 39w?” éCSwfiJJm SMQEJAW‘M @100 {2Q Name Make swam“ have , , L v P nun—>00 " IfLim 1’"—”—exists and is greater than 1 (or infinite), the series diverges. n—wo’ p" Show all work: gm“? Te» fl .‘ 1 {im ham 1 ’x {fits-bx _ 1 12+ p2 + ....+pn + be a series ofpositive terms. Vaflfum PM exists and is less than 1; converges. Cxé’weiré [AD/’7 V‘ng ff;- / fiar‘zwgr ua flair: g Z i Z i J a? (3L: axe/m cam OE, M408DTest1Fall’06pg2bfnb 2) a. Determine whether the series is converge or divergent. If it is convergent, find its sum. Show all work. (8 pt (2)“ + 6.33 ififinLfiifiaf/é) L: o - ft 73 “f 3mm“ w/ 1*: 5/2; Ag M408DTest1Fall’07pg3bfnb l 3) Use the integral test to determine whether'the series is convergent or divergent. (10 pts) Show all work. Make sure you can use the integral test. 0° 3 n w I x f} 3 — W7) Inf}: é en . >< y: t 11:1 fl~?5‘0 g j" . n 5 .3 x 63;" X 5 "312 z’: X“ e“ 1:555?» ‘5 W m if: l w . t: a » “ex. 3 x r l 5" " ,1“ m r; 2 m r: , m r: v I V) “" G”; if V} a“ .21?” f: "“r .. G x .1 / w i a i m :5 ’0 7pg4bfnb 4) Determine whether the series converges orvdiverges. (10 pts) °° sin2(n) n2+1 éirfiqu); 5— ! ! M4 08DTest1Fall ’07pg5bf nb \ 3 i i ‘i ‘3 ‘i' E? m 47% V 5)ShowthatT13-+-il-3—+3i3—f;+3%+g;+m (three positive terms alternating with one L3,) > 50+: negative term) converges. Mar/mm ‘ ééfl‘éfi 75' M408DTeSt1Fall’07pg6bfnb 1 6) How many terms of the series do we need "to add > in order to find the sum to the indicated accuracy? oo (_ 1 )n+l I - v , lerrorl < 0.001 ‘5’ Ema» n3 3! j 408DTest1Fall’07pg7bfnb 7) A car is moving with speed 21 m/s, acceleration 1 m/szand jerk .05 m/s3 at a given instant. Using a third degree Taylor polynomial, estimate how far the car moves in the next second. gigs} * a: {£3} 3 ire/5:“ ' i 3 g m; (m a» _ W f~ " "- lg {a} r: 2! + f: T b (090' (>- = mom +9300 +53 - mmwxmma-tbnw-wv M4 08DTestI Fall ’0 7pg8bf nb 8) Find the radius of convergence and the interval of convergence for the series. I °° (7x—3)” M4 08DTest1 F all ’0 7 pg9b f nb 9) Find a power series representation for the function and determine the interval of convergence. .. i _ V ,g EWMW {€M(XL\5EI ‘ E5" ,f’ ,1 ‘ i M408DTest1Fall'07pg10bfnb 10) Approximate f by a Taylor polynomial with degree n at a. f(x)=exz, c220, 1122, 05x:0.1 :3 o5 - ,3; ll feagvfamrm Use Taylor's Inequality to estimate the accuracy of the approximation of T 2(x) to f (x). ...
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