Midterm 3 PExam Key

Midterm 3 PExam Key - Math 1272 30"PRACTICE"...

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Unformatted text preview: Math 1272 - 30 "PRACTICE" MIDTERM EXAM 3 11 April 2011 1.) Determine whether the series below are convergent or divergent. If convergent, find its sum. Justify your answer and state the test used. a.) ~~ 22n s,-n a.~. T ,/ = f "f\ <f'" 5 - en-i) t ~ - 'f({1" PI I (9 points) '"L _~,J-,' ) '~) , ,r-- L 1 ~l u-~-~ J-~7 1 L ,/'.-( J =1 lQ"ylQ( S b.) - Q ---=--l - ..,- tfI -~ s - - - ~OJ '+ f (8 points) =- ~ - ~~~ (~) '14 ar_ I 0+1 [);.~ 6# Ted W D,JJ~!jc'1ce 2.) Determine whether the series below converge or diverge. Show work and state test used. a.) (8 points) b.) Page 2 of 5 (8 points) t ., oJJ (8 points) ~ ~~ O t.- ;f-j'~""'kll P ~ i ~i ~ JJ~~1 Page 3 of 5 e.) ~oo Lm=l n! e n2 . (8 points) - - ' . ---- f.) Lm=l nvmn IF ~oo 1 (8 points) o Page 4 of 5 3.) Find the radius of convergence, R, and the interval of convergence, I, of the series below. (20 points) - rp- SiJ'rlO,! I . \ W1 A' A. r ->; ~)v-P4pJ -~ . a. Ul\_J...L.( - 4.) Find a power series rep . Page 5 of 5 res entation for the fu ti convergence, R, and the interval of nc on below and determine the radius of convergence, I,0f the power series 3 ( [ex) = x _ 7 'vI (' \ ) . (15 points) 4x 2 + 1 ") (\ --;>)(' 7 , 1 - '2. ~ \+ X " t - (- ~~) \ cfJ 3;><: ~ (-'fx1\ = c rP ---~'~- I cfD C-t)" if x VI 2 >O V\ -::.. O -:;. .:2. ( 0'" VI - ~O __ 3 , tf"' )( '2-"+ '---J l ~+y1. \ )'1 -\ <L ~ i lL{-t~ ~ i ~Y- ~ Jw k ~;) teeJ- i#~,J ~ /tJ-~ vJ- ~.J- W Ufi'1'4CR!}o,, ' j k uuilR- 1M, AjS sfjll IY\. ~y-1'c... ~f, ...
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