MAC 2312 Exam 3 Spring 2011 Key

MAC 2312 Exam 3 Spring 2011 Key - znt3 t-z) x x3 z-N rVs...

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MAC 2312 Name EXAM 3 SpnrNc 2011 SHO\M ALL WORK TO RECEIVE FULL CREDIT. Please state any named theorems that you use. Problem 1is worth 12 points, 2*4rs worth 6 points each. The bonus is worth 3 points. 1. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ^[r^l ='lT- =+ -- o' drn+po So , *he seixs is abso tul ab| ca\vWen+ hi Poot Test 0)p,qg f*l =l 89)\. F1 o)' n! 0+\) I _lo 1- n+l r0 ht\ -+ o <l AS nttF 5o . *lte .ft ries i s a6s (anvfient @ |*{{tt' fest '
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(c) Determine whether the series i + is absolutely convergent, conditionally n=o 5n convergent, or divergent. l*\ =\% #l = 50, Ar Jerit{ is b""ry bJ 2. Find a power series representation for the functio " #Uand determine the interval of ln*l^,1' .+f ++ asn)F I n'+\ Po-b io Iest . 1-rx'l ' l -l <4'< I -i. t' . J, (* -st" ,- -+.x < ltr=t q€(-4, +) So, *hs intstYal o+ Go'tvouJ is f-+,4) convergence. xt .-_,,.-- 4x1z I .-- I +ZX' I " | _ 6"-zx.) 5- (-r x') " , nlo g,tfx'n nk n
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Unformatted text preview: znt3 t-z) x x3 z-N rVs r=---LYW-_t--zt z l+x+tl < fts X=-4 P" = h;t So , th e in'ft"vout "{ hYlwgwcx 8F: this '-' co^"'n6fant bJ fi+a,r^rt,>g **uH. i-#+ is obs 'fiffi', \ 3. Find the radius of convergence and the interval of convergence of the series. $. (ar + 1)" I ontr | - I (+rlll*' . i-1" t-n;I=l@@l- l# '1+x+r)f :2 l+x+ rt as n-o-I + -l <+x{l<.l -) *{<x<o ) ,"F=l (-l)n n' f,,=o, ,S incr t # is d' nve*ga^t , thgrf.r @*uo'gont ' e *!)^ = 9+ ffi n' nz\ Th is is eonv<ge"t ' I2s n=l fi5 is f {, oJ @*+l n' 4. Find the Taylor series for /(r) = cosr centered at, a: r. (Do not find the radius of convergence or the interval of convergence.) n {'"'(r) {"'tn) CroSX-l I *SinX o z- CoSx 3 5in X 4 (ros X-l "r * Si', X BONUS: Find the sum of the series * iP lll.o-\ {r.)(T) n! +!+, s-Tv) OssX=-tt ft-r/' 4! , j-n)b +-' b! 1+rnr*ry.s+. =r+S+91S* e (hr)" .? nl {\eo lr t =e* =W...
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This note was uploaded on 10/13/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.

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MAC 2312 Exam 3 Spring 2011 Key - znt3 t-z) x x3 z-N rVs...

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