MAC 2312 Exam 3 Spring 2011 Key

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

This preview shows pages 1–4. Sign up to view the full content.

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 '

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online