152 Exam II answers FA 11

152 Exam II answers FA 11 - EXAM MATHI52 Mrs. Bonny Tighe...

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MATHI52 Mrs. Bonny Tighe ,i/ i' \':Ps EXAM II \IAME 150 points 7 .8-1 1.1 I L r;r{-<*.*-- Section Mon. lll2ln}Tl and it,are series with positive terms. 1'. (10 points)_Fill in the Name for each ofthe following "t--l*-rf F*r ti*** lf tima,*g *"n io, irdivergent tl d"."ltg ., S" -"' t"*ose f is " **,fr"rs, poritirre, decreasing function on [, m ) and let a, = f (n) then the series io, i"convergent if and only if n=l the improper integral -[f @la*i"convergent. :-) "l # -'.'"-;d.'-*i$*u suppose ar, : .f(k) where f is a continuous, positive, decreasing function for x) n and. i o" i, convergent. If R, - S - S,, then n=l and ii) \4b, - 0 Then the series I f- t)'-'b, rs convergent ':Iijr"' e i"'"'"'*4h nL--toe* 'T*"'n*+ ":l l5'*, .gr''n-* {,-f"'i.'l -C- -.r,,;;''FJ;'r'"" i o (r\,-, iS la,(r)"-t is convergent if Irl . t and divergent if |rl = t e) i) ii) tt i{ is convergent and, a,3bn forall n, then ir, i, also convergent n=l n=l @@ rc \n, is divergent and an ) bn for all n, then la, isalso divergent ,d^ *"r;**"-f*t .*& -tuppose nn f;r, *,u' f,u,are series with positive terms . ,t t*ff= 6 where c is a finite number ahd c > 0, then either both series converge or both diverge. .,,n"-3 [ * F{#l .i# rf h*lgr{ n+aol Q n then lo, is absolutely convergent then la, ri divergent then the test is inconclusive Ir.r jt ,, lL =t dF*&'E ' q'EF€-' I *-# r. h**' i\,t h) -1,
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ar E #- *'5 E .f{r \ r.+ E *.. \.f i :ftw fr.? p a. ? t ! $ J_ *fe" -o"-"''"'"'* -.-'t'i' .--\ i drl \ \ &f \ i' 2. ! \ iFJ \ *j : { l}o-} J *, f *-g f '',,. cJ*\ - J ,.,,.'' \'r -.t. '*'-=.- *F" 'ergent. j* t*f - /s +- div : ry) )nt or cl\ *s; K-ss: verg #- )on >c E-.t' # r-- co is ct i $ E s.>, \d B .f a *1 g q*id' gral tl *ts ti f*l * F fF, fi Eg the inte; \ rd* / f\ \{ \ trL rdr'#s4.{v@- i* i4p i"tr !5 ij' \ 1f- ,*--i nteg K re in \ r4 \ trL -#s<#:4.* { 1 1.r iJ rf ! 1.; 2. (20 points) a) Determine whethe ;2 _v l- x-/: dx {'} s Jo rv 'vaJv t-x.,t^- \L+,,* f, +,-f$f ?=; n\ 'tlt*-: fr* X 4 \ *.'H*** Wa*+ *w Keq E ;i \tsJ. V d. ffi 'b,ts l"f*-Li* i u-o L.r'-.i the sum. i t Hr= +n \ *-!** --6a ft k*-t *aill ) --^""'f f r i"f i.t' - - td t F4,' F-! tE \j ^ *"f #**"=-oaift*' $f u '''*'F --f,T: \ "€' ._. 4*o', $ q**. i *-"s ,-Li fr-e # \c,zc "v* 9^;-j "fl, Y*" aP*t* t3.*6,J C"0.^ *+r'-y;zF \ b) Determine whether the series is convergeat or divergent and if it is convergent find *il* ffi- 3*G; rylnr\) *-Bn;t fo= \ {a'* *I {q i .*' e+ FFt a.+F E -?-* tJ ts -*n'l - r/ F 7--5 Y ! 5e $.*q & S"a#-* F*- --=- i n-1 q i e"v { aF i,i - " . ."$rt+- i t'-b, _€* Fi r+ t ."s' -* rF i *-. f -] h->; i --"* l{ i f : z'*x f g:fle**;'ff" E"ntf; E v ' u {-"*r\ -d -. i,*d
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152 Exam II answers FA 11 - EXAM MATHI52 Mrs. Bonny Tighe...

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