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practice quiz 3

# practice quiz 3 - San Jose I'Cit}r College Name July 1 EMS...

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Unformatted text preview: San Jose I'Cit}r College Name July 1?, EMS Quiz 3 {Sections 3.1-3.4} Mathematics T2 1. For each of the following series determine whether the given series converges or diverges using the integral test. Explain why you can use the integral t:st in this eases. {4 points} Eh ﬂag? :— é 2x1. CD I; ‘2: ‘2": Jam ’r "Me "' F“ i = "‘ 8 (ﬂights: FosiiiVej g Inlearaﬂ eD‘l { 4 4 4 =3: cont'EW U.) for dx 5 do, .5..— “l \ -———-‘"" "“ ﬂu 1‘ t “I or 2— nﬂanDE e xfgn x) usﬁnﬁ :: “LL“?- east“: 9) comartyio 2 Use the ratio test or the root test to determine whether the following series converge or diverge. If the tests are inconclusive, use other test to determine the convergence to points) i n ‘1 I h. n (nu-III)" __ on: m ﬂan-T.— .- R was late wﬁl’ ’teﬁl lm‘t ﬂtil “‘1 l. nﬁﬂoﬁ {2n+4} E . —,t I'll-TED a ; ljﬂ—llz "ﬁll: n—‘rco I’H' . C * wall 8 4 1: [ml {3:11 am>1 iii—UHW mmho’m’t hr‘n ‘ﬂ‘\=*"t;;§ ‘ns‘ name l3- ”-1 Err-P4 “Firm CH 8 ti‘ diveroge * c. i l g. n -. °° 1 n+1 = I‘m -——-— ... e 2? er mitn’resi' hm 5: new {,mn'l "L new 3.— Express the following repeating decimal as an inﬁnite geometric series and express the sum as an exact fractional form: HSTSTSTSTSTST. . . . . {2 points} J a. U- 54. -— \$hd-Dt Gﬁq‘ ‘fm 'll'lﬁ Mlm m n Doc's-"l cash—t -" + 3“); r" o seem 0W :35 W ' 'l‘ E use ﬁnenelrie W95 d r: .L .54 g 5:} _~——~——- wH’thE'l a" W98=T it? os-tsitsimw- m 'l we {-13 4— Prove the convergence of the alternating series 3: 2 Hon many terms would he neededinapartral sum 3. to estimate the l” l [Predator-1 a? to :3 actual sum 5? (Hint: use the remainder formula for alternating series}. {3 points] _ . —3 PlHErnthg remainder ‘Fbl'ﬂlugﬁ. an l'l'lrtl < lam = J" 1: l [mull l0 4 3 (Nit): to ,-> 11-11 = 5-62: kin-14.62. Sewcre'uml ur in ﬁmlﬂoe 1 lN‘JSl H.int: after using partial fractions to separate it in two terms. you get a 5.- Find the sum of the following series 5: 21 “Elm —l} telescopic series) {2 points} 1 . 1._.\$_. _ ] U53 n?=s'ﬂ[n-1 n+1) é Suﬁ {2% l [NJ on :J. = 4+i+l+l+¢ 1 :1 3 1.. 4 s ; sear—1;— 53 __ .l_+—l~—l»..l+* 2.1%“ 3 4 s air-a 6. Determine the divergence or convergence of the following series. Justify carefully your reasoning and include all the steps. (Hint: you may use the comparison test in your arguments). [4 points} . - anti 2— On_ “In _9 ﬂ ml'm ‘l‘eJ'l' 11m -"' 1o“ —s W new din l0 I?“ r all“ — "m “T"??? a) new in l1 “‘1 «1 in“ In!“ :7... to“ q.” lo (ll- '55“) .. 2_ a n .——-——-g" ' . a n l nil" 4' lti:I (Pi-r) I 11-1114 +1 “4&1 3,11. l0“ ? 7‘1 ril'-'l 11m 0311‘:- iél‘émlwﬁl’ “if: 4 ti: ' El" new 0’1“ 10 n l omits "le‘e’lelm Z “”5 We raw ...
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