finding_limits_of_riemann_sums_examples

finding_limits_of_riemann_sums_examples - Exmmfik l 2 Find...

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Unformatted text preview: Exmmfik l 2 Find the area-L under the curve y = I frum r = 2 DU 1* = 5. 5’ ’ ngiclx - 7 3r WW“ 1 1. a 2n’MkA‘ Nok‘ Hm Omen of ls‘hkfld Rhink/VHI "*l‘lnklw.) and" "Dy—A‘Afi‘c hkcs ,L / I _ 1-H ‘HH' :lp-nvm '- f R rk—x {Thar Varkfiofl 5 —‘__«|———l—\—’—i'—'|——J—’l‘i—’ 2/ 466') ' Ax (Ingram-3 - {Ni-3W3 1 . 2d,) 5 ah/g) / fix‘ 14(1) x._,.—- / “3(a) \I/ Nok: Ax=5;—_Z=; in xfhem I" In fifl‘fi’ cnhfu'uflv [at r A H4 i“ M: iakrvd. S KIA: = hm 2‘“)!va 1 "-9.9 I"-\ So Xff II 12ml! 13mm?" " lig‘ [2*E(};‘) ' " A " A an “I 72f62.“'- b‘fl'bi) = z“: " Z 1?: = “I” flame); 43,);ij ,— ’— hm 5; 11E“ 2’ 4%) i‘] r\/ A n “w I A 72ml?- 2 c4; -— a Zq; ‘- \im "i 4' Zn + 2 it] / ’— H' P“ flaofl 'l‘—| {1| 1'11 2 3(2 \) a “* ] : hm +%_2:‘|1 +1‘étfll’) I n [I I‘ ha!) Y =n Etc H= I: 3 [4.“ ,, %_n(n+l§ 4, a_1.n_fy;\,__ :7: Z -= HMO c lli-Tflfi z ‘7' L 7 A 'L |_ Ell + '30.“) J, a = n(n+2(2n+\3 “ 'm T 2w n L '1 “0 2C1 = (‘1. II”) I:: T ,_ (SM-H) . 7tm+|)(?fl+') ' J 7— + I ’— ‘n:w| \nd‘. n " as” an am} In and... E—XAME‘C 2— Fiml the Ell'UEl 1111111111 113' the e111‘1-‘e y = r3 — F 111111 the ext—1131111 between :1? = [} te I = :3. Nok‘ H12 011101 of EMA" Nc+°M§k nkav: Ha: X-qfls +n\€ts H1: :Fonn'. BUJ‘ “0+6, #0903“. 00"” be M346“ when x1< V? 1H?) ‘ Ax So 011101 SoujH' shun Le! “Hiram” _ (udfiq ‘W 2 —S x"—s h *3 {£531 -5 '55. W" \_’—~(—/ am bdow Mu ah"- ‘0 So 1»: wk? MON! 4'0 3m Hus omccJ Ir} v} 7‘“) 5 13-53:: in! 01le 31v“ 61 m1 b 01 a 3’ “Mr. \ 2n’mlvn‘ I’finwvd i’“ 1.. WI i . A” n‘l‘lnkm.) Read“! Vfifkfiun : —_‘__+——i—\—’—i'—l——"—’l‘)b—/ rk—x “/ so AX‘bJ—A n L" “‘59 a1+£(l';"l) {I K \ \ n+3”? \ {r \o n Clnoasima :1: ‘ha he ‘Hne J X'L'Sax - 1320a Z :F(X:)47( m H. {Aaraclfi a! H“ A A ial i Ink/val, w: \nm-c‘ (1—9.0 I=| = ("111" '2; 0134-3 1 1L1“)! 4. sap/+07%; + (4:9)SL-3 _5.] élcni célq; fl ’- 'm 1L“) 2.11M W be); + 342mm (ear; 1] = lim (b;a) [lag—$014 4- 3fi1{b_:“) “0”” 4—3A (17:3)1‘ "(MOM-4H) +(l,__1.)g "2014-011 é i1= (fl+l)( n+1) neck A 2 V‘ 6 ‘I [11 a I‘ 1— ” n L 2 (:1 = {‘1 [ll-l) 5 6—433— (q3_r) +3q1[b'q) _ VIZ/"47?) + sq ‘0!)7. I +0 + (bFOD—s I n1[ I}! Li w M " n9“) [[qz'g) + 3‘109'0 4' 4024.31 4-[b’n03] 7 ‘-f 3 So 58X3-§dx = 3.]?[-€+o + o 4-9;] = -5st=+%3{§, D :2 112—3 L! @- 4“) 3173-”: = (2'35) [0 + 5155(24714 + V; (2,5f5'5)1+ (2-9,?)5J if} 2 cf =(1~"’J?) [Ha—s -%(5) + ‘f?(4—‘f’fi+’fz’r) +- 3412? +e’fE—s’] I." =(2-5fl‘) [395! "g- +“I%-"I§rz:§ 4—5‘ 4—2 ~3'5f§'+}2_5/2} -g] 41%) [Jawsw’rg —;] =3JE—f4-23f-f'zz —§z:-?/z_{+.¢7_%_' v. ,6 Real] I 441C Qrfia w: sick 1;: —S {Lg 2" +5 x3_S-J, Em3 The force required to stretch :1. spring I nnitr-c I" Puma” ("AMP'U/ we in”) H" [Md-Mj IV" ‘1 heyentl its natural length of l-i 8111 is. found #5" red-“9d” we“ at H” 1"" to he Fir) = 251 How 11111Cl1 work is done in v Htretching the spring from its natural length lea ) 'A’L Refinins, all (“"56 ‘H'g‘i' to a. length of 18 em? hfifi‘w . MAM" Areal —_— (h£15k+)x [MAJ-In) \a lo in)” a bcfinm inkfijk\ al- Hne for... S :Hxxéx For A Cans'l'm‘l' ion!) know Hun!- ‘3 3 o. worit = (Forcc)x (Disylnam‘l') NOR: HM“! '15 mart 'Hlam 0M. MIA-3 ‘l'b C.th X‘v in ring 21-9Mnn. So in HM 5am our-3 M Wish 41. 2%“; HQ lim§kn Sum 54- Sum. 3 ass:le chain; we maritca I J j r Small «noun-‘1 oi wall! We ‘Hfll-l- 41k: 4"“! film: M 74 ‘aweb’ can:th Ana blufl. 0i rum“l ‘Hw3 all kc.) +1, 44L: Some CamclUSram . . . Pb?) - AX W W #5,“ . disylncemfvrl' 6+ rm) W A5 such] we geek 43 fl”) : @MHRA)I.WLA/‘l o '-+ 2‘ ‘l 'f I F60); -: y 25', a, Lplqzc {Fr‘vub an x—qaus a 0 So en) 3: ad- a whm 4+ «5+. N ‘k bi 1- Lt? = i \ a n n litwvgfa é}; mzplrain‘i' (ow-emf): 51i- lc‘H/njfl an39034+;\ D _\ - h / f \ = Lip}. _ Z V! n 13’ at" is thoscn +n be 2'7- 5-16") Hie Nih- cgéea'm-l- 5f— emln Q_—_—"_/ Suh'm‘l‘zrvnd’ 11L“ Ne km“... W 11 x'u clause-A 4-: L: 4+: (13%} enJFoml- 54 +11: 1"" 5119;44:1er ,1, It! x' is choir-n halve HI: MIAPmn‘i' Hm. we haw-t 6i- end suhM-Hrwd) Hm. we he. ._, fly—(:04, —. qusx A; q I, q R l’ If ° ° 5 ram —- 5 m Ag Tm» = Salim-ix " ll _ a = \m 22§(%u—I>)-(%) =13,“ g mama) H) = I'm,“ imam [la-o |-‘ A465 '-' n» ia- ¢1M ‘gén-u) by. 2;? Z(z:~ll ‘ lira “iv—.095 0—5-9 "‘ new 5=' new u = 1m — —— hm whiz — in] —— in 102mg“) 17:3 Add, in Hana "1 |-_. r—. "4.0 Hz 2 | = hm 4%[ani'l ’ A] = “M 2% Z 110;”) , A] A"°“ ""9 0H1" choice! jar x" tau” lac. mile — iemlin +0 H16 SQMIE : I qUDAOI-D'n _ “1&1 = , ZObOH-D , w] 3 in. l 2m A1 ‘3; “n— n "M- I‘ N e 0 ‘ 0 |\ N O D “ N O O I D H N O 0 0n& shoul) no'I-t’ however, Hm)- ‘fflf yalvnnwfial $Umch‘wu, Hm ri7h+ “dram-i i5 filtu—hfi'lj Easier alaghlnicaib. ...
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finding_limits_of_riemann_sums_examples - Exmmfik l 2 Find...

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