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13th - 10.7 ARICA ANI LENGTHS IN POLAR COORDINATES 3 A = 2...

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Unformatted text preview: 10.7 ARICA ANI) LENGTHS IN POLAR COORDINATES 3. A = 2 full-'4 cos2 26‘ d6 =10 —] ' C3548 d9 = [6‘ — Sia‘w] EH :% 8.1' landr 25in9 »25in9 1 »sin6 2:» 6‘ = % or 57” ; therefore . 5 .7 l5 A=7r(l)2—J .13[(25in 99— 121cm 3.: 6 : Tr — 2 singf) — d9 _ ( = Tr— (1 —c0526— .13] d6 2% 1::603—00529] dfizw— [ge— “123] :31“ =rr (i: %sin (.2 3mg) = I) 15.1' 63ndr 3csc6‘ »6sin9 3 »sin9 6 .5536 2:» :lorS—I;th61'cforcA:j_ 3—,[63—9csc‘l‘JJdfi 6 6 m a r -3 m a run-r. m; x : Isa-#118 — E0302 6‘] d6 = [186 — % cot 6‘] =(15vr—gx/5) —(3?r—%\,/§) =12?r—9\,/§ _ . I: ,1 I) _ . 3 ._ 2 1r d: _ —2.51n3 . _ - 2 ‘ —2.su13 24- 1 — E (- 9 (- '*T => @ — ’ wereme Length — V (m) — d9 _1—cosé“ "' .1 4 ' 2a "' 2 : j;_.-2\l|" (1—0053]3 (1— ( 5m ) d6 21,32 l—cosé‘ v cos rsm d6 1—0058}? (1—m53P : ($1110: 1 —cosfi 27-“- Oonfi < 6 < Tr] 2 j-TI_I2(1_1053] V WM .: "I --.7 .-.: : Z 2 jq_.-g(l—]cos&) V d6 = 2 E]- ccrlifll“ : 2V/Eju2 [2 mfg)“: 21:32 csc‘ d6 ., I I -.:.-'2 I = “2 CSC“(§) d6 = (smce csc g 2* Don 4. r9 < GT) 2 I,“ csc‘udu 2 (use tables) .31 - 1)] _cscucotu FI'3_]_j-'7'II2 _A, ‘J _ ‘J_ _ NIH—3 _a-, 'J _1_ 2([ 2 ]m.4 2 M cscudu>—_ [glnlcscu n::otu|]w._4 —_ 72- 21:1 \. Zy/E—InO—x/E) 31. 13 = cos 26 2:» r = ; \f cos 26‘ ; user : Vcos 26‘ on [0, :> $ = 330205. 26‘)_]"2(— sin 26)(2) : fl; . 2:31 [Ir—HI . 5 34 :— thcrcfore Surface Area = 2 10 (2mg cos 26") (sin 6) V cos 26 — d6 = 41?er Vans 26 (sin 6) V 005123 (16 : 4w jjusin F) d8 = 47rl— cos 9].?” = 4N [— — (— 1)] = 27r (2 — V6) 10.8 CONIC SECTIONS IN POLAR COORDINATES 4. 1'c05(l‘9— [:— =4 2:» 1'cos(r9—%) :4 ::> 1'(cosr9cos%—sinfisin =4 =:> flrcosfi—‘Tiirsi11624 =5» ‘.—i§x—‘.—i§y=4 =5» V6x—V’2y28 =5» y=x—4\,/2 I) _ 3-0 _ 1—5 sin 5‘ > CHAPTER 11 INFINITE SEQUENCES AND SERIES 11.] SI‘IQUI‘ZNCI‘ZS _l—l_ , _1—2_ 1._1—3_ ‘ _l—4_ 3 1- a'J—T—flaJB— 3: ——:,J:i—3—3——E,fl4—T——fi a a 1 [—4.]: 1 q I, 1 1 Ia-fl] mile —I.-‘J:i —§.04 '_]' gun —-.-‘J.T may; —I.flu —§.flm=§ 18. anzn—4,n:l,2,.u 2Ve’fi I a - 211I]_ - __._.I . L6. “ling” — 11ml?” —,_IF_ U — rx :> dnerges \_.'II 5]. Iim (:3 I'Dn : Iim 1013'“ - "I'm : l - I : l :> converges (Theorem 5,#3 and #2} 11 —v :)<_'- 11 —v :)<_'- -'l\ . Fl— I- . : Inn : oc- => (lwelges eIn n _ e In I: \ 4. ['1 _ 3c. - 7’2. Iim sinh (In H} : Iim — :)<_'- ‘ n — :)<_'- 11.2 INFINITE SERIES 1 _ '_2]ll . . . ' 4. Sn : " v ,21 geometric serles whele |r| .> I =:> dwergence I — [—4.1 ID. 5 — — % — a? — . .. ,the sum of this geometric series is : 4 -. 4 _ 1 1 1 1 1 “Hm—O «5) («a «3) (a «i1 \ . _ . _ ] _ 2:) 11119130 5“_ nl—l‘ngn (1 anr1)_] 27. film,” cos(mr) = (—1)“ ;’ 0 2:» diverges 42- (—11nK2n = [—XBJH; fl =1, 1': —x3;converges to n—0 n-0 54. 0.32;?) %(f_flj“= ]_ i) 2% 1 3x2 f0r|x| <1 ...
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