MATH 201 Notes Part 2, Spring 2017

becond MC Hed - ££ (kac(tw) = a (* [ee a (a= Ince Defarhes Soltuthhon! “SX v ) = Pe > a yA nN [ea cle &)] or? Fee * Fey t > TE re Rh 70 = = dey “tde- Tey tt _ ay ae =" ~ = ok o 470 L C gen nel Examolt 3: 6 2 Ad Power series -% Lely tion! Use foe po of y rs) abouf ro = 2, oe r oh oe fe (-22)" Az=l as 4 -* = 2 H Azo a PF Rae. R Sor aly n | Extra: Find the m~ _n2 th 1OT* derived Ve of fa)= 4€ atO Sexton, fr, — = Coctcat of 2'? which (6 aero (oe DAH =O ip" a n # aa (aheger, Fo). (-)?a" Uh” U7!) L?*) affront of a ® ection: Why (50 # thot et: ee > epee FY) a - fet), a news fd §,eu = maa (a a azo NM “ad bs, must be AY), : yan (1-0) (pla) > eChor pf pL ertot =o, thea Pall Fortes =e) Aj ~ Suppose See and pa(tal sus, The y ape not epltal but he dane btfiueen prem te the errors Ran) if L Rand 20, forn)as Hey, (- pov @% 20, an decreas ikg Lyre fe Keygen GLa] € Sori (23SEP20(6) heotus et Ernr in alternating Ser Ces a=) Seley" Fey a -V i a e4 —— _ Tf ~e heave S_ the \f fof = err A rr (Oo, ~ IES | (4, (epbonased berm Cxanple J Vad 2: CI) Ann wheel paral sur ea We app mxinate Ac3 n 7 Fre Ly hnl(atd gb Wwe (k*ow (Ln 1 Sb 2 al - fer (880 | xample 21 40 PS: Qe ey rl | , “nr. lerrmer[< ~¢% a= . ; ~Fad n Sueh tha f Sele 2 IS-G |< — ofabs | n ot | ra enn =>) azb arty) (0% he EES, Side role on & cha tlea gg prodlem (valelafed) Yt bas n nn, bi 9 <]) => 4% ¢) na J Meco > ata én nz! R cr) there acc< 7) fy | (< M Atl or] K er or Exangle 1 Tn the Taye exp cation of cosx Qbeut &50 [?! Voy 2d 67 i? 12 0,(, Fig te So tart Crrer < co - Answer: (a +0 |e. Cy a)| ele) ja-af”"" —* A-¢()/ See hu) = cece < y, > (ney + Ch 4 ‘ “00 Few) " f cas2 ne eee ue ce <[ = AtS ” the ° , i C [Rav] ¢ [a] Se SCR D Such thet ous. | en ce! fea AA WNRELA TE O ; Ct rs: n AG _ a x " ne en? soe f x20 Chea © 7 ay -e = [*%€5- 3 Pete ' j A A Choost xan ZS i => at > G) nA (265EP20(6) decture 10 . fue (ley% we, XER Crhis a meclusen efter) 36TEPS ede culleg wmomt | reriec ) 4 5 : frye Uy 2-! | write Fey (of exp 24 Sdoa! fiap= & Clea) od a2 X(«-1) it A + Heol LK NDt-2),5 la a) = ok (k- YC 4%) 3 : ! 31 “(4 = k(d- YEP Note! (y (attopert, thes Server converges for (a(<] Exoryled step x = 4 2 Brvyig 43.2% ntTE OO €O.... (ta*= p+ 4x t 44 +> al aa S kIn general, if l= AA and MUS Gp ositeve m fey er, the Aporston ts Anite, Cleve < [+ X BG of (WG a a t.. CA Iherna 1749 SCL), How fo fread [eylor expeation «a Hout a ath xd S) 2H book chapter (0.10 (The fable] HE C(ta) By ar = ‘foving” Mom tits feteote :e sed Cost eSine les. 7? pie Ure e*: tent t. terror < A SMy > Koad nates \ Compine wl th t , 3 cosa [—k? ha "_ yg p | LO - Find all p fer which Bente) comverges USI Ag C In X Need a Cawarcttan 4°! t 6¢f een A AAG Cine eo in Mea <(‘dp)* now vselLcer:! = ~- sin (fo a =f (OG 0) aor he he AD rik a aye _)*s (4)" wheck peraves £7 Re Peel: E(u! > gorc0% (2gset20u) dequre tl Find Teyl or Stfies of fea) = —- ban (x) qhouf 2 ~For baa 'ex) = — bent = —. =a Se reve Chen fe | dL “ ; _ CAD a0 2a+/ A, 2A 2a ‘ . ye “dé = yb. Sey € 0 Itt L c i Eo y b SL aat( A bela) S (ex Mende. JCae 26 we) then i ieee term by bern, 3 ~ The o/€m : (2 a, % NE x") = e anon tab tt an be A509 chapter ((: Polar coord nether nell Cot fesiga CoofdeAafes : Gemetlf fraaly tle 4 =-Pod = ( _ Siarqnt Lie - set PF setts ———_ te © ») D (a, 0) ~ Circle fineere7z (Ceater, (ed?vy) h, ik), Peg * aA yas Q oe b- LN im -h)t = - Pofabolas p a ; pelipse gree tebatc of pa ey? CaYy* C og a- h)* tgs) (y-(9) ( whyerbleis at GE Example ! ae Cyrte)t_ a ae A 437, =( Polar cootdnater of P: - r(48) PI, B) same er PLL, AE er . ‘ a er J ©) ee oR shngeleree y (wv) p02,-¢) (c+) (4; -4) Q Some Histor y f a7 Garth 4 ur Pa 2 P F re F m4 Example f(t c= means efecle gerber O Padus C Example) * Ono MOQAS rey going through the oreg'9 4 e (arlesian Polar eZ 4 Example 3! (2 2Qeos O change be Car fesian ep ua ftea a > L> rcos @ 2 rsh’ a ghey? So fedws@ so pa Drease banOet ; 1f¢0 Ay x) After completing the Sta7® . (acs) £Y? =| (clvele ceater Cl, o) rt) Ee ba geas 2 2) cos O (30 SEP Qeib) Aecture (2 Example l- Sieetch 77 (tCosO ist Qtudy symmeffy |! Fils i SY J ca ltcasC C= ltlos & repece & by ~& then e 2 Pont S cre) f(r, -9) on CaPVe Le ‘ Os _ o Replee by tO cugve 15 a re (tcos(w-8) 262-0 O Oat sp poh gunetic wrth pespetl ort nid . U3 AF 15 1° 0,5 03 0,2 O § Ketch: called Gu died Si (LA ; r> l-cos cr [45a 0 cel-sud Example): Sieet ch! cz sing re! cos F Find af pots of rn ten sectvon J a ree cheer far (0,0) acne > [ECs D6=T,C y) ooh cos & : ges (Z) at ALS ( z 6 cs - wee fot & =0 (6 ban & - a ortg!s iJ p° 2 2 Oe Chapter (2 Adwadnic Surfleves Tr the plane an epeatiéa between X ard ¥ repleSert acarve e4 .a % t5Y tc =O Cr Pofats Needed) 2. Qn? eaytebn tcyt dae nea ceater and radfus Xe Ta 3d space, a points given by 3 nun bers (1, 9,2) 2 Ccircle) ' sphere Cea tr (h&O radios =R > euele ceater (YOY radcup = R = (4-9 + 6-k) + (2-2 Rk if h,KJ afe Ze fhen arty? t2°= R 4(glinder La the plane the oe¢ 2, frp] rorzef *Taspoe > f¢nyz)s artytetf (base! wey) z } Mofe: acylinder dvecn't have te be else Lke @ Sodg OX | g {ey 2)/ asy'} Z ra of points Such that m*ty" 7¥ ty eadrele (CO) a L£ J ) & also acylin der . (030CT 206) olectare (3 [o2wov2016 7 In3h16] Curves mspece & Like categrals Ny Sd, Doman 2 IR” (10d), yCb), xL)) a c (veay 9¢3)2(4) f ¢) infevva/ owe 1 5 % EC i , : & Notation: | ftogians #03 hie m= tit jt XU i baat Example £: , > ¥ jek @el aye ce tT eee MG, 40> 1, 90° Ee -27- Example: = —) > Bey acosket smb ye bP os (£27 Alt) = coo sOnaueS rege | which means the prof & fee of the oats On the 1- — ceccle P y Plane 6% ab) = center (0,°) ,. Pads us = i Sue 202E oS es2e.3 a r(t) : position vector (No Fe: thes (F more than 27) Example YY fv heoltx a or _ Canppequty ar dt = [frat > e+ = Qrt2 fo) ) 6 - Alc Length fom atot D deaoled c® ab Lat She, o€) fl Vey a & Nelo: fees ie Iv a Fore ejyeer less Example 5? For helix angle | Find Vit), arc Length ant ieee t = feats fot 7 =f t LEP, vty) (pee 5 _ Oe fire