1.6 powers, polynomials, and rational fcns

1.6 powers, polynomials, and rational fcns - I t . 5.11;...

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WHTUa/iy grows more rap/ally 7717417 g: 10326 5 (y: Mm. / \ Polynomial Funméns i300: ann+fln4Yi4+...+4/X+flo whera 72 = deerea (5 an = @4520? 6%??qu ° ani—O . ~ 71, Is a pastrive )fl’lzeer - each member is calLed aim/m. 0 each a; Is CaLLed a. 006%d611 . am Is coated The, Commrfir 176mm 0 czan Ts catled+hc leadlrg Term . th‘Ls 13 Could W Sfandard "QM/m .1 . 2 , . nu. 11111115 1,114? 5- W1 n=3 m: if “:5 4 Gimme cub zc QuaVfiC ammo 99 When Viewed on a lame enough 564/6, 7%@ W}? 07” "W WWW/77W fix) was me me jmph 074 #76 finer/m 9:- an)” [a Wfl ). 77773 Is 64/64 #76 M397 .MA/ or My ~7Lem 56m (#0)" 070 776a fl 44704414/ EX 67mph y(x)=>(3+><2 on [~2,2jU[~)7lj 8—- than an [-55] U [750,150] than 0n Emmi] U E1000, [000] Ex Why do W0 knaw gar-8x6“ 3X5+4x2_/ W23 +7100 zeros (MMS)(30IY)3)B o $(o)=-) . Evem-uauy cam x, 3x“ Whléh looks “MU! u‘fibD’“ jcalculufi , n M p0m7poI)/nom/dz§,mnénd/§ .\ 5 .\ Zeros 07¢ VO/znombb o 11¢ a 495 are, numbers (6 if 61953-0 than a, or b [or be???) mam QZUd/ 26m. 2? 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SW'fEf‘déé’ @ 2 -_I , ‘2‘ 37061-006 5), mama/gs F If r can be bun/772W) as five mm 01” ‘ polynomials 'p (5 3: . _ PM) ‘ r‘ .r —— ‘ (x) gm then Nx) 75 a Par/0M vibmfion [am/MW 500450). 3 EX 3 X+A "2 g X—s : x+3~ 2— : X~3 (er} _ ; _)<+x«§98 X”; ' (x-zv (x—z) x—zg /‘= E For lame, enoth valwg 014- X (pas. or my) W 0P Wx) )UOKS like fine “(2mm 01¢ a. power 45mm. The long—run behavfar '13 éylvam by leadm mm OHM) leading WM 010 30c) g“ V00: L79 )coks )HEC 3:) 74% Wye “ x+2 / 5 => horizonml asympmk. i : A WK): 3M} IooKs JJKc g: 3X- Mia'zfm’i 35500 /-6 It“! ‘ go um (nu o The. zeros of fix) are Hm scam, 45 1591a 26% OF We numerafor P00. . The 9mm 0# mo has a Winch/l as)! mpmm 61+ each 0F #76. zeros at We QJenomimFbr 600 . LC 1907‘?) My) £0 36x) have zero: m’ the same X— values ) Hfla rat/Giza} jaoncmn may behave d/PWenflg, 37H probaby be a bO/é- 2 _ Ex: M): if," 1 r. (x-DMHZ) x-I : (H27 For any xzfl )we can Gama! (630 Wflzwrlj w— New x2! 2 MO is Undéfme‘d.’ . M pow,.polynb/mcszlgmzmmls /0‘, g m) - __§’_5______ 7:55 [X+37/X'331 ( No): 25/)8 ‘ I X: 2 X3 3 ° No 267233 . VQH‘. qumpfOfESG) K: *2?) K33 . near 12-2, 1+”)! ioot’mcc 1/)(+2_ 0 mar K=3 ) PH 1001: Ma l/(X-fil a Long run WCLVMf [S “Q ZS/Xg 1/183 0L W12. asymp. @ 3:0. 'A 37%”?— Ex : la“ (Mu/H27 .y-Wrercepf @ (or/7 » xvmmrcaw (43 [—ng )0) a Two Vet/Na! avymprafes X2); X3 “2 ._ mar each one) loaks M66 Ska/95 y; 21 . Far larqex 3 Eu: 28 g agonggm/z MW at? 00 k-m // ., W The graph 0P a Var/mid fl/ncn'm max/w Grasses g; vemia/ asym/Wafz, m vow/ms 0% 50/776 Mir/WW f funmmvs can cross bomzonfd/ asympfafeg . My ,7 Well) Vem‘cal asymp. Ma whm A l 7000 T3 undefined, /Jr box/{‘2‘ Mymp‘ T3 #76 W29th i haw/tornflfi OK Ma 3% Mm 7LM+ 561Vch value @ ...
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This note was uploaded on 03/26/2012 for the course MAC 2233 taught by Professor Smith during the Fall '08 term at University of Florida.

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1.6 powers, polynomials, and rational fcns - I t . 5.11;...

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