sol8scan - "6 CA givfnj I(4 mm = I ~(PW/D 1‘ 0(w7 V...

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Unformatted text preview: "6) CA. givfnj I (4 mm = I ~ {- (PW/D 1‘ 0((w7) V NO‘EQ’ Wt’H‘ ‘kfl (,Lo’vjk of Wrti’aL-f { is qul‘mw 4" I L ,. L, J;*\('(+W/L) : C¢J({) : “it 4’ OCE) m ><‘>TT/Z [424/ , a! M CA’CU ((37%;wa w H Lam 0:1" (axTXw) Z V”- «£4 M L/ft art/(V Tailor- figmmlrn‘ér f M ca 64 9" 7 " +5+1+5+om> Mwo fl 2 I + x 1 ( 2.1 Colbd “ I - 2:: +5: + 0&1“) 04 X“) (3‘ 55.; Z cm”, \jg «My, {DJ ”M profile/5‘ Z 1 L; ‘ +£~i+0k> 1 LI 551; Va We 1m M 4% Wu 4 ‘30“) (o) it?» n: 0‘) [‘1’51‘1/Sl 711 M10 Vat: (I give»: 7(93<0) 1‘ a (0) 2 I To TLM 2L”(O7)=sa'(0)'/ = 24/ : / PW h‘l ) \m‘ N—w‘l 0M QxIQMJrJA 'é” 7“ )LJLGCL M mix 1)? gaffe/“41,177 ffi atzdwmi \d’((\,§) :xa ~7<+l yum : y16<1~l+0 ‘ * x*l)‘L ‘A - 1 1 (X")‘~‘Z(x") H '3 1 ‘ {“{m (x-Q ‘ ( M “ 7 b“) ”i vc CeCl, [.53 Jo 1H = 12°: s 3.. :1 5 e 3 '3 3 7L IKIU‘SH é g—(w-n «.— 33— (a : ,Lzoum 2‘! W5 T917 [vars mayor». aggro/K1166: ‘l’fi wan/(OWL? @540qu 4312/ our effimk: 3 g 3’; s In (If) 4 ’23-; is 0333 3 'Im Us”) 5 ofl/u, 3M, In (L r) a 0. t/ 057 ’9) In owl-V 4—9 gUaM kg “Cow—:7 A ‘GW (11qu [7(an (\rx our 077pr‘vfimjlv; uri Nu! J“ ( 3' pm . 41M! V\ In W 1 fine; “(“ng $12”! “2“ ("m 4 0.00009- 1% )é“zq\gww, e i . 3 JJ Niki I, ‘m LCJI', )R“ Qt?” S (5%)“ (a VL mole/IL .—H\ w Ltvt. W30“) g2}, ({Y3004r56' W y» /0 1) +“A’Q Z J. ’l10 w ()0qu 0'11!»- ZLJQMr M )Rq 05)} ‘ Io (A ’ 0 £w5’1vv‘ l w”: % m3 210(0): 0 661) [> T2:=convert(tay1or(cos(x), x=0, 3 ), po1ynom); LTZ := 1-1/2*xA2 :>-T4:=convert(tay1or(cos(x), x=0, S ), polynom); 2T4 == 1-1/2*XA2+1/24*xA4 ;:> T6:=convert(tay1or(cos(x), x=0, 7 ), po1ynom); :T6 := l-1/2*xA2+l/24*XA4-l/720*XA6 :>-p1ot({cos(x), T2, T4, T6}, x=-4..4); 5f> ém> #Zooming in, we estimate the va1ue at which the po1ynomia1 L, approximation 1eaves the enve1ope: ;>-p1ot({cos(x)—O.1, cos(x)+0.1, T2}, x=1.2..1.3); 045 0.4 Q35 03 025 02 015 1.2 1.225 1.25 1.275 1.3 §> # this occurs at about 1.265, so the desired accuracy ho1ds over [ g —1.26, 1.26] :> ;> #b ‘:> 1> TT2:=convert(tay1or(exp(x)*cos(x), x=0, 3 ). po1ynom); ;TT2 := 1+x } >~TT6:=convertCtay1or(exp(x)*cos(x), x=0, 7 ), polynom); gTT6 := 1+x—1/3*XA3—1/6*xA4-1/30*XA5 j > TT12:=convert(tay1or(exp(x)*cos(x). x=0, 13 ), po1ynom);, jTTlZ := 1+x—l/3*xA3—l/6*xA4—1/3O*XA5+1/63O*XA7+1/2520*XA8+1/22680*XA9 ;—1/1247400*xA11-1/7484400*xA12 ;> #eva1uating: 5 >-eva1f(subs(x=Pi/2, TT2)); 32.570796327 1>reva1f(subs(x=Pi/Z, TT6)); {-0.545804063e-1 §> eva1f(subs(x=Pi/2, TT12)); 30.353760767e—5 L> L > if> Comparing with the function va1ue of zero, we see the acturacy ‘ improving dramatica11y ...
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