Mat-C.1 harj2 25.4. 2012 Sis\303\244llys: Suorita View LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEoJnNyYXJyO0YnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkYtRiw2LlEifkYnRi9GMkY1RjhGOkY8Rj5GQEZCRkRGR0YyCollapse all sections.

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Maple Matlab a) Lausekkeena: 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 Sama hoituu yhdell"a eval-komennolla: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= x=-2; f=1+sin(x)./(1+x.^2); f x=linspace(-5,5); f=1+sin(x)./(1+x.^2); plot(x,f) b) M"a"aritell"a"an f funktioksi: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= f=@(x) 1+sin(x)./(1+x.^2) f(-2) fplot(f,[-5 5]) % tai x=linspace(-5,5); plot(x,f(x))

Paraabelin 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ja suoran 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rajoittaman alueen pinta-ala? LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRitGK0YvToki voitais x ja y vaihtaa, kuvion kierto ja peilaus pystyakselin suhteen ei muuta alaa. Tehd"a"an t"ass"a kuitenkin alkup. koordinaatistossa, mutta integroidaan ""alykk"a"asti". 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Huom! Tyoarkkia uudelleen ajettaessa ratk-joukon alkioiden j"arjestys saattaa vaihtua! 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Talletettiin ellipsin kuva muuttujaan ellkuva. 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Osoittautuu, ett\303\244 t\303\244ss\303\244 on puutteita. Siksi voitaneen suositella tinkimist\303\244 eleganssista ja pit\303\244ytymist\303\244 lhs-rhs-tyyliin (vrt. seuraava kohta:"Yht\303\244l\303\266iden muokkausta"). Toki toimiviksi tiedetyt voi hoitaa yll\303\244 olevalla eleganssilla. Hyv\303\244 puoli on, ett\303\244 toimimattomista tulee huutavat punaiset virheilmot. JSFH

T"ass"a aiemman ws:n jono/lista-oppia. T"ass"a on tiivistettyin"a jonoihin ja listoihin liittyvi"a operaatioita, jotka voi k"ayd"a itsen"aisesti l"api. 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Edellisess\303\244 huomattiin, ett\303\244 yht\303\244l\303\266iss\303\244 derivointi ja yhteenlasku toimivat puolittain. Miten yleisesti vastaava p\303\244tee? 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Sanoisko, ett\303\244 semisimppeli\303\244 tai semivaivalloista, riippuen n\303\244k\303\266kumasta. JSFH

T\303\244ss\303\244 aika riemukasta Maple-tekniikkailoittelua. a) K\303\244sittely lausekkeena: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElcGxvdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYwLUY2NiYtRiM2Ky1GLDYlUShoZXJwb2x5RidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSVkaWZmRidGL0YyLUY2NiQtRiM2J0Y+RkEtRiw2JVEieEYnRi9GMi8lK2V4ZWN1dGFibGVHRklGRUZFRkFGZm4tRjY2JC1GIzYpRj5GQUZdb0ZBRl1vRmBvRkVGRUZgb0ZFRkUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGQUZdby1GQjYtUSI9RidGRUZHL0ZLRklGTEZORlBGUkZUL0ZXUSwwLjI3Nzc3NzhlbUYnL0ZaRmFwLUZCNi1RKiZ1bWludXMwO0YnRkVGR0ZfcEZMRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRicvRlpGZ3AtSSNtbkdGJDYkUSMuNUYnRkUtRkI2LVEjLi5GJ0ZFRkdGX3BGTEZORlBGUkZURmZwL0ZaRlgtRmpwNiRRJDEuNUYnRkVGQS1GLDYlUSZjb2xvckYnRi9GMkZccC1GNjYmLUYjNiktRiw2JVEkcmVkRidGL0YyRkEtRiw2JVEmZ3JlZW5GJ0YvRjJGQS1GLDYlUSVibHVlRidGL0YyRmBvRkVGRUZmb0Zpb0Zgb0ZFRkVGYG9GRQ== b) K\303\244sittely funktiona: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEkZDJwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEiREYnL0YwRj1GOS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRI2RwRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjktRiw2I1EhRidGZW5GOQ== Huomaa, ett\303\244 D operoi funktioon ja palauttaa funktion. Siten p, dp ja d2p ovat nyt funktioita. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVEoaGVycG9seUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJXN1YnNGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2KC1GLDYlUSprZXJ0b2ltZXRGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJwRidGL0YyLUZTNiQtRiM2JS1GLDYlUSJ4RidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjlGZm9GOUY5LUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGaG4vRk5GaW5GaG9GaG8tRjY2LVEiI0YnRjlGO0Y+RkBGQkZERkZGSEZobkZbcC1GLDYlUUN+VCYjMjI4O3NzJiMyMjg7fnZhc3RhfnRhcnZpdHRpaW5+RidGL0YyLUYsNiZGUUYvLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnRjItRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORltxLUYsNiVRKWtvbWVudG9hRidGL0YyLUY2Ni1RIi5GJ0Y5RjtGPkZARkJGREZGRkhGaG5GW3BGZm9GOQ== JSFH

Maple Matlab LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZA 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 x=linspace(-2,2,30); y=linspace(-1,1,30); [X,Y]=meshgrid(x,y); Z=sin(3*Y-X.^2+1)+cos(2*Y.^2-2*X); mesh(x,y,Z) figure surf(x,y,Z) figure surfc(x,y,Z),colorbar figure contour(x,y,Z) % Korkeusarvoja piirrokseen: [cs,h]=contour(x,y,Z) clabel(cs,h,'manual') % Hiiriasetus LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

T\303\244ss\303\244 tehd\303\244\303\244n enemm\303\244n kuin pyydet\303\244\303\244n. Maplessa on valmis interpolointifunktio, joka palauttaa interpolaatiopynomin valitsimella s\303\244\303\244dett\303\244v\303\244ss\303\244 muodossa. ?curvefitting[PolynomialInterpolation] Opettavaista on kirjoittaa oma Lagrangen interpolaation toteuttava funktio, alla lagint, jonka apufunktiona on Lagrangen kertojapolynomin m\303\244\303\244rittelev\303\244 L. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVErY3VycmVudGRpckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUStjdXJyZW50ZGlyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiZGKy1JI21zR0YkNiNRSy9tL2hvbWUvaG9tZTc5L2FwaW9sYS91bml4LzIwMTJrZXZhdC9tYXBsZUYnRisvRjhRJ25vcm1hbEYnRkNGQ0YrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVErY3VycmVudGRpckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA 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 T\303\244m\303\244 meni mystiikan puolelle, miksei toimi! LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2L1ElcmVhZEYnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZILUkobWZlbmNlZEdGJDYkLUYjNictSSNtaUdGJDYjUSFGJy1JI21zR0YkNiNRMk1hdEMxa29vZGl0MTIubXBsRidGUC8lK2V4ZWN1dGFibGVHRjkvRjNRJ25vcm1hbEYnRlpGWEZa 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 Muuta polku, omaksesi. Koodit ovat my\303\266s alla olevassa laatikossa, joten ei tarvitse temppuilla polkujen kanssa. Vie osoitin laatikkoon ja CTR-E (CMD-E), [E - execute]. linspace:= (a,b,n)->[seq(a+iii*(b-a)/(n-1),iii=0..n-1) ]: # Lagrangen kertojapolynomi: L:=proc(j,xd,x) local oso,nimi,i,j1; j1:=j+1; oso:=product((x-xd[i]),i=1..nops(xd))/(x-xd[j1]); nimi:=subs(x=xd[j1],oso); oso/nimi; end: lagint:=(xd,yd,x)->add(yd[j+1]*L(j,xd,x),j=0..nops(xd)-1): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmcHJpbnRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSlsaW5zcGFjZUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZARj1GQA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmcHJpbnRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSdsYWdpbnRGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQEY9RkA= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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Tutkitaan interpolaatiovirhett\303\244, verrataan virhearviota todelliseen virheeseen. 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Probe-info -> cursor position => LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEobWF4ZGVyN0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSkmYXBwcm94O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZTLUkjbW5HRiQ2JFEnMjc2MDAwRidGOUY5 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEobWF4ZGVyN0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEnMjc2MDAwRidGOS8lK2V4ZWN1dGFibGVHRj1GOQ== 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suhteen (ja muutenkin) on t"ass"a tapauksessa k"aytt"okelvottoman karkea, johtuen 7. derivaatan valtavasta maksimista. (Eih"an se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NTg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYyv"altt"am"att"a (l"ahimainkaan) siihen max-kohtaan osu, mutta kun siit"a ei mit"a"an tiedet"a, ei yleisell"a kaavalla parempaa arviota max-virheelle saada.) JSFH 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 Huom! Virhearvion uskottavuuden suhteen t\303\244m\303\244 ei ollut ihan paras teht\303\244v\303\244 n\303\244in alkajaisiksi. Toki on hyv\303\244 n\303\244hd\303\244 t\303\244llainenkin tapaus. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZA LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRInhGJ0YvRjItRjY2LVEoJnNyYXJyO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRJmV2YWxmRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNidGTy1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl5vLUkmbWZyYWNHRiQ2KC1GIzYmLUYsNiVRImZGJ0YvRjItRmZuNiQtRiM2JUZPLyUrZXhlY3V0YWJsZUdGPUY5RjlGXHBGOS1GIzYnLUYsNiVRIkRGJy9GMEY9RjktRmZuNiQtRiM2JUZlb0YvRjJGOS1GZm42JC1GIzYlRk9GL0YyRjlGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZhcS8lKWJldmVsbGVkR0Y9RlxwRjlGOUZccEY5 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnbHByaW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEmTnN5bWJGJ0YvRjItRjY2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGR0ZERkdGR0ZERkc= Siirret\303\244\303\244n t\303\244m\303\244 kaava Matlab-ikkunaan (copy/paste) Matlab-ikkuna: >> syms x >> vectorize(x+(x*cos(x)-sin(x)-1)/(x*sin(x))) x+(cos(x).*x-sin(x)-1)./sin(x)./x >> N=@(x) x+(cos(x).*x-sin(x)-1)./sin(x)./x >> x=6; >> format long >> x=N(x) % Toista n-nappaimella. x = 2.993463587028939 >> x=N(x) >> x=6.5 x = 6.500000000000000 >> x=N(x) x = 10.170723934666555 >> x=N(x) x = 11.299466443472243 >> x=N(x) x = 10.990110316129204 >> x=N(x) x = 10.995575700223300 >> x=N(x) x = 10.995574287564367 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRidGQC1JI21vR0YkNi1RIjtGJ0ZALyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGPUZA 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 Teht\303\244v\303\244ss\303\244 ei pyydetty, mutta tehd\303\244\303\244n graafinen havainnollistus piirt\303\244m\303\244ll\303\244 tangentteja sivuamispisteest\303\244 x-akselin leikkauspisteeseen. T\303\244ss\303\244 on riemastuttavan k\303\244tev\303\244 mahdollisuus m\303\244\303\244ritell\303\244 grafiikka-arvoinen funktio: 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 display-komennolle annetaan jono n\303\244it\303\244 kuvia, kunkin kuvan "kantapiste" on ao. iteraatiojonon piste. Alla olevassa kuvajonossa esiintyv\303\244 uusi display tarvitaan siksi, ett\303\244 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Selvemmin prosessi n\303\244kyy animaationa, se saadaan lis\303\244\303\244m\303\244ll\303\244 edelliseen valitsin insequence=true Koska haluamme kuvaajan n\303\244kyv\303\244n jokaisessa animaatiokehyksess\303\244, jouduimme lis\303\244\303\244m\303\244\303\244n display(fkuva,...) muuten fkuva pyyhkiytyisi seuraavassa kehyksess\303\244 pois. 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 Klikkaamalla kuvaa, saat animaatiovalikon. Newton suppenee n\303\244ill\303\244 arvoilla turhan nopeasti. Voi kokeilla muita l\303\244ht\303\266arvoja. T\303\244ss\303\244 on joka tapauksessa hyvin k\303\244tev\303\244 yleinen tekniikka, jolla erilaisia iteraatioita on tavattoman helppo graafisesti havainnollistaa. b) 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 Taulukon saa k\303\244tev\303\244sti INSERT-valikon INSERT TABLE-valinnalla. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 N\303\244ytt\303\244is silt\303\244, ett\303\244 arvolla y(0)=c=-0.5 ratkaisuk\303\244yr\303\244 = vakio = 0, mutta vain "n\303\244ytt\303\244is", kts. alla. Kun c > -0.5, niin 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Kun c <-0.5, niin 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 Mutta, eih\303\244n siin\303\244 parvessa vakioratkaisua voi olla. 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aivan pipariksi. 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