y= cosx approssimazione della funzione coseno con un polinomio intorno a zero
[br][br]Vogliamo approssimare, in un intorno di x=0, la funzione y= cosx con un polinomio.[br][br]Ripassiamo le proprietà della funzione y= cosx[br][list][*]La funzione [math]y=cosx[/math] ha come dominio tutti i reali, come codominio l'insieme [math][-1,+1][/math][/*][*]E' una funzione periodica di periodo [math]2\pi[/math] [/*][*]La funzione [math]y=cosx[/math] è una funzione pari[/*][/list][br]Per rispettare la simmetria della funzione, anche l’approssimazione deve essere fatta con un [b]polinomio pari[/b] (cioè con solo potenze pari: [math]x^o[/math], [math]x^2[/math], [math]x^4[/math], [math]x^6[/math], ...) perchè avrebbe la stessa proprietà di simmetria.[br]Un polinomio con termini dispari romperebbe questa simmetria, quindi le proprietà della funzione coseno.
la funzione [math]y=cosx[/math] è una funzione [b]pari[/b]. Giustifica la risposta da un punto di vista analitico e grafico
da un punto di vista grafico , la funzione è simmetrica rispetto all'asse delle ordinate[br]da un punto di vista algebrico f(-x)=f(x)
Quanto vale y=cosx in x=0?[br]Scrivi in modo formale la risposta
[list][*]Approssimiamo la funzione [math]y=cosx[/math] con un polinomio di grado zero, primo polinomio di grado pari. Un polinomio di grado 0 è semplicemente una [b]retta orizzontale[/b]: ovvero [math]P_0\left(x\right)=q[/math] Se calcoliamo il [b]polinomio di grado 0 in[/b][math]x=0,[/math] abbiamo [math]P_0\left(0\right)=q[/math] , quindi la retta sarà passante per la quota [math]y=q[/math].[/*][/list]Di conseguenza il polinomio approssimante di grado zero è: [math]P_0\left(x\right)=q[/math][br]Ci chiediamo quale potrebbe essere il il valore di [math]q[/math] che renda l'approssimazione del coefficiente del termine di grado zero migliore possibile.[br]Per determinare il valore di [math]q[/math], coefficiente del termine di 0° grado, possiamo fare valutazioni di diversa natura:[br][list][*]una valutazione intuitiva utilizzando Geogebra[/*][*]una valutazione algebrica utilizzando un foglio di calcolo[/*][/list]
Ti sembra che il polinomio [math]P_0\left(x\right)=1[/math], rappresenti una buona approssimazione della funzione y= cosx intorno a x=0?[br]Dove ti sembra comincino a separarsi? Per dare una risposta, aiutati completando la tabella presente nel foglio elettronico del file di geogebra che segue; per meglio valutare l'approssimazione , sono visualizzati i valori con 5 cifre decimali
La funzione coseno in [math]x=0[/math] vale [math]1[/math] ([math]cos\left(0\right)=1[/math]). Quindi se vogliamo approssimare la funzione con un polinomio di grado 0, necessariamente anche il polinomio calcolato in x=0 deve valere 1 cioè [math]P_0\left(0\right)=1[/math]. Tale polinomio è una retta parallela all'asse delle ascisse. Se rappresenti entrambe le funzioni su un file di geogebra, ti accorgerai che l'approssimazione è buona solo in un intorno piccolissimo di [math]x=0[/math]. Infatti, fissa un valore di[math]x[/math], a tale valore corrisponderà un punto C sulla curva esponenziale e un punto P sulla funzione polinomiale. La [b]distanza CP[/b] tra le ordinate di tali punti (|[math]\left|y_C-y_P\right|[/math]) può fornire una indicazione del grado di approssimazione tra le due curve: più la distanza CP tra le due curve è piccola più è buona l'approssimazione. [br]Completa la seguente tabella inserendo opportune formule nel foglio di calcolo. [br]Nella finestra grafica, invece, sposta il punto P (e quindi la sua ascissa) e visualizza come l'approssimazione indicata dalla distanza CP , tra la funzione coseno e il polinomio, migliori man mano che l'ascissa di P si avvicina a 0.
Usando geogebra costruisci, la visualizzazione della distanza che c'e tra la funzione [math]y=cos\left(x\right)[/math] e il polinomio approssimante al variare delle [math]x[/math] prese in un intorno di [math]x=0[/math]. [br]N.B. devi:[list=1][*]traccia la funzione coseno [math]y=cos\left(x\right)[/math];[/*][*]traccia la funzione polinomiale [math]y=1[/math];[/*][*]traccia la retta [math]x=a[/math];[/*][*]si introdurrà automaticamente uno slider che mi farà variare le[math]x[/math] scelte; [/*][*]visualizzare, con il comando intersezione, i punti C e P che appartengono rispettivamente alle due funzioni e corrispondenti alla [math]x[/math] scelta;[/*][*]visualizzare il segmento CP che rappresenta la distanza tra tali punti;[/*][*]visualizzare il valore numerico di tale distanza.[/*][/list]
Siccome la funzione y= cosx è pari, il polinomio che potrebbe migliorare l'approssimazione dovrebbe essere di 2° grado. Aggiungiamo al polinomio di grado 0 , un termine di secondo grado. Tenedo conto della concavità della funzione di y =cosx intorno a x=0, che segno dovrebbe avere il termine aggiuntivo di secondo grado? Inserisci il polinomio che ritieni più adatto. Inseriscilo nella forma [math]P_2\left(x\right)=1+bx^2[/math]
L'idea è la seguente: determiniamo il valore di [math]b[/math] ( coefficiente del termine di secondo grado del polinomio) seguendo un ragionamento molto semplice : [br] [br][list][*]Prendiamo un valore di [math]x[/math] abbastanza vicino allo zero, per esempio [math]x=0,2[/math][/*][*] calcoliamo la funzione coseno in [math]x=0,2[/math]: [math]y=cos\left(0,2\right)[/math] [/*][/list][list][*] calcoliamo il valore del Polinomio di 2° grado in [math]x=0,2[/math] : [math]P_2\left(0,2\right)=1+b\left(0,2\right)^2[/math][/*][*]ricaviamo [math]b[/math] risolvendo la seguente equazione : [math]P_2\left(0,2\right)=cos\left(0,2\right)[/math][/*][/list]se risolviamo, rispetto ad [math]b[/math] l'equazione [math]1+b\left(0,2\right)^2=cos\left(0,2\right)[/math], otterremo [math]b=0,49834[/math] [br][br]Se ripeti la stessa procedura per un valor di [math]x[/math] che si avvicina ulteriormente a 0, otterrai un valore di [math]b[/math] sempre più vicino al valore che ti permette di approssimare meglio la funzione coseno con un polimonio [math]P_2(x)[/math]. Usa il foglio excel per ricavare [math]b[/math] (con un'approssimazione di cinque cifre decimali) per i seguenti valori :[math]x=0,1[/math] ;[math]x=0,01;x=0,001;x=0,0001;x=0,00001[/math][br]
In seguito alle valutazioni fatte scrivi di seguito il polinomio approssimante, inserendo [math]b[/math] come numero frazionario
Il polinomio che potrebbe migliorare l'approssimazione deve essere di 4° grado. Aggiungiamo perciò al polinomio precedente di grado 2° , un termine di quarto grado. [br]Chiamiamo il nuovo polinomio approssimante : [math]P_4\left(x\right)=1-\frac{1}{2}x^2+cx^4[/math][br][br]Per determinare il valore del coefficiente [math]c[/math] del termine di secondo grado , possiamo fare anche qui valutazioni di diversa natura:[br][list][*]una valutazione intuitiva usando Geogebra[/*][*] una valutazione algebrica[/*][*]una valutazione di natura geometrica (una valutazione globale), ovvero, scegliendo un intorno di zero non troppo piccolo e minimizziamo l'area sottesa tra il polinomio e la funzione coseno usando Geogebra[/*][/list]
Usa Geogebra: [br][list=1][*]inserisci la funzione coseno [math]y=cos(x)[/math];[/*][*]inserisci il polinomio [math]P_4\left(x\right)=1-\frac{1}{2}x^2+cx^4[/math][br][/*][*]si crea automaticamente uno slider [math]c[/math] [/*][/list]Per capire quale potrebbero essere il segno e il valore di [math]c[/math], fai dei tentativi, variando il valore dello slider . Ricordati che puoi anche "animare" lo slider , regolando la velocità del movimento, per osservare meglio la posizione reciproca tra il polinomio e la funzione. [br]
Per determinare il coefficiente del polinomio di secondo grado, seguiremo un ragionamento molto semplice : [br] [br][list][*]Prendiamo un valore abbastanza vicino allo zero, per esempio x=0,2[/*][*] calcoliamo il coseno di 0,2 , [/*][/list][list][*] calcoliamo il valore del Polinomio di quarto grado in x=0,2 [/*][*]ricaviamo b risolvendo la seguente equazione : [math]P_4\left(x=0,2\right)=cos\left(0,2\right)[/math][br][/*][/list]
[list=1][*] Quale è il segno di [math]c[/math]? [/*][*]Quale valore di [math]c[/math] ti sembra possa essere adeguato per una buona approssimazione? [/*][/list]
Ti sarai reso conto che, pur variando il valore dello slider, sembrerebbe non semplice capire l'esatto valore del coefficiente [math]c[/math]. [br]Analizziamo un altro tipo di valutazione:[br]
L'idea è la seguente: determiniamo il valore di [math]c[/math] ( coefficiente del termine di 4°grado del polinomio) seguendo un ragionamento molto semplice : [br] [br][list][*]Prendiamo un valore di [math]x[/math] abbastanza vicino allo zero, per esempio [math]x=0,2[/math][/*][*] calcoliamo la funzione coseno in [math]x=0,2[/math]: [math]y=cos\left(0,2\right)[/math] [/*][/list][list][*] calcoliamo il valore del Polinomio di 4° grado in [math]x=0,2[/math] : [math]P_4\left(0,2\right)=1-\frac{1}{2}\left(0,2\right)^2+c\left(0,2\right)^4[/math][/*][*]ricaviamo [math]b[/math] risolvendo la seguente equazione : [math]P_4\left(0,2\right)=cos\left(0,2\right)[/math][/*][/list]se risolviamo, rispetto ad [math]c[/math] l'equazione [math]1-\frac{1}{2}\left(0,2\right)^2+c\left(0,2\right)^4=cos\left(0,2\right)[/math], otterremo [math]c=0,416112[/math] [br][br]Se ripeti la stessa procedura per un valor di [math]x[/math] che si avvicina ulteriormente a 0, otterrai un valore di [math]c[/math] sempre più vicino al valore che ti permette di approssimare meglio la funzione coseno con un polimonio [math]P_4(x)[/math]. Usa il foglio excel per ricavare [math]c[/math] (con un'approssimazione di almeno cinque cifre decimali) per i seguenti valori :[math]x=0,1[/math] ;[math]x=0,01;x=0,001;x=0,0001;x=0,00001[/math][br]
In seguito alle valutazioni fatte su [math]c[/math] indica il valore di [math]c[/math] sotto forma di frazione algebrica e scrivi il polinomio di 4° grado, [math]P_4\left(x\right)[/math] che meglio approssima, in[math]x=0[/math], la funzione coseno:
Passiamo ad un altro tipo di valutazione, basato sull'area sottesa tra le due funzioni in un intervallo fissato. L'idea sulla quale si basa questa valutazione è che "più le due funzioni sono vicine", più l'area "racchiusa" tra le due funzioni è piccola; man mano che le due funzioni si avvicinano l'area diminuisce.[br][br]Per questo tipo di valutazione , utilizziamo Geogebra: [br][list][*]Inserisci le due funzioni: la funzione esponenziale [math]y=cosx[/math]e il polinomio [math]P_4(x)=1-\frac{1}{2}x^2+cx^4[/math]. [/*][*]Scegli un intorno di 0, per esempio [math]-1\le x\le1[/math] , [/*][*]usa il comando di Geogebra che si chiama [b]IntegraleTra, [/b] [math]IntegraleTra(f,P_4(x),-1,1)[/math] per determinare l'area racchiusa tra le due funzioni nell'intervallo scelto. [/*][/list]
Passiamo ad un altro tipo di valutazione, basato sull'area sottesa tra le due funzioni in un intervallo fissato. L'idea sulla quale si basa questa valutazione è che "più le due funzioni sono vicine", più l'area "racchiusa" tra le due funzioni è piccola; man mano che le due funzioni si avvicinano l'area diminuisce.[br][br]Per questo tipo di valutazione , utilizziamo Geogebra: [br][list][*]Inserisci le due funzioni: la funzione esponenziale [math]y=cosx[/math]e il polinomio [math]P_4(x)=1-\frac{1}{2}x^2+cx^4[/math]. [/*][*]Scegli un intorno di 0, per esempio [math]-1\le x\le1[/math] , [/*][*]usa il comando di Geogebra che si chiama [b]IntegraleTra, [img]data:image/png;base64,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[/img][/b] per determinare l'area racchiusa tra le due funzioni nell'intervallo scelto. [br] [/*][/list]
Passiamo ad un altro tipo di valutazione, basato sull'area sottesa tra le due funzioni in un intervallo fissato. L'idea sulla quale si basa questa valutazione è che "più le due funzioni sono vicine", più l'area "racchiusa" tra le due funzioni è piccola; man mano che le due funzioni si avvicinano l'area diminuisce.[br][br]Per questo tipo di valutazione , utilizziamo Geogebra: [br][list][*]Inserisci le due funzioni: la funzione esponenziale [math]y=cosx[/math]e il polinomio [math]P_4(x)=1-\frac{1}{2}x^2+cx^4[/math]. [/*][*]Scegli un intorno di 0, per esempio [math]-1\le x\le1[/math] , [/*][*]usa il comando di Geogebra che si chiama [b]IntegraleTra, [img]data:image/png;base64,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[/img][/b] per determinare l'area racchiusa tra le due funzioni nell'intervallo scelto. [br] [/*][/list]
Ti sembra che l'"idea" possa funzionare? ti sembra che la valutazione di b sia più accurata?
Dalla valutazione algebrica puoi dedurre il valore di [math]c[/math]. Scrivi tale valore decimale anche in forma frazionaria:
Confronta i polinomi usati per approssimare la funzione esponenziale intorno a [math]x=0[/math]:[br][math]P_0(x)=1[/math];[br][math]P_2(x)=1-\frac{1}{2}x^2[/math];[br][math]P_4(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4[/math];[br][br]aggiungiamo altri polinomi approssimanti per aiutarti nelle osservazioni:[br][br][math]P_6(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6[/math];[br][br][math]P_8(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6+\frac{1}{40320}x^8[/math][br] [br]...[br][br]Come avrai notato, man mano che aumenta il grado del polinomio, l'approssimazione migliora. In altre parole: [br][b]1)[/b] [b]il grafico del polinomio “tocca” quello di [math]y=cosx[/math] in [math]x=0[/math] con un contatto sempre più accurato man mano che aumenta il grado del polinomio approssimante. [br][b]2) l’approssimazione è particolarmente buona vicino a x=0[/b] e l’intervallo in cui il polinomio approssima bene la funzione [b]si allarga aumentando il grado[/b].[/b][br]Ma quale altra osservazione si potrebbe fare?
[list][*][b]Confronta i polinomi usati per approssimare la funzione coseno intorno a [math]x=0[/math]:[br][br][math]P_0(x)=1[/math];[br][math]P_2(x)=1-\frac{1}{2}x^2[/math];[br][math]P_4(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4[/math];[br][br][math]P_6(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6[/math];[br][br][math]P_8(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6+\frac{1}{40320}x^8[/math][br] [br]...[br][/b][/*][/list][list][*][b]1) Che segno hanno i termini dei polinomi? Scrivi delle osservazioni.[/b][/*][/list]
[b][b]Confronta i polinomi usati per approssimare la funzione esponenziale intorno a [math]x=0[/math]:[br][br][math]P_0(x)=1[/math];[br][math]P_2(x)=1-\frac{1}{2}x^2[/math];[br][math]P_4(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4[/math];[br][br][math]P_6(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6[/math];[br][br][math]P_8(x)=1-\frac{1}{2}x^2+\frac{1}{24}x^4-\frac{1}{720}x^6+\frac{1}{40320}x^8[/math][br] [br]...[/b][/b][list=1][*][b]Qual è la potenza di [math]x[/math] più alta che compare in [math]P_0(x)[/math]?[/b][br][br][/*][*][b]Qual è la potenza più alta in [math]P_2(x)[/math]?[/b][br][br][/*][*][b]Qual è la potenza più alta ina [math]P_4(x)[/math]?[/b][br][br][/*][*][b]Che relazione c’è tra il numero del polinomio [math]P_n\left(x\right)[/math] e la potenza più alta di [math]x[/math]?[/b][/*][*][b]Quali potenze di [math]x[/math] compaiono nel polinomio [math]P_4(x)[/math]?[/b][/*][*][b]Mancano potenze tra [math]x^0[/math] e [math]x^4[/math]?[/b][br][/*][/list]
Scrivi per esteso il polinomio approssimante [math]P_{10}(x)[/math]
Scrivi il polinomio approssimante P_10(x) attraverso l'uso dell'operatore di sommatoria. [br]( si suggerisce di utilizzare Inserisci Equazione in Microsoft Word usando la scheda INSERISCI -> Equazione[br][img]data:image/png;base64,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[/img][br]Fare poi uno screenshot della formula, incollarla su un foglio di word, rimpicciolire la formula, copiarla ed incollarla nella zona risposta
Scrivi il polinomio approssimante P_10(x) attraverso l'uso dell'operatore di sommatoria. [br]( si suggerisce di utilizzare Inserisci Equazione in Microsoft Word usando la scheda INSERISCI -> Equazione[br][img]data:image/png;base64,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[/img][br]Fare poi uno screenshot della formula, incollarla su un foglio di word, rimpicciolire la formula, copiarla ed incollarla nella zona risposta
Utilizza geogebra per visualizzare il polinomio approssimante. [br]Segui le seguenti istruzioni:[br][list][*]inserisci [math]y=cosx[/math][br][/*][*]inserisci il polinomio [math]P(x)[/math] nel seguente modo: usa la formula [b]somma: [/b][/*][/list]La [b]formula somma (espressione, variabile, valore iniziale, valore finale) [/b]rappresenta una sommatoria matematica (spesso indicata con il simbolo [img]data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==[/img][math]\Sigma[/math] - sigma maiuscolo), utilizzata per calcolare la somma dei valori di un'espressione al variare di una variabile tra un limite inferiore e uno superiore.[br]inserisci :[br]=somma([math]...,k,0,a[/math]) . Lasciamo a te il compito di individuare l'espressione corretta della formula; [math]a[/math] è uno slider che automaticamente comparirà, che ti permetterà di aumentare a tuo piacere i termini della somma e avere polinomi che sempre più si adagiano sulla funzione esponenziale intorno allo zero. Nelle impostazioni dello slider assegna ad [math]a[/math] come valore minimo lo zero e come valore massimo un valore alto, per esempio 50. Ti accorgerai che il polinomio con un grado alto , approssimerà molto bene la funzione esponenziale non solo in un intorno di [math]x=0[/math] [br]