Nella lezione 1 (y=cosx, approssimazione della funzione coseno , attraverso un polinomio), abbiamo determinato il polinomio di grado dodicesimo che approssima la funzione [math]y=cosx[/math] , in un intorno di [math]x=0[/math].[br][br][b]La sua espressione finale è: [br][/b][br][b][b][math]P_{12}(x)=1-\frac{1}{2!}x^2+\frac{1}{4!}x^4-\frac{1}{6!}x^6+\frac{1}{8!}x^8-\frac{1}{10!}x^{10}+\frac{1}{12!}x^{12}[/math][br] [/b][/b]
Per la funzione coseno, [b] viene lasciato a te [/b]il compito di scrivere il polinomio [math]P_{12}(x)[/math] in forma sintetica! A tale scopo proponiamo tre quesiti che possono guidarti. Arriverai alla determinazione della espressione sintetica del polinomio [math]P_{12}(x)[/math], facendo uso del simbolo di sommatoria[br][br]Ricordiamo alcune [b]osservazioni[/b] fatte precedentemente, lo sviluppo polinomiale del coseno prevede: [br][list][*][size=100][size=200][size=150] [b]segni alternati[/b] per i termini posti in ordine crescente; [/size][/size][/size][/*][*] [b]solo le potenze pari[/b] poste in ordine crescente; [/*][*][b] denominatori [/b]dei vari termini[b] [/b]possono essere scritti utilizzando l'operatore fattoriale.[/*][/list]
Abbiamo già osservato la [b]sequenza dei segni[/b] nello sviluppo del polinomio approssimante.[br][br] [img width=101,height=22]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAWBAMAAAAr5E+TAAAAAXNSR0IArs4c6QAAACRQTFRFAAAAAAAAADqQOpDbZgA6kDoAkNv/tmZm25A62/////+2///bNuiSOAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUElEQVQ4T2NgGAXAEOAwQA8GwiKEVWCaO3j1bBUEAk1gKBDNUKBzuG2FxRGYAQpJPCKEVWCaAtWzJAGaFsAMkD14RKBKy2DJhxjGaI5jYAAAKTgdqLK7WgQAAAAASUVORK5CYII=[/img] ....[br]che equivale alla seguente sequenza: [br][br] [img width=113,height=22]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAWCAMAAADAUYMAAAAAAXNSR0IArs4c6QAAAEVQTFRFAAAAAAAAADo6ADqQOgAAOpDbZgAAZgA6Zjo6ZpC2ZpDbZrb/kDoAkGY6kNv/tmZm25Bm27Zm2/+22////9uQ//+2///bG+k0XgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAkklEQVRIS+2UyQqAMAxE477vtv//qQqKjEog1oAHm1NhXjIhbUPkw0/AdQK2qbhUlPSwIQ44R5T0sL4YU8YRJVXMcI5EKCliiqXW9yCphoytgz2i6ZKuiEm6EjYvxL5ytHVy/5VbM5uE5wv5CKM5Xy8uLPeyp1Io6WGHhclabvOg9B47XDrWkFB6j7kuY5/38wksAhMNRona1/IAAAAASUVORK5CYII=[/img]....[br]che equivale a:[br][br] [img width=202,height=22]data:image/png;base64,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[/img][br][br]Scrivi una [b]potenza[/b] [b]generica[/b], con base -1, che produce questa sequenza di segni?[br][br]
1. L'affermazione [b]“solo potenze pari” [/b]significa scrivere l'esponente [math]n[/math] della potenza generica con un numero pari. Quale espressione indica che [math]n[/math] è un numero pari? [br] [br]2. Come puoi scrivere la potenza [b]generica [math]x^n[/math], con esponente pari, [/b]che compare nel polinomio approssimante?[br][br]
Da osservazioni precedenti, abbiamo dedotto che al [b]denominatore[/b] del coefficiente numerico di ogni termine del polinomio[math]P_{12}(x),[/math] compare il fattoriale dell'esponente. [br][br][math]P_{12}(x)=1-\frac{1}{2!}x^2+\frac{1}{4!}x^4-\frac{1}{6!}x^6+\frac{1}{8!}x^8-\frac{1}{10!}x^{10}+\frac{1}{12!}x^{12}[/math][br]Come puoi scrivere il denominatore generico che compare nei termini del polinomio [math]P_{12}(x)[/math]?[br]
Dopo aver trovato qual è :[br][list][*][b]l'espressione generica che esprime l'alternanza dei segni del polinomio;[/b][/*][*][b]l'espressione generica delle potenze pari , nella base x del polinomio;[/b][/*][*][b]l'espressione generica che descrive il denominatore del coefficiente numerico dei termini del polinomio;[/b][/*][/list]1) indica la forma del generico termine del polinomio e [br]2) scrivi, [b]in modo sintetico, il polinomio [math]P_{12}(x)[/math], utilizzando il simbolo di sommatoria. [br][/b][br]N.B. Ricorda che puoi scrivere agilmente la formula utilizzando [b]Equation di Word [/b]e poi incollandola nello spazio risposta.[br]Alleghiamo immagine della schermata che avrai a disposizione per scrivere formule con Microsoft word :[br][img]data:image/png;base64,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[/img][br][br]
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_{12}(x)[/math] usando il comando [b]somma, [/b]considerato che trovato l'[b]espressione[/b] [b]generica[/b] del singolo termine del polinomio: [/*][/list]il comando [b]somma (espressione, variabile, valore iniziale, valore finale) [/b]rappresenta un operatore matematico (spesso indicata con il simbolo [img]data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==[/img][math]\Sigma[/math] - sigma maiuscolo), utilizzato per esprimere la somma di termini dello stesso tipo che compaiono in una [b]espressione [/b] (termine generico della somma); tale termine dipenderà da un indice (nel comando viene detto [b]variabile)[/b]; al variare di tale indice (che assume valori numerici interi) si avranno i vari termini da sommare. Tale indice parte da un [b]valore iniziale[/b] (che viene posto come limite inferiore della sommatoria) e ogni volta verrà incrementato di 1 sino ad un valore finale (che viene posto come limite superiore della sommatoria) che dovrà essere tale da dare il grado voluto del polinomio.[br]inserisci :[br]=[b]somma([/b][math]...,k,0,6[/math][b]) [/b]. [br]Potrai così osservare quanto sia già buona l'approssimazione della funzione y=cosx attraverso il polinomio [math]P_{12}\left(x\right)[/math]) , non solo in un intorno di [math]x=0[/math] [br]
Come per la funzione esponenziale , aggiungendo termini al polinomio approssimante, ovvero aumentando il grado del polinomio, otterremo una approssimazione migliore della funzione [math]y=cosx[/math]. [br]Scrivi, utilizzando il simbolo di sommatoria , il polinomio approssimante la funzione [math]y=cosx[/math], con un limite superiore non fisso, ma variabile. Chiamaiamo [math]a[/math] tale limite superiore. In questo modo potremo avere un polinomio del grado voluto.
Utilizza geogebra per visualizzare il polinomio approssimante di grado [math]n[/math], variabile. [br]Segui le seguenti istruzioni:[br][list][*]inserisci [math]y=cosx[/math][br][/*][*]inserisci il polinomio [math]P_n(x)[/math] nel seguente modo usando la formula [b]somma: [/b][b] [/b]=somma([math]...,k,0,a[/math]) . [/*][*] [math]a[/math] è uno slider che automaticamente comparirà e 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] [/*][/list]
Esprimi le tue considerazioni finali sull'argomento svolto