contin.py

Created on April 24, 2025

605 Bytes

°f continue en x = a 
lim f(x) = lim f(x) = f(a)
x->a-      x->a+     

°TVI 
f def sur I = [a;b]
*f continue sur I 
*0 e [f(a);f(b)] alors il existe 
alpha e [a;b] tq f(alpha) = O 

°Corollaire du TVI
Il faut que f soit strict croiss
ou decroiss car f(alpha) = 
admet une unique solution 

°Petit th du point fixe 
*Un+1 = f(Un)
*f continue sur I 
*f(I) c I 
*Un converge vers l 
alors l verifie f(l)=l

Méthode 
*exprimer un+1 sous la forme 
f(Un)
*verifier que f est continue 
sur I 
*verifier que les images de f
appartiennent à I
*Résoudre sur I f(x)=x
*appliquer le th du pts fixe

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contin.py