Culegere de probleme de Analiz˘a numeric˘a
Culegere de probleme de Analiz˘a numeric˘a
Culegere de probleme de Analiz˘a numeric˘a
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10.1. Ecuat¸ii în R 157<br />
Ecuat¸ia<br />
are două rădăcini<br />
x 0<br />
ξ ξ′<br />
f(x 0 )<br />
ξ x x ′<br />
1<br />
1 ξ′<br />
Figura 10.4: Cazul c) al <strong>probleme</strong>i 10.1.3<br />
f(x0) = 1<br />
2 f′′ (x0)(x−x0) 2<br />
<br />
x1 = x0 − − 2f(x0)<br />
f ′′ (x0)<br />
x ′ 1 = x0<br />
<br />
+ − 2f(x0)<br />
f ′′ (x0)<br />
care sunt abscisele punctelor <strong>de</strong> intersect¸ie cu axa Ox ale parabolei (figura 10.4,<br />
dreapta)<br />
Y = f(x0)+ 1<br />
2 f′′ (x0)(x−x0) 2 .<br />
Observat¸ia 10.1.4 Avem <strong>de</strong> fapt două cazuri <strong>de</strong> interes date <strong>de</strong> I s¸i II.<br />
Problema 10.1.5 Determinat¸i o rădăcină a ecuat¸iei<br />
x 3 −x−1 = 0<br />
folosind metoda aproximat¸iilor succesive.
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