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<font size="3">Considereu la funció següent <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#f«/mi»«/math»</span>. Aquesta funció té un zero entre x=#a i x=#b.<br />Feu un pas del mètode de la bisecció per reduir l'interval inicial [#a,#b] a la meitat. </font><br /><br />
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<font size="3">1. El teorema de Bolzano ens diu que si f(x) és una funció contínua en un interval tancat [a,b] i f(a)*f(b)<0 llavors f(x) té un zero dins l'interval.<br /><br />2. El mètode de la bisecció divieix l'interval original [a,b] en un interval de la meitat de la meitat de la longitud on podem assegurar que hi ha un zero.<br />Per això es calcula el punt mig m=(a+b)/2 i s'avalua f(a)*f(mig) i f(b)*f(mig):<br />- Així si f(a)*f(mig)<0 llavors el nou interval és [a,mig].<br />- Així si f(b)*f(mig)<0 llavors el nou interval és [mig,b].</font><br />
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#dolent
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Thursday, 10 December 2015, 10:53 AM
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