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categoryرياضيات
schoolبكالوريوس
event_available2026-07-13
السؤال
Transcribed Image Text:
Q2.
Most functions can be rearranged in several ways to give x = g(x) with which to
begin the fixed-point method. For f(x)=e* -2x², one g(x) is
a.
x=±√√e* 12
Show that this converges to the root near 1.5 if the positive value is used
and to the root near - 0.5 if the negative value is used.
b. There is a third root near 2.6. Show that there is no convergence to this
root even though values near to the root are used to begin the iterations.
Where does it converge if x =2.5? If x?
2.7?
C. Find another arrangement that does converge correctly to the third root.
Use Aitken Acceleration method to help you finding the root faster.
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