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Kamila [148]
2 years ago
9

Use Newton’s Method to find the solution to the equation

Mathematics
1 answer:
Scorpion4ik [409]2 years ago
6 0

f(x) =  - x {}^{2}  + 18 \\ f'(x) = - 2x

x_{n + 1} = x_{n} -  \frac{f(x_{n})}{f'(x_{n})}

x_{2} = 3  -  \frac{f(3)}{f'(3)}  = 4.5

x _{3}= 4.5 -  \frac{f(4.5)}{f'(4.5)}  = 4.25

x_{4} = 4.25 -  \frac{f(4.25)}{f'(4.25)}  ≈4.242647

x_{5} = 4.242647 -  \frac{f(4.242647)}{f'(4.242647)}  ≈4.242640 \\

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