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Natasha2012 [34]
2 years ago
8

PLEASE HELP!

Mathematics
1 answer:
emmainna [20.7K]2 years ago
5 0

Use the given recursion and starting value of x_0 = 2.4 to find x_1 :

x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45

Do the same for x_2 and x_3 :

x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949

x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}

(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)

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