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Helpppp pleasee

You can use the recursion xn=(xn-1+10/xn-1)/3
the process of iteration to estimate the value of
V10 without using a calculator. What is the value
of the 2nd iterate if x0 = 3.1? Carry out your
answers to the 5th decimal place.

Helpppp pleasee You can use the recursion xnxn110xn13 the process of iteration to estimate the value of V10 without using a calculator What is the value of the class=

Respuesta :

Using the recursion equation, it is found that the value of the 2nd iterate is:

[tex]x_2 = 3.16228[/tex]

What is the recursive equation?

The value of the nth iteration is given by:

[tex]x_n = \frac{x_{n-1} + \frac{10}{x_{n-1}}}{2}[/tex]

The initial estimate is:

[tex]x_0 = 3.1[/tex]

Hence, the 1st iterate is given by:

[tex]x_1 = \frac{x_0 + \frac{10}{x_0}}{2} = \frac{3.1 + \frac{10}{3.1}}{2} = 3.1629[/tex]

The 2nd iterate is:

[tex]x_2 = \frac{x_1 + \frac{10}{x_1}}{2} = \frac{3.1629 + \frac{10}{3.1629}}{2} = 3.16228[/tex]

Thus, the fourth option is correct.

You can learn more about recursive equations at https://brainly.com/question/6561461

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