Question
Asked Nov 13, 2019
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f(x) 2-10
a) Use algebraic methods to find the exact roots of f(x) and assign ro the value of the closest
integer to your positive root. Example: If your roots were ±5.34 then x= 5
b) Write the formula for Newton's method for f(x) given above, ie. Tn+1=. ...
Simplify your answer completely
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f(x) 2-10 a) Use algebraic methods to find the exact roots of f(x) and assign ro the value of the closest integer to your positive root. Example: If your roots were ±5.34 then x= 5 b) Write the formula for Newton's method for f(x) given above, ie. Tn+1=. ... Simplify your answer completely

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Expert Answer

Step 1

We are given the function f(x) = x2-10.

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(a) Using algebraic methods to find the exact roots of f(x) So, to find the roots, x2 10 0 => (x-V10)(x + V10) = 0 => x = 10,-V10 => x 3.1623,-3.1623 According to the question, we will be assigning xo the value of closest integer to the positive root. So, xo = 3

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Step 2

Now,

...
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(b) Newton's method: Let the initial value is xo f (xn) is repeated until a sufficiently f'(xn) Then by the Newton's method, xn+1 = Xn precise value is reached Here we are given that f (x) x2 10 Now f'(x)( -(x2 10) f'(x) 2x So, by using the above formula, f (x) f'(xo) f (3) => x1 3 - f'(3) (-1) => x1=3 6 => x1 3.167 = 0.167 Here, x

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