Question

Use Newton''s method to find the second and third approximation of a root of x^3 + x + 3= 0 starting with x1 = -1 as the initial approximation.
The second approximation is x2= ?
The third approximation is x3= ?

Answer 1

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Answer:

  see attachment

Step-by-step explanation:

The iterator for Newton's method gives the next approximation (x') as ...

  x' = x -g(x)/g'(x) . . . . . where g'(x) is the derivative of g(x)

We have defined g(x) = x^3+x+3, the function we want the zero of. We have defined the iteration function to be f(x).

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Additional comment

Modern graphing calculators not only make the iteration trivially simple, they also give a first approximation good to 2 or 3 decimal places in many cases.