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Thread: Newton's Method to approximate the real root of f(x)=2x^7-1 to 3 decimal places.

  1. #1

    Post Newton's Method to approximate the real root of f(x)=2x^7-1 to 3 decimal places.

    Hi so I have been having some issues with Newton's Method. I understand what you have to do, however, I was solving this one equation, yet no matter what I did I could not arrive at the correct answer.

    The question was to use Newton's method to approximate the real root of f(x)=2x^7-1 to 3 decimal places. I see x1=1 and when I do it I get 0.928571429. What I am supposed to get is 0.907343 as my x2. What do I do?

    Also this one problem I cannot figure out at all. Use Newton's Method to find the value of squareroot7 until two consecutive terms of the sequence are within 0.0001. (Hint squareroot7 is a root of what function?) I'm very confused on this problem, any help is appreciated.

    Edit I have fixed my error in the first problem, I was too stupid to not keep going. However, the second confuses me still, I've tried multiple methods to solve it but cannot come up with anything.
    Last edited by LANavjeet; 10-25-2017 at 10:17 AM.

  2. #2
    Elite Member
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    Quote Originally Posted by LANavjeet View Post
    Hi so I have been having some issues with Newton's Method. I understand what you have to do, however, I was solving this one equation, yet no matter what I did I could not arrive at the correct answer.

    The question was to use Newton's method to approximate the real root of f(x)=2x^7-1 to 3 decimal places. I see x1=1 and when I do it I get 0.928571429. What I am supposed to get is 0.907343 as my x2. What do I do?

    Also this one problem I cannot figure out at all. Use Newton's Method to find the value of squareroot7 until two consecutive terms of the sequence are within 0.0001. (Hint squareroot7 is a root of what function?) I'm very confused on this problem, any help is appreciated.
    How do you know that? What is x2?

    If x2 is 2nd approximation - then your calculation is correct.

    After five iteration the answer will converge.

    Hint for the second problem: What are the roots of y = x^2 - b ('b' is a real constant)?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    Let us not forget that this method relies on a steep slope. If you are too near horizontal, you are out of luck.

    Did you use your hint? [tex]\sqrt{7}[/tex] is a solution to what equation? Use your best algebra.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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