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Use Newton’s Method to approximate 3^(√7) to four decimal places.
Use x1 = 2 as your seed. Round off intermediate iterates to five decimal place

  • Math -

    let f(x) = x^3 - 7
    so f(∛7) = 0


    just enter your function, its derivative, and initial guess.

  • Math -

    the answer I should get is 18.2955

    let x = 3^√7
    then x^(1/√7) = 3
    x^(1/√7) - 3 = 0

    let y = x^(1/√7) - 3 = x^.3779645 - 3
    dy/dx = (1/√7)^(1/√7 - 1) = .3779645 x^-.62204

    iteration expression:

    x - (x^.3779645 - 3)/(.3779645x^-.62204)

    x = 2 -----> 15.06815
    x = 15.06815 --->18.10237..
    x = 18.10237.. ---> 18.294858..
    x = 18.29456 ----> 8.2955 , which was my calculator answer.

    I find this a very strange question.
    There is no practical way to do the above calculations without using a scientific calculator.
    So why not find that scientific calculator to find the answer in the first place ?

  • Math -

    Good job, Reiny. I keep seeing 3^√ being used as cube root, so maybe I was way off.

    In any case, the problem is solved.

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