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Math Help - finding roots in Iteration method and newton raphson,

  1. #1
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    finding roots in Iteration method and newton raphson,

    hello, everyone i just want to know how to find roots in iteration and as well as newton raphson method. actually this two methods comes after bisection method and false position method,( this are all numerical methods to solve problems)
    i know how to solve problems in bisection and false position method very well.
    but i dont know how to solve in this two methods(i,e iteration and newton raphson)

    Actually,I missed the classes, so please i request u to explain in detail, i know how to find derivates very well,.

    ok heres the problem,
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  2. #2
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    Quote Originally Posted by avengerevenge View Post
    hello, everyone i just want to know how to find roots in iteration and as well as newton raphson method. actually this two methods comes after bisection method and false position method,( this are all numerical methods to solve problems)
    i know how to solve problems in bisection and false position method very well.
    but i dont know how to solve in this two methods(i,e iteration and newton raphson)

    Actually,I missed the classes, so please i request u to explain in detail, i know how to find derivates very well,.

    ok heres the problem,
    1. Iteration means repetition of the same method. So the Newton method is an example of an iterative way to find the zeros of a differentiable function. Have a look here: Newton's method - Wikipedia, the free encyclopedia

    2. Tranform the equation into the equation of a function:

    2x-\log_{10}(x) = 4~\implies~2x-\log_{10}(x) - 4=0

    Therefore f(x)=2x-\log_{10}(x) - 4

    3. Now use the Newton method:

    x_{n+1} = x_n-\dfrac{f(x_n)}{f'(x_n)}

    Use x_0 = 2

    4. After 4 steps you should have reached x_4 \approx 2.168032...
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