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Math Help - Functions and Newton-Raphson formula

  1. #1
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    Functions and Newton-Raphson formula

    Howdy, the forum looks great.

    I have the below question.

    http://i.imgur.com/xMJ7fs3.jpg


    I'm looking for someone to break down it down for me as I don't have any solved examples to work off. I only have the questions, so having one with a break down should hopefully help me solve the others.

    Hope that makes sense.
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  2. #2
    MHF Contributor

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    Re: Functions and Newton-Raphson formula

    The first part is easy- f(0)= 0- 3cos(0)= -1 and f(\pi/2)= \pi/2- 3(cos(\pi/2))= \pi/2. Since f is negative at 0, positive at \pi/2, and f is continuous, it must be 0 some place in between.

    As for the second, do not know what the "Newton-Raphson" algorithm is? If your text has this question, surely it at least defines it?

    The Newton-Raphson algorithm, to solve the equation f(x)= 0, requires that you define a sequence of x values, \{x_n\}, where x_0 is some chosen value, hopefully near a root, and then x_{n+1}= x_n- \frac{f(x_n)}{f'(x_n)}.
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