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C3 Edexcel, Proving degree of accuracy via iterative formula watch

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    Hey guys,
    A question that seems to pop up a lot on the past papers I have been given is giving proof to the degree of accuracy of 'x' to say 3 significant figures.

    The general layout of the questions is usually the iterative formula and they give you a starting 'x' value to substitute into the formula until you converge to the degree of accuracy they've stated so let's say I've got 'x' to 1.61 but I have to then proof that it's not 1.60 or 1.62 by using the values 1.605 and 1.615. e.g.

    Xn+1 = 12/7*ln(2Xn+5) -2

    'n' and 'n+1' are notations.

    So basically if I want to prove it's 1.61 I do this :

    1.605 - 12/7*ln(2*1.605 + 5) + 2 = around zero
    and the same for 1.615, but when I do this I never get the same answer as they do on the mark scheme but conveniently enough I always get the correct value closer to zero to prove the degree of accuracy of my answer... Basically is the way I'm doing this wrong or is there another way?

    I get for x=1.605 , -4.176*10^-3

    and for x=1.615, 1.653*10^-3

    but mark scheme says for 1.605 , −0.0073 and for 1.615, 0.0029

    Thanks Guys.
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    You substitute the two numbers (1.605 and 1.615) into the original equation (f(x) , or y = ..), not the iterative formula. You should get two results, one a positive and one a negative, this therefore shows that the 1.61 is a root to 3 decimal places.
 
 
 
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Updated: January 17, 2010

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