iterative formula Watch

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sarah12345
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#1
Report Thread starter 13 years ago
#1
using the iterative formula

x=12/7 ln(2x+5) -2

with xo=1.5 find the solution correct to 3sf - did this bit and got 1.61

then it says to justify the accuracy of your answer
think i have to work out f(1.605) and f(1.615) but dont get the right answer

thanks alot
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Christophicus
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#2
Report 13 years ago
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(Original post by sarah12345)
using the iterative formula

x=12/7 ln(2x+5) -2

with xo=1.5 find the solution correct to 3sf - did this bit and got 1.61

then it says to justify the accuracy of your answer
think i have to work out f(1.605) and f(1.615) but dont get the right answer

thanks alot
sorry to be rude, but could you type out the iterative formula again?
Is it x_n+1 = (12/7)ln(2x_n+5)^-2 ?
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Fermat
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I used the formula,

x_(n+1) = (12/7)ln(2x_n + 5) - 2

and that gave the iterative value, viz. x = 1.61

f(x) = x - (12/7)ln(2x+5) + 2

f(1.605) = -4.2*10^-3
f(1.615) = 1.6*10^-3

There is a change in sign in f(x) in the region [1.605, 1.615], so the root lies in this region.
:. x = 1.61 is accurate - to 3 s.f.
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sarah12345
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#4
Report Thread starter 13 years ago
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thats what i got but the answer says that f(1.605)=-.0073 and f(1.615)=.0029 and i didnt get what fomula they used to get those answers
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Christophicus
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#5
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(Original post by sarah12345)
thats what i got but the answer says that f(1.605)=-.0073 and f(1.615)=.0029 and i didnt get what fomula they used to get those answers
answers are wrong. I get the same answers as fermat.
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