Newtons method error approximation

1. Mar 30, 2012

TyErd

1. The problem statement, all variables and given/known data
I've attached the question

2. Relevant equations
x(n+1) = x(n) - f(x(n)) / f '(x(n))

3. The attempt at a solution

okay so x2= 1.3517323300 and i've already calculated x3 to be 1.3483949227

then how do i estimate the error in x2? do i subtract or something?

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2. Mar 31, 2012

scurty

I assume they want a percent error as an answer. To do that you do $\displaystyle\left|\frac{\text{true value} - \text{estimated value}}{\text{true value}}\right| \times 100$

So while your third iteration isn't the "true" value (it's still an approximation), it's more accurate than your second iteration so that's why you would divide by it.

3. Mar 31, 2012

TyErd

nah its not a percent error. Its says |error in x2| =< ....

so if i didn't multiply by 100 it would give me decimal answer.
so it would be | (1.3483949227 - 1.351732330) / 1.3483949227 | yeah??

4. Mar 31, 2012

TyErd

and that equals 0.002475.