Newtons method error approximation

[TyErd]

Homework Statement

I've attached the question

Homework Equations

x(n+1) = x(n) - f(x(n)) / f '(x(n))

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?

 

[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.

 

[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??

 

[TyErd]

and that equals 0.002475.