Thread: Consider the function...

Need help revising on this question. Not sure what to search for :s.


Consider the function f(x) = x + lnx - 2 = 0.

1. Find two appropriate rearrangement for the equation x + lnx - 2 = 0 in the form of x_n-1 = g(X_n):
2. By considering the derivative of g(x) explaining which one of the rearrangement is likely to converge to a suspected root near x = 1.4.

Originally Posted by passingtime

Not sure what to search for

... iterative methods.

There are two ways to make one of the x's in the equation the subject.

(One way is to add 2 to and subtract lnx from both sides, and the other is to add 2, subtract x and then take the exp of each side.)

Label the subject term x_n+1 and the other x term x_n. Then iterate.

In general the method fails if absolute value of g'(x_n) is greater than 1 near the root.

So if you proceed as suggested in step 2 you'll see which arrangement is going to work near 1.4.

I'll get back to u on this. This seems a little complicated right now.

Thanks a lot for the reply it has helped.