Consider the function f(x) = x- 4 In x

Show that the equation f(x) = 0 has a solution in the interval (1,2)

Show that for this function f the Newton - raphson method formula can be expressed as xn +1 = 4x n (1-4 In x)/4 - x n (n = 0,1,2....).

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- Jul 11th 2006, 03:17 PMfair_lady0072002Help- Newton - Raphson Method
Consider the function f(x) = x- 4 In x

Show that the equation f(x) = 0 has a solution in the interval (1,2)

Show that for this function f the Newton - raphson method formula can be expressed as xn +1 = 4x n (1-4 In x)/4 - x n (n = 0,1,2....). - Jul 11th 2006, 05:09 PMSoroban
Hello, fair_lady0072002!

I'll do the second part . . . it's trickier.

And I believe there's an extra "4" is the answer . . .

Quote:

Consider the function:

(b) Show that for this function , the Newton- Raphson method formula

can be expressed as: .**?**for

Formula: .

I'm going to drop the subscripts (temporarily) . . .

We have: .

Then: .

Multiply top and bottom of the fraction by

Get a common denominator: .

Factor: .

- Jul 11th 2006, 05:27 PMfair_lady0072002My mistake....sorry and thanx
second part should be

x n+1 = 4x n (1- Inx n)/4-x n - Jul 12th 2006, 07:49 AMSoroban
Hello again, fair_lady0072002!

I hope this suffices as a solution . . .

Quote:

Consider the function:

Show that the equation has a solution in the interval (1,2)

It can shown that is continuous for all

We find that: .

. . . . . . and: .

Since the*continuous*function changes from positive to negative over the interval,

. . it must achieve somewhere on the interval.