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....).
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....).
Hello, fair_lady0072002!
I'll do the second part . . . it's trickier.
And I believe there's an extra "4" is the answer . . .
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: .
Hello again, fair_lady0072002!
I hope this suffices as a solution . . .
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.