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I know how to use it using variables, but when it comes to problems like:
Use Newton's method to approximate the value of
(42)^(1/3)

as follows:
Let x1=3 be the initial approximation.
The second approximation x2 is _____?

2007-12-10 07:56:49 · 3 answers · asked by Anonymous in Science & Mathematics Mathematics

3 answers

Look the problem over.
Go to kitchen and open refrigerator.
Remove milk and pour glass.
Replace milk and close refrigerator.
Open cupboard and remove box of fig newtons.
Alternate eating newtons and drinking milk until you forget problem.

2007-12-10 08:02:02 · answer #1 · answered by gebobs 6 · 0 2

Newton's method finds roots of equations. So, to answer a question of the type you have been given, you have to devise an equation for which your number is a root. If you are trying to approximate the value of 42^(1/3), then note that this number is the one real root of the equation

x^3 - 42 = 0.

So, apply Newton's method to that. Cheers!

2007-12-10 08:06:21 · answer #2 · answered by acafrao341 5 · 0 0

you need to see this as f(x) = x^3 -42 and you want to solve f(x) = 0

f ' (x) = 3x^2

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

2007-12-10 08:05:16 · answer #3 · answered by lienad14 6 · 0 0

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