Newton interpolary difference formula

fonseh
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Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :

f(x1 ,x2 ) - f(x0 , x1 ) / ( x2 -x0 )
=
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143
 

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fonseh said:

Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143

Do not post images; type out your work.
 
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Ray Vickson said:
Do not post images; type out your work.
It's just the notes ... For my trial , i didnt post images ...
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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