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Problem: Divided Difference, {{0,1},{1,0},{2,1},{3,10}},x=2.1 [ Calculator, Method and examples ]

Solution:
Your problem -> Divided Difference, {{0,1},{1,0},{2,1},{3,10}},x=2.1

The value of table for X and Y

 X Y 0 1 2 3 1 0 1 10

Numerical divided differences method to find solution
Newton's divided difference table is as follows.
 X Y(X) 1^(st) order 2^(nd) order 3^(rd) order 0 1 -1 1 0 1 1 1 2 1 4 9 3 10

The value of x at you want to find the f(x) : x = 2.1

Y(x) = y_0 + (x - x_0) f[x_0, x_1] + (x - x_0)(x - x_1) f[x_0, x_1, x_2] + (x - x_0)(x - x_1)(x - x_2) f[x_0, x_1, x_2, x_3]

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