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Problem: Langrange's Interpolation, {{0,1},{1,0},{2,1},{3,10}},x=2.1 [ Calculator, Method and examples ]

Solution:
Your problem -> Langrange's Interpolation, {{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

Langrange's Interpolating Polynomial
The value of x at you want to find P_n(x) : x = 2.1

Y(x) = ((x - x_1)(x - x_2)(x - x_3))/((x_0 - x_1)(x_0 - x_2)(x_0 - x_3)) xx y_0 + ((x - x_0)(x - x_2)(x - x_3))/((x_1 - x_0)(x_1 - x_2)(x_1 - x_3)) xx y_1 + ((x - x_0)(x - x_1)(x - x_3))/((x_2 - x_0)(x_2 - x_1)(x_2 - x_3)) xx y_2 + ((x - x_0)(x - x_1)(x - x_2))/((x_3 - x_0)(x_3 - x_1)(x_3 - x_2)) xx y_3

Y(2.1) = ((2.1 - 1)(2.1 - 2)(2.1 - 3))/((0 - 1)(0 - 2)(0 - 3)) xx 1 + ((2.1 - 0)(2.1 - 2)(2.1 - 3))/((1 - 0)(1 - 2)(1 - 3)) xx 0 + ((2.1 - 0)(2.1 - 1)(2.1 - 3))/((2 - 0)(2 - 1)(2 - 3)) xx 1 + ((2.1 - 0)(2.1 - 1)(2.1 - 2))/((3 - 0)(3 - 1)(3 - 2)) xx 10

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