Home

 Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution will be displayed step by step (In 2 parts)
Solution
Problem: Langrange's Interpolation, 2x^3-4x+1, [2,4], x=2.1, N=4 [ Calculator, Method and examples ]

Solution:
Your problem -> Langrange's Interpolation, 2x^3-4x+1, [2,4], x=2.1, N=4

Equation is f(x) = 2x^3-4x+1.

h = (b-a)/N

h = (4 - 2) / 4 = 0.5

The value of table for X and Y

 X Y 2 2.5 3 3.5 4 9 22.25 43 72.75 113

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 - x_4))/((x_0 - x_1)(x_0 - x_2)(x_0 - x_3)(x_0 - x_4)) xx y_0 + ((x - x_0)(x - x_2)(x - x_3)(x - x_4))/((x_1 - x_0)(x_1 - x_2)(x_1 - x_3)(x_1 - x_4)) xx y_1 + ((x - x_0)(x - x_1)(x - x_3)(x - x_4))/((x_2 - x_0)(x_2 - x_1)(x_2 - x_3)(x_2 - x_4)) xx y_2 + ((x - x_0)(x - x_1)(x - x_2)(x - x_4))/((x_3 - x_0)(x_3 - x_1)(x_3 - x_2)(x_3 - x_4)) xx y_3 + ((x - x_0)(x - x_1)(x - x_2)(x - x_3))/((x_4 - x_0)(x_4 - x_1)(x_4 - x_2)(x_4 - x_3)) xx y_4

Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me