Find the lagrange polynomials that approximate f(x) = x3 a ) Find the linear interpolation polynomial...

Find the lagrange polynomials that approximate f(x) = x³

a ) Find the linear interpolation polynomial P₁(x) using the nodes x₀= -1 and x₁ = 0

_b) Find the quadratic interpolation polynomial P2(x) using the nodes x₀= -1 and x₁ = 0 and x₂ = 1

c) Find the cubic interpolation polynomial P₃(x) using the nodes x₀= -1 and x₁ = 0 and x₂ = 1 and x₃=2

d) Find the linear interpolation polynomial P₁(x) using the nodes x₀= 1 and x₁ = 2

e) Find the quadratic interpolation polynomial P₂(x) using the nodes x₀= 0 and x₁ = 1 and x₂ = 2

Expert Solution

Colby Messinger answered 2 years ago

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