Let f (x) = x3 − e−x, x0 = 0.5, x1 = 0.7, x2 = 1.0. Find the Lagrange Polynomial, P2(x), of degree at most 2 for f (x) using x0, x1, x2. Evaluate P2(0.8) and compute the actual error |f (0.8) − P2(0.8)|

Let f (x) = x3 − e−x, x0 = 0.5, x1 = 0.7, x2 = 1.0. Find the Lagrange Polynomial, P2(x), of degree at most 2 for f (x) using x0, x1, x2. Evaluate P2(0.8) and compute the actual error |f (0.8) − P2(0.8)|

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let f (x) = x³ − e^−x, x₀ = 0.5, x₁ = 0.7, x₂ = 1.0.

Find the Lagrange Polynomial, P₂(x), of degree at most 2 for f (x) using x₀, x₁, x₂.
Evaluate P₂(0.8) and compute the actual error |f (0.8) − P₂(0.8)|

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