Let V=R2[x] be the real vactor space of polynomials of degree most 2. B={f0 ,f1 ,f2 } where f0(x)=1, f1(x)=1, and f2(x)=x2 be the standard basis of V. The inner product <.,.> on V is defined by = integral 1_0 f(x)g(x)dx. (i) Find the best quadratic approximation to f(x)=x4 on [0,1]

Let V=R2[x] be the real vactor space of polynomials of degree most 2. B={f0 ,f1 ,f2 } where f0(x)=1, f1(x)=1, and f2(x)=x2 be the standard basis of V. The inner product <.,.> on V is defined by = integral 1_0 f(x)g(x)dx. (i) Find the best quadratic approximation to f(x)=x4 on [0,1]

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 V=R₂[x] be the real vactor space of polynomials of degree most 2. B={f₀ ,f₁ ,f₂ } where f₀(x)=1, f₁(x)=1, and f₂(x)=x² be the standard basis of V. The inner product <.,.> on V is defined by

<f,g> = integral 1_0 f(x)g(x)dx.

(i) Find the best quadratic approximation to f(x)=x⁴ on [0,1]

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