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Let P,(R) be the space of all polynomial functions on R of degree at most n with the inner product (f,9) = (t)g(t)dt. Consider the linear functional G : P2(R) →R defined by G(f) = f(0) + f'(1), where f' is the derivative of f. Find a vector he P2(R) such that G(f) = (f,h) for all %3D fE P2(R).

Let P,(R) be the space of all polynomial functions on R of degree at most n with the inner product (f,9) = (t)g(t)dt. Consider the linear functional G : P2(R) →R defined by G(f) = f(0) + f'(1), where f' is the derivative of f. Find a vector he P2(R) such that G(f) = (f,h) for all %3D fE P2(R).

Advanced Engineering Mathematics
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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5. Let P(R) be the space of all polynomial functions on R of degree at most n with the inner product (f, g) = | /)g(t)dt. Consider the linear functional G: P2(R) R defined by G(f) = f(0) + f'(1), where f' is the derivative of f. Find a vectorhe P2(R) such that G(f) = (f,h) for all fe P2 (R).
Transcribed Image Text:5. Let P(R) be the space of all polynomial functions on R of degree at most n with the inner product (f, g) = | /)g(t)dt. Consider the linear functional G: P2(R) R defined by G(f) = f(0) + f'(1), where f' is the derivative of f. Find a vectorhe P2(R) such that G(f) = (f,h) for all fe P2 (R).
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