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Consider the inner product (p(x), q(x)) := C p(x)q(x)dx on the vector space V of real polynomials with degree less than 2. The linear functional f :V → R is defined by f(p(x)) = p'(5) + 5p(-4). According to the Riesz Representation Theorem, there is an r(x) E V such that f(p(x) = (p(x), r(x)) for all p(x) E V. Find this r(x). r(x)

Consider the inner product (p(x), q(x)) := C p(x)q(x)dx on the vector space V of real polynomials with degree less than 2. The linear functional f :V → R is defined by f(p(x)) = p'(5) + 5p(-4). According to the Riesz Representation Theorem, there is an r(x) E V such that f(p(x) = (p(x), r(x)) for all p(x) E V. Find this r(x). r(x)

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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Consider the inner product (p(x), q(x)) := S p(x)q(x)dx on the vector space V of real polynomials with degree less than 2. The linear functional f:V → R is defined by f(p(x)) =p' (5) + 5p(-4). According to the Riesz Representation Theorem, there is an r(x) E V such that f(p(x) = (p(x),r(x)) for all p(x) E V. Find this r(x). r(x) =
Transcribed Image Text:Consider the inner product (p(x), q(x)) := S p(x)q(x)dx on the vector space V of real polynomials with degree less than 2. The linear functional f:V → R is defined by f(p(x)) =p' (5) + 5p(-4). According to the Riesz Representation Theorem, there is an r(x) E V such that f(p(x) = (p(x),r(x)) for all p(x) E V. Find this r(x). r(x) =
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