Define a weighted inner product on continuous functions on [-2, 2] by2- 2)f(x)g(x) dr.(a) Find an expression ax? + bæ + c so that 2 is a set of mutually orthogonal functions withrespect to this weighted inner product.Choose your answer so that a is the smallest positive integer that will produce an answer with a,b, and c all integers.az? + bx +c= 3x^2-2(b) Find an expression ar³ + ba? + cx +d so that this new polynomial is orthogonal to all thefunctions in part (a) with respect to this weighted inner product.Choose your answer so that a is the smallest positive integer that will produce an answer with a,b, c, and d all integers.ax³ + bæ² + cx + d =

Solution of part (b): The inner product on continuous functions on -2,2 is defined by…

(b) Find an expression az + ba? + ca +d so that this new polynomial is orthogonal to all the functions in part (a) with respect to this weighted inner product. Choose your answer so that a is the smallest positive integer that will produce an answer with a, b, c, and d all integers. az³ + bæ? + cz +d

(b) Find an expression az + ba? + ca +d so that this new polynomial is orthogonal to all the functions in part (a) with respect to this weighted inner product. Choose your answer so that a is the smallest positive integer that will produce an answer with a, b, c, and d all integers. az³ + bæ? + cz +d

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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