(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
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Define a weighted inner product on continuous functions on [-2, 2] by
2- 2)f(x)g(x) dr.
(a) Find an expression ax? + bæ + c so that 2 is a set of mutually orthogonal functions 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, 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 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.
ax³ + bæ² + cx + d =
Transcribed Image Text:Define a weighted inner product on continuous functions on [-2, 2] by 2- 2)f(x)g(x) dr. (a) Find an expression ax? + bæ + c so that 2 is a set of mutually orthogonal functions 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, 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 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. ax³ + bæ² + cx + d =
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