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  3. 8 equip v c1 with the following inner product dx...

Question: 8 equip v c1 with the following inner product dx...

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8- Equip V C(-1,) with the following inner product: dx For n-0, î , 2, . . . define T, (x) = cos (narcos x). Prove that the set S-(To(x), ή (x), T2(x), . . . } is an orthogonal set in V Remark. Note that To(x)-1 and Ti(x)-x. Later we will prove that for each n, T,(x) is indeed a polynomial. These polynomials are called Chebyshev polynomials

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