Question 1. (a)Verify that the sequence1Un(x) = cos (n + ;)x),n e Nform an orthogonal set of functions on [0,1]. That is, prove| Un(x)Um(x)dx = 0, for n # m.(The formula cos(a) cos(b) = ¿(cos(a – b) + cos(a + b)) may be useful).(b) ILet ø be a C' function, and suppose$(x) = > b„Un(x)., ø"(x) = > cnUn(x).%3Dn=1n=1Express the coefficients c, in terms of b, and the values ø(0), ø(7), Ø'(0), ø'(n).

Consider the given information: Let Un(x)=cosn+1/2x, n∈ℕ be the given sequence To prove that,…

Question 1. (a) Verify that the sequence U„(x) = cos (n + x) n e N form an orthogonal set of functions on [0, 7]. That is, prove Un(x)Um(x)dx = 0, for n + m. (The formula cos(a) cos(b) = 3(cos(a – b) + cos(a + b)) may be useful). (b) 1 Let ø be a C' function, and suppose 00 $(x) = b„Un(x), $"(x) = enUn(x). n=1 n=1 Express the coefficients c, in terms of b, and the values ø(0), ø(1), Ø'(0), Ø'(n).

Question 1. (a) Verify that the sequence U„(x) = cos (n + x) n e N form an orthogonal set of functions on [0, 7]. That is, prove Un(x)Um(x)dx = 0, for n + m. (The formula cos(a) cos(b) = 3(cos(a – b) + cos(a + b)) may be useful). (b) 1 Let ø be a C' function, and suppose 00 $(x) = b„Un(x), $"(x) = enUn(x). n=1 n=1 Express the coefficients c, in terms of b, and the values ø(0), ø(1), Ø'(0), Ø'(n).

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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