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categoryالرياضيات schoolبكالوريوس event_available2026-07-15

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[3] Let X = C(0,1;C)={q:[0,1]⇒C : (•) is continuous}. Consider the differential operator AD : D(A) ≤ X→X defined by A₂[º(·)](x) = ø″(x), with domain D(A) = {(•) = C² (0,π; C) : q(0) = 0, &(7) = 0} . Circle the correct eigenvalue and eigenfunction pair for AD (i) V₁ = −N²л², V√(x) = sin(Nлx), N = 1,2,3,... (ii) (iii) Y₁ = −[2N−1]², √(x) = sin([2N −1]x), N=1,2,3,... Y₁ = -N², V√(x) = cos(Nx), N = 0,1,2,3,... N (iv) none of the above

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