Problem 1. Let Ao be the collection of admissible functions on [a,b], i.e., Ao = {v : [a, b] → R | v(a) = 0 = v(b)} Suppose that uЄC+1 ([a, b]). Prove that u(x) is a polynomial of degree at most n if and only if for all vЄ A₁ we have d" u v'(x)dx = 0. dan Hint: Make sure you prove both directions of this statement.
Problem 1. Let Ao be the collection of admissible functions on [a,b], i.e., Ao = {v : [a, b] → R | v(a) = 0 = v(b)} Suppose that uЄC+1 ([a, b]). Prove that u(x) is a polynomial of degree at most n if and only if for all vЄ A₁ we have d" u v'(x)dx = 0. dan Hint: Make sure you prove both directions of this statement.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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