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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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