Process write complete write yourself clearly do not miss the topic Problem 1.Let Ao be the collection of admissible functions on [a,b], i.e.,A0 = {v : [a, b] → R | v(a) = 0 = v(b)}Suppose that u € C+1 ([a, b]). Prove that u(x) is a polynomial of degree at most n if and only if for allv € A₁ we haved" uv'(x)dx= 0.danHint: Make sure you prove both directions of this statement.

problem : 1 Given that also given that first we assume that is a polynomial of degree at most n…

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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