Question: (a) Consider the second-order boundary-value problem, (d) Find u esuch that for all u E H such that t (O)-o(1) 0. Discuss properties of the

(a) Consider the second-order boundary-value problem, (d) Find u esuch that

(a) Consider the second-order boundary-value problem, (d) Find u esuch that for all u E H such that t (O)-o(1) 0. Discuss properties of the classes of test and trial functions for each of bound ary-value problems (b), (c), and (d) so that these problems correspond to the given problem (a). In addition, suppose that f.g, and h are the three functions shown below: and the following weak boundary-value problems: (b) Find u e such that u(0)u0 and (-u" -x)v dx 0 for all v E H f(x) 8(x) (c) Find u e such that (uw'-xv) dx = 0 for all u E H h(x) The function h is given by h(x) For each of problems (b), (c), and (d), determine whether or not f,g, and h belong to either the appropriate class of trial functions or test functions

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