数学期末考试练习代写 Math 132代写 数学考试助攻 数学代写
195Math 132 Final exam practice 数学期末考试练习代写 Directions. This is not an assignment to be turned in. These questions are meant to provide practice for the final exam. Directions. This ...
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数学final代考 Directions: • Write your names and student number on the top right-hand corner of this page. • Open this booklet only when directed to do so.
• Write your names and student number on the top right-hand corner of this page.
• Open this booklet only when directed to do so.
• Check that you have all 7 pages including this one.
• Write all your answers in the space provided.
• You may use the backs of sheets for rough work, or if you need additional space for your answer.
• Each question is worth 16 points. (Total: 100 points)
• No cheating sheets may be used.
• This examination is two days (48 hours) in duration.
Determine whether the following statements true or false. Give reasons.
(a) Every bounded sequence in Rn has a convergent subsequence.
(b) The dual space of (Rn, ∥· ∥1) is (Rn, ∥· ∥1).
(c) In a Hilbert space, every bounded sequence has a convergent subsequence.
Suppose that the sequence (xn)n∈N in H satisfies
(a) There exists M > 0 such that for every n ∈ N, ∥ xn∥ ≤ M.
(b) For every y ∈ M, limn→∞ 〈xn, y〉exists.
(c) M is total in H.
Prove that for every y ∈ H, limn→∞ 〈xn, y〉 exists.
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Math 132 Final exam practice 数学期末考试练习代写 Directions. This is not an assignment to be turned in. These questions are meant to provide practice for the final exam. Directions. This ...
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