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(15 points) (a) Dene What it means for a sequence {f : D > IR} to converge uni formly to the function f : D ) IR. (b) For each n E N, let fn...

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7. (15 points) (a) Define What it means for a sequence {ffl : D —> IR} to converge uni—
formly to the function f : D —) IR. (b) For each n E N, let fn : IR —> IR be given by fn(m) 2 502+ $2. in.
Prove that the sequence {fn} converges uniformly on IR to the function f : IR —> IR given by f(a:) = |LE|. (c) Give an example, with proof, of a domain D and a sequence of func—
tions which converges pointvvisej but not uniformly on D.

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