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    Taylor series, the convergence of sequence, and series of functions

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    Let ƒn : R2  R be ƒn (x,y) = (x+y) / n
    a. Show that ƒn  0 , but convergence is not uniform.
    b. Show that the convergence ƒn  0 is uniform on bounded sets.

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    https://brainmass.com/math/real-analysis/convergence-sequence-series-functions-15063

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    1. Let ƒn : R2  R be ƒn (x,y) = (x+y) / n
    a. Show that ƒn  0 , but convergence is not uniform.
    Proof. Given , for any we know that there exists when , we have
    .
    So, , i.e., ƒn  0.

    But from the proof, we know that ...

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