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Math Help - uniformly on compact subsets

  1. #1
    Member thaopanda's Avatar
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    uniformly on compact subsets

    For each n \in N, let F_{n} : (0,1) \rightarrow R be given by F_{n}(x) := x^nsin(\frac{1}{x^{n-1}}). Show that F_{n} \rightarrow F as n \rightarrow \infty uniformly on compact subsets of (0,1) where F \equiv 0.
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  2. #2
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    Let K \subset (0,1) compact then x^n attains a maximum, say at x_0, in K and \vert f(x) \vert \leq \vert x^n \vert \leq \vert x_0 ^n \vert < \epsilon as long as n> \frac{ \ln ( \epsilon )}{ \ln (x_0)}
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