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Thread: convergence

  1. #1
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    convergence

    Let
    f, g, h : A$\displaystyle \subseteq$R$\displaystyle \rightarrow$R be functions such that g(x)$\displaystyle \leq$f(x)$\displaystyle \leq$h(x) for all x$\displaystyle \in$A. Let p be an accumulation point of A: Prove that If limx$\displaystyle \rightarrow$p g(x) =limx$\displaystyle \rightarrow$p h(x) = l; where l $\displaystyle \in$R: Then limx$\displaystyle \rightarrow$p f(x) =l.

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  2. #2
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    Why not learn to post in symbols? You can use LaTeX tags.
    I do not think that any of us can read that garbage.
    If you are really a serious question the learn to post it is proper notation.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by janae77 View Post
    Let
    f, g, h : A$\displaystyle \subseteq$R$\displaystyle \rightarrow$R be functions such that g(x)$\displaystyle \leq$f(x)$\displaystyle \leq$h(x) for all x$\displaystyle \in$A. Let p be an accumulation point of A: Prove that If limx$\displaystyle \rightarrow$p g(x) =limx$\displaystyle \rightarrow$p h(x) = l; where l $\displaystyle \in$R: Then limx$\displaystyle \rightarrow$p f(x) =l.

    Quote Originally Posted by Plato View Post
    Why not learn to post in symbols? You can use LaTeX tags.
    I do not think that any of us can read that garbage.
    If you are really a serious question the learn to post it is proper notation.
    All she stated is the squeeze theorem.
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