Quick Analysis Question

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  1. lilman91's Avatar
    1 11-02-2010  23:29
    • Adored and Respected Member
    • Location: London
    • Posts: 530
    Quick Analysis Question
    I am asked what is the definition of f(x) \rightarrow \infty as x\rightarrow\infty? Would this be right...

    \forall l ,\forall \epsilon, \exists N\in\mathbb{R} such that \forall x\geq N, |f(x)-l|>\epsilon
  2. Zhen Lin's Avatar
    2 11-02-2010  23:50
    • Vengeful, Imperial Overlord of The Student Room
    • Posts: 4,791
    Re: Quick Analysis Question
    No. \forall N > 0 \, \exists M > 0 \, \forall x > M \left[ f(x) > N \right]. What you have there is almost, but not quite, the definition of f(x) \to l as x \to \infty.
  3. Icy_Mikki's Avatar
    3 12-02-2010  00:05
    • Benevolent Member
    • Location: Glos
    Re: Quick Analysis Question
    Yeah, there's a few flaws in your definition- you can just completely ignore the "l" because it's not needed. Also your modulus signs mean that the function could wildly jump between very large positive values and very large negative values, which is not really want you want. "Tending to infinity" generally means only positive infinity.

    The definition Zhen Lin gave you is much better.
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