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  1. MHB Craftsman

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    #1
    If any one value in an expression is approaching 0, does the entire expression equal 0?

    So for example, for the limit $\lim_{{z}\to{q}} z ln(z) f(z)$. If $\lim_{{z}\to{q}}f(z) = 0$, then does $\lim_{{z}\to{q}} z ln(z) f(z)$ equal 0?

  2. Perseverance
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    #2
    Not necessarily. There is (at least) the indeterminate form $0\times\infty$ to consider.

  3. Pessimist Singularitarian
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    #3
    Yes, suppose we have:

    $ \displaystyle L=\lim_{x\to a}\left(f(x)\cdot g(x)\right)$

    Now, in order to write:

    $ \displaystyle L=\lim_{x\to a}\left(f(x)\right)\cdot\lim_{x\to a}\left(g(x)\right)$

    We require that both $ \displaystyle \lim_{x\to a}\left(f(x)\right)$ and $ \displaystyle \lim_{x\to a}\left(g(x)\right)$ exist.

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