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

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

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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