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math: add division derived important thing limit

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eggy 2020-10-14 12:00:25 -04:00
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@ -367,6 +367,9 @@ Substituting a variable in for the variable to be solved and then solving in ter
= \frac{1}{16} = \frac{1}{16}
$$ $$
!!! note
If $lim_{x \to a} \frac{f(x)}{g(x)}$ exists, $x - a$ *must* be a factor of both $f(x)$ and $g(x)$. Therefore, $f(a) = 0$ and $g(a) = 0$.
### Limits and continuity ### Limits and continuity
If a function has holes or gaps or jumps (i.e., if it cannot be drawn with a writing utensil held down all the time), it is **discontinuous**. Otherwise, it is a **continuous** function. A function discontinuous at $x=a$ is "discontinuous at $a$", where $a$ is the "point of discontinuity". If a function has holes or gaps or jumps (i.e., if it cannot be drawn with a writing utensil held down all the time), it is **discontinuous**. Otherwise, it is a **continuous** function. A function discontinuous at $x=a$ is "discontinuous at $a$", where $a$ is the "point of discontinuity".