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math: clarify why f(x)=g(x)

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eggy 2020-10-19 15:23:36 -04:00
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@ -371,7 +371,7 @@ Substituting a variable in for the variable to be solved and then solving in ter
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!!! 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 $g(a) = 0$.
If $\lim_{x \to a} \frac{f(x)}{g(x)}$ exists and direct substitution is not possible, $x - a$ *must* be a factor of both $f(x)$ and $g(x)$ so that the discontinuity can be removed. Therefore, $f(a) = 0$ and $g(a) = 0$.
### Limits and continuity