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math: clarify discontinuity

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eggy 2020-10-05 20:54:45 -04:00
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@ -383,7 +383,7 @@ $$\lim_{x \to a^-} f(x) ≠ \lim_{x \to a^+} f(x)$$
An **infinite discontinuity** occurs when both one-sided limits are infinite. It is common when functions have vertical asymptotes. It can be expressed as when An **infinite discontinuity** occurs when both one-sided limits are infinite. It is common when functions have vertical asymptotes. It can be expressed as when
$$\lim_{x \to a} f(x) = ± ∞$$ $$\lim_{x \to a} f(x) = ± ∞$$
Therefore, a function is only continuous if all of the following are true: Therefore, a function is only continuous at $a$ if all of the following are true:
- $f(a)$ exists - $f(a)$ exists
- $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$ - $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x)$