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Mark44

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I would call it an infinite discontinuity. A simpler example than your graph shows is

##f(x) = \begin{cases} 1 & \text{if } x \le 0 \\ \frac 1 x & \text{if } x > 0\end{cases}##

In my example, ##\lim_{x \to 0^-} f(x) = 1##, but ##\lim_{x \to 0^+} f(x) = \infty##

Another site I found would agree with me -- http://www.milefoot.com/math/calculus/limits/Continuity06.htm

I believe that their definition would also include the case where both one-side limits are infinite. If so, their definition would be clearer if it said "when at least one of the one-side limits of the function is infinite."Aninfinite discontinuityexists when one of the one-sided limits of the function is infinite.

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This is what I assumed. When I learned Calculus 1, we classified this as an essential discontinuity, compared to the removable discontinuity. Obviously we went over infinite discontinuities but they typically were asymptoticIf so, their definition would be clearer if it said "when at least one of the one-side limits of the function is infinite."

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