Address continuity at the boundary of a function's domain

[Alex-Jordan]

Version 3.0 defines continuity at a point for a point inside an open interval in f's domain. Some homework questions ask if a function is continuous at a boundary point of f's domain. Some content needs to be added/edited to address this. May have ripple effects.

Discussion at https://groups.google.com/d/msg/apexactive-calculus-mbx-conversion/g-siVEjzIAc/kFVEuPdbAgAJ with ideas from Greg, David, Carly, and Alex

[CVollet]

Another way I thought that would fix it (but might be a bit more subtle) would be to say that if $f(x)$ is not defined on one side of $c$, then we take $lim{x \to c} f(x)$ to mean the appropriate one sided limit. For example, when evaluating $\lim{x \to 0}\ln(x)$, we would take that to mean $\lim_{x \to 0^+}\ln(x)$.

You could then remove the part about being defined on an open interval containing c and then just consider continuity as being $\lim_{x \to c} f(x)=f(c)$. This would also help with being able to say things like all algebraic functions are continuous on their domains? (Which BTW I would like to add to APEX).