A question about continuity: If a function is defined with the domain [a,b] is this function continuous on the point (a,f(a))? By definition I think it isn't, since there is no left limit and there is one from the right. But, still, if this is true, then it is also not differentiable on it. Therefore it would not be a differentiable equation, because not all of the points of the functions have a defined differentiation. Am I right or is my logic wrong? If it is wrong, why?

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phi · Answer

I think people deal with this by saying let
f(x) be defined on the domain [a,b] and differentiable in the domain (a,b)