The other thing your missing about limits is functions like tangent where they approach different values on each side of a value.
The reason limits are introduced in calculus is you need a Continuous function for the basic assumptions that allow integration/differentiation to work. Basically, the limits for all points you care about need to agree or you can't take the derivative. In other words f(x) ~= f(x + 1/ infinity) ~= f(x - 1/ infinity) for all x.
Yup. That is continuity and one-sided limit which I would cover in the next article. I actually mentioned that in the comment above.
Other things that you would find in a lot of calculus textbooks but I didn't cover are complex function, the application of calculus (e.g. in Newtonian physics, in optimization problems) and stuff like L'Hospital's Rule, Squeeze theorem, etc. I didn't want to get into too much of the details in this article because my plan was to be concise and get straight to the points. I want to write it in a way that anyone who is new to calculus can grasp the concepts and have an idea of what calculus is about in the shortest time possible. On a side note, most of the functions they will be dealing with are elementary functions, which are continuous over their domains.
The reason limits are introduced in calculus is you need a Continuous function for the basic assumptions that allow integration/differentiation to work. Basically, the limits for all points you care about need to agree or you can't take the derivative. In other words f(x) ~= f(x + 1/ infinity) ~= f(x - 1/ infinity) for all x.
http://en.m.wikipedia.org/wiki/Continuous_function
http://en.m.wikipedia.org/wiki/Fundamental_theorem_of_calcul...
PS: I still like the overall presentation.