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**Is this function continuous? Edit: Fixed - function should load now**

[tex]

f\left( x \right) = e^{\left[ x \right]}

[/tex]

Where the argument of the exponential is the greatest integer less than or equal to x.

For the function to be continuous at a point x = a we need [tex]\mathop {\lim }\limits_{x \to a} f(x) = f(a)[/tex]. For this particular function, f(x) at x = a is just f(a) where a is an integer? But what about the limit? As far as I can see this function is like a sequence so that if I looked at the graph I would just see some dots. Is it possible to take any limits with this function? For example, can I actually take lim(x->3)f(x) and get a finite value? Further, could I take lim(x->2.5)f(x) for this particular function. Any help appreciated.

Edit: Fixed f(x)...it should look right now.

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