(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is this function continuous?

**Physics Forums | Science Articles, Homework Help, Discussion**