# with floor functions

• Jun 8th 2008, 06:50 AM
tombrownington
with floor functions
Show that the function:

$f(x) = \frac{x - \lfloor x \rfloor}{x + \lfloor x \rfloor +1}$ is:

a) always upper-semicontinuous;
b) has a derivative for all x belonging to N (natural numbers).

Thanks in advance for the help all you mathwizzes out there.
• Jun 8th 2008, 09:43 AM
tombrownington
sorry folks I made a terrible typing mistake.

the question's part b should be:

b) for all x not belonging to Z.
And now that I come to think of it the solution is rather simple, so I take back the question to this part.

However part a) is still puzzling me (and I'm sure there are no typos here) Any ideas?