Define:
where denotes the greatest integer function, or floor function. Sketch the graph of
for
and
. Evaluate
Is it possible to define in a way that makes
continuous at 0.
First, we sketch the graph of on the requested intervals.
As ,
takes on arbitrarily large positive values.
As ,
takes on arbitrarily large negative values.
There is no way to define to make
continuous at 0.