Consider the function
We can perform long division to obtain
but this is not equal to
The reason is that if
becomes
which is not defined, but
We can sketch the graphs ofand
This is done below.
The graph of
is not defined at
and this is indicated by an empty circle at the point on the graph where
We can however define the limit of the functionas
tends to 1.
The graphitself is not defined atbut it does not need to be. As long astends to some limit, we can define the limit ofatby considering