Example 4.3.2
Let

. This function has no limit at 0:
- Take
. Then
and
.
- Take
. Then
and
.
As the limit of a function is unique ( v.s. Prop.
1.2 ),
it cannot be equal both to 0 and to 1, therefore

has no limit at 0 (in Figure
8 we show two drawings of the graph of

, zooming to show how ``messy'' looks the graph for

close to 0).
Figure 8:
![\begin{figure}\centering
\mbox{
\subfigure[]{\epsfig{file=sin1_x-01.eps,height=...
...uad\qquad
\subfigure[]{\epsfig{file=sin1_x-02.eps,height=4cm}}
}\end{figure}](img578.png) |