Oscillating Function
Shown is the graph of
This sketch demonstrates why the limit of this function does not exist at 0. The function oscillates between -1 and 1 increasingly rapidly as . In a way you can think of the period of oscillation becoming shorter and shorter. Click the "Zoom In" button to see what happens as we get closer to . The graph becomes so dense it seems to fill the entire space. For this reason, the limit does not exist as there is no single value that the function approaches.
does not exist.