Shown is the graph of [math]f(x)=\sin\frac{1}{x}[/math][br][br]This sketch demonstrates why the limit of this function does not exist at 0. The function oscillates between -1 and 1 increasingly rapidly as [math]x\rightarrow0[/math]. 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 [math]x=0[/math]. 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.[br][br][center][math]\lim_{x\to0}f\left(x\right)[/math] does not exist.[/center]