We want to evaluate
[tex]\lim _{x\to0}\cos (\frac{1}{x})[/tex]
As 'x' tends to 0, the argument of the cosine function (1/x) tends to infinity.
The range of the cosine function varies between -1 and 1, and we don't know the behavior of infinity on this function. Then, this limit is undefined.
For the plot of this graph, we have
It comes from the value of 1, and starts oscilating near the y-axis increasing its frequency.
