Answer
We can see a graph of the function $y = sin(\frac{\pi}{x})$ on the interval $[-1, 1]$
As we zoom toward the origin, we can see that the graph moves up and down between the values of $-1$ and $1$ infinitely many times on shorter and shorter intervals.
Work Step by Step
We can see a graph of the function $y = sin(\frac{\pi}{x})$ on the interval $[-1, 1]$
As we zoom toward the origin, we can see that the graph moves up and down between the values of $-1$ and $1$ infinitely many times on shorter and shorter intervals.
Since the function does not converge on a single point as $x$ approaches 0, $\lim\limits_{x \to 0}sin(\frac{\pi}{x})$ does not exist.
Also, the function is undefined at $x=0$
