Limit Demo #4

Here f(x) = sin(π/x).
What happens to f(x) as x approaches 0?
Does the limit of f(x) as x approaches 0 make sense?

Note that even though 0 = f(1) = f(1/2) = f(1/3) = f(1/4) = f(1/5) = .....,
we cannot say that the limit of f(x) at 0 is 0, because in between these numbers the function keeps oscillating wildly - i.e the function does not uniformly approach one number as x approaches 0.
After learning about continuity you will see that this f(x) has a discontinuity at x=0 which is not removeable, infinite or a jump discontinuity.

Jason McCullough, Created with GeoGebra