6.3. Discontinuous Functions
What kind of discontinuity does the function f(x) = cos(1/x) have at x = 0 ?
|f(x) = cos(1/x)|
By looking at sequences involving integer multiples of or / 2 we can see that the limit of f(x) as x approaches zero from the right and from the left both do not exist. Hence, f(x) has an essential discontinuity at x = 0.