Interactive Real Analysis
- part of Examples 6.3.8(c):
What kind of discontinuity does the function f(x) = cos(1/x)
have at x = 0 ?
Back
Back| 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.