6.3. Discontinuous Functions

Examples 6.3.8(c):

What kind of discontinuity does the function f(x) = cos(1/x) have at x = 0 ?

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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.

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