Question

Question #c66df

Answer 1

A function, `f(x)` is discontinuous at a point `x=hatx`
if

`f(hatx)` does not exist; but `f(hatx+-epsilon)` does exist for arbitrarily small values of `epsilon >0`

or

`lim_(hrarr0) f(hatx+-h) != f(hatx)`

Some simple examples:
`f(x) = 1/x` is discontinuous at `x=0` since the function is not defined at the at point

`f(x) = "Integer"(x)` is discontinuous since (for example)
`f(3-h) = 2 " for all " h>0`
but
`f(3) = 3`