If the `limit`

command
cannot compute a limit of a function at a particular point and also
cannot prove that the limit is not defined at this point, the command
returns an unresolved limit:

limit(gamma(1/x)*cos(sin(1/x)), x = 0)

If `limit`

can prove that the limit is undefined
at a particular point, then it returns `undefined`

:

limit(exp(x)*cos(1/x), x = 0)

The function `exp(x)*cos(1/x)`

also does not
have one-sided limits at `x = 0`

:

limit(exp(x)*cos(1/x), x = 0, Left); limit(exp(x)*cos(1/x), x = 0, Right)

The plot shows that as `exp(x)*cos(1/x)`

approaches ```
x
= 0
```

, the function oscillates between
and
:

p1 := plot::Function2d(exp(x)*cos(1/x), x = -PI/4..PI/4): p2 := plot::Function2d(exp(x), x = -PI/4..PI/4, Color = RGB::Red): p3 := plot::Function2d(-exp(x), x = -PI/4..PI/4,Color = RGB::Red): plot(p1, p2, p3)

To get the interval of all possible accumulation points of the
function `exp(x)*cos(1/x)`

near the singularity ```
x
= 0
```

, use the option `Intervals`

:

limit(exp(x)*cos(1/x), x = 0, Intervals)

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