# Documentation

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## If Limits Do Not Exist

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

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)`