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If a limit of a function at a particular value of a variable
does not exist, the `limit`

command
returns `undefined`

. For example, `tan(x)`

does
not have a bidirectional limit at
:

limit(tan(x), x = PI/2)

The plot of this function shows that the function can have two
different limits as the variable `x`

approaches the
value
from
the left and from the right:

plot(tan(x), x = -PI..PI)

To compute one-sided limits of a function, use the options `Left`

and `Right`

:

limit(tan(x), x = PI/2, Left); limit(tan(x), x = PI/2, Right)

If the function has a bidirectional limit at some point, one-sided limits are equal at this point. They also are equal to the bidirectional limit at this point:

Left = limit(abs(tan(x)), x = PI/2, Left); Right = limit(abs(tan(x)), x = PI/2, Right); Bidirectional = limit(abs(tan(x)), x = PI/2)

plot(abs(tan(x)), x = 0..PI)

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