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Compute Right and Left Limits

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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