This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

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)

Was this topic helpful?