# Wolfram Language™

## Investigate the Limit Behavior of a Univariate Function

Univariate function limits have been improved to include support for undirected limits as well as richer classes of functions for limits that can be computed. In addition, for the first time, there are functions and algorithms that can compute lower and upper limits. See this blog post for more on the new limit functionality.

Investigate the limit behavior of a univariate function near zero.

Visualize near zero.

Show that the undirected limit of at zero does not exist.

Compute the limit of as approaches zero from below.

Compute the lower limit and the upper limit of at zero.

Investigate the limit behavior of a piecewise function.

Visualize near zero.

Compute the limit of as approaches zero from below.

Compute the limit of as approaches zero from above.

The directed limits are different, hence the two-sided limit does not exist.

Here are some limits that can be computed thanks to the newly added algorithms.