Limits are the underlying tool used in calculus, appearing in the definitions of continuity, derivatives and integrals. Wolfram|Alpha has the power to compute bidirectional limits, one-sided limits and multivariate limits. More information, such as plots and series expansions, is provided to enhance mathematical intuition about a limit.


Compute limits numerically and symbolically.

compute a limit

take the limit of a difference quotient

compute a limit involving abstract functions

More examples

One-sided Limits

Compute one-sided limits from a specified direction.

compute one-sided limits at a point of discontinuity

specify direction of approach

More examples

Limit Representations

Express functions in terms of limits.

find limit representations for a function

More examples