Examples for


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:

Limit Representations

Express functions in terms of limits.

Find limit representations for a function:

One-sided Limits

Compute one-sided limits from a specified direction.

Compute one-sided limits at a point of discontinuity:

Specify the direction of approach: