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, supremum and infimum limits, discrete limits and multivariable 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:
Explore limits of expressions in two or more dimensions.
Compute a multidimensional limit:
Find the value of a nested limit:
Evaluate limiting behavior of sequences.
Compute discrete limits:
Compute discrete supremum or infimum limits:
Compute one-sided limits from a specified direction.
Compute one-sided limits at a point of discontinuity:
Specify the direction of approach:
Express functions in terms of limits.
Find limit representations for a function:
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Find the limiting upper and lower bounds of functions.