Limit

Computes the limit of an expression as a variable approaches a value.

Independently checkable: an answer for this function is re-derived by a different route and compared - the workbench and the verify tool do this automatically, so a wrong answer is caught rather than trusted. History →

Forms

Limit[f, x -> x *]

Limit[f, {x1 -> , …, xn -> }]

Limit[f, {x1, …, xn} -> {, …, }]

Verified examplesLimit[(1 + 1/n)^n, n -> Infinity] → E Limit[(Sin[x] - x)/x^3, x -> 0] → -1/6 Limit[x/(x + Sqrt[x]), x -> Infinity] → 1 Limit[(3 x^(3/2) + x)/(2 x^(3/2) - 1), x -> Infinity] → 3/2 Limit[(a x + b)/(c x + d), x -> Infinity] → a/c Limit[(x + Sqrt[x])/(x - Sqrt[x]), x -> 0] → -1 Limit[1/x^2, x -> 0] → Infinity Limit[1/x^3, x -> 0] → Indeterminate Limit[1/x, x -> 0, Direction -> "FromAbove"] → InfinityOptions

Assumptions — default $Assumptions
Direction — default Reals
GenerateConditions — default Automatic
Method — default Automatic
PerformanceGoal — default "Quality"

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Used in

Magnitude response of selected windows - 2 steps
Compute a limit - 6 steps
N integrate integration strategies double exponential oscillatory integration - 6 steps
Evaluate infinite sums and products - 7 steps

Topics

Asymptotics - Asymptotic Limit Functions
Calculus - Vector Calculus »
Multiplicative Number Theory - Operations
Series Expansions - General
Symbolic Arrays - Array Limits

Used in

Topics

Related