Function reference · Calculus

`limit`

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

Nerdamer first uses direct evaluation where possible, then applies symbolic strategies for supported indeterminate forms and common rational, logarithmic, and exponential growth patterns. One-sided limits are available through the optional direction argument.

When the limit cannot be resolved by the supported methods, the operation remains symbolic.

Examples

These examples use Nerdamer Notation.

Resolve the standard removable singularity at zero.

limit(sin(x)/x,x,0)
// → 1

Compare leading polynomial terms at infinity.

limit((4*x^2-x)/(3*x^2+x),x,Infinity)
// → 4/3

Recognize that linear growth dominates logarithmic growth.

limit(log(x)/x,x,Infinity)
// → 0

Interfaces

The same operation is available through the interfaces below.

Nerdamer Notation · nerdamer API · Direct API

Nerdamer Notation

Use this form inside input passed to nerdamer(...).

limit(expression, variable, value[, direction])

Parameters

expression — Expression whose limit should be evaluated.
variable — Variable approaching the requested value.
value — Value approached by the variable.
direction — Optional one-sided or two-sided limit direction.

`nerdamer.limit`

Call the operation through the default nerdamer import.

nerdamer.limit(expr: ExpressionInput, x: ExpressionInput, val: ExpressionInput, dir: LimitDir, depth: number): Expression

Parameters

Name	Type	Description
`expr`	`ExpressionInput`	Expression whose limit is sought.
`x`	`ExpressionInput`	Independent variable.
`val`	`ExpressionInput`	Finite value or positive/negative infinity to approach.
`dir`	`LimitDir`	Two-sided, left-sided, or right-sided approach.
`depth`	`number`	Internal recursion depth. Defaults to zero.

Returns

Expression — The resolved limit or an unevaluated `limit(...)` Expression.

Browse the nerdamer API →

Direct JavaScript / TypeScript API

Import the operation directly from its package entry point.

import { limit } from 'nerdamer/calculus';

limit(expr: ExpressionInput, x: ExpressionInput, val: ExpressionInput, dir: LimitDir, depth: number): Expression

Parameters

Name	Type	Description
`expr`	`ExpressionInput`	Expression whose limit is sought.
`x`	`ExpressionInput`	Independent variable.
`val`	`ExpressionInput`	Finite value or positive/negative infinity to approach.
`dir`	`LimitDir`	Two-sided, left-sided, or right-sided approach.
`depth`	`number`	Internal recursion depth. Defaults to zero.

Returns

Expression — The resolved limit or an unevaluated `limit(...)` Expression.

Browse nerdamer/calculus →

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