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nerdamer.limit
nerdamer.limit(expr: ExpressionInput, x: ExpressionInput, val: ExpressionInput, dir: LimitDir, depth: number): ExpressionComputes a symbolic finite or infinite limit. The implementation combines direct substitution, side-aware pole analysis, simplification, bounded L'Hopital recursion, indeterminate-form rewrites, composition rules, dominant-growth analysis at infinity, and a table of known limits.
'left' and 'right' request one-sided limits; 'both' is the default
two-sided direction. Direction is significant for poles and piecewise
functions such as sign. When the available strategies cannot establish a
result, the function returns an unevaluated limit(expr, x, val, dir)
Expression. That form can therefore mean unsupported, undefined, or
non-existent; it is not a proof that a limit exists.
The implementation primarily reasons about real signs and real growth.
Oscillatory and branch-sensitive complex cases are intentionally left
symbolic unless a specific rule resolves them. Decimal input is preserved in
the formatting of a resolved result.
depth is an internal recursion counter and should normally be omitted.
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.