Limits and Series
limits_seriesCompute limits and series expansions of mathematical expressions with support for one-sided limits, infinite limits, and Taylor/Maclaurin series expansions. Specify expression, variable, point, operation, series order, and direction.
Instructions
Compute limits and series expansions using SymPy.
Examples:
CLASSIC LIMIT: expression="sin(x)/x", variable="x", point=0, operation="limit" Result: limit=1
LIMIT AT INFINITY: expression="1/x", variable="x", point="oo", operation="limit" Result: limit=0
ONE-SIDED LIMIT: expression="1/x", variable="x", point=0, operation="limit", direction="+" Result: limit=+∞ (approaching from right)
REMOVABLE DISCONTINUITY: expression="(x^2-1)/(x-1)", variable="x", point=1, operation="limit" Result: limit=2
MACLAURIN SERIES (at 0): expression="exp(x)", variable="x", point=0, operation="series", order=4 Result: "1 + x + x^2/2 + x^3/6 + O(x^4)"
TAYLOR SERIES (at point): expression="sin(x)", variable="x", point=3.14159, operation="series", order=4 Result: expansion around π
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| context | No | Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification. | |
| output_mode | No | Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details. | full |
| expression | Yes | Mathematical expression to analyse (e.g., 'sin(x)/x', 'exp(x)') | |
| variable | Yes | Variable for limit/expansion (e.g., 'x', 't') | |
| point | Yes | Point for limit/expansion (number, 'oo' for infinity, '-oo' for -infinity) | |
| operation | No | Operation: limit=compute limit, series=Taylor/Maclaurin expansion | limit |
| order | No | Series expansion order (number of terms) | |
| direction | No | Limit direction: +=from right, -=from left, +-=both sides | +- |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| result | Yes |