calculate_limit
Calculate the limit of a mathematical expression as a variable approaches a specified point, with support for one-sided and two-sided limits to analyze steady-state, boundary, and asymptotic behavior.
Instructions
Calculate the limit of an expression.
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🆕 NOT AVAILABLE IN SYMPY-MCP!
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Use cases:
- Steady-state analysis (t → ∞)
- Boundary behavior (x → 0)
- Asymptotic behavior
- L'Hôpital's rule situations
Args:
expression: The expression to take limit of
variable: The variable approaching the point
point: The point to approach (can be "oo", "-oo", "0", "1", etc.)
direction: Direction of approach
- "+-" or "": Two-sided (default)
- "+": From the right (x → 0⁺)
- "-": From the left (x → 0⁻)
Returns:
Limit result with LaTeX
Examples:
# Steady-state concentration
calculate_limit("C0 * exp(-k*t)", "t", "oo")
→ {"result": "0", "latex": "0"}
# Indeterminate form (0/0)
calculate_limit("sin(x)/x", "x", "0")
→ {"result": "1", "latex": "1"}
# One-sided limit
calculate_limit("1/x", "x", "0", direction="+")
→ {"result": "oo", "latex": "\infty"}
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| point | Yes | ||
| variable | Yes | ||
| direction | No | +- | |
| expression | Yes |
Output Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||