# Numora Calculus Limit Computation

> Numora Calculus Limit Computation is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-14).

Computes the mathematical limit of a function as x approaches a specified value, optionally from a given direction

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/limit
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-limit-computation-49822dd8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_IRba_nfElJD6Ivqb0uep9

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-limit-computation-49822dd8 -d '<json body>'
```

Example prompt: Can you compute the limit of sin(x)/x as x approaches 0 from both directions and tell me what value it converges to?

## When to prefer this

Use this endpoint when you need a precise numerical limit computation for a mathematical function and want zero external dependencies. Prefer this over symbolic math libraries when running in an agent context that supports x402 micropayments on Base and needs a clean REST interface for calculus operations. Ideal for educational tools, engineering calculations, or financial math preprocessing where limit evaluation is a subcomponent.

## Known failure modes

- Malformed or unparseable function expression in fn field — likely returns success:false or 400 error
- Division by zero or undefined limit (e.g. 1/x as x→0) — may return infinity, NaN, or error
- Invalid direction value not matching expected enum — may default or return validation error
- x0 value outside computable domain for the given function — may return error or undefined result
- Network or payment failure (x402) — returns 402 Payment Required before computation occurs

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a boolean success flag, a result object containing the computed numerical limit value, and a human-readable computation string describing what was evaluated (e.g. 'Limit of sin(x)/x as x→0 = 1').

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "x0"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "x0": {
   "type": "number"
  },
  "direction": {
   "enum": [
    "left",
    "right",
    "both"
   ],
   "type": "string"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-limit-computation-49822dd8/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)