# Taylor Series Calculator API

> For the complete documentation index, see [llms.txt](/llms.txt).

Taylor series expansion of common functions about any center a, using exact shifted-derivative formulas, with optional evaluation.

Use this endpoint to add the tool to your app, site, workflow, or agent without rebuilding formulas, validation, examples, and docs.

- Slug: `taylor-series-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 65536 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/taylor-series-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/taylor-series-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `func` | `str` | no | exp | sin | cos | sinh | cosh | ln | reciprocal | sqrt Choices: exp, sin, cos, sinh, cosh, ln, reciprocal, sqrt |
| `center` | `float` | no | Expansion point a (must be > 0 for ln/sqrt, nonzero for reciprocal) |
| `n_terms` | `int` | no |  |
| `eval_x` | `float | None` | no |  |

## Example request

```json
{
  "func": "sin",
  "center": 1.0,
  "n_terms": 6,
  "eval_x": 1.2
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/taylor-series-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"func":"sin","center":1.0,"n_terms":6,"eval_x":1.2}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "taylor-series-calculator",
  "tool_version": "2026-04-22",
  "credits_used": 1,
  "result": {}
}
```

## Errors

Errors are RFC 7807 `application/problem+json`. Branch on `code`, not `title`.

## MCP

Agents can discover and call this tool through `https://api.miniwebtool.com/mcp` or `https://api.miniwebtool.com/v1/mcp` using MCP `tools/list` and `tools/call`.

## Frequently asked

### What does the Taylor Series Calculator API do?

Taylor series expansion of common functions about any center a, using exact shifted-derivative formulas, with optional evaluation. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.

### How much does one call cost?

1 credit per successful call. Failed calls do not bill.

### What parameters are required?

Required fields: (none). Full schema at `https://api.miniwebtool.com/v1/openapi.json`.

### Is this deterministic?

Yes. Same input, same output. Tool version: 2026-04-22.