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Math & Numbers

Newton-Raphson Root Finder

Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.

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Quick start

Call this tool from your code in three languages.

cURL
curl -X POST 'https://api.elysiatools.com/en/api/tools/newton-raphson-root-finder' \
  -H 'Content-Type: application/json' \
  -d '{"fxExpr":"x^2 - 2","dfxExpr":"","x0":1,"tolerance":1e-10,"maxIter":50,"decimalPlaces":10}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP
POST https://api.elysiatools.com/en/api/tools/newton-raphson-root-finder

Parameters

NameTypeRequiredDescription
fxExprtextYesThe function whose root is sought, in the variable x. Supports + - * / ^, parentheses, and functions like exp, sin, cos, sqrt, ln.
dfxExprtextNoOptional analytic derivative; when blank a central difference (h ≈ 1e-7) is used.
x0numberNoStarting point of the iteration.
tolerancenumberNoConvergence threshold on |f(x)| and on the step size.
maxIternumber

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json
{
  "mcpServers": {
    "elysiatools-newton-raphson-root-finder": {
      "name": "newton-raphson-root-finder",
      "description": "Newton-Raphson iteration for f(x) = 0 with analytic or numeric derivative, full iteration table, and explicit convergence/divergence reporting.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=newton-raphson-root-finder",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list
{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call
{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "newton-raphson-root-finder",
    "arguments": {
  "fxExpr": "x^2 - 2",
  "dfxExpr": "",
  "x0": 1,
  "tolerance": 1e-10,
  "maxIter": 50,
  "decimalPlaces": 10
}
  }
}
Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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No
Hard cap on the number of iterations (2–200).
decimalPlacesnumberNo—

Response format

Text result

JSON
{
  "result": "Processed text content",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}