curl --request POST \
  --url https://api.iotools.cloud/v1/tool/taylor-series-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "f": "sin(x)",
  "a": "0",
  "n": "5",
  "x0": "1"
}
'

{
  "tool": "taylor-series-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "series": "x - 0.166667·x^3 + 0.00833333·x^5",
    "approxValue": "0.841667",
    "actualValue": "0.841471",
    "error": "0.000195682",
    "steps": "f(x) = sin(x), center a = 0, degree 5\nf(x) = sin(x)  →  value at a = 0, c0 = 0\nf^(1)(x) = cos(x)  →  value at a = 1, c1 = 1\nf^(2)(x) = -sin(x)  →  value at a = 0, c2 = 0\nf^(3)(x) = -cos(x)  →  value at a = -1, c3 = -0.166667\nf^(4)(x) = sin(x)  →  value at a = 0, c4 = 0\nf^(5)(x) = cos(x)  →  value at a = 1, c5 = 0.00833333\nTaylor polynomial: P(x) = x - 0.166667·x^3 + 0.00833333·x^5\nAt x = 1: P(x) ≈ 0.841667, actual f(x) = 0.841471, |error| = 0.000195682"
  },
  "credits_used": 5,
  "credits_remaining": null
}