curl --request POST \
  --url https://api.iotools.cloud/v1/tool/maclaurin-series-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "func": "exp",
  "nTerms": "6",
  "x0": "1"
}
'

{
  "tool": "maclaurin-series-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "series": "1 + x + 1/2·x^2 + 1/6·x^3 + 1/24·x^4 + 1/120·x^5",
    "coefficients": [
      {
        "n": "0",
        "coefficient-exact-fraction": "1",
        "term": "1"
      },
      {
        "n": "1",
        "coefficient-exact-fraction": "1",
        "term": "x"
      },
      {
        "n": "2",
        "coefficient-exact-fraction": "1/2",
        "term": "1/2·x^2"
      },
      {
        "n": "3",
        "coefficient-exact-fraction": "1/6",
        "term": "1/6·x^3"
      },
      {
        "n": "4",
        "coefficient-exact-fraction": "1/24",
        "term": "1/24·x^4"
      },
      {
        "n": "5",
        "coefficient-exact-fraction": "1/120",
        "term": "1/120·x^5"
      }
    ],
    "radius": "∞ (Converges for every real x.)",
    "approxValue": "2.71667",
    "actualValue": "2.71828",
    "error": "0.00161516",
    "steps": "f(x) = eˣ\nGeneral term: aₙ = xⁿ / n!\nRadius of convergence: ∞  (Converges for every real x.)\nn = 0: coefficient = 1\nn = 1: coefficient = 1\nn = 2: coefficient = 1/2\nn = 3: coefficient = 1/6\nn = 4: coefficient = 1/24\nn = 5: coefficient = 1/120\nMaclaurin series: P(x) = 1 + x + 1/2·x^2 + 1/6·x^3 + 1/24·x^4 + 1/120·x^5\nAt x = 1: P(x) ≈ 2.71667, actual f(x) = 2.71828, |error| = 0.00161516"
  },
  "credits_used": 5,
  "credits_remaining": null
}