Maclaurin Series Calculator

Maclaurin Series Calculator

Try these examples:



Find Maclaurin Series Expansions Instantly

This calculator computes the Maclaurin series expansion (special case of Taylor series at x=0) for common mathematical functions.

Supported Functions Include:

  • sin(x), cos(x), tan(x)
  • eˣ, aˣ
  • ln(1+x)
  • arcsin(x), arctan(x)
  • (1+x)ᵏ (binomial series)

How to Use:

  1. Type your function (examples below)
  2. Select polynomial degree (3-10 recommended)
  3. Click “Expand”
  4. See the series + convergence radius

Example Inputs:

  • sin(x) → x – x³/6 + x⁵/120 – …
  • e^x → 1 + x + x²/2 + x³/6 + …
  • 1/(1-x) → 1 + x + x² + x³ + … (for |x|<1)

[EMBED CALCULATOR HERE]
(Use WordPress ‘Custom HTML’ block or a calculator plugin shortcode)

Key Features:
✔ No installation required
✔ Handles both elementary and special functions
✔ Shows convergence information
✔ Step-by-step examples included

Common Questions:
Q: What’s the difference between Taylor and Maclaurin series?
A: Maclaurin series are Taylor series centered at x=0.

Q: Why does my series stop at a certain term?
A: Higher-degree terms become negligible for approximation.

Q: Can I use this for multivariable functions?
A: This tool is for single-variable functions only.

Mathematical Note:
All expansions are computed using exact coefficients rather than decimal approximations for maximum precision. The calculator automatically determines the radius of convergence where applicable.