# Taylor Polynomial Calculator

> Calculate the nth-degree Taylor polynomial (or Maclaurin series) of any differentiable function about a center point with step-by-step derivatives.

**URL:** https://www.calculatoranswers.com/taylor-polynomial-calculator
**Category:** Education

## Quick Answer

Calculate the nth-degree Taylor or Maclaurin polynomial approximation of a function about a center point, with step-by-step symbolic derivatives.

## Definition

A Taylor polynomial calculator computes the polynomial approximation of a differentiable function around a specified center point using Taylor's theorem. It calculates successive symbolic derivatives of the function, evaluates them at the center point, divides by the corresponding factorial to find the coefficients, and assembles the polynomial term-by-term. When centered at zero, the result is known as a Maclaurin polynomial.

## How to Use

1. **Enter the function** — Type the function f(x) you wish to approximate (e.g., sin(x), exp(x)).
2. **Set center and degree** — Input the center point (a) and the desired degree of approximation (n).
3. **Evaluate at a point** — Optionally enter an x-value to compare the exact function value with the polynomial approximation.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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