Taylor Expansion Calculator
Compute the Taylor series expansion of a function around a point up to a specified order. Enter a function f(x), the expansion point a, and the order n to get the polynomial approximation.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator computes the Taylor polynomial approximation of a function f(x) around a point a up to a specified order n.
- Enter the function f(x) in standard mathematical notation. Use
^for exponents (e.g.,x^2), and common functions likesin(x),exp(x),cos(x). - Set the expansion point a (a real number, e.g., 0).
- Choose the order n (integer from 0 to 10). Higher orders give more accurate approximations.
- Click Calculate.
Output: The result shows the polynomial Pn(x) with coefficients rounded to 4 decimal places. Terms with negligible coefficients are omitted.
Note: Use * for multiplication only when needed (e.g., 2*x). The calculator uses numerical differentiation, so very high orders may have slight numerical errors.
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Frequently Asked Questions
A Taylor expansion approximates a function as an infinite sum of terms calculated from its derivatives at a single point. It provides a polynomial approximation that becomes more accurate as more terms are added.
You can input standard mathematical functions like sin(x), cos(x), exp(x), log(x), x^2, etc. Use JavaScript syntax (e.g., Math.sin, Math.exp). The calculator evaluates numerically.
The calculator uses numerical differentiation with finite differences to approximate derivatives. This works for most smooth functions but may have rounding errors for very high orders.
