Taylor Series Calculator
Compute the Taylor series expansion of a function around a point up to a specified order. Enter the function, expansion point, and order to get the polynomial approximation.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Taylor Series Calculator
- Enter the function in the "Function f(x)" field using JavaScript syntax. Examples:
Math.sin(x),Math.exp(x),x*x,Math.log(x+1). - Set the expansion point "a" (a number). Default is 0.
- Choose the order "n" (integer from 0 to 10). Higher orders give more terms.
- Click "Calculate".
Output: The polynomial approximation Pn(x) is displayed, along with each derivative value and coefficient used in the expansion.
Tips:
- Use
Math.for functions:Math.sin(x),Math.cos(x),Math.exp(x), etc. - For powers, use
x^2orx*x(JavaScript exponentiation works). - All inputs are required. Order must be between 0 and 10.
- Derivatives are computed numerically (finite differences), so ensure your function is smooth near point a.
Previous Results
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Frequently Asked Questions
A Taylor series is an infinite sum of terms that represent a function as a polynomial around a point. It is used to approximate functions.
Use JavaScript syntax. For example, sin(x) becomes Math.sin(x), exp(x) becomes Math.exp(x), and x^2 becomes x*x or Math.pow(x,2).
The order can be from 0 to 10. Higher orders may be less accurate due to numerical differentiation errors.
