Taylor Polynomial Calculator
Calculate the Taylor polynomial of a function at a given point up to a specified degree. Enter the function, center point, and degree to get the polynomial and evaluate at a point.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Taylor Polynomial Calculator
This calculator computes the Taylor polynomial approximation of a function f(x) around a center a up to a given degree n, and evaluates it at a point x.
- Enter the function f(x) in the first field. Use
xas the variable. Supported operations:sin, cos, exp, log, sqrt, ^(for power). Example:sin(x)orx^2 + exp(x). - Set the center
a(the point around which the polynomial is built). Default is0. - Choose the degree
n(0 to 10). Higher degrees give more accuracy but more terms. - Enter the evaluation point
xwhere you want to approximate the function. - Click Calculate.
Results:
- Result: The approximate value of f(x) using the Taylor polynomial.
- Polynomial: The full expression of the Taylor polynomial.
- Step-by-step: Shows each derivative and coefficient used in the calculation.
Tip: Use ^ for exponents (e.g., x^3). The calculator uses numerical derivatives, so functions must be differentiable at the center.
Previous Results
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Frequently Asked Questions
A Taylor polynomial approximates a function near a point by a polynomial of degree n, using the function's derivatives at that point.
Supported functions include polynomials, sin, cos, exp, log, sqrt, and combinations using +, -, *, /, and ^ for powers.
The calculator uses finite difference formulas with a small step size, providing good accuracy for smooth functions up to degree 6. Higher degrees may have reduced accuracy.
