Taylor Series Expansion Calculator
Compute the Taylor series expansion of a function up to a specified order around a point.
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isCalculator Editorial Team
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How to use this tool?
How to Use the Taylor Series Expansion Calculator
- Enter the function in the Function f(x) field. Use standard JavaScript math syntax, e.g.,
sin(x),exp(x),x^2,cos(x). - Set the center point a (where the series is expanded). Default is 0.
- Choose the order n (number of terms). Must be a non-negative integer. Higher orders give better accuracy but slower computation.
- Enter the x-value where you want to evaluate the series approximation.
- Click Calculate to see the approximate result and a breakdown of each term.
Tips:
- Use
^for exponentiation (e.g.,x^3). - All numeric inputs accept decimals.
- The result shows the approximated value of f(x) using the Taylor series up to order n.
- The detailed steps show each term’s derivative and contribution to the sum.
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Frequently Asked Questions
A Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point.
You can enter any valid JavaScript expression using x, e.g., sin(x), exp(x), x^2, log(x), etc.
Derivatives are approximated using finite difference formulas for orders up to 4.
