Taylor Series Calculator
Generate Taylor and Maclaurin series expansions. Visualize polynomial approximations of functions.

Use 0 for Maclaurin series

Function vs Polynomial Approximation
sin(x)Taylor Polynomial
Approximation Result
0.84147101
Taylor Approximation
0.84147098
Actual sin(x)
Absolute Error
2e-8
Percent Error
0%
Series Expression
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + x^9/9! + ...

General term: (-1)^n * x^(2n+1) / (2n+1)!

Term Values at x = 1
nCoefficientPowerTerm Value
01.00e+011
1-1.67e-13-0.16666667
28.33e-350.00833333
3-1.98e-47-0.00019841
42.76e-690.00000276

Common Taylor/Maclaurin Series

e^x = 1 + x + x²/2! + x³/3! + ...
sin(x) = x - x³/3! + x⁵/5! - ...
cos(x) = 1 - x²/2! + x⁴/4! - ...
ln(1+x) = x - x²/2 + x³/3 - ...
1/(1-x) = 1 + x + x² + x³ + ...

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