Taylor, Maclaurin, Fourier Series
Expand a function in a Taylor, Maclaurin or Fourier series with a graph of the approximation.
Which series:
f(x) =
x
Order n =
Taylor and Maclaurin up to order 10, Fourier up to 30 harmonics.
This calculator expands a function in a Maclaurin, Taylor or Fourier series and compares the approximation with the function on a graph.
f(x) = Σ f(k)(a)/k! · (x − a)k
Example. ex ≈ 1 + x + x²/2 + x³/6 + …
Taylor coefficients use exact derivatives, and Fourier coefficients are numerical. The calculator does not study the convergence of the series.
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