Taylor & Maclaurin Series
Expand functions as Taylor and Maclaurin series, with derivatives evaluated at the centre and the general term shown. Try “Maclaurin series of eˣ up to x⁴”.
Try an example:
How the Taylor & Maclaurin Series works
- Compute the derivatives of f at the centre point (0 for Maclaurin).
- Substitute into f(a) + f′(a)(x − a) + f″(a)/2!·(x − a)² + …
- Simplify the terms and state the radius of convergence.
Frequently asked questions
What is the difference between Taylor and Maclaurin?
A Maclaurin series is a Taylor series centred at x = 0.
What is the Maclaurin series of eˣ?
1 + x + x²/2! + x³/3! + x⁴/4! + …, which converges for every x.
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