Taylor & Maclaurin Series Explorer

We evaluate each derivative f^{(k)}(a) symbolically and report c_k = f^{(k)}(a)/k!. If symbolic rules fail, the tool switches to a least-squares fit around a and reports approximate values instead.

Fallback triggers when derivatives are undefined or unstable (for example abs at 0 or logarithms of negative numbers). The polynomial is then estimated from nearby samples, and the step log highlights the switch.

Enter a function and choose an expansion point. Then start with a low order such as 3 or 5 so you can compare the polynomial against the original function before increasing the degree.

The calculator keeps internal precision and rounds only for display. Agreement depends on the expansion point, the truncation order, and how far x is from the center of the series.

Different tools may expand around a different center, stop at a different order, or switch between symbolic and numeric derivative handling. Match those assumptions before comparing coefficients or plots.