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.