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Taylor & Maclaurin Series Explorer

Build P_n(x) at x = a with symbolic derivatives, fall back to a least-squares fit when rules run out, and compare f and P_n with error summaries, steps, LaTeX, CSV, and shareable links.

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Input parameters

Graph near a

Result

How it's calculated

    FAQ

    How are the coefficients c_k computed?

    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.

    When does the numeric fallback activate?

    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.