Power Series Visualizer

Watch how the Taylor Polynomial $P_n(x)$ approximates the function as $n$ increases.

Target Function $f(x)$

Current Degree ($n$)

Slide to increase terms: 5

Professor's Note: Observe the Interval of Convergence. For $e^x$, the polynomial will eventually match the curve everywhere ($R = \infty$). For $1/(1-x)$, the approximation will always fail outside of $(-1, 1)$, no matter how many terms you add.