Track the wild convergence of Newton's Method. Place an initial guess x0 and watch iterative tangent lines slice toward the true polynomial root. Place the guess at a local minimum (f'(x)=0) to provoke absolute visual divergence.
Interactively approximate definite integrals using left, right, and midpoint Riemann sums. Adjust the number of rectangles to watch the approximation converge to the true area under the curve.