Watch polynomial approximations converge to transcendental functions — term by term
A Taylor series expands a smooth function as an infinite sum of polynomials: f(x) = Σ f⁽ⁿ⁾(a)/n! · (x−a)ⁿ. Convergence depends on the radius of convergence — entire for sin, cos, eˣ; only |x|<1 for ln(1+x).