Taylor series provide a method to approximate non-polynomial functions near a specific point using infinite sums of polynomial terms constructed from the function's derivatives evaluated at that point. The core theoretical principle relies on matching higher-order derivatives (slope, curvature, rate of change of slope) between the original function and its approximating polynomial by dividing derivative values by corresponding factorials to account for power rule cascading effects. This concept belongs to mathematical analysis within calculus, specifically extending Taylor polynomials into convergent series that translate local derivative information at a single point $a$ into global approximation behavior around that input with defined domains of convergence.
Taylor series provide a method to approximate non-polynomial functions near a specific point using infinite sums of polynomial terms constructed from the function's derivatives evaluated at that poin…