Given a function f(x) and a point 'a', the n-th order Taylor series of f(x) around 'a' is defined as: T_n(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2 /...

Taylor series are used to approximate functions, analyze behavior, solve problems in physics/engineering, perform efficient computations, and expan...

The limitations of Taylor's series include poor convergence for some functions, accuracy dependent on number of terms and proximity to expansion po...