To determine the remainder or error term in Taylor's theorem, you use the Lagrange form of the remainder, given by \\( R_n(x) = \\frac{f^{(n+1)}(\\xi)}{(n+1)!} (x-a)^{(n+1)} \\), where \\(\\xi\\) is some point between \\(a\\) and \\(x\\). This formula calculates the error between the Taylor polynomial of degree \\(n\\) and the actual function value.