This project investigates the accuracy of Taylor approximation using computational methods. Taylor polynomials of degree 1, 3, and 5 were applied to the functions e^x, sin x, and ln(1+x), all centere..
This project investigates the accuracy of Taylor approximation using computational methods. Taylor polynomials of degree 1, 3, and 5 were applied to the functions e^x, sin x, and ln(1+x), all centered at x=0. Using C++, we generated both numerical data and graphical visualizations to analyze the absolute error∣f(x)−Tn(x)∣. The results show that higher-degree polynomials provide better approximation near the expansion point, while the error increases as the distance from the center grows. In addition, the study reveals that the effectiveness of Taylor approximation depends not only on the polynomial degree but also on the structure of the function. In particular, ln(1+x) exhibits rapid error growth near x=−1, demonstrating the limitations of local approximation.
