[br]Simple Taylor Polynomial approximation to a function.[br]Enter a function in the green entry box.[br]Move the orange plus symbol on the x-axis for the central point of the expansion.[br]Move the slider to change the order of the approximation (number of terms)[br][br]What happens near the expansion point as the number of terms is increased?[br]What happens far away from the expansion point as the number of terms increases?[br][br]Function suggestions:[br][br][list][*]x^2 + 4x + 1[/*][*]sin(x)[/*][*]exp(x)[/*][*]atan(x)[/*][*]sqrt(x)[/*][*]tan(x)[/*][*]nroot(x,3)[br][/*][/list][br]Take special note of the radius of convergence where the expansion point, [math]a[/math], is close to 0 for the square-root and cube-root functions. Another interesting set of expansion points is points near [math]\left(2k-1\right)\frac{\pi}{2}\text{ for }k\text{ an integer}[/math].