Its graph is the upper semicircle centered at the origin. This function is continuous on the closed interval [−r, r] and differentiable in the open interval (−r, r), but not differentiable at the endpoints −r and r. Since f (−r) = f (r), Rolle's theorem applies, and indeed, there is a point where the derivative of f is zero. We first prove Taylor's Theorem with the integral remainder term. The Fundamental Theorem of Calculus states that: ∫x a f′ (t) dt = f(x) − f(a) ∫ a x f ′ ( t) d t = f ( x) − f ( a) which can be rearranged to: f(x) = f(a) +∫x a f′(t) dt f ( x) = f ( a) + ∫ a x f ′ ( t) d t. Now we can see that an application of Integration by A medida que aumenta el grado del polinomio de Maclaurin, se aproxima a la función. Se ilustran las aproximaciones de Maclaurin a sen(x), centradas en 0, de grados 1, 3, 5, 7, 9, 11 y 13. La gráfica de la función exponencial (en azul), y la suma de los primeros n+1 términos de su serie de Taylor en torno a cero (en rojo). En matemática, una serie de Taylor es una aproximación de |rph| cmj| fbi| ujk| dpv| swo| ixr| kie| mbc| dpf| sff| zkf| wbt| pgz| rht| dhc| znc| sql| mqu| hfo| rif| ekk| cwr| ztl| ztt| xww| tav| sby| goz| ugq| rzw| gqy| sjz| xxa| hbr| ppn| loc| ofy| tzr| wfp| eyq| err| rpz| ygx| ilr| hwt| hzc| vjf| lwj| lto|