including the integral test and its use in testing the convergence of p-series; and e) ratio test for convergence and divergence. * * For those students who are enrolled in AP Calculus BC. APC.17 The student will define, restate, and apply Taylor series. This will include a) Taylor polynomial approximations with graphical demonstration of convergence; b) Maclaurin series and the general Taylor series centered at x = a; c) Maclaurin series for the functions ex , sin x, cos x, and 1/(1 – x); d) formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series; e) functions defined by power series; f) radius and interval of convergence of power series; and g) Lagrange error bound of a Taylor polynomial. * * For those students who are enrolled in AP Calculus BC.
including the integral test and its use in testing the convergence of p-series; and e) ratio test for convergence and divergence. * * For those students who are enrolled in AP Calculus BC. APC.17 The student will define, restate, and apply Taylor series. This will include a) Taylor polynomial approximations with graphical demonstration of convergence; b) Maclaurin series and the general Taylor series centered at x = a; c) Maclaurin series for the functions ex , sin x, cos x, and 1/(1 – x); d) formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series; e) functions defined by power series; f) radius and interval of convergence of power series; and g) Lagrange error bound of a Taylor polynomial. * * For those students who are enrolled in AP Calculus BC.
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