AP^® Calculus

Working with a table of parametric velocity values: Given a table of derivative values for one parametric coordinate and an algebraic expression for the other parametric coordinate, students calculate and approximate associate values, interpreting them in the context of the problem. Euler’s Method is one approximation technique used, and the tabular values are also used in creating a Taylor polynomial approximation.

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Taylor polynomials and Maclaurin series: Given the graphs of a function f and its tangent line at x=0, as well as some higher derivative values at 0, this problem asks for terms of Taylor polynomials and Maclaurin series of several functions, as well as approximations using them.

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A power series question: Given the Maclaurin series for a function, one is asked to find the series for a related function, an interval of convergence, and an upper bound on a function value approximation using alternating series bound.

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