MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Define p(x)=e3xcosx.
(a) Derive a Maclaurin polynomial for p that includes all terms up to and including degree 4.
(b) Use the polynomial found in part (a) to approximate p(0.2) to five decimal places.
(c) Write the first term that was omitted when forming the polynomial in part (a). Use this term to obtain an explicit upper bound for the absolute error in the approximation from part (b).