Which statement best explains why the Maclaurin polynomial for contains only even…
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Which statement best explains why the Maclaurin polynomial for cosx contains only even powers of x?
(a) Because cosx is a periodic function, its Maclaurin series repeats every 2π, which forces all odd powers of x to cancel.
(b) Only even–order derivatives are used when building a Maclaurin polynomial, so odd–power terms never appear.
(c) All odd–order derivatives of cosx evaluated at x=0 are equal to 0.
(d) Because cosx is even, it cannot have non-zero derivatives at x=0, so all coefficients of odd powers vanish.