The function is approximated at by its fourth‐degree Maclaurin polynomial
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The function f(x)=e−x2 is approximated at x=0.2 by its fourth‐degree Maclaurin polynomial. Which statement correctly describes the error‐bound options available for this approximation?
(a) Only the Lagrange error bound can be used, because the series does not alternate in sign.
(b) Both the Lagrange and alternating–series error bounds can be used, since the derivatives are bounded on [0,0.2].
(c) Only the alternating–series error bound can be used, because the terms decrease to 0.
(d) Neither error bound can be applied, because the radius of convergence of the series is unknown.