A third–degree Maclaurin polynomial is used to approximate
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A third–degree Maclaurin polynomial is used to approximate ln(1.3). Which statement correctly identifies the error‐bound guarantee for this approximation?
(a) The alternating–series error bound cannot be applied because the third‐degree polynomial ends with a positive term.
(b) The Lagrange error bound must be used because all derivatives of ln(1+x) remain finite on [0,0.3].
(c) The alternating–series error bound applies, since for 0<x≤0.3 the terms of the Maclaurin series for ln(1+x) alternate in sign and decrease in magnitude.
(d) No error estimate is needed because ∣0.3∣<1 guarantees that the Maclaurin series converges to ln(1.3).