Let be the 5th–degree Maclaurin polynomial for

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let T5(x)=x−x33!+x55!T_5(x)=x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!} be the 5th–degree Maclaurin polynomial for sin⁡x\sin x. For what largest symmetric interval about x=0x=0 does T5(x)T_5(x) approximate sin⁡x\sin x with an error less than 10−710^{-7}? (a) ∣x∣≤0.40|x|\le 0.40 (b) ∣x∣≤0.32|x|\le 0.32 (c) ∣x∣≤0.28|x|\le 0.28 (d) ∣x∣≤0.22|x|\le 0.22

Related theory

Browse the problem library