Let . The quadratic Taylor polynomial about is used to estimate . Determine an upper…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

f(x)=\ln(1+x)

. The quadratic Taylor polynomial about

x=0

is used to estimate

f(0.5)

. Determine an upper bound for the magnitude of the error, expressing your answer as an exact decimal or simplified fraction.