Let be the second-degree Maclaurin polynomial for

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Calculus · Calculus

Problem

Let

P_{2}(x)=1-\dfrac{x^{2}}{2}

be the second-degree Maclaurin polynomial for

\cos x

. Consider the approximation of

\cos 1

P_{2}(1)

. Which statement about the error is true? (a) The actual error is approximately

-0.0403

, which exceeds in magnitude the theoretical bound of about

0.0417

. (b) Using the next term, the theoretical bound is about

0.0417

, so the actual error equals this bound. (c) The actual error is approximately

0.0403

and is less than the theoretical bound of about

0.1667

. (d) Treating

1

as a degree measure gives an actual error of nearly

0.500

, which is greater than the theoretical bound of

0.1667