Question

The Taylor polynomial of degree 6 is approximated for cos(x). Then the interval in which the function can be accurately calculated using Taylor series (center = 80π)?

(a) [-3π, 3π]

(b) [77.5π, 83.5π]

(c) [-2.5π, 2.5π]

(d) [77π, 83π]

The question was posed to me in final exam.

This interesting question is from Taylor Mclaurin Series in portion Differential Calculus of Engineering Mathematics

Answer 1

Right option is (b) [77.5π, 83.5π]

Explanation: Given the Taylor polynomial has degree 6 we must have 6 roots.

The symmetry point is at the center of the Taylor polynomial (which is 80π).

The cos(x) function has roots at nπ/2

Hence, the interval over which the roots approximately coincide is [77.5π, 83.5π].