Question

Let τ(x) be the taylor Series centered at 0. Let the Taylor series be approximated to fifth degree polynomial only, which is the interval over which f(x) = sin(x) can be accurately calculated.

(a) (-∞, ∞)

(b) [-2π, 2π]

(c) [-4π, 0]

(d) It is accurate for any interval

This question was addressed to me in an interview for job.

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

Answer 1

The correct choice is (b) [-2π, 2π]

The best explanation: The function sin(x) is known to have a root at every x = nπ The center is at 0. The Taylor polynomial also has five roots, spread symmetrically around the origin. After the polynomial crosses the roots it goes outward to infinity, But the sine function is bounded.

Hence, the interval where the roots of sine and polynomial approximately coincide is [-2π, 2π].