Find the Maclaurin polynomial of degree 3 for f(x) = xcos(x)

Question

Find the Maclaurin polynomial of degree 3 for f(x) = xcos(x)

A	x - x3
B
C
D

Answer 1

Solution.

f(x) = x cos x

= x (1 − x²/2! + x⁴/4! ···)

= x − x³/2 + x⁵/24 ···

So the Maclaurin polynomial of degree 3 for f(x) is x − x³/2.

Answer: B