Question Detail
Question
The nth term of the Maclaurin series expansion of cos x is...
Correct Answer
Option D is the correct answer.
Detailed Explanation
The Maclaurin series expansion for cos x is given by:cos x = Σ [fⁿ(0) / n!] xⁿ = 1 - x²/2! + x⁴/4! - x⁶/6! + ...The general term (n-th term, starting from n=0) for this series is (-1)ⁿ x²ⁿ / (2n)!.For n=0: (-1)⁰ x⁰ / 0! = 1For n=1: (-1)¹ x² / 2! = -x²/2!For n=2: (-1)² x⁴ / 4! = x⁴/4!And so on.
Hint
Recall the standard Maclaurin series for cos x and identify the pattern for the general nth term (starting with n=0).