Question Detail
Question
The 8th term of the Maclaurin series of eˣ.
Correct Answer
Option A is the correct answer.
Detailed Explanation
The Maclaurin series for eˣ is given by the formula: eˣ = Σ [fⁿ(0) / n!] * xⁿ. For eˣ, all derivatives at x=0 are 1. So, eˣ = Σ [1 / n!] * xⁿ = 1 + x/1! + x²/2! + x³/3! + ... + xⁿ/n! + ...The term corresponding to xⁿ is xⁿ/n!. If the '8th term' refers to the term containing x⁸, then n=8, and the term is x⁸/8!.
Hint
Recall the general formula for the Maclaurin series of a function f(x) and specifically for eˣ. The Maclaurin series for eˣ is 1 + x/1! + x²/2! + x³/3! + ...