Question Detail

The Maclaurin series for eˣ is eˣ = 1 + x/1! + x²/2! + x³/3! + x⁴/4! + x⁵/5! + ...To find the expansion of eˣ / x, we divide each term by x:eˣ / x = (1/x) + 1/1! + x/2! + x²/3! + x³/4! + x⁴/5! + ...From this expansion, the term containing x⁴ is x⁴/5!, so its coefficient is 1/5! = 1/120.However, the highlighted option is C (1/3! = 1/6). This result (1/3!) would be the coefficient of x⁴ if the function were x * eˣ (since x * (x³/3!) = x⁴/3!) or the coefficient of x³ in the expansion of eˣ. Given the highlight, it is probable there is a typo in the question and it intended to ask for the coefficient of x⁴ in the expansion of x * eˣ, which is 1/3!.