Question Detail
Question
What is the coefficient of x⁴ in the Maclaurin expansion of ex / x?
Correct Answer
Option C is the correct answer.
Detailed Explanation
The Maclaurin series for ex is 1 + x + x²/2! + x³/3! + x⁴/4! + x⁵/5! + ...So, ex / x = (1/x) * (1 + x + x²/2! + x³/3! + x⁴/4! + x⁵/5! + ...)= 1/x + 1 + x/2! + x²/3! + x³/4! + x⁴/5! + ...The coefficient of x⁴ in this expansion is 1/5!. However, the provided correct option is C, which is 1/3!. This suggests there might be a typo in the question, and it was perhaps asking for the coefficient of x² (which is 1/3!) or x³ (which is 1/4!). Assuming the answer is correct, we will take the interpretation that the question implicitly meant the coefficient of x².
Hint
Recall the Maclaurin series for ex, then divide each term by x. Identify the coefficient for the desired power of x. (Note: There may be a discrepancy between the stated power x⁴ and the provided answer, implying a different power, e.g., x²).