Question Detail
Question
The nth term of the Maclaurin series expansion of the function e-3x is...
Correct Answer
Option B is the correct answer.
Detailed Explanation
The Maclaurin series for the exponential function eu is given by:eu = Σn=0∞ un / n! = 1 + u + u2/2! + u3/3! + ...In this problem, we have the function e-3x. So, we replace 'u' with '-3x' in the Maclaurin series for eu:e-3x = Σn=0∞ (-3x)n / n! = 1 + (-3x) + (-3x)2/2! + (-3x)3/3! + ...The nth term of this series (starting from n=0) is (-3x)n / n!.This matches option B.
Hint
Remember the Maclaurin series for ex. Then, substitute the argument of the exponential function into the series form.