What is the coefficient of x^4 in the Maclaurin series for e^x?

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Multiple Choice

What is the coefficient of x^4 in the Maclaurin series for e^x?

Explanation:
The exponential function e^x expands as a Maclaurin series with terms x^n over n!, so each power comes with a coefficient 1/n!. For x^4, that coefficient is 1/4! = 1/24. Writing out the start of the series shows the pattern: 1 + x + x^2/2 + x^3/6 + x^4/24 + …; the denominators are 0!, 1!, 2!, 3!, 4!, respectively. The other numbers correspond to different powers (for example, 1/6 is for x^3, 1/120 is for x^5), so the x^4 term has coefficient 1/24.

The exponential function e^x expands as a Maclaurin series with terms x^n over n!, so each power comes with a coefficient 1/n!. For x^4, that coefficient is 1/4! = 1/24. Writing out the start of the series shows the pattern: 1 + x + x^2/2 + x^3/6 + x^4/24 + …; the denominators are 0!, 1!, 2!, 3!, 4!, respectively. The other numbers correspond to different powers (for example, 1/6 is for x^3, 1/120 is for x^5), so the x^4 term has coefficient 1/24.

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