Which of the following is the coefficient of x2 in the expansion of the Maclaurin series for f(x) = e5x?

Question

 

Which of the following is the coefficient of x² in the expansion of the Maclaurin series for f(x) = e^5x?

	25

Answer 1

e^x = 1 + x/1! + x²/2! + ...

e^{5x = 1 + 5x + 25x^2/2 + ...}

^{So we have coefficient of x^2 is 25/2}