Which of the following is the coefficient of x3 in the Maclaurin series for f(x) = e-x

Question

Which of the following is the coefficient of x³ in the Maclaurin series for f(x) = e^-x 

A
B
C
D	1

Answer 1

In general the n-th term of the McLaurin series for f is

f⁽ⁿ⁾xⁿ / n!

where the derivative is evaluated at x=0.

f(x) = e^-x

f'(x) = -e^-x

f"(x) = e^-x

f(3)(x) -e^-x

Therefore the coefficient of x³ is

-e^-0/3! = -1/6