Find the first four nonzero terms in the Maclaurin series for the function.
-$e ^ { - 6 x }$
A) $1 - 6 x + \frac { 36 x ^ { 2 } } { 2 ! } + \frac { - 216 x ^ { 3 } } { 3 ! } + \ldots$
B) $x - 6 x + \frac { - 6 x ^ { 2 } } { 2 ! } + \frac { - 6 x ^ { 3 } } { 3 ! } + \ldots$
C) $1 - 6 x + \frac { - 6 x ^ { 2 } } { 2 ! } + \frac { - 6 x ^ { 3 } } { 3 ! } + \ldots$
D) $- 6 x - 216 x ^ { 3 } - 7776 x ^ { 5 } - 279,936 x ^ { 7 } + \ldots$

Question

Quizplus · Accepted Answer

The Maclaurin series for $e^{ax}$ is $1 + ax + \frac{(ax)^2}{2!} + \frac{(ax)^3}{3!} + \ldots$. Substituting $a = -6$, we get $1 - 6x + \frac{(-6x)^2}{2!} + \frac{(-6x)^3}{3!} + \ldots$, which simplifies to $1 - 6x + \frac{36x^2}{2!} + \frac{-216x^3}{3!} + \ldots$.

Find the First Four Nonzero Terms in the Maclaurin Series e−6xe ^ { - 6 x }e−6x

Find the First Four Nonzero Terms in the Maclaurin Series $e ^ { - 6 x }$