Find the Maclaurin polynomial of degree 4 for the function. $$f ( x ) = e ^ { 9 x }$$
A) $1 + 9 x + \frac { 81 } { 2 } x ^ { 2 } + \frac { 243 } { 2 } x ^ { 3 } + \frac { 2187 } { 8 } x ^ { 4 }$
B) $1 - 9 x + \frac { 27 } { 2 } x ^ { 2 } + \frac { 243 } { 2 } x ^ { 3 } + \frac { 2187 } { 8 } x ^ { 4 }$
C) $1 - 9 x + \frac { 27 } { 2 } x ^ { 2 } - \frac { 243 } { 4 } x ^ { 3 } + \frac { 2187 } { 16 } x ^ { 4 }$
D) $1 + 9 x + \frac { 27 } { 2 } x ^ { 2 } + \frac { 243 } { 4 } x ^ { 3 } + \frac { 2187 } { 16 } x ^ { 4 }$
E) $1 + 9 x + \frac { 81 } { 2 } x ^ { 2 } + \frac { 729 } { 4 } x ^ { 3 } + \frac { 2187 } { 2 } x ^ { 4 }$

Question

Quizplus · Accepted Answer

The Maclaurin series for $e^{9x}$ is given by $1 + 9x + \frac{9^2}{2!}x^2 + \frac{9^3}{3!}x^3 + \frac{9^4}{4!}x^4 + \cdots$, which simplifies to $1 + 9x + \frac{81}{2}x^2 + \frac{243}{2}x^3 + \frac{2187}{8}x^4$.

Find the Maclaurin Polynomial of Degree 4 for the Function f(x)=e9xf ( x ) = e ^ { 9 x }f(x)=e9x

Find the Maclaurin Polynomial of Degree 4 for the Function $f ( x ) = e ^ { 9 x }$