Find the Taylor polynomial of order 3 generated by f at a.
-$$f ( x ) = e ^ { - 6 x } , a = 0$$
A) $P _ { 3 } ( x ) = 1 - 36 x + \frac { 1296 x ^ { 2 } } { 2 } - \frac { 46,656 x ^ { 3 } } { 12 }$
B) $P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 6 }$
C) $P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 3 }$
D) $P _ { 3 } ( x ) = 1 - 6 x + \frac { 36 x ^ { 2 } } { 2 } - \frac { 216 x ^ { 3 } } { 18 }$

Question

Quizplus · Accepted Answer

The Taylor polynomial of order 3 for $f(x) = e^{-6x}$ at $a = 0$ is derived using the derivatives of $f(x)$ evaluated at $x = 0$. The correct polynomial is $1 - 6x + \frac{36x^2}{2} - \frac{216x^3}{6}$.

Find the Taylor Polynomial of Order 3 Generated by F f(x)=e−6x,a=0f ( x ) = e ^ { - 6 x } , a = 0f(x)=e−6x,a=0

Find the Taylor Polynomial of Order 3 Generated by F $f ( x ) = e ^ { - 6 x } , a = 0$