Find the fourth degree Maclaurin polynomial for the function. $$f ( x ) = \frac { 1 } { x + 4 }$$
A) $\frac { 1 } { 4 } + \frac { 1 } { 16 } x - \frac { 1 } { 64 } x ^ { 2 } + \frac { 1 } { 256 } x ^ { 3 } - \frac { 1 } { 1024 } x ^ { 4 }$
B) $\frac { 1 } { 4 } + \frac { 1 } { 16 } x + \frac { 1 } { 64 } x ^ { 2 } + \frac { 1 } { 256 } x ^ { 3 } + \frac { 1 } { 1024 } x ^ { 4 }$
C) $4 + 16 x + 64 x ^ { 2 } + 256 x ^ { 3 } + 1024 x ^ { 4 }$
D) $4 - 16 x + 64 x ^ { 2 } - 256 x ^ { 3 } + 1024 x ^ { 4 }$
E) $\frac { 1 } { 4 } - \frac { 1 } { 16 } x + \frac { 1 } { 64 } x ^ { 2 } - \frac { 1 } { 256 } x ^ { 3 } + \frac { 1 } { 1024 } x ^ { 4 }$

Question

Quizplus · Accepted Answer

The Maclaurin series for $f(x) = \frac{1}{x+4}$ is derived by expanding the function around $x=0$. The coefficients are determined by the derivatives of $f(x)$ evaluated at $x=0$. The correct polynomial is $\frac{1}{4} - \frac{1}{16}x + \frac{1}{64}x^2 - \frac{1}{256}x^3 + \frac{1}{1024}x^4$.

Find the Fourth Degree Maclaurin Polynomial for the Function f(x)=1x+4f ( x ) = \frac { 1 } { x + 4 }f(x)=x+41​

Find the Fourth Degree Maclaurin Polynomial for the Function $f ( x ) = \frac { 1 } { x + 4 }$