Find the terms in the Maclaurin series for the function $f ( x ) = \ln ( 1 + x )$ , as far as the term in $x ^ { 3 }$ .
A) $1 - x + x ^ { 2 } - x ^ { 3 }$
B) $x - x ^ { 2 } + x ^ { 3 }$
C) $1 - x + \frac { 1 } { 2 } x ^ { 2 } - \frac { 1 } { 6 } x ^ { 3 }$
D) $x - \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } x ^ { 3 }$
E) $1 + \frac { 1 } { 2 } x + \frac { 2 } { 3 } x ^ { 2 } + \frac { 5 } { 6 } x ^ { 3 }$
F) $x + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 }$
G) $1 + \frac { x } { 2 } + \frac { 1 } { 6 } x ^ { 2 } + \frac { 1 } { 24 } x ^ { 3 }$
H) $x - \frac { 1 } { 24 } x ^ { 2 } + \frac { 1 } { 120 } x ^ { 3 }$

Question

Find the terms in the Maclaurin series for the function $f ( x ) = \ln ( 1 + x )$ , as far as the term in $x ^ { 3 }$ .
A) $1 - x + x ^ { 2 } - x ^ { 3 }$ 
B) $x - x ^ { 2 } + x ^ { 3 }$ 
C) $1 - x + \frac { 1 } { 2 } x ^ { 2 } - \frac { 1 } { 6 } x ^ { 3 }$ 
D) $x - \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } x ^ { 3 }$ 
E) $1 + \frac { 1 } { 2 } x + \frac { 2 } { 3 } x ^ { 2 } + \frac { 5 } { 6 } x ^ { 3 }$ 
F) $x + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 }$ 
G) $1 + \frac { x } { 2 } + \frac { 1 } { 6 } x ^ { 2 } + \frac { 1 } { 24 } x ^ { 3 }$ 
H) $x - \frac { 1 } { 24 } x ^ { 2 } + \frac { 1 } { 120 } x ^ { 3 }$

Quizplus · Accepted Answer

The Maclaurin series for $f(x) = \ln(1+x)$ is given by $x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \cdots$, which matches option D.

Find the Terms in the Maclaurin Series for the Function f(x)=ln⁡(1+x)f ( x ) = \ln ( 1 + x )f(x)=ln(1+x)

Find the Terms in the Maclaurin Series for the Function $f ( x ) = \ln ( 1 + x )$