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

question 41

Multiple Choice

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) \(x - \frac { 1 } { 24 } x ^ { 2 } + \frac { 1 } { 120 } x ^ { 3 }\)

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