Find the Terms of the Maclaurin Series For $f ( x ) = \frac { 1 } { \sqrt { 1 + 2 x } }$

question 332

Multiple Choice

Find the terms of the Maclaurin series for $f ( x ) = \frac { 1 } { \sqrt { 1 + 2 x } }$ , as far as the term in $x ^ { 3 }$ .

• A) \(1 - x + x ^ { 2 } - x ^ { 3 }\)
• B) \(1 + x - \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } x ^ { 3 }\)
• C) \(1 - x + \frac { 3 } { 2 } x ^ { 2 } - \frac { 5 } { 2 } x ^ { 3 }\)
• D) \(1 + x + 3 x ^ { 2 } + 5 x ^ { 3 }\)
• E) \(1 - x + \frac { 3 } { 2 } x ^ { 2 } - \frac { 7 } { 3 } x ^ { 3 }\)
• F) \(1 + x + \frac { 1 } { 2 } x ^ { 2 } + \frac { 7 } { 3 } x ^ { 3 }\)
• G) \(1 - x + \frac { 5 } { 2 } x ^ { 2 } - \frac { 7 } { 3 } x ^ { 3 }\)
• H) \(1 + x + \frac { 7 } { 2 } x ^ { 2 } + \frac { 11 } { 3 } x ^ { 3 }\)

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