Find the First Four Terms in the Maclaurin Series For f

question 157

Multiple Choice

Find the first four terms in the Maclaurin series for $f ( x ) = x e ^ { - x }$ .

• A) \(x - x ^ { 2 } + x ^ { 3 } - x ^ { 4 }\)
• B) \(x - \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 3 } x ^ { 3 } - \frac { 1 } { 4 } x ^ { 4 }\)
• C) \(x - x ^ { 2 } + \frac { 1 } { 2 } x ^ { 3 } - \frac { 1 } { 6 } x ^ { 4 }\)
• D) \(x - 2 x ^ { 2 } + 3 x ^ { 3 } - 4 x ^ { 4 }\)
• E) \(x + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 6 } x ^ { 3 } + \frac { 1 } { 24 } x ^ { 4 }\)
• F) \(x + x ^ { 2 } + \frac { 1 } { 3 } x ^ { 3 } + \frac { 1 } { 8 } x ^ { 4 }\)
• G) \(x + x ^ { 2 } + \frac { 1 } { 2 } x ^ { 3 } + \frac { 1 } { 6 } x ^ { 4 }\)
• H)\(\frac { 1 } { 2 } x - \frac { 1 } { 6 } x ^ { 2 } + \frac { 1 } { 24 } x ^ { 3 } - \frac { 1 } { 120 } x ^ { 4 }\)

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