Find the First Four Nonzero Terms in the Maclaurin Series $e ^ { 4 x } \sqrt { 1 + x }$

question 230

Multiple Choice

Find the first four nonzero terms in the Maclaurin series for the function.
- $e ^ { 4 x } \sqrt { 1 + x }$

• A) \(1 - \frac { 9 } { 2 } x + \frac { 79 } { 8 } x ^ { 2 } - \frac { 683 } { 48 } x ^ { 3 } + \ldots\)
• B) \(1 + \frac { 3 } { 2 } x + \frac { 7 } { 8 } x ^ { 2 } + \frac { 17 } { 48 } x ^ { 3 } + \ldots\)
• C) \(2 + \frac { 9 } { 2 } x + \frac { 63 } { 8 } x ^ { 2 } + \frac { 515 } { 48 } x ^ { 3 } + \ldots\)
• D) \(1 + \frac { 9 } { 2 } x + \frac { 79 } { 8 } x ^ { 2 } + \frac { 683 } { 48 } x ^ { 3 } + \ldots\)

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