Determine the First Four Non-Zero Terms of the Taylor Series $f ( x ) = x e ^ { ( 1 / 2 ) x }$

True/False

Determine the first four non-zero terms of the Taylor series at x = 0 for $f ( x ) = x e ^ { ( 1 / 2 ) x }$ .
Is x - $\frac { x ^ { 2 } } { 2 }$ + $\frac { x ^ { 3 } } { 2 ^ { 2 } \cdot 2 ! }$ - $\frac { x ^ { 4 } } { 2 ^ { 3 } \cdot 3 ! }$ the correct answer?