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

Question

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The Taylor series for f(x) = 1 + $x e ^ { x }$ at x = 0 is given by:$$f(x) = 1 + x + x ^ { 2 } + \frac { x ^ { 3 } } { 2 ! } + \frac { x ^ { 4 } } { 3 ! } + \cdots$$The first four non-zero terms of this series are 1, x, x^2, and x^3/2!.

Find the First Four Non-Zero Terms of the Taylor Series xexx e ^ { x }xex

Find the First Four Non-Zero Terms of the Taylor Series $x e ^ { x }$