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Let  $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$.

  1. $1 + x + x^{2} + x^{3} $
  2. $1 + x +\frac{3}{2} x^{2} + x^{3} $
  3. $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $
  4. $1 + x +3 x^{2} + 7x^{3} $
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