Let \(f\left( x \right) = \;{e^{x + {x^2}}}\) 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 + x + \(\frac{3}{2}\) x2 + x3

1 + x + \(\frac{3}{2}\) x2 + \(\frac{7}{6}\) x3

Let \(f\left( x \right) = \;{e^{x + {x^2}}}\) for real x. From among

1.	Let \(f\left( x \right) = \;{e^{x + {x^2}}}\) 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.
A.	1 + x + x2 + x3
B.	1 + x + \(\frac{3}{2}\) x2 + x3
C.	1 + x + \(\frac{3}{2}\) x2 + \(\frac{7}{6}\) x3
D.	1 + x + 3x2 + 7x3
Answer» D. 1 + x + 3x2 + 7x3

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Let \(f\left( x \right) = \;{e^{x + {x^2}}}\) 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.

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