Use the formula for the Taylor polynomial approximation to the function $g(x)=e^{x}$ about $x_{0}=0$ to construct a polynomial approximation of degree 6 for $f(x)=e^{x^{2}}$ .Use the first four nonzero terms of this approximation to estimate the value of $e^{(0.3)^{2}}$ .Give your answer to 5 decimal places.

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The Answer of Use the formula for the Taylor polynomial approximation to the function $g(x)=e^{x}$ about $x_{0}=0$ to construct a polynomial approximation of degree 6 for $f(x)=e^{x^{2}}$ .Use the first four nonzero terms of this approximation to estimate the value of $e^{(0.3)^{2}}$ .Give your answer to 5 decimal places.

Use the Formula for the Taylor Polynomial Approximation to the Function