Use Theorem 1.13 (Taylor) to find fourth and fifth order polynomials that are approximations to the standard

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Use Theorem 1.13 (Taylor) to find fourth and fifth order polynomials that are approximations to the standard normal distribution function \(\Phi(x)\). Is there a difference between the approximations? What can be said in general about two consecutive even and odd order polynomial approximations of \(\Phi(x)\) ? Prove your conjecture using the results of Theorem 1.14.

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