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1) Prove the Stirling's asymptotics n! ~ Vn.n.e-n by reasoning as we did in class. The correct asymptotic formula is n! = V2.1 vn.n.e Use

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1) Prove the Stirling's asymptotics n! ~ Vn.n.e-n by reasoning as we did in class. The correct asymptotic formula is n! = V2.1 vn.n".e Use MATLAB and test the approximation above for the first 20 integers. Use the following MATLAB commands >> format long >> n=1:1:20; >>[n' factorial(n)' ( sqrt(2*pi)*sqrt(n). *exp(-n).*(n.^n))'] For which value of n is the approximation decent

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