Determine how large a problem can be solved in 1 second, Computer Engineering

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Determine how large a problem can be solved in 1 second

(A) Prove

3ⁿ = O(n!)

(B) In each of the following cases, determine how large a problem can be solved in 1 second using an algorithm that requires f(n) operations, where each operation is carried out in 10^-9 seconds:

i. f(n) = vn

ii. f(n) = n³

iii. f(n) = 5n

(C)If you have time could you please give your very simpliest proof that the halting problem has no solutions. you can only find complicated ones online!

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Computer Engineering: Determine how large a problem can be solved in 1 second

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