Proof of the smoothness rule by providing details of the proof that t (n) ∈ Ω(f(n))...

Proof of the smoothness rule by providing details of the proof that t (n) ∈ Ω(f(n)) whenever (n) is a smooth function and t(n) is an eventually nondecreasing function such that

t(n) ∈ Θ(f(n) | n is a power of b).

Expert Solution

Smoothness rule can be used to simplify the analysis of efficiency for divide and conquer algorithm.

It provides order of growth for all values of n.

Below is the proof of soothness rule ,which is based on smooth function and eventually non-decreasing function.

venereology answered 1 month ago

proof: L t^(n+1)f(t)=(-1)^(n+1)(d^(n+1)/ds^(n+1))*F(s)

proof: L t^(n+1)*f(t)=(-1)^(n+1)*(d^(n+1)/ds^(n+1))*F(s)

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