Show that f(n) is Θ(g(n)) for the correct function g(n). Prove your result using the definitions from class, including an explicit value for k justifying your statement is true for all n ≥ k. f(n) = n 1.5 log(2n) + n 2 log(n 2 ) + √ n

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Q: Given T1(n)=O(f(n)) and T2(n)=C(g(n)). Find T1(n).T2(n)

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Q: how many months

A: Given:

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A: Solving:

Q: If g(n) = O(f(n)),by using the definition of Big-Θ, prove that f(n) + g(n) = Θ(f(n)).

A: Hence proved. Show explanation below.

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.