ASYMPTOTIC NOTATION doubt


#1


#2

option d is correct
f(n) is O(g(n))


#3

f(n) = 3n^sqrt(n) = theta(n^sqrt(n))
g(n) = theta(2^(sqrt(n)log(n)))
h(n) = n! = O(n^n)
so
h(n) > ( f(n) , g(n) )
f(n) = g(n)
n^sqrt(n) = 2^(sqrt(n)log(n))
…apply log base2 both sides
sqrt(n)log(n) = sqrt(n)log(n).

f(n),g(n) both are asymptotically equal.
option D is true.