1. Using the definition of big-O, show that 2n element of O(6*n^2)
2. Using the definition of big-O, show that 6n^2 not element of O(2n)
3. Show that 6n^2 element of THETA(n^2)
Do not use limits, just the big O and big Theta definitions.
Please show the definitions.© BrainMass Inc. brainmass.com October 10, 2019, 3:32 am ad1c9bdddf
Big-O definition: We say f(n) = O(g(n)), if we can find a sufficiently large constant M>0, such that for sufficiently large n, we have f(n) <= M*g(n).
1. Let M = 1. For all n>=1, we have 6n^2 - 2n = n(6n - 2) >= 1*(6*1 - 2) = 4 > 0. Thus 2n <= ...
Big O and big Theta definitions are illustrated.