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show that the function f(n) = |n^2 sin n| is in neither O(n) nor (n) Show...

show that the function f(n) = |n^2 sin n| is in neither O(n) nor \Omega (n)

Show that the function f(n) = |n^2 sin n| is in neither O(n) nor \Omega(n)
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Answer:

f(n) = | n^2sinn |

Let we assume that f(n) = n^2 for even and f(n) = 0 for odd

Now , say f(n) = O(n) , it will be less than c *n * c*n , where c is constant and c > 0 and similarly f(n) = Omega(n) is not possible also because it will be less than c*n . So both the cases are not possible.

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