# Math Help - Discrete Math Problem

1. ## Discrete Math Problem

For each of the following two functions f(n), determine a simple function g(n)
such that f(n) = Θ(g(n))

• f(n)=(n5 −13n4 +n2logn)(logn+25).

• f(n)=(2n +n2)(n3 +3n).

More problems after this is solved.

2. One man's simple function is another man's nightmare

If you have a sum $h_1(n)+h_2(n)$ where $h_1(n)$ dominates, i.e., $h_2(n)=O(h_1(n))$, then $h_1(n)+h_2(n)=\Theta(h_1(n))$. For example, $a_kn^k+a_{n-1}n^{k-1}+\dots+a_1n+a_0=\Theta(n^k)$.

It is customary to write n^2 for $n^2$. It is even better to surround math with $$tags, e.g., [tex]f(n)=(2n +n^2)(n^3 +3n)$$ for $f(n)=(2n +n^2)(n^3 +3n)$.

Also, you are supposed to show some effort in solving a problem. At least write what you know and what your difficulty is.