Problem 8. We can extend the big- O notation to multiple variables. In this problem, we will focus on two variables, but the idea extends to more variables in a straightforward manner. Formally, let f(n,m) and g(n,m) be functions of variables n and m satisfying f(n,m)0 and g(n,m)0. We say f(n,m)=O(g(n,m)) if there exist constants c1 and c2 such that f(n,m)c1g(n,m) holds for all nc2 and mc2. Prove: - n2m+100nm=O(n2m). - n2m+100nm2=O(n2m+nm2)