1 (20 points) In this problem, you may assume the log function is computed with any base you like, but state the base you are assuming. (a) (5 points) n log n O(g(n)) for which of the following definitions of g(n)? Circle all that apply: g(n)= n g(n)= nlogn g(n) = n2-n log n g(n)= n2 log n (b) (5 points) n log n-(g(n)) for which of the following definitions of g(n)? Circle all that apply: g(n) = n g(n)= n log n g(n) = n2 log n (c) (5 points) n log n = (g(n)) for which of the following definitions of g(n)? Circle all that apply: g(n)=1 g(n)= n g(n) = n log n g(n) n2-n log n 1(n)= n2 logn (d) (5 points) Using limits and L'Hpital's rule, provide a proof that 1000 log n = ( log (n-c) ) where c is some positive constant (independent of n and c