2. Determine whether each of the following is True or False. (12 points) (1) T(n) = n* (n + 5 *log(n) is O(n*log(n)) (2) T(n) = (n+1)(n+2)/2 + 1 is O(n?) (3) 1000n+4 is O(23+2n2) (4) If f(x) is O(n?) and g(x) is O(n), then f(x) is O(g(x)) (5) Linked lists are efficient for binary search. (6) Insertion to a stack (implemented normally) takes O(1) time. 3. Prove that n* cos(n)+ 20 is O(n), using the formal definition of big-O notation. (12 points)