2. Asymptotic Notation (8 points) Show the following using the definitions of O, N, and O. (1) (2 points) 2n + n2 +4 (ny) (2) (2 points) 3n4 9n2 + 4n E O(n4) (Hint: careful with the negative number) (3) (4 points) Suppose f(n) E O(gi(n)) and f(n) E (92(n)). Which of the following are true? Justify your answers using the definition of O. Give a counter example if it is false. (a) f(n) E O( 5.91(n) + 100 ) (b) f(n) E O( gi(n) + 92(n)). (c) f(n) O( 93(n) ) (d) f(n) E O( max(91(n), 92(n)) )