3. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(r2) (a) 100r 1000 (b) 10021000 (c) - 1000r2 (d) rlogr (2) (2 points) Use the definition of to show that 5n5+4n +3n3+2n2+ne (3) (2 points) Use the definition ore to show that 2n3-n + 10 (n*). (4) (3 points) Let f, g, h : N R+. Use the definition of big-Oh to prove that if f(n) E O(h(n) and g(n) E O(h(n)) then f(n) + g(n) O(h(n)). You should use different letters for the constants (i.e. don't use c to denote the constant for each big-Oh)