3. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x2). Proof is not requi

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3 Growth Of Functions 11 Points 1 4 Points Determine Whether Each Of These Functions Is O X2 Proof Is Not Requi 1 (43.26 KiB) Viewed 46 times

3. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x2). Proof is not required but it may be good to try to justify it (a) 100x1000 (b) 100x² + 1000 (c)-1000x² (d) x log x (2) (2 points) Use the definition of O to show that 5n5 +4n²+3n³+2n² +n € 0(n³). (3) (2 points) Use the definition of to show that 2n³- n + 10 € (n³). (4) (3 points) Let f, g, h: N→ R+. Use the definition of big-Oh to prove that if f(n) = O(h(n)) and g(n) = 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).