2. Suppose that the functions f1, f2, 91, 92 : N → R20 are such that f₁ = O(91) and ƒ2 € О(92). Prove that (fi + ƒ₂) € ☹(max{91, 92}). Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}. 3. Let nЄ N\{0}. Describe the largest set of values n for which you think 2n < n!. Use induction to prove that your description is correct. Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! = O(n log n).
2. Suppose that the functions f1, f2, 91, 92 : N → R20 are such that f₁ = O(91) and ƒ2 € О(92). Prove that (fi + ƒ₂) € ☹(max{91, 92}). Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}. 3. Let nЄ N\{0}. Describe the largest set of values n for which you think 2n < n!. Use induction to prove that your description is correct. Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! = O(n log n).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Please help me with this question. I am having trouble understanding what to do. Please show all your work on paper
Course: Discrete mathematics for CS
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![2. Suppose that the functions f1, f2, 91, 92 : N → R20 are such that f₁ = O(91) and ƒ2 € О(92).
Prove that (fi + ƒ₂) € ☹(max{91, 92}).
Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
3. Let nЄ N\{0}. Describe the largest set of values n for which you think 2n < n!. Use induction to
prove that your description is correct.
Here m! stands for m factorial, the product of first m positive integers.
4. Prove that log2 n! = O(n log n).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5354a32c-ee07-469b-96d5-42a00c955615%2Fe71c76e3-3685-43d7-938e-6630a01052b3%2Frfwm5us_processed.png&w=3840&q=75)
Transcribed Image Text:2. Suppose that the functions f1, f2, 91, 92 : N → R20 are such that f₁ = O(91) and ƒ2 € О(92).
Prove that (fi + ƒ₂) € ☹(max{91, 92}).
Here (f1f2)(n) = fi(n) + f2(n) and max{91, 92}(n) = max{91(n), 92(n)}.
3. Let nЄ N\{0}. Describe the largest set of values n for which you think 2n < n!. Use induction to
prove that your description is correct.
Here m! stands for m factorial, the product of first m positive integers.
4. Prove that log2 n! = O(n log n).
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