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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Please do this in excel please
Please help me with this question if you know how to use the R software. I am very confused and my teacher tells me to type ?longley in the software but I still struggle to understand this question and answer it properly. Any help would be tremendously ap.p/reciated! Please don't answer it if you answered my question before!!!!>>
Briefly explain the procedure you may adopt to summarize data set obtained from field study.
Give an example of a refinement in mathematical modeling with contextual explanation.
I was doing my homework but look for an example but I don't know how they get the class midpoint
How do you make the z-tables that go with this question?
I want it in writing hard to understand
What is the measure of ∠x in this diagram?
Based on the data in both images. show how the values are acquired.
Can someone explain x-bar to me?
APA spell is the one used to cite the sources of for information gathered from different reference materials. What does APA mean?
What is curve fitting and polynomial interpolation