[Problem 1] Prove the following statements formally. a) Let f(n) b) Let f(n) = = log2 (n) and g(n) = loge(n). Prove that f(n) = O(g(n) n² +n and g(n) 7n². Prove that f(n) = N(g(n)). =
[Problem 1] Prove the following statements formally. a) Let f(n) b) Let f(n) = = log2 (n) and g(n) = loge(n). Prove that f(n) = O(g(n) n² +n and g(n) 7n². Prove that f(n) = N(g(n)). =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Prove all in detail please
![[Problem 1] Prove the following statements formally.
a) Let f(n)
b) Let f(n)
log₂ (n) and g(n)
n² +n and g(n)
=
loge(n). Prove that f(n) = O(g(n)).
7n². Prove that f(n) = (g(n)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc630a04b-52cd-42f4-994f-7132aebc4d04%2F4cc748f1-fc47-46eb-8374-3eaff5c85e15%2Fwuty5nu_processed.png&w=3840&q=75)
Transcribed Image Text:[Problem 1] Prove the following statements formally.
a) Let f(n)
b) Let f(n)
log₂ (n) and g(n)
n² +n and g(n)
=
loge(n). Prove that f(n) = O(g(n)).
7n². Prove that f(n) = (g(n)).
![[Problem 2] Using substitution method
a) T(n) = 9T(n/3) + 7 is O(n²)
b)
T(n) =
T(n) = T(n − 1) + 5n is (n²)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc630a04b-52cd-42f4-994f-7132aebc4d04%2F4cc748f1-fc47-46eb-8374-3eaff5c85e15%2Fh0qqmq_processed.png&w=3840&q=75)
Transcribed Image Text:[Problem 2] Using substitution method
a) T(n) = 9T(n/3) + 7 is O(n²)
b)
T(n) =
T(n) = T(n − 1) + 5n is (n²)
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