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[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)). =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 26RE
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[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)).
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)
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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