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Problem 2. Solve the following questions, 2(A) & 2(B). Show that 13 + 23 + 33 + +n is O(n*). Show that the function f(r) = (r+ 2) log(r² + 1) + log(r³ + 1) is O(r log r).

Problem 2. Solve the following questions, 2(A) & 2(B). Show that 13 + 23 + 33 + +n is O(n*). Show that the function f(r) = (r+ 2) log(r² + 1) + log(r³ + 1) is O(r log r).

Advanced Engineering Mathematics
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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Problem 2. Solve the following questions, 2(A) & 2(B). Show that 13+ 23 +33 + ...+n is O(n). Show that the function f(x) = (r+ 2) log(r² + 1) + log(r³ + 1) is O(x log r). %3D
Transcribed Image Text:Problem 2. Solve the following questions, 2(A) & 2(B). Show that 13+ 23 +33 + ...+n is O(n). Show that the function f(x) = (r+ 2) log(r² + 1) + log(r³ + 1) is O(x log r). %3D
Expert Solution
Step 1

Given : To prove 13+23+33+⋯+n3 has the order O(n4)formula: (1) Choose k=1(2) Assuming n>k=1, find the value of λ such that  f(n)≤O(g(n))=λg(n)(3) Arrive at the conclusion that ∀n>k=1⇒ f(n)≤λ(g(n))

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