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Tell whether each of the following statements is true or false. i n² +3 = 0(n²) ii 19n = 0(n) iii log, n = 0(log3 n) iv 34n3 + 2 = O(

Tell whether each of the following statements is true or false. i n² +3 = 0(n²) ii 19n = 0(n) iii log, n = 0(log3 n) iv 34n3 + 2 = O(

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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Tell whether each of the following statements is true or false. No explanation is needed. i \( n^2 + 3 = O(n^2) \) ii \( 19n = O(n) \) iii \( \log_2 n = O(\log_3 n) \) iv \( 34n^3 + 2 = \Theta(\frac{n}{1000}) \) v \( 123 = O(n!) \) vi \( n^2 = \Omega(n^2 + 4) \) vii \( n^2 = \Omega(123) \) viii \( 3 \log_2 n = \Theta(n \log_3 n) \) ix if \( f(n) = \Theta(g(n)) \) then \( f(n) = O(g(n)) \) x if \( f(n) = \Omega(g(n)) \) then \( f(n) = O(g(n)) \) xi if \( f(n) = O(g(n)) \) then \( g(n) = O(f(n)) \)
Transcribed Image Text:Tell whether each of the following statements is true or false. No explanation is needed. i \( n^2 + 3 = O(n^2) \) ii \( 19n = O(n) \) iii \( \log_2 n = O(\log_3 n) \) iv \( 34n^3 + 2 = \Theta(\frac{n}{1000}) \) v \( 123 = O(n!) \) vi \( n^2 = \Omega(n^2 + 4) \) vii \( n^2 = \Omega(123) \) viii \( 3 \log_2 n = \Theta(n \log_3 n) \) ix if \( f(n) = \Theta(g(n)) \) then \( f(n) = O(g(n)) \) x if \( f(n) = \Omega(g(n)) \) then \( f(n) = O(g(n)) \) xi if \( f(n) = O(g(n)) \) then \( g(n) = O(f(n)) \)
Expert Solution
Solution:

i Given: n2+3=On2   True

n2+3≤n2+3≤n2+3n2≤4n2

 

ii Given: 19n=On  True

19n≤19n

 

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