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Tell whether each of the following statements is true or false. No explanation is needed. (a) n2 + 3n + nlog, n = 0(n²) (b) 7n + log, n = O(n?) (c) log, n+ 3n = 0(log3 n)

Tell whether each of the following statements is true or false. No explanation is needed. (a) n2 + 3n + nlog, n = 0(n²) (b) 7n + log, n = O(n?) (c) log, n+ 3n = 0(log3 n)

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. (a) n2 + 3n + n log, n = O(n2) (b) 7n + log, n = O(n²) (c) log,n+ 3n = 0(log3 n) (d) 3n3 + 12n = O( n3 (1000) %3D (e) 25 = O(1) (f) = Q(n²) (g) 4n log, n= Q(3n²) (h) 30n log, n=0(log,n) (i) if f(n) = O(g(n1)) then f(n) = O(g(n)) (j) if f(n) = O(g(n)) then g(n) = Q(f (n)) (k) if f(n) = O(g(n)) then g(n) = Q(f(n))
Transcribed Image Text:Tell whether each of the following statements is true or false. No explanation is needed. (a) n2 + 3n + n log, n = O(n2) (b) 7n + log, n = O(n²) (c) log,n+ 3n = 0(log3 n) (d) 3n3 + 12n = O( n3 (1000) %3D (e) 25 = O(1) (f) = Q(n²) (g) 4n log, n= Q(3n²) (h) 30n log, n=0(log,n) (i) if f(n) = O(g(n1)) then f(n) = O(g(n)) (j) if f(n) = O(g(n)) then g(n) = Q(f (n)) (k) if f(n) = O(g(n)) then g(n) = Q(f(n))
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