Theorem: Assume that f1(x) is O(g1(x)) and f2(x) is O(g2(x)). Then, (i) (f1 + f2)(x) is O(g(x)) where g(x) = max(lg1(x)l, Ig2(x)l) for all x. (ii) (fjf2)(x) is O(g1(x)g2(x)). Using the theorem above give a big-O estimate for n log(n² + 1) + n² logn

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Theorem: Assume that f1(x) is O(g1(x)) and f2(x) is O(g2(x)). Then,
(i) (f1 + f2)(x) is O(g(x)) where g(x) = max(lg1(x)l, Ig2(x)) for all x.
(ii) (fif2)(x) is O(g1(x)g2(x)).
Using the theorem above give a big-0 estimate for n log(n² + 1) + n² logn
Transcribed Image Text:Theorem: Assume that f1(x) is O(g1(x)) and f2(x) is O(g2(x)). Then, (i) (f1 + f2)(x) is O(g(x)) where g(x) = max(lg1(x)l, Ig2(x)) for all x. (ii) (fif2)(x) is O(g1(x)g2(x)). Using the theorem above give a big-0 estimate for n log(n² + 1) + n² logn
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