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f(n)
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= 8 ( 5 n2 + 7 n5 + 2) / ( (1/2) n2 )
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given a computational complexity function f(n)
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= 16( 5 n2 + 7 n5 + 2) / n2
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by mulpiplying 2 to both numerator and denominator
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≤ 16( 5 n5 + 7 n5 + 2 n5) / n2
for all n ≥ 1
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since n5 ≥ 1 and n5 ≥ n2 for all n ≥ 1
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= 16( 14 n5 ) / n2
for all n ≥ 1
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= 16( 14 n3 )
for all n ≥ 1
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since nc / nd = n(c−d) for all n ≥ 1 when d ≠ 0
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= 224 n3
for all n ≥ 1
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an upper bound O(n3) derived
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