Mathematics, 20.09.2019 21:30 winterblanco
Let ƒ(n) and g(n) be asymptotically positive functions. prove or disprove each of the following conjectures.
a ƒ(n)∈o(g(n)) implies g(n)∈o(ƒ(
b ƒ(n)+ g(n)∈θ(min(ƒ(n),g(
c ƒ(n)∈o(g(n)) implies lg(ƒ(n))∈o(lg(g( where lg(g(n))≥1 and ƒ(n)≥1 for all sufficiently large n.
d ƒ(n)∈o(g(n)) implies 2^(ƒ(n))∈o(2g(
e ƒ(n)∈o((ƒ(n))^2).
f ƒ(n)∈o(g(n)) implies g(n)∈ω(ƒ(
g ƒ(n)∈θ(ƒ(n/
h ƒ(n)+ o(ƒ(n))∈θ(ƒ(
Answers: 3
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Let ƒ(n) and g(n) be asymptotically positive functions. prove or disprove each of the following conj...
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