Exercises on O and Θ

5n log n ∈O((n^2))

Plot[Tooltip[{5 n Log[n],(n^2)}],{n,1,10}]

Limit[5 n Log[n]/(n^2),n -> ∞]

Plot[Tooltip[{5 n Log[n],(n^2)}],{n,1,20}]

log n ∈O((n^0.1))

Plot[Tooltip[{Log[n],(n^(.1))}],{n,1,10}]

Limit[Log[n]/(n^(.1)),n -> ∞]

Plot[Tooltip[{Log[n],(n^(.1))}],{n,1,10000000000000000}]

n log n ∈O((n^1.1))

More exercises

5n+ n cos((Sqrt[n])/100)∈ Θ (5n-4n cos log n)

Plot[Tooltip[{5n+ n Cos[(Sqrt[n])/100],5n-4n Cos[Log[n]]}],{n,1,100}]

Limit[(5n+ n Cos[(Sqrt[n])/100])/(5n-4n Cos[Log[n]]),n -> ∞]