algorithms Asymptotic Notations

Question

2. Fill the following blanks with the notations $O, o, \Omega, \omega$, or $\Theta$. Use $o$ if both $O$ and $o$ are applicable. Use $\omega$ if both $\Omega$ and $\omega$ are applicable. Use $\Theta$ if both $\Omega$ and $O$ are applicable. To distinguish $O$ and $o$, write "big-O" for $O$.
a) $n=$ $\qquad$ $(2 n)$.
b) $0.2 n=$ $\qquad$ (2 $\log n$ ).
c) $2^{n}=$ $\qquad$ $\left(n^{6}\right)$.
d) $2 n \log n=$ $\qquad$ $\left(n^{2}\right)$.

Comments

Thetha
small omega
small omega
small o

Answer 1

a) Theta

b) Both Big and small Omega applicable --> small Omega

c)Both Big and small Omega applicable --> small Omega

d)Both Big and small O applicable --> small O

Comments

@VS Can you elaborate a method behind your answer?

---

@VS how exponential function (2^n) is smaller than polynomial function(n^6)?