$2\mathrm{.}1$ Order the following functions by growth rate: $N,\sqrt[\phantom{2}]{N},N^{1\mathrm{.}5},N^2,$NlogN, NloglogN,$Nlo{g}^{2}N,$Nlog$(N^2),\frac{2}{N},2^N,2^{\frac{N}{2}},37,N^{2}logN,N^3.$ Indicate which functions grow at the same rate.

$2\mathrm{.}2$ Suppose $T_1(N)=O(f(N))$ and $T_2(N)=O(f(N)).$ Which of the following are true?

a$.T_1(N)+T_2(N)=O(f(N))$

b$.T_1(N)-T_2(N)=o(f(N))$

c$.\frac{T_1(N)}{T_2(N)}=O(1)$

d$.T_1(N)=O(T_2(N))$

$2\mathrm{.}3$ Which function grows faster: NlogN or $N^{1+lo\frac{n}{\sqrt[\phantom{2}]{logN}}},lon>0?$