Reading the long list, Xianghu and Jordan realized that things were not as simple as they thought, and felt

really upset. Could you help them with the following problems? $($You don't need to explain your answer for

this entire problem.$)$

$(1)(1$pt$)$ What does polynomial mean $($use $O(*),(*),(*),(*),o(*)$ to present your answer$)?(2$pts$)$

Which of them are polynomial?

$(2)(1$pt$)$ What does polylogarithmic mean $($use $O(*),(*),(*),(*),o(*)$ to present your answer$)?(2$pts$)$

Which of them are polylogarithmic?

$(3)(1$pt$)$ What does sublinear mean $($use $O(*),(*),(*),(*),o(*)$ to present your answer$)?(2$pts$)$ Which

of them are sublinear?

$(4)(1$pt$)$ What does superlinear mean $($use $O(*),(*),(*),(*),o(*)$ to present your answer$)?(2$pts$)$

Which of them are superlinear?

$(5)(2$pts$)$ Which of the above $20$ functions grow the fastest $($if you think there are multiple answers, list

all of them$)?$

$(6)(6$pts$)$ Finally, please rank all the functions by ascending order of growth; Group together those func$-$

tions that are big$-$Theta of one another.