$(10$ points$)$ Place these functions in order from slowest asymptotic growth to fastest asymptotic

growth. Justify the claimed order for each pair of consecutive functions that appear in your ordered

list. For instance, if you claim that $()<()$ in growth rate for some choice of the functions $()$

and $(),$ show that the limit test yields lim

$$ $()/()=0.$

Hint: Try and simplify the functions algebraically before comparing them.

NB: The notation lg $$ stands for log$2.$