Homework about function growth rate

Question

Please order a function that matches the growth rate.

n ^ 1.5
n ^ 0.5 + log n
n log ^ 2 n
n log ( n ^ 2 )
n log log n
n ^ 2 + log n
n log n
n

ps: Sorting by growth rate means that as n gets bigger and bigger, this function will ultimately be higher in value than others.

ps2. I ordered most of the functions: n, n log log n, n log n, n log ^ 2 n, n log (n ^ 2), n ^ 1.5

I just don’t know how to order: n ^ 2 + log n, n ^ 0.5 + log n, these 2 values

Can anyone help me? thank you

Answer 1

, , ( , Maxima, Wolfram Alpha). , , - n , .

Answer 2

, , , " " , . , , ( ), , .

Answer 3

!

, http://faculty.ksu.edu.sa/Alsalih/CSC311_10_11_01/3.3_GrowthofFunctionsAndAsymptoticNotations.pdf

Answer 4

, .

, . , , ?

Answer 5

, - .

, :

f1(n) = n log n
f2(n) = n

f3 (n) = f1 (n)/f2 (n), n .

, f2 (n) , f1 (n).

, , f1 (n) , f2 (n).

Answer 6

n ^0,5 ( n ^1/2) n. , , n ².

Answer 7

let say n = 4 then we get 
n ^ 2 + log n       = 16.6020599913
n ^ 1.5             =  8
n                   =  4
n log ( n ^ 2 )     =  4.81
n ^ 0.5 + log n     =  2.60205999133
n log n             =  2.4
n log ^ 2 n         = ? 
n log log n         = -0.8