Arrange the Functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$

question 7

Short Answer

Arrange the functions $n ^ { 3 / 2 } , \log \left( n ^ { n } \right) , \left( n ^ { 100 } \right) ^ { n }$ and $\log ( n ! )$ in a list so that each function is big- $O$ of the next function .

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Definitions:

Per-unit Costs

The average cost for each unit of product produced, calculated by dividing the total cost of production by the number of units produced.

Social Inhibition

Not expressing emotions that risk others’ disapproval; overlaps with introversion.

Reluctance

The feeling of hesitancy or unwillingness to do something.

Disapproval

The act of expressing an unfavorable opinion about something or someone, often leading to social or personal consequences.