Determining the order of a function with big Oh

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Discussion Overview

The discussion revolves around determining the order of various functions using Big Oh notation. Participants analyze three specific functions and attempt to classify their growth rates, addressing both theoretical and practical implications of their findings.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant proposes that Ta(n) = 20^2 + (n + 4)^3 has an order of Θ(n^3).
  • Another participant suggests that Tb(n) = (6n + 4)^2 + 3nlog2(n) has an order of Θ(n^2).
  • A claim is made that Tc(n) = (7n + 1)^2log10(n) has an order of Θ(n^2log10(n)).
  • One participant expresses confidence in their answers but seeks verification, particularly regarding the third function.
  • Another participant confirms that they do not see any issues with the proposed orders.
  • A later reply indicates that the initial participant's confidence has increased after receiving feedback.

Areas of Agreement / Disagreement

Participants generally agree on the proposed orders for the functions, with no significant disagreement noted. However, there is some uncertainty expressed about the third function's classification.

Contextual Notes

Participants mention doubts regarding the use of brackets in their calculations, indicating potential limitations in their reasoning or assumptions.

ZERO_COOL
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Homework Statement



Give the order of the following functions,

1. Ta(n) = 20^2 + (n + 4)^3

2. Tb(n) = (6n + 4)^2 + 3nlog2(n)

3. Tc(n) = (7n + 1)^2log10(n)


Homework Equations





The Attempt at a Solution



I got the following orders:-

1. Θ(n^3)

2. Θ(n^2)

3. Θ(n^2log10(n))

Number 2 is the most effecient for very large values of n because it is higher up the Big Oh ranking table.
 
Last edited:
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ZERO_COOL said:

Homework Statement



Give the order of the following functions,

1. Ta(n) = 20^2 + (n + 4)^3

2. Tb(n) = (6n + 4)^2 + 3nlog2(n)

3. Tc(n) = (7n + 1)^2log10(n)


Homework Equations





The Attempt at a Solution



I got the following orders:-

1. Θ(n^3)

2. Θ(n^2)

3. Θ(n^2log10(n))

Number 2 is the most effecient for very large values of n because it is higher up the Big Oh ranking table.
Do you have a question?
 
Looks ok to me.

EDIT: HAHAHA! Seems as if we're going for exactly the same threads tonight Mark!
 
Last edited:
Yep LOL,

I was hoping someone could verify my answers, the brackets have me doubting my answers and I'm a bit dubious about my response to the third one.
 
I don't see anything wrong with any of them.
 
Thanks Mark and phyzmatix.

I was about 80% confident in my answers now I'm 100% :)
 

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