Growth Functions - Need help making this statement true

May 2010
6
0
Virginia
The section of my book that this problem comes from is on the Growth of Functions.

I need to fill in the blanks to make a true statement out of the following:

[FONT=&quot]n2 + log2n ϵΘ (n2) because ___ * n2 ≤ n2 + log2n ≤ ____ * n2 for all n ≥ ____[/FONT]

I barely know how to approach this, but one question I have would be, how do you put [FONT=&quot]log2 [/FONT]into a graphing calculator? I have a TI-83 Plus. (Yes, it's not the best). I think I might have an idea of what to do if I knew how to put it into the calculator. But I could still use a lot of help on this one. Thanks in advance!

Katie

PS, this didn't post right. All of the "n2"s are supposed to be n^2, (n squared), and the "log2n"s are supposed to be log sub 2 times n. Thanks.
 
Oct 2009
255
20
St. Louis Area
The section of my book that this problem comes from is on the Growth of Functions.

I need to fill in the blanks to make a true statement out of the following:

[FONT=&quot]n2 + log2n ϵΘ (n2) because ___ * n2 ≤ n2 + log2n ≤ ____ * n2 for all n ≥ ____[/FONT]

I barely know how to approach this, but one question I have would be, how do you put [FONT=&quot]log2 [/FONT]into a graphing calculator? I have a TI-83 Plus. (Yes, it's not the best). I think I might have an idea of what to do if I knew how to put it into the calculator. But I could still use a lot of help on this one. Thanks in advance!

Katie

PS, this didn't post right. All of the "n2"s are supposed to be n^2, (n squared), and the "log2n"s are supposed to be log sub 2 times n. Thanks.
Choose C1 = 1 and C2 = 2 and k = 2.
 

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Oct 2009
255
20
St. Louis Area
I forgot to let you know how to calculate logs to other bases.



So log x to base 2 would be log x base 10 divided by log 2 base 10.

It's very easy to get confused and forget the conversion when working on a problem like that.

If you are a student and have around $100, you should consider purchasing MATLAB for your computer. Check it out on their website and I can show you where to purchase it at the student price.
 
May 2010
6
0
Virginia
Choose C1 = 1 and C2 = 2 and k = 2.

Thank you for your help so far.... What do you mean by choosing these values for C1, C2, and k? I don't see those in my original equation. If you can't tell, I'm horrible at this stuff.
 
Oct 2009
255
20
St. Louis Area
Thank you for your help so far.... What do you mean by choosing these values for C1, C2, and k? I don't see those in my original equation. If you can't tell, I'm horrible at this stuff.
No problem. With the growth of functions, you have BIG O, BIG OMEGA, and BIG THETA. You are working with BIG THETA which combines BIG O and BIG OMEGA. (Look these up in either your text or Google them)

The idea for BIG THETA is that you can find a function that will create an envelope around \(\displaystyle n^{2}+log_{2}n\). So looking at the graph, 1 * \(\displaystyle n^2\) is always below \(\displaystyle n^{2}+log_{2}n\) which is always below 2 * \(\displaystyle n^2\) for n greater than or equal to 2.

C1 = 1 goes in the first blank, C2 = 2 goes in the second blank, and k=2 goes in the last blank.

Good luck!
 
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May 2010
6
0
Virginia
No problem. With the growth of functions, you have BIG O, BIG OMEGA, and BIG THETA. You are working with BIG THETA which combines BIG O and BIG OMEGA. (Look these up in either your text or Google them)

The idea for BIG THETA is that you can find a function that will create an envelope around \(\displaystyle n^{2}+log_{2}n\). So looking at the graph, 1 * \(\displaystyle n^2\) is always below \(\displaystyle n^{2}+log_{2}n\) which is always below 2 * \(\displaystyle n^2\) for n greater than or equal to 2.

C1 = 1 goes in the first blank, C2 = 2 goes in the second blank, and k=2 goes in the last blank.

Good luck!

Ohhhh allright. I do remember reading about The BIG O in my book but I was having trouble relating it to this problem. Thanks so much, that really helps. :)