# Homework Help: Help with comparsion

1. Oct 24, 2008

### Gear2d

1. The problem statement, all variables and given/known data

k is a constant where k1 < k2

Is the relation between the two <. > or = to:

A = nk1 + k2n

B = nk2 + k1n

3. The attempt at a solution

I did this problem said that A > B, and I got it wrong. I am having a hard time telling if nki or kin is greater.

2. Oct 24, 2008

### jhicks

Do you mean *n* is a constant? I don't see a k. Also, you have given us insufficient information to solve the problem because depending on k1 and k2 relative to n the answer will change. For example, n=10, k1=1, k2=2 and n=2, k1=10, k2=11.

Last edited: Oct 24, 2008
3. Oct 24, 2008

### Dick

If n=1 then A>B. If n=2, k1=1 and k2=2 then A>B. If n=2, k1=3 and k2=4, then A<B. Do you know something about n you aren't telling us? What makes you think there is a definite relation between the two?

4. Oct 26, 2008

### Gear2d

Sorry about that, n can be any number, does not have to be fixed like the k's. So, for example nk1 < nk2.

5. Oct 26, 2008

### Dick

That doesn't help. You've already been given examples where A<B and B>A.

6. Oct 26, 2008

I think that k's are fixed value for a give problem, and that as n-> infinite that one of those will be >, <, or =. I think that is what gear2d is asking.

7. Oct 26, 2008

### Dick

You might be right. If that's the real question, I wish Gear2d would clarify.

8. Oct 27, 2008

### Gear2d

Thanks Ad2d you said what I wanted to say. So how would one approach this problem?

9. Oct 27, 2008

### Dick

Figure out which term is dominant. Take n^k1 and k2^n. The logs are k1*log(n) and n*log(k2). Which is larger as n gets large? I.e. what is lim n->infinity (k1*log(n))/(n*log(k2))? Is it zero or infinity? Think l'Hopital.

10. Oct 27, 2008

### Gear2d

Thank you, that makes sense. Don't know why I did not see that. Thanks again.