Disproving Homework Statement | Homework Equations | Attempt at Solution

  • Thread starter Melodia
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In summary: For the second problem, there is a fixed value of c that works, but it gets smaller and smaller as n gets larger.In summary, the conversation discusses two math problems and the concept of a fixed value of c in relation to the growth of two functions. The first problem does not have a fixed value of c that satisfies the inequality for all values of n, while the second problem has a fixed value of c that works but decreases as n increases. The suggestion to graph the functions is also mentioned as a helpful tool.
  • #1
Melodia
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Homework Statement



Thanks for the help on the last problem. Here is the final problem set I'm stuck on:


SYPzV.jpg


Homework Equations





The Attempt at a Solution



To me it seems that there will always be a positive c so that cg(n) is greater or equal to f(n). No matter how large n is, since there's no limit to how large c can be (can even be a decimal), wouldn't that always be possible?

Thanks.
 
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  • #2
First off, g is not a polynomial, as it is not the sum of multiples of integral powers of n. It might be helpful for you to graph the two functions, because you would see that for n larger than about 20, the linear function dominates the other function. Although f(n) = 2n + 3 is a linear function and grows at only a constant rate, that rate is larger than that of the other function, for large enough n.
 
  • #3
Oooh I see. Since c is fixed and chosen before the n, then there will always be an n that contradicts the statement right?

I'm guessing the same thing applies to this other problem right?

8cBSM.jpg
 
Last edited:
  • #4
Yes, essentially. For the first problem, there's no fixed value of c that works because you can always make n large enough so that the inequality doesn't hold. In other words, no such c exists.
 

What is the purpose of "Disproving Homework Statement"?

The purpose of "Disproving Homework Statement" is to critically analyze a given homework assignment and determine whether or not it is valid, accurate, and/or relevant. This process involves examining the homework statement, identifying any necessary equations or formulas, and attempting to solve the problem using those equations.

What are "Homework Equations"?

"Homework Equations" refer to the mathematical formulas and principles that are necessary to solve a given homework problem. These equations may be provided by the teacher or may need to be identified by the student through research and understanding of the subject matter.

How do you approach "Attempt at Solution" in the process of disproving a homework statement?

When attempting to disprove a homework statement, it is important to first carefully read and understand the given problem. Then, the equations and principles that are relevant to the problem should be identified and used to attempt a solution. If the attempted solution is incorrect or does not align with the given homework statement, the statement may be considered disproven.

What are some common reasons for disproving a homework statement?

There are several reasons why a homework statement may be disproven. Some common reasons include: incorrect or incomplete information given in the statement, incorrect use of equations or principles, or a logical error in the problem-solving process.

How can disproving a homework statement benefit students?

Disproving a homework statement can benefit students by helping them develop critical thinking skills, improve their understanding of the subject matter, and identify any errors or gaps in their knowledge. It also encourages students to question and analyze information rather than simply accepting it at face value.

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