Limitations of Comparing t/U and t^2/U Variables

  • Thread starter mvww
  • Start date
  • Tags
    Variables
In summary: Bai5GK2Q9JA&feature=relmfuDonAntonioIn summary, the limit of t/U tends to 0, and the limit of t^2/U tends to 1.
  • #1
mvww
9
0
Let U and t be independent real variable.
In the limit:
[itex]t/U \rightarrow 0[/itex]
Can I say that
[itex]t^2/U \rightarrow 0[/itex]
too? Or I can compare only same powers of both?

Regards.
 
Last edited:
Physics news on Phys.org
  • #2
mvww said:
If
[itex]t/U \rightarrow 0[/itex]
can I say that
[itex]t^2/U \rightarrow 0[/itex]
too? Or I can compare only same powers of both?

Regards.


You don't say what is t, what is U, the limit of what tending to what...are we to guess?

DonAntonio
 
  • #3
DonAntonio said:
You don't say what is t, what is U, the limit of what tending to what...are we to guess?

DonAntonio

Fixed. thanks.
 
  • #4
First of all, you still did not explain anything. What does the limit tend to, what is t, what is U? Is t dependent or U, or for example they both are dependent on some arbitrary variable x?
 
  • #5
Millennial said:
First of all, you still did not explain anything. What does the limit tend to, what is t, what is U? Is t dependent or U, or for example they both are dependent on some arbitrary variable x?

they are both independent variables. U is much bigger than t, in the sense that
[itex]t/U \rightarrow 0[/itex]
 
  • #6
mvww said:
they are both independent variables. U is much bigger than t, in the sense that
[itex]t/U \rightarrow 0[/itex]


Ok, please DO PAY ATTENTION! You have to tell what in the name of Newton is tending where!
Is it [itex]\,t\to 0\,\,,\,t\to\infty\,\,,\,U\to 0...[/itex] ? Common...

DonAntonio
 
  • #7
mvww said:
Let U and t be independent real variable.
In the limit:
[itex]t/U \rightarrow 0[/itex]
Can I say that
[itex]t^2/U \rightarrow 0[/itex]
too? Or I can compare only same powers of both?

Regards.

[itex]\displaystyle\ \lim_{x\to\infty} \frac{x}{x^2} = 0[/itex]

but

[itex]\displaystyle\ \lim_{x\to\infty} \frac{x^2}{x^2} = 1[/itex]

Note that I specified what variable is going to what limit, which is an essential part of this question, as Don Antonio's pointing out.
 
  • #8
I think this may have to see with the "Big O " class that the expression belongs to,

i.e., how fast does the expression go to 0 ?
 
  • #9
SteveL27 said:
[itex]\displaystyle\ \lim_{x\to\infty} \frac{x}{x^2} = 0[/itex]

but

[itex]\displaystyle\ \lim_{x\to\infty} \frac{x^2}{x^2} = 1[/itex]

Note that I specified what variable is going to what limit, which is an essential part of this question, as Don Antonio's pointing out.

To use SteveL27's example: A limit is used to describe what value(s) a funcation approaches as x reaches a specific value. Steve's first example
[tex]\lim_{x\to\infty} \frac{x}{x^2}[/tex]
says that as x approaches infinity, for the function [itex]\frac{x}{x^2}[/itex] is equal to zero. although the function never quite reches this point, that's what value the function approaches, as x gets closer and closer to infinity. 1/12=1, 2/22=0.5, 3/32=0.33.3...155/1552=0.006451612903...12,347,222/12,347,2222=8.098987 X 10-8.
It gets closer and closer to zero. yet never acually gets to the point that f(x)=0.

Limits can be used for any part of any function, even simple ones (even thought there isn't any reason to waste time with evaluating limits for simple, continuous function), for example:

[tex]\lim_{x\to 1.5} 5x-{x^2}=5.2[/tex]

limits are usually used to describe breaks in non-continous functions, functions approaching (+ or -) infinity, or specific x values that make the y value spike up to (+ or -) infinity.

Here are some videos that may help:

http://www.youtube.com/watch?v=UkjgJQaGx98&feature=relmfu
 
Last edited by a moderator:

1. What is the concept of t/U and t^2/U variables?

The concept of t/U and t^2/U variables is a statistical method used to compare two different groups or populations. The t variable represents the difference between the means of the two groups, while the U variable represents the standard deviation of the two groups. The t^2 variable is the square of the t variable, which is used to account for the variability in the data.

2. What are the limitations of comparing t/U and t^2/U variables?

One of the main limitations of comparing t/U and t^2/U variables is that it assumes the data follows a normal distribution. If the data is not normally distributed, the results of the comparison may not be accurate. Additionally, this method does not take into account other factors that may affect the comparison, such as sample size and variance of the two groups.

3. Can t/U and t^2/U variables be used to compare more than two groups?

No, t/U and t^2/U variables are typically used to compare only two groups. Comparing more than two groups using this method can lead to inaccurate results and is not recommended. In such cases, other statistical methods such as ANOVA (analysis of variance) should be used.

4. Is there a minimum sample size required for comparing t/U and t^2/U variables?

Yes, there is a minimum sample size required for accurate results when using t/U and t^2/U variables. The recommended minimum sample size is 30 for each group, but this may vary depending on the specific data and research question.

5. Are there any alternatives to using t/U and t^2/U variables for comparison?

Yes, there are other statistical methods that can be used for comparison, such as non-parametric tests like the Mann-Whitney U test or the Kruskal-Wallis test. These methods do not require the data to be normally distributed and can handle comparisons of more than two groups. However, it is important to consult with a statistician to determine the most appropriate method for your specific research question and data.

Similar threads

Replies
33
Views
2K
Replies
5
Views
979
Replies
17
Views
2K
  • Calculus
Replies
5
Views
1K
Replies
9
Views
882
  • Calculus
Replies
3
Views
636
Replies
5
Views
1K
  • Calculus
Replies
13
Views
1K
Replies
4
Views
609
Back
Top