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Evaluate limit

  1. Aug 29, 2012 #1
    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: Aug 29, 2012
  2. jcsd
  3. Aug 29, 2012 #2

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

    DonAntonio
     
  4. Aug 29, 2012 #3
    Fixed. thanks.
     
  5. Aug 29, 2012 #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?
     
  6. Aug 29, 2012 #5
    they are both independent variables. U is much bigger than t, in the sense that
    [itex]t/U \rightarrow 0[/itex]
     
  7. Aug 29, 2012 #6

    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
     
  8. Aug 29, 2012 #7
    [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.
     
  9. Aug 30, 2012 #8

    Bacle2

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    Science Advisor

    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 ?
     
  10. Sep 1, 2012 #9
    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, thats 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 isnt any reason to waste time with evaluating limits for simple, continous 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: Sep 25, 2014
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