Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

TuringTest

\[\lim_{x\to\infty}x=?\]

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. Math4Life
    Best Response
    You've already chosen the best response.
    Medals 0

    What does that mean?

    • 2 years ago
  2. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    are we allowed to say this limit Does not exist? or is that an incorrect statement?

    • 2 years ago
  3. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    must we say the limit exists, and it is \(+\infty\) ?

    • 2 years ago
  4. Math4Life
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry i'm not that advanced in math yet

    • 2 years ago
  5. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    @FoolForMath @JamesJ @Zarkon @Mr.Math please clear up a technicality @Freckles here is our question

    • 2 years ago
  6. Math4Life
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest what is your question?

    • 2 years ago
  7. freckles
    Best Response
    You've already chosen the best response.
    Medals 1

    The question is can you interpret the limit being infinity as the limit does not exist?

    • 2 years ago
  8. freckles
    Best Response
    You've already chosen the best response.
    Medals 1

    And I'm not saying if the limit does not exist, then the limit is infinity Remember the logic stuff we learned in Discrete math p->q does not imply q->p

    • 2 years ago
  9. freckles
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm saying if the limit is infinity, then the limit does not exist

    • 2 years ago
  10. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    I think the limit does exist, and it is \(=\infty\) freckles says that you can also say the limit does not exist because \(\infty\) is not a number I just want to get some more input

    • 2 years ago
  11. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 0

    i posted this in the other thread, but since we moved here here we go The limit of f(x) as x approaches a is L if and only if, given e > 0, there exists d > 0 such that 0 < |x - a| < d implies that |f(x) - L| < e can we apply this as a formal definition?

    • 2 years ago
  12. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    that would probably help clear up the matter if we can do it right ^

    • 2 years ago
  13. freckles
    Best Response
    You've already chosen the best response.
    Medals 1

    No amistre64 is not allowed to talk. :p

    • 2 years ago
  14. eigenschmeigen
    Best Response
    You've already chosen the best response.
    Medals 0

    if we do accept that as our definition i see a potential problem: |f(x) - L| < e so we want |f(x) - infinity| < e which is a bit weird

    • 2 years ago
  15. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    there are more than 1 cardinality of infinity; so i believe its DNE since it cannot have a definitive value

    • 2 years ago
  16. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    hm... good point

    • 2 years ago
  17. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    does the limit settle to infinity? if so, which infinity are we discussing :)

    • 2 years ago
  18. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    but still... I am not completely convinced (perhaps I never will be) this seems to undermine the difference between things like\[\lim_{x\to\infty}\sin x\]and the one I posted...

    • 2 years ago
  19. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    sin(x) doesnt settle to anything; much less infinity

    • 2 years ago
  20. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    if we cant determine the limit that it settles down to; it is undefined

    • 2 years ago
  21. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    this is getting interesting

    • 2 years ago
  22. freckles
    Best Response
    You've already chosen the best response.
    Medals 1

    I think DNE can be used whenever the function is oscillating, left limit does not equal right limit, the limit is infinity

    • 2 years ago
  23. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    in sin(x) we have a bound; but in x we are boundless is the only diff i see

    • 2 years ago
  24. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    clearly lim sinx to infty DNE oh... Zarkon came online, I beet he can help!

    • 2 years ago
  25. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    sin(x) doesnt need to act like x(x) does it?

    • 2 years ago
  26. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    right, so why can we say they both DNE ? that seems to vague to me...

    • 2 years ago
  27. amistre64
    Best Response
    You've already chosen the best response.
    Medals 0

    becasue neither one of them has a point that they settle down to

    • 2 years ago
  28. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 2

    the limit does not exist. you are not using the correct formal definition of a limit (as \(x\to\infty\))

    • 2 years ago
  29. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 2

    you can say that the limit diverges to infinity

    • 2 years ago
  30. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    hm... so "blah, blah diverges to +/- infty" implies that the limit also DNE ?

    • 2 years ago
  31. Zarkon
    Best Response
    You've already chosen the best response.
    Medals 2

    for a limit to converge it has to converge to a number...infinity is not a number

    • 2 years ago
  32. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    Freckles wins! I concede, happy to have learned something :)

    • 2 years ago
  33. experimentX
    Best Response
    You've already chosen the best response.
    Medals 0

    It seems, 0 < |x - a| < d implies that |f(x) - L| < e |x - infinity| < d <----- looks like this 'd' buddy cannot be defined exactly should imply |f(x) - infinity| < e <---- and same goes to 'e' buddy

    • 2 years ago
  34. FoolForMath
    Best Response
    You've already chosen the best response.
    Medals 0

    I would say that the limit of \(f(x)=x\) as x tends to infinity is \(+\infty\) and save the DNE (does not exist) for those cases where left hand limit \(\neq \) right hand limit.

    • 2 years ago
  35. FoolForMath
    Best Response
    You've already chosen the best response.
    Medals 0

    Precisely where there is a hole in the graph or there is no graph at all.

    • 2 years ago
  36. FoolForMath
    Best Response
    You've already chosen the best response.
    Medals 0

    To me undefined and infinity are two different things.

    • 2 years ago
  37. FoolForMath
    Best Response
    You've already chosen the best response.
    Medals 0

    There is a nice discussion on this in M.SE: http://math.stackexchange.com/questions/36289/

    • 2 years ago
  38. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    "To me undefined and infinity are two different things." yes, that's how I felt as well, but apparently if the limit tends to infinity it technically does not exist. I guess just saying that the limit is infinity is a more specific way, or at least a reason for, stating that the limit DNE

    • 2 years ago
  39. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 7

    @FoolForMath wow, that's a very thorough answer from Qiaochu, and actually helped me understand ideas like rings and fields

    • 2 years ago
  40. FoolForMath
    Best Response
    You've already chosen the best response.
    Medals 0

    @TuringTest: Yes, the limit tends to infinity is technically does not exist, I see people often use thee two interchangeably, it's fine because technically \( ∞∉\mathbb{R}\). And I agree, that's a dainty answer :)

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.