A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

anyone good at limits? lim(1+2/x)^x x-(infinity)

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[e^{-2}\]is my guess

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

    any work to go with it?

  3. myininaya
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    he might be right i remember that limit i think it was either as x->0 or infinity cant remember

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

    lim(1+3h)^(1/h) h->0

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry it is e^2

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

    \[e=lim_{x->\infty}(1+\frac{1}{x})^x\]

  7. myininaya
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if he is right about that one then this second one should be e^(1/[3h]) i believe

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and so of course \[e^2=lim_{x->\infty}(1+\frac{2}{x})^x\]

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you other one is e^3

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    for exactly the same reason

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

    so then lim 3^(-x) x->+(infinity)

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if you want we can work this out step by step.

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sure,

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

    step one is take the log get \[ln(1+\frac{1}{x})^x=xln(1+\frac{1}{x})\]

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

    let 1/u=3h as h->0 then u->infinity so we have as u->infinity then (1+1/u)^u->e^u but u=1/(3h) so the limit is e^{1/(3h)}

  16. myininaya
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh wiat nvm

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

    wait. myininaya i think it is just e^3

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we do it the donkey way

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

    take the log, take the limit using l'hopital, see that we get 3 and then conclude that it is e^3

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

    which one do you want to do?

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

    u r right

  22. myininaya
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its not fair u shouldn't always win

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

    fancy which one would you like worked out?

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lim 3^-x x-> +(infinty

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

    i want to see both :)

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[lim_{x->\infty}3^{-x}\]

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

    nothing to that one. that is \[lim_{x->\infty}\frac{1}{3^x}=0\]

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is the pain: (1+2/x)^x

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but we knock it out

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why 0

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    as x gets large 3^x gets really large. huge denominator,1 in the numerator, very close to zero

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    back to (1+2/x)^x because i gotta go

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

    limx-.2+ ln(x-2)

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

    take the log get xln(1+2/x) take the limit as x -> infinity get infinity times 0 so rewrite

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

    as \[\frac{ln(1+\frac{1}{x})}{\frac{1}{x}}\]

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

    now we have 0/0 so use l'hopital

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

    ooo ojkak

  38. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ooo ojkak

  39. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i made a mistake and wrote 1 instead of 2. when you take the derivative of to bottom you get \[-\frac{1}{x^2}\]

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

    when you take the derivative of the top you get \[\frac{1}{1+\frac{2}{x}}\times-2\frac{1}{x^2}\]

  41. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    everything cancels leaving you with \[\frac{2}{1+\frac{1}{x^2}}\]

  42. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then let x -> infinity and get 2

  43. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and since we took the log in the first step the answer is not 2, but e^2

  44. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so many questions, so little time

  45. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.