A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

find limt lim x approaches infinity 1/(5x+4)

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

    0

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

    denomiator gets bigger, numerator stays one. think of \[\frac{1}{1000000}=.000001\]

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

    bigger the denominator gets, the smaller the fraction.

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

    ok so anything that deals with infinity could possibly be zero

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

    well it depends on the function, but it certainly could be 0 in the limit.

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

    ok. i have another one simliar but mor complex

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

    shoot

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

    \[ \lim \rightarrow \infty (1- x-x^2)/(3x^2-4)\]

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

    ok in this case you have a polynomial of degree 2 in the numerator, and a polynomial of degree 2 in the denominator. when the degrees are the same, as in this case, just take the ratio of the leading coefficients.

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

    leading coefficient of the numerator is -1, and the leading coefficient of the denominator is 3 so the limit as x goes to infinity is -1/3

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

    what could be easier?

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

    ok..so basically you look into the coefficent of both numerator and denominator and computer it to become a -1/3...so the -4 in the denomintor and the numerator dont neccessary needs anything

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

    not a thing. lets do a simple example: \[lim_{x->\infty}\frac{x^3+9x}{2x^2+x^2}\]

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

    ok

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

    and lets let x = 100 which is not even that big

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

    ok cool

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

    the numerator is \[100^3+9\times 100=1000900\]

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

    the denominator is 2010000

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

    the ratio is \[\frac{1000900}{2010000}\]

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

    right and the denomator would be 2010000....

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

    which is certainly not exactly \[\frac{1}{2}\]

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

    ok..

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

    but you can see that it is close. you can also see that the 9x term and the x^2 term meant nothing as far as the magnitude of the numerator and denominator

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

    there are way down there in the decimal places.

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

    i need a lot of practice on this function

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

    and that was just for 100. we are taking the limit as x -> infinity. imagine what it would look like if x was 10000000000

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

    very very close to 1/2

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

    this is not how it is explained in your book. i am just pointing out that the numbers show you that you will get closer and closer to 1/2

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

    i see becuase you can basically pick any number in the infinity column and it would still be the coeffiencet

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

    now if the degree of the denominator is bigger than the numerator, then the limit is 0

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

    think of \[\frac{10^3}{10^5}\]

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

    numerator has degree 3, denom has degree 5 and this number is small. it is .01

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

    it would be zero because the 10^5 and large

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

    last possibility is that the degree of the numerator is higher. in this case the limit is infinty

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

    yes you are right.

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

    now think of degree of the numerator bigger. for example \[\frac{10^5}{10^2}=1000\]

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

    and that is just for 10! as x -> infinity this will get huge. so the rules are as follows (and very simple) lim x-> infity p(x)/q(x)

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

    if deg p > deg q, limit is infinity if deg p < deg q limit is 0 if deg p = deg q ratio of leading coefficients

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

    that is it!

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

    ok no i see thanks again!!

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

    welcome!

  42. 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.