A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

idku

  • one year ago

I have a question about growth ranking

  • This Question is Closed
  1. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, we are taking about different growths. From smallest to greatest 1) Polynomials - linear growth - quadratic polynomial (with positive coefficient) - cubic polynomial (with positive coefficient) - etc... (some nth degree polynomial) 2) Exponential function f(x)=a(b)\(^x\) - this exponential eventually exceeds the polynomial 3) factorial 4) n\(^n\)

  2. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, would I put hyperbolic functions in the exponential? what I want to propose is that a hyperbolic function (as lim x→∞) is smaller than or equivalent to e\(^x\), and larger than any other exponential function if the base of this exponential function is less than e.

  3. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  4. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    (and of course is base is bigger than e, this exponential is certainly exceeds hyperbolic)

  5. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh yes? nice

  6. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    define hyperbolic function

  7. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well, it consists of some e^x componenets

  8. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cosh(x) for example is the average between e^X AND E^-X

  9. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So... `hyperbolic function` ≥ `(a)^x; where a≤e` `hyperbolic function` < `(a)^x; where a>e`

  10. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if the difference is the base, then yes

  11. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, with same x exponent... tnx (I was just thinking of different growths)

  12. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can wolfram alpha it to make sure

  13. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    test it with one concrete condition where a>e

  14. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I started this proposal when I proved that e^x is greater than cosh(x)

  15. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1435300335244:dw|

  16. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    saying, as x-> infinity

  17. nincompoop
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    correct

  18. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then sinh(x) is certainly smaller

  19. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -e^-x<e^x

  20. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -e^x is always >0 e^x is always <0 :)

  21. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -e^-x is always >0, (correction). but that is always >0 as well.

  22. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wwhat wouldn't have?

  23. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    other functions are also obviously less than e^x.

  24. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I want to change my statment a bit

  25. idku
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    `hyperbolic function` < `(a)^x; where a≥e ` `hyperbolic function` > `(a)^x; where a<e`

  26. 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.