A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

17x/(x^4 + 1)^1/4...what are the horizontal asymptotes. only the denominator is raised to 1/4

  • This Question is Closed
  1. Mertsj
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Since the lead exponents are equal, the horizontal asymptote is the ratio of the coefficients of the leading terms.

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

    what mertsj said, with the sophistication that as x gets large \[\sqrt[4]{x^4+1}\] behaves like \[\sqrt[4]{x}=x\] so you might as well pretend you have \[\frac{17x}{x}=17\]

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

    oh i see. how do i find y2

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

    What do you mean, y2?

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

    y1= and y2= where y1>y2

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

    And don't forget there are two fourth roots of one so there are two horizontal asymptotes, y = 17 and y=-17

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

    thats what i meant, thanks

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

    \[y=\frac{17x}{(x^4+1)^{\frac{1}{4}}}\] Rearrange to get x in term of y: \[y(x^4+1)^{\frac{1}{4}} =17x\] \[y^4(x^4+1) = 83521x^4\] \[\frac{(x^4+1)}{x^4} = \frac{83521}{y^4}\] \[\frac{1}{x^4} = \frac{83521}{y^4}-1=\frac{83521 - y^4}{y^4}\] So \[x =\pm \left(\frac{y^4}{83521 - y^4}\right)^{\frac{1}{4}}\] So the value of y where the denominator is zero is the value at which the horizontal asymtote occurs... \[y^4 = 83521\] so \[y = \pm 17\]

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

    that's how you prove it the long way round I think...

  10. 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.