Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

badreferences

  • 2 years ago

Bored?\[f:\mathbb R\to\mathbb R\mid e^{x-\int f\left(x\right)}=\int f\left(x\right)\]Find:\[\lim_{x\to\infty}\left(f\left(x\right)\right)^x\]

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

    The answer is 0. And I'm still bored -_-

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

    Haha! I'm right aren't I?

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

    No, lol, I hope that isn't a real question. XD

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

    -_- You are clearly misunderstanding me <-- (see what I did there?) The answer is F.

  5. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i don't even understand the question

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

    Also, I should've specified a \(dx\) in the integrals, so it's clear they aren't an operation of \(f\). But I think you all knew that already.

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

    I didn't. So you misunderstood me again :D

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

    what is \( dx \)? :P

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

    We're given conditions \(f:\mathbb R\to\mathbb R\) which means the function maps reals into reals. We know that \(\int f\left(x\right)\,dx=e^{x-\int f\left(x\right)\,dx}\). We want to find the limit asked knowing this much.

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

    Could you repeat that?

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

    @LifeIsADangerousGame You are a snarky one, aren't you?

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

    It's my job. It's what I do.

  13. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Solution? ಠ_ಠ

  14. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @Mr.Math SAVVEE MEE!

  15. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Ishaan94 I will come back to it later and see if I can do it. I feel tired now.

  16. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\mathsf{ \color{yellowgreen}{\text{Okay}}}\]

  17. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    By taking ln of both sides we have \[x-\int f(x)dx=\ln(\int f(x)dx)) \implies 1-f(x)=\frac{f(x)}{\int f(x)dx}\] \[\large \implies f(x)=\frac{\int f(x)dx}{\int f(x)dx+1}.\] Because \(\int f(x)dx>0\), we have \( 0<f(x)<1\). Hence \[\large \lim_{x\to \infty} (f(x))^x=0.\]

  18. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Oh, I did the same but read above, badref rejected Zero as the answer :/

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

    ISHAAN GET IN CHAT IF U R NOT HELPIN...

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

    :D intrestin lookin R u got there

  21. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, he/she should post the answer then.

  22. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Post the Answer! Post the Answer! Post the Answer!

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

    Lol, I actually mistyped the question. I think the answer for this is actually \(0\), my bad.

  24. Mr.Math
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is the question then?

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.