Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

dgamma3 Group Title

limit question. lim (x - > 5) 1/(x-5)^4

  • one year ago
  • one year ago

  • This Question is Closed
  1. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{x \rightarrow 5} 1/(1+5)^4\]

    • one year ago
  2. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    woops. the 1 is an x

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

    It would be infinity

    • one year ago
  4. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh

    • one year ago
  5. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    why so?

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

    Do you know L'Hopital's rule

    • one year ago
  7. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    nope. is it the only way?

    • one year ago
  8. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer is infinity. just have no clue how to work it out.

    • one year ago
  9. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok what you can do is:

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

    wait i just noticed

    • one year ago
  11. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    u mean it's x-5 in the denominator right? otherwise it wouldn't be infinity

    • one year ago
  12. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, x-5

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

    \[\lim_{x \rightarrow 5} \frac{x}{(x-5)^4}\]\[=\lim_{x \rightarrow 5} \frac{x}{(x-5)^4}\]\[=\lim_{x \rightarrow 5} \frac{x}{(x-5)^2(x-5)^2}\]\[=\lim_{x \rightarrow 5} \frac{x}{(x-5)(x-5)(x-5)(x-5)}\]\[=\lim_{x \rightarrow 5} \frac{x/x}{(x/x-5/x)(x/x-5/x)(x/x-5/x)(x/x-5/x)}\]\[=\lim_{x \rightarrow 5} \frac{1}{(1-5/x)(1-5/x)(1-5/x)(1-5)}\]

    • one year ago
  14. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oops the last factor should also be (1-5/x)

    • one year ago
  15. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome, thanks for your effort! just wondering line 6. why are you diving everything by x?

    • one year ago
  16. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I hope you see that the bottom factors are (1-1) when substituting x=5, so you get like "1/0" -> infinity

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

    hm it's true that was a useless step

    • one year ago
  18. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I was thinking that it was going to x->infinity at first, but i realized it was x->5 after lol

    • one year ago
  19. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ahhh, yes. i see that. thank you. is that a legal move though? because you are changing the function?

    • one year ago
  20. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    for example, (x-5) doesn't equal (1-5/x)

    • one year ago
  21. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, i guess it is. just would have never thought of that!

    • one year ago
  22. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Nope :) If you divide the top and bottom by x, it is perfectly valid (it's like you are dividing by "1") Example: \[\frac{2}{3} = \frac{\frac{2}{x}}{\frac{3}{x}}=\frac{2}{x}*\frac{x}{3}=\frac{2}{3}\]

    • one year ago
  23. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I divided the numerator by x as well: I did x/x = 1 in the numerator, and divided the whole denominator by x

    • one year ago
  24. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    if you divide the numerator, you MUST also divide the denominator!

    • one year ago
  25. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome, this is just amazing. never would have figured out this.

    • one year ago
  26. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you will learn a neat theorem called "L'hopital's rule" later which will make the computation even easier :)

    • one year ago
  27. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    k. thanks for your time. im now 'a fan' haha.

    • one year ago
  28. kirbykirby Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Hehe awesome ;) Good luck with everything

    • one year ago
  29. dgamma3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    cheers

    • one year ago
    • Attachments:

See more questions >>>

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.