Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

tonykart44

  • 2 years ago

Hi everyone, I'm currently studying for my calculus test tommorow and I have some problems which I have no clue how to solve. 1) Lim (cos 2x)^(csc^2 2x) x-> 0 Any help at all is very much appreciated, as I truly have no idea how to get started this excercise. I'm sorry for not saying this earlier but L'Hopitals rule is not allowed.

  • This Question is Open
  1. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    this looks like \(1^{\infty}\) so you can use l'hopital after you take the log

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

    when you see an exponential function like this, you usually have to take the log first and work with that one either that, or rewrite as \[e^{\csc^2(2x)\ln(\cos(2x)}\]

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

    i would take the log, get \[\csc^2(2x)\ln(\cos(2x))\] then rewrite as \[\frac{\ln(\cos(2x))}{\sin^2(2x)}\] to put it in the form \(\frac{0}{0}\) now you can use l'hopital

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

    when you get your answer to this, make sure to remember to raise \(e\) to that power, as you took the log as the first step

  5. tonykart44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you very much for your fast answer but unfortunately we are not allowed to use L'Hoptials rule yet. I'm sorry I didn't specify that, is there another way to solve this problem?

  6. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont know whether it help take the whole expression = y and take log on both sides try to simplify

  7. tonykart44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That looks like it could work. I'll try that.

  8. tonykart44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But isn't that for solving derivatives?

  9. tonykart44
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok so I got this one in the form (1-2sin^2 x)^(1/2sin^2 2x) but i don't know how to go on from there. I know i'm almost there but i don't know how to get rid of the 2x above, I know it's silly, but i just don't see it.

  10. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1-2sin^2x = cos2x

  11. 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.