A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

lim x→0 cos 9x − cos^2 *9x / 9x

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

    \[lim~x\rightarrow \infty\{ \cos(9x) -\frac{\cos^2(9x)}{9x}~\text{?}\]

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

    on the homework its setup like lim x -> 0 ........ cos(9x) - cos^2 9x / 9x

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

    break it into smaller parts... 1. \[\lim_{x \rightarrow \infty} \cos(9x) - \lim_{x \rightarrow \infty} \cos^2(9x)/9x\]

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

    okay, well you can separate this into two distinct limits, one is very easy to deal with because we know what it turns out to be: like this \[lim~ x \rightarrow 0~~cos(9x) - lim~x \rightarrow 0~~\frac{cos^2(9x)}{9x)}\] the other one resembles the sin function you asked about a few questions ago, the same methods should work

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

    atleast I think it was you that asked about it

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

    so should it be 1/9 0r 1/81

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

    the cos^2(9x) may use l'hopitals rule...

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

    im thinking the 9's match like cos(9x)/ 9x = 1 and then cos 9x *cos 9x / 9x = 1 am i on the right track?

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

    campbell, no you can't you don't have a case of 0/0,0/infinity,infinity/0 or infinity/infinity, you have 1/0

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

    well lim of cos(9x) = 1 as x ==> 0

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

    is it 3?

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

    if you try plotting this one you can see pretty clearly that as x -> 0 the function approaches infinity. there's another pretty useful property of limits that says the limit of a product of two functions is the product of the limits. so what you'd have in this case is \[1-\{lim~x\rightarrow 0~(\cos^2(x))\}*\{lim~x\rightarrow0(\frac{1}{9x})\}\] the limit of one of these is one, while the other is infinity, and 1 times infinity is infinity.

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

    http://www.wolframalpha.com/input/?i=limit+as+x+-%3E0+of+cos^2%28x%29%2Fx

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

    I dont think its infinity, i put it into the thing at it said an x, but i think its 3

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

    but its 9(x)

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

    use the idea that that the sum of the limits \[\cos ^{2}(9x) = 1 - \sin^2(9x)\] then is \[\lim_{x \rightarrow \infty} \cos(9x) - \lim_{x \rightarrow \infty} (1 - \sin^2(9x))/9x\]

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

    \[\lim_{x \rightarrow \infty} \cos(9x) - \lim_{x \rightarrow \infty} 1/9x + \lim_{x \rightarrow \infty} \sin^2(9x)/9x\]

  18. 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.