A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

clara1223

  • one year ago

find the limit as x approaches 0 of (sin(4x))/(x(cos(x))) a) -1 b) 0 c) 4 d) 1/4 e) does not exist

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

    have you tried graphing the equation and trying to solve it graphically yet?

  2. clara1223
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, not yet.

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

    i would suggest that as the answer may become apparent to you when you graph it

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

    \[\large\rm \lim_{x\to 0}\frac{\sin(4x)}{x \cos x}=\quad \lim_{x\to 0}\frac{\sin(4x)}{x}\cdot \lim_{x\to 0}\frac{1}{\cos x}\]Maybe this can help get us started. When I break them up this way, that first limit looks an awful lot like an identity doesn't it?

  5. clara1223
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    graphically it says that x is undefined at 0 but I need to prove it on paper

  6. clara1223
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @zepdrix then I can pull a 4 out of the first limit and the answer is 4, I'm not sure how to get the second limit though

  7. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This is how you should think about limits in your brain: Step 1: Plug the limit value directly into the function. Step 2: If there is a problem, back up, and do some algebra. Step 3: Plug the limit directly in and check again.

  8. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So for the second limit, do step 1, .... and you're done with it.

  9. clara1223
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok 1/cos(0) is 1 so the overall answer is 4 correct?

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

    yay good job \c:/

  11. 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.