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

LolWolf Group Title

Show that the limit as x->0 of 3x^2/(\sin(4x^2))=3/4. Thanks. (Without l'Hospital's)

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. henpen Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    \[Lim(x \rightarrow 0)\frac{3x^2}{(\sin(4x^2)}\]

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

    Use\[Lim (x \rightarrow 0) \frac{sinx}{x}=1\rightarrow sinx=x\]

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

    Why is this true? It's obvious if you graph it http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJzaW4oeCkiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoieCIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMH1d sinx=x when you move closer to the origin.

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

    Yes, but, remember that \[nx\] is not of the form \[nx^2\] so the equivalent does not necessarily apply. :( Now, were we to show that \[\sin nx^2 \sim x^2, x \to 0\] that would make more sense... How would we ago about doing that, though?

    • 2 years ago
  5. experimentX Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \lim_{x \rightarrow 0}\frac{4x^2}{\sin(4x^2)} \times {3 \over 4} \\ \lim_{4x^2 \rightarrow 0}\frac{4x^2}{\sin(4x^2)} \times {3 \over 4} = {3 \over 4}\]

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

    \[ \lim_{4x^2 \rightarrow 0}\frac{1}{\frac{\sin(4x^2)}{4x^2}} \times {3 \over 4} = {3 \over 4} \]

    • 2 years ago
  7. henpen Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    Or\[\lim(x \rightarrow 0) \frac{3x^2}{\sin(4x^2)}=\lim(x \rightarrow 0) \frac{3x^2}{4x^2}=\lim(x \rightarrow 0) \frac{3}{4}\]

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

    Ahh, yes, again, although I don't know how to prove they're asymptotically equal, I should be able to solve it, now, thanks.

    • 2 years 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.