Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Show that the limit as x>0 of 3x^2/(\sin(4x^2))=3/4.
Thanks. (Without l'Hospital's)
 one year ago
 one year ago
Show that the limit as x>0 of 3x^2/(\sin(4x^2))=3/4. Thanks. (Without l'Hospital's)
 one year ago
 one year ago

This Question is Closed

henpenBest ResponseYou've already chosen the best response.2
\[Lim(x \rightarrow 0)\frac{3x^2}{(\sin(4x^2)}\]
 one year ago

henpenBest ResponseYou've already chosen the best response.2
Use\[Lim (x \rightarrow 0) \frac{sinx}{x}=1\rightarrow sinx=x\]
 one year ago

henpenBest ResponseYou've already chosen the best response.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.
 one year ago

LolWolfBest ResponseYou've already chosen the best response.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?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \lim_{x \rightarrow 0}\frac{4x^2}{\sin(4x^2)} \times {3 \over 4} \\ \lim_{4x^2 \rightarrow 0}\frac{4x^2}{\sin(4x^2)} \times {3 \over 4} = {3 \over 4}\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \lim_{4x^2 \rightarrow 0}\frac{1}{\frac{\sin(4x^2)}{4x^2}} \times {3 \over 4} = {3 \over 4} \]
 one year ago

henpenBest ResponseYou've already chosen the best response.2
Or\[\lim(x \rightarrow 0) \frac{3x^2}{\sin(4x^2)}=\lim(x \rightarrow 0) \frac{3x^2}{4x^2}=\lim(x \rightarrow 0) \frac{3}{4}\]
 one year ago

LolWolfBest ResponseYou've already chosen the best response.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.
 one year ago
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
 Engagement 19 Mad Hatter
 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.