A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Show that the limit as x>0 of 3x^2/(\sin(4x^2))=3/4.
Thanks. (Without l'Hospital's)
anonymous
 4 years ago
Show that the limit as x>0 of 3x^2/(\sin(4x^2))=3/4. Thanks. (Without l'Hospital's)

This Question is Closed

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Use\[Lim (x \rightarrow 0) \frac{sinx}{x}=1\rightarrow sinx=x\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Why is this true? It's obvious if you graph it http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJzaW4oeCkiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoieCIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMH1d sinx=x when you move closer to the origin.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes, 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?

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

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

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ahh, yes, again, although I don't know how to prove they're asymptotically equal, I should be able to solve it, now, thanks.
Ask your own question
Sign UpFind 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
 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.