A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

Bomull
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim (x>0) \frac{ \sin(x) }{ \sin(2x) }\] ?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{x\to 0}\frac{\sin x }{\sin 2x}\] We know that \[\lim_{x\to 0}\frac{\sin x }{x}=1\] Could you use this here to solve ? @Bomull

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, I'll explain you \[\lim_{x\to 0} \frac{\sin x}{\sin 2x}\] Let's multiply and divide by x \[\lim_{x\to 0} \frac{\sin x}{\sin 2x}\times \frac x x\] \[\lim_{x\to 0} \frac{\sin x}{x}\times \frac{x}{\sin 2x}\] Do you understand till here?

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{x\to 0} \frac{\sin x}{x}\times \frac{x}{\sin 2x}\] Let's multiply and divide by 2 \[\lim_{x\to 0} \frac{\sin x}{x}\times \frac{2x}{\sin 2x}\times \frac 1 2\] We know that \[\lim_{x\to 0}\frac{\sin x}{x}=\lim_{x\to 0}\frac{nx}{\sin nx}=1\] so we get \[\lim_{x\to 0} \frac{\sin x}{x}\times \frac{2x}{\sin 2x}\times \frac 1 2\] \[1\times 1 \times \frac 1 2=\frac 1 2\]

ash2326
 2 years ago
Best ResponseYou've already chosen the best response.1Do you understand this?

Bomull
 2 years ago
Best ResponseYou've already chosen the best response.0ah ok thanks! \[\lim_{x \rightarrow 0} \frac{ nx }{ \sin nx }\] is good to know. I think I got it
Ask your own question
Ask a QuestionFind 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.