Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Open

NoelGreco Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow 0}\frac{ \sin x }{ x }=1\] because the graph of y=x and sin x get closer and closer to each other as they approach zero. I assumed that's what you meant.
 one year ago

snuderl Group TitleBest ResponseYou've already chosen the best response.0
Use L'hopitals rule. If\[ \lim_{x \rightarrow a} \frac{ a(x) }{ b(x) }= \frac{ 0 }{ 0 }\] then \[\lim_{x \rightarrow a} \frac{ a(x) }{ b(x) }=\lim_{x \rightarrow a}\frac{ a(x) ' }{ b(x) ' }\]
 one year ago

Topi Group TitleBest ResponseYou've already chosen the best response.0
To use L'Hopitals rule you need to know the derivative of sin(x), but to derivate sin(x) you need to know what is the limit of sin(x)/x when x approaches 0, so this is circular proof and thus not valid. Here is one proof that starts from the geometrical fact that if x is in radians and positive but less than pi/2 then sin(x) <= x <= tan(x). If we divide this inequity by sin(x) (>0) we get: 1 <= x/sin(x) <= 1/cos(x) If we take the inverse of this we get: 1>= sin(x)/x >= cos(x) If we now let x approach 0 we get: 1>= sin(0)/0 >= cos(0) So because cos(0) = 1 sin(0)/0 = 1.
 one year ago

dinnertable Group TitleBest ResponseYou've already chosen the best response.0
Here's another interesting geometric proof using the squeeze theorem. http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx
 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.