A community for students.
Here's the question you clicked on:
 0 viewing
TrojanPoem
 one year ago
Limits question :
TrojanPoem
 one year ago
Limits question :

This Question is Closed

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1limit sin x/ x x> 0 this one is 0/0 but assume x = 1 /t limit tsin1/t 1/t > 0 so t>0

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Now i got the second in my exam limit tsin1/t which is obviously not 0/0

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1My teacher told me you can assume t= 1/x and it will be sinx/x which makes me insane.

phi
 one year ago
Best ResponseYou've already chosen the best response.1limit as x>0 of (sin x) / x is a famous limit The derivation of this limit that I have seen rely on geometric arguments https://www.khanacademy.org/math/differentialcalculus/limits_topic/squeeze_theorem/v/prooflimsinxx

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1but mustn't it be 0/0 in any case to apply this

phi
 one year ago
Best ResponseYou've already chosen the best response.1I assume you mean the problem is limit t sin1/t as t>infinity rewrite as x=1/t , x> 0 and the problem is limit sin(x)/x as x>0 which = 1

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1Lol , I never thought sinx/ x was proved with a triangle tanx = sinx/x LAWL !

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1my mistake t > infinite

phi
 one year ago
Best ResponseYou've already chosen the best response.1The other way to find the limit of sin x / x is to use the series definition of sin x https://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions sin x = x  x^3/3! + x^5/5!  ... now divide by x sin x / x = 1  x^2/3! + x^4/5!  .... now let x>0 to get limit sin x / x = 1

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1The series definition is out of my curriculum :o

TrojanPoem
 one year ago
Best ResponseYou've already chosen the best response.1You know what was wrong ? it was written as 1/t > 0 and I dumbly turned it into t> 0 so it was meaningless .
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.