A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
for the function sinc(x)=sinx/x , why is the point x=0 defined ?
I know the limit as x>0 of sinx/x=1 , but still there is a 0 in the denominator at x=0 , so how does this work ?
anonymous
 one year ago
for the function sinc(x)=sinx/x , why is the point x=0 defined ? I know the limit as x>0 of sinx/x=1 , but still there is a 0 in the denominator at x=0 , so how does this work ?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think that the answer is that sinc would be discontinuous at x = 0, if sinc wasn't defined to be 1 at 0. Sinc does what you would expect except at zero where it is defined so as to make it useful for making things happen.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought that too , since the discontinuity is removable , but then shouldn't sinc(x) be defined in 2 different pieces , namely sinx/x for x different than 0 , and 1 for x=0 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Again, I'm guessing here, but sinc is defined piecewisely; 1 is the value when x=0, sinx/x otherwise. Isn't it a matter of what you want the function to do? In some cases, sinc without a value at zero might be useful, in others, not so much?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perhaps , but the way I encountered the function was simply sinc(x)=sinx/x , without the 1 at x=o part , so that's why I am asking : ))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I see your point, indeed.... Are you watching 18.01 at MIT's Open Course Ware?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes, the value of sinc(0) is defined to be the limit x>0 of sinc(x) i.e. 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@against.names yeah , I've followed all the lectures a year ago , but I found out about the 18.01SC just recently , so I thought I'd do the practice problems and the problem sets :)) @phi what about the ctg(x) at x=0 ? I never see it defined separately for x=0

mytyl
 one year ago
Best ResponseYou've already chosen the best response.0I guess it's because when x>0, sin(x) >0 at the same time(and when x=0, sin(x)=0 too), that's why sin(x)/x=1
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.