quick limit Q for math gurus :)

[Jeff Moote]

You can show that lim (t->0) sin(t)/t = 1 with the squeeze theorem (which I'm sure you've seen). This is normally how it is shown in early calculus courses. Of course, L'Hôpital's rule works and is easier.

+1

 

[Poop-Loops]

Dunno what squeeze theorem is. My high school calc teacher was a literature major.

 

[Geoff St. Germaine]

Dunno what squeeze theorem is. My high school calc teacher was a literature major.

That's unfortunate. For sin(t)/t you could write that sin(t) < t and also that t < tan(t) (for small t). Then you just slap them together: sin(t) < t < tan(t) and manipulate that to get 1 < t/sin(t) < cos(t).

http://en.wikipedia.org/wiki/Squeeze_theorem

 

[Figjam]

l'hopital's *

 

[Figjam]

That's unfortunate. For sin(t)/t you could write that sin(t) < t and also that t < tan(t) (for small t). Then you just slap them together: sin(t) < t < tan(t) and manipulate that to get 1 < t/sin(t) < cos(t).

http://en.wikipedia.org/wiki/Squeeze_theorem

We called that the sandwhich theorem.

 

[Jeff Moote]

We called that the sandwhich theorem.

Well that has the same implications, espeically considering it's a colloquially derived name to begin with. Squeeze theorem is what I generally see in textbooks.

 

[Poop-Loops]

Wow, I've never heard of that. Weird.

 

[Brad Barker]

You can show that lim (t->0) sin(t)/t = 1 with the squeeze theorem (which I'm sure you've seen). This is normally how it is shown in early calculus courses. Of course, L'Hôpital's rule works and is easier.

series expansion ftw.

 

[Ericman197]

Wow, I've never heard of that. Weird.

It's kinda cool. In layman's terms, they're saying that at the point of interest, the three functions converge like so:

If you know the limits of the top and bottom functions, you can find the limit of the middle function (either as a single point or as the range between the Y values of the top and bottom functions).

 

[MCBTunes]

That's unfortunate. For sin(t)/t you could write that sin(t) < t and also that t < tan(t) (for small t). Then you just slap them together: sin(t) < t < tan(t) and manipulate that to get 1 < t/sin(t) < cos(t).

http://en.wikipedia.org/wiki/Squeeze_theorem

yeah i've seen the squeeze?