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Babynini
 one year ago
Squeeze Theorem greatest integer function
Babynini
 one year ago
Squeeze Theorem greatest integer function

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from \(\pi \) to \(\frac{\pi}{2}\) cosiene goes from \(1\) to \(0\) so it would be identically \(1\) on that interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then on \(\frac{\pi}{2}\) to \(0\) it goes from \(0\) to \(1\) so on that interval it would be \(0\)

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Might be fun to play here, the greatest integer function is sometimes called the ceiling function. https://www.desmos.com/calculator/fdipg03oxv

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do those funky brackets mean the least integer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0on the interval \(0\) to \(\frac{\pi}{2}\) it goes from \(1\) to \(0\) so it is 0 there as well

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So if I were to draw one cosine it would be just one mountain

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@empty i though greatest integer was floor

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0greatest integer less than like \(\lfloor 2.4\rfloor=2\)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444265853694:dw like that!..? haha i'm such an artist.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why can't they use the standard \[\lceil \cos x \rceil\] for ceiling and \[\lfloor \cos x \rfloor\]for floor?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0who said art was dead that is cosine though not \(\lfloor \cos(x)\rfloor\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0"greatest integer" to me means "greatest integer less than" so "floor" whereas "least integer" means "least integer greater than i.e. "ceiling"

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Oh floor ceil, whatever haha yeah I agree with @ospreytriple I wouldn't have messed up if they just wrote \[\left\lfloor \frac{1}{\sec x} \right\rfloor\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Wait, so how is cos(x) looking then? o.o

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Almost identical but shifted https://www.desmos.com/calculator/cowtkonbwe

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0hmm..shifted how? Like the only difference seems to be that there's lines across the bottom and top.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is identically \(1\) on \((\pi,\frac{\pi}{2})\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then it is \(0\) on \(\frac{\pi}{2},\frac{\pi}{2}\) except it is 1 at \(0\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=floor%28cos%28x%29%29%2C+pi..pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can't see the \((0,1)\) on wolfram, but it is there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There seems to be some confusion above somewhere. The greatest integer function is also called the floor function, the greatest integer that is less than or equal to the argument.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ospreytriple that is what i think as well

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So there's no..normal curve. Ah yeah @Empty showed me the desmos one but I don't get it really haha it looks like a cosine but with lines on the hills/indents

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So the graph is nor a normal curve?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Is it just a point at (0,1)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's definitely it @satellite73 . The ceiling function mentioned above is also called the least integer function, the smallest integer that is greater than or equal to the argument.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444266645781:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Is what ..i'm imagining. By what yall are saying 0.0

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah that's right, it's what we're saying. :)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444266755110:dw like dis?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0The line on 0 being all but the point (0,0)

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah, since the greatest integer function says [[0]]=0 Looks good to me.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Fabulous! phew. part b!

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So for this one, the rules we used for the previous problem (ie: a, or a1) do not apply? or do they?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the reason that desmos thing threw you off is that they graphed both the floor function and cosine on the same graph

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0floor is a step function

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I'm wondering about the part b now. Because I know the rules, which you stated for the last problem. But I wasn't sure if those applied here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\to 0}f(x)=0\] for sure, since it is identically 0 to the right and to the left

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0b: i) 0 ii) if the rules apply then.. 0.57 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the fact that \(f(0)=1\) does not effect the limit

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what does "rules apply" mean? this thing never approaches 0.57 it is either 0 or 1

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0the rules of if it approaches from the left it = a  1 and if it approaches from the right it = a but for this one I guess we just use the graph.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\to \frac{\pi}{2}}f(x)=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok typo there hold on

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \lim_{x\to \frac{\pi}{2}^}f(x)=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since it is identically 0 on the interval to the left

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0They all look like they're ultimately approaching 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no, from the right it is \(1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444267958342:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \lim_{x\to \frac{\pi}{2}^+}f(x)=1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and since the right and left hand limits are not the same, the limit does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0k good to answer the last question, the limit exists everywhere except at those two jumps

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So I should probably write that in some form of interval haha the two jumps meaning.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no limit at \(\frac{\pi}{2}\) and \(\frac{\pi}{2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0at those to points it jumps form 1 to 0 and from 0 to 1 receptively

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1444268282111:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0hahah awesome. Art lives!!
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