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Babynini
 one year ago
greatest integer functions. Help!
Babynini
 one year ago
greatest integer functions. Help!

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.1@SolomonZelman you free? :)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2do you know how the greatest integer function is defined?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Mm I know what the graph of it looks like. But not quite sure how it's defined

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2http://mathbits.com/MathBits/TISection/PreCalculus/GraphGreatestIntFunction.html the basic idea is that the input x could be any real number the output is always a whole number (positive or negative). You round down to the nearest whole number

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2greatest integer function = floor function

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2think of the number line written vertically dw:1444263692393:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2if we plug in x = 1.7 then [[x]] = [[1.7]] = 1 we round down to the nearest whole number which in this case is 1 dw:1444263763896:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2now let's say we plugged in x = 0.16 that would move to 1 because we're moving down the ladder or building dw:1444263816583:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1approaching it from either the positive or negative side we always do that?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Here are the properties, which follow just from logic: *[1]* \(\Large\color{black}{ \displaystyle \lim_{x~\to~a^+} \left[\left[x\right]\right]=a }\) *[2]* \(\Large\color{black}{ \displaystyle \lim_{x~\to~a^} \left[\left[x\right]\right]=a1 }\) where *a* is an integer.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2let's try an example if f(x) = [[x]], then what is f(8.3125) equal to?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes, how about f(8.99999)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2good, so if the number is positive, you just chop off the decimal portion

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2now let's try f(2.462)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Would that round up? to 3?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I think you meant 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2look back to the vertical number line

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2dw:1444264095476:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2think of each whole number as a floor in a building 2.462 is between the two floors the floor function moves 2.462 down to the nearest floor

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so approaching 2 from the right = 2 and from the left = 2 ?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1because there's no decimals o.o

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2look at the rules SolomonZelman posted

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Ahh ok. Approaching  2 from the right = 2 approaching  2 from the left = ...1?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2idk how you jumped from 2 to +2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2\[\Large \lim_{x \to 2^{+}} [[x]] = 2\] \[\Large \lim_{x \to 2^{}} [[x]] = 3\] looks good

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, my brains are not working haha =.=

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2does \[\Large \lim_{x \to 2^{}} [[x]]\] exist?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1and then as x approaches 2.4 it = 3

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1because the points aren't meeting

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes, specifically because \(\Large \text{LHL} \ne \text{RHL}\) LHL = left hand limit RHL = right hand limit

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so 51(a)(ii) does not exist

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1for c) the answer is: for all noninteger values of a, yeah?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2`for c) the answer is: for all noninteger values of a, yeah?` agreed

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2part b) is very similar to what SolomonZelman wrote out

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Okay, I wasn't sure if that was too "simple" So b: i) n1 ii) n

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Oh I thought this was going to be another squeeze theorem thing, but in case you come across one soon, I think you might be entertained: \[x \le [[x]] \le x+1\] So if you're given like find the limit of \(x [[x]]\) as x approaches 0 you already know: \[x^2 \le x[[x]] \le x^2+x\] So \[\lim_{x \to 0} x[[x]] = 0\] Anyways there are a lot of problems with squeeze theorem and this rounding function in it so I thought it'd be fun to share real fast for fun.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1hahah my next problem is that! i'll tag you in it ;)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Though from all you said here I think I could get it.
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