greatest integer functions. Help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

greatest integer functions. Help!

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

#51
1 Attachment
@SolomonZelman you free? :)
do you know how the greatest integer function is defined?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Mm I know what the graph of it looks like. But not quite sure how it's defined
http://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
greatest integer function = floor function
think of the number line written vertically |dw:1444263692393:dw|
if 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|
now 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|
approaching it from either the positive or negative side we always do that?
Here are the properties, which follow just from logic: *[1]* \(\Large\color{black}{ \displaystyle \lim_{x~\to~a^+} \left[\left[x\right]\right]=a }\) *[2]* \(\Large\color{black}{ \displaystyle \lim_{x~\to~a^-} \left[\left[x\right]\right]=a-1 }\) where *a* is an integer.
let's try an example if f(x) = [[x]], then what is f(8.3125) equal to?
8?
yes, how about f(8.99999)
8 still
good, so if the number is positive, you just chop off the decimal portion
now let's try f(-2.462)
Would that round up? to 3?
I think you meant -3
look back to the vertical number line
yes yes sorry o.o
|dw:1444264095476:dw|
think 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
so approaching -2 from the right = -2 and from the left = -2 ?
because there's no decimals o.o
look at the rules SolomonZelman posted
Ahh ok. Approaching - 2 from the right = 2 approaching - 2 from the left = ...1?
idk how you jumped from -2 to +2
*-2 and -3
\[\Large \lim_{x \to -2^{+}} [[x]] = -2\] \[\Large \lim_{x \to -2^{-}} [[x]] = -3\] looks good
Sorry, my brains are not working haha =.=
does \[\Large \lim_{x \to -2^{}} [[x]]\] exist?
and then as x approaches -2.4 it = -3
No, it doesn't.
why not?
because the points aren't meeting
yes, specifically because \(\Large \text{LHL} \ne \text{RHL}\) LHL = left hand limit RHL = right hand limit
so 51(a)(ii) does not exist
ahh gotcha. Okay!
Part b!
for c) the answer is: for all non-integer values of a, yeah?
`for c) the answer is: for all non-integer values of a, yeah?` agreed
part b) is very similar to what SolomonZelman wrote out
Okay, I wasn't sure if that was too "simple" So b: i) n-1 ii) n
looks good
Thank you so much :)
sure thing
Oh 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.
hahah my next problem is that! i'll tag you in it ;)
Though from all you said here I think I could get it.

Not the answer you are looking for?

Search for more explanations.

Ask your own question