#Interval of Continuity

242 messages · Page 1 of 1 (latest)

drowsy mulch
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never was taught this and am confused, probably easy but no idea how to look for it

IMG_5387.jpg
gritty crystalBOT
idle isle
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Here you're being asked to define the interval of where x is continuous and you have to identify what the graph is telling you

drowsy mulch
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is that like like circles

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?

idle isle
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The circles are holes where x is not defined

drowsy mulch
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so whats not the circles

idle isle
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Yes but what does it mean if there is a circle and full circle on the same x value

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Is it still defined at this point?

drowsy mulch
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like the dark one

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isnt the open one like it isnt actually that point

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and the dark one the absolute

idle isle
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Yeah open circle means it's undefined and a closed or dark circle means it's defined at that point

drowsy mulch
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so do i list the dark circles?

idle isle
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Yep

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List the intervals or sections of x where your think it's defined

drowsy mulch
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hm i tried putting the coordinates for the dark circles

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but that didnt work out

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hmm

idle isle
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It's not asking for coordinates it's asking for intervals

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The question is asking where is x continuous on the graph

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So you need to give it a domain of where x exists

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Have you learned interval notation yet or does that not sound familiar

drowsy mulch
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probably a while ago like months i havent done math in a while

idle isle
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That's fine I can teach it to you quick

drowsy mulch
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ok epic

idle isle
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Interval notation is just a fancy way of giving the set of points where a function exists

drowsy mulch
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ye

idle isle
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The functions you're familiar with like y=x always continuous and has the interval notation of (-∞, ∞)

drowsy mulch
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ye i seen those

idle isle
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" (" denotes that it goes up to but does not include because you can't reach infinity

drowsy mulch
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so u can see better

IMG_5388.jpg
idle isle
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Let's say we had a function that existed between x=-10 and x=10 we would give it the interval of [-10,10]

drowsy mulch
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why [

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i thought it was between and odesnt include -10,10

idle isle
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"[" denotes that it goes up to and includes 10

drowsy mulch
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oh ok

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how do i tell that on a graph though

idle isle
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You just have to ask yourself does this include the point or not

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Can you tell me the first interval to look at

drowsy mulch
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i just see the 2 dark ones

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at 2,2 and 3,0

idle isle
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It's not just the closed circles we have to at it's the open circles

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Is the function defined at 0?

drowsy mulch
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no

idle isle
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Does it include all the points leading up to 0

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From 1

drowsy mulch
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like in between

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1 and 0

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yeah i suppose

idle isle
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Yeah

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So that's your first interval

drowsy mulch
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so

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do i write

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0 then 1

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or 1 then 0

idle isle
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In internal notation we always start lowest than highest

drowsy mulch
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ok epic

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so (0,1)

idle isle
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That's right but why did you pick ( instead of [

drowsy mulch
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doesnt include 0 or 1

idle isle
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Okay perfect what's your next interval

drowsy mulch
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oh snap i see (1,2) but also there is a dark circle too so idk what to do witht hat one

idle isle
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Well we know that it starts at (1,

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We just have to ask ourselves if x is defined at 2

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Does f(2) exist?

drowsy mulch
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with the dark circle yes

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but is this just for the line

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?

idle isle
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That line and dot is the same function

drowsy mulch
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dang then how do we decide

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cause with those 2 points it looks defined and undefined

idle isle
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Well it's not defined at the first open circle but it is defined in the other

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Since the function is defined that means x does exist

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You can think of the open circle as saying the function doesn't exist there but can still exist if told otherwise

drowsy mulch
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ok

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so

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so far

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(0,1),(1,2]?

idle isle
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Yeah let's keep going

drowsy mulch
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[2,3]?

idle isle
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That's right you're using the same logic

drowsy mulch
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and then [3,4)

idle isle
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Yes put them all together and then we wills simplify

drowsy mulch
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(0,1),(1,2],[2,3],[3,4)

idle isle
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Since (1,2],[2,3],[3,4) have touching brackets we can just combine them

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Can you explain why we can do this

drowsy mulch
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oh we can do [2,4)?

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cause 3 in there either way

idle isle
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Yep and we can continue with (1,2],[2,4)

drowsy mulch
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so is that the final

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of it all

idle isle
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Yeah what's your final answer

drowsy mulch
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(1,4)

idle isle
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And

drowsy mulch
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(0,1),(1,4]

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?

idle isle
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Close

drowsy mulch
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dang

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i actually have no clue

idle isle
idle isle
drowsy mulch
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oh lol

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mindless

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mistake

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i just didnt notice

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so just (0,1),(1,4)

idle isle
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Alright give that answer a shot if you think it's right

drowsy mulch
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?

idle isle
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You can submit that answer lol

drowsy mulch
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oh i did what in the world they had the right one as the long one lol

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make sit easier i guess one second

idle isle
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Lol oops maybe we should done the long one

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Wasn't sure if they simplified

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But now you should know how to do interval notation and more

drowsy mulch
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new ine

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one

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i got

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(0,1),(1,2],[2,3],[3,4)

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does that seem right

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i think they want me to simplify a little

idle isle
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Yep looks right

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Couple answers you can send here just try a few

drowsy mulch
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apperantly the correct answer was (0,1),(1,2),(2,3],(3,4)

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idk how

idle isle
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Uh I guess it wants each of the lines

whole spoke
idle isle
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Damn I'm scammed this dude 😭

whole spoke
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$f(x) = \begin{cases}1 \text{ if }x =0 \ 0 \text{ if } x\neq 0\end{cases}$

carmine gulchBOT
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artemetra

474467399207223307.png
whole spoke
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this function is defined for all real x but is not continuous

idle isle
whole spoke
# drowsy mulch idk how

think of continuity around some point as having very close values to that point if you go left or right

drowsy mulch
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can u explain in terms of this

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💀

whole spoke
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in this case, the answer key writes (1,2) instead of (1,2] is because there is a discontinuity right at x=2

drowsy mulch
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how do u arrive to answer

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then

whole spoke
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okay so you got the (0,1) covered

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now

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oh wait it's a different graph nvm

drowsy mulch
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(0,1),(1,2)

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for this one so far

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i see

whole spoke
# drowsy mulch

unshaded circle = not defined
shaded circle = defined to be exactly that and not where the unshaded circle is

drowsy mulch
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so which one do i listen to

whole spoke
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i looked at the wrong graph

drowsy mulch
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ok

whole spoke
drowsy mulch
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so is it only whats on the line

whole spoke
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precisely

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that's a good way to put it

drowsy mulch
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what about the other line

whole spoke
# drowsy mulch

is it (2,3) or (2,3]? let's break it down
if you look at the graph to the immediate left of x=3, you can see that the function gets closer and closer to y=3. however, AT x=3, y=2 (cuz shaded circle). so there's a sudden jump → discontinuity
which means that the correct interval is (2,3), the one excluding the 3

drowsy mulch
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maybe (1,2)(2,3)(3,4],(4,5)

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idk

whole spoke
drowsy mulch
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ye

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dang

whole spoke
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lol

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any more questions?

drowsy mulch
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wait why it say wrong on the site RIP

whole spoke
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bruh

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what now

drowsy mulch
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didi i miss something

whole spoke
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doesn't look like it

drowsy mulch
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BRUH

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LLOL

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ITS CUAS

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EI FORGOT

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TO WRITE COMMAS

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R U SRS

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BRO

whole spoke
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💀💀💀

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that's terrible

drowsy mulch
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one second

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new one

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was aboe to do this part

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what about this second part

whole spoke
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i won't tell you the full answer but I'll say it's A

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what value should go in the box there?

drowsy mulch
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see

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thats what i was wondering

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i mean

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whats teh continuous part

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cause ik it stops

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so is it

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like

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right before the definite

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?

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idk

whole spoke
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it's continuous from the left

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very important

drowsy mulch
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how do i look for the ik from the left

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so going to the right

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but like

whole spoke
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this question is basically asking you to find an interval like "(a, b]"

drowsy mulch
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idk

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(3,4]??

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idk

whole spoke
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yes!

drowsy mulch
whole spoke
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which number do you put in out of the two?

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you can't put 3 and 4 there

drowsy mulch
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wym

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ohh

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3

whole spoke
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why

drowsy mulch
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well see i thought it was because it went right from there and the 4 was definite n stuff but apperantly it is not 3 bleakkekw

whole spoke
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it is 4

drowsy mulch
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is it because the 3 isnt real

whole spoke
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why? the continuous part is to the left of 4

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that too

drowsy mulch
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oh i thought it reverse

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like starts left

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going right

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bruh'

whole spoke
drowsy mulch
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ok

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now it asksa

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the same

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but from the right

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is it

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there are none

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i dont see any definite

whole spoke
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correct

drowsy mulch
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me rn

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ok thanlks

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that was all

whole spoke
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no problem!

whole spoke
drowsy mulch
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.solved