Do you know how to solve quadratic equations?
#help-0
limpid turret
broken wraith
Do you know how to solve quadratic equations?
Yeah but the answers would be with roots and I din don't know how to solve these
Don't*
limpid turret
Yup. You basically were on the right path all along. You were just misled for a little while
broken wraith
Yeah but the answers would be with roots and I din don't know how to solve these
......
limpid turret
Yeah but the answers would be with roots and I din don't know how to solve these
I'm confused. Are you saying "yes you know how to solve quadratic equations" but "no you dont know how to solve with roots"?
!nosols
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
broken wraith
I'm confused. Are you saying "yes you know how to solve quadratic equations" but...
I Tried and I couldn't ok? 😭
limpid turret
I Tried and I couldn't ok? 😭
Boruto, i promise you i am not asking you to attack or ridicule you or make you feel bad. I simply want to be sure i understand what you are telling me so i can best help you.
I am sorry if my messages sound hostile but i promise you that is not my intention. i am not judging you negatively. I'm here to help 
molten pewter
Two solutions
their point is that just giving away the answer without explanation is frowned upon here -- the idea is to guide people through the process
golden osprey
Fair point
broken wraith
Boruto, i promise you i am not asking you to attack or ridicule you or make you ...
Well what's the answer
golden osprey
Simplify the expression first and then use the quadratic formula. Hope that helps
broken wraith
I tried do the quadratic equation and I failed
golden osprey
If solving the quadratic equation directly doesn't work, use the quadratic formula
broken wraith
What's that
limpid turret
Well what's the answer
An equation like $x^2-4x+2=0$ is known as a quadratic equation. There are a few ways to solve quadratic equations. You can try factoring, but not every quadratic can be simply factored. But there is another method that always works, the quadratic formula. In this specific problem, it is what you would need
limpid turret
Another way to find the solution is by a method known as "completing the square". But that method is how we end up with the quadratic formula. So if you are not familiar with formula already, I'm guessing you may not know about the quadratic formula yet
broken wraith
Try me
limpid turret
@broken wraith permit me to ask, from where did you get this problem? By that, i mean, what else are you learning in the class where you were assigned this problem? If you do not know quadratic formula, then maybe you are expected to solve this in some other way. And it might help me to get some idea of what other things you are learning in your math classes
broken wraith
Class?, I get way more easier math in the class, dad wants to Test me and if I gave up he'd tell me the answer as I give up. But he's not with me anymore so I tried to solve it alone and I failed, I tried asking you guys and I failed as well
To be more clear dad gave me this as wants me to solve it
limpid turret
Class?, I get way more easier math in the class, dad wants to Test me and if I g...
Not with you? My deepest condolences if you mean that in the permanent sense
broken wraith
He's alive so don't think far
limpid turret
To be more clear dad gave me this as wants me to solve it
I see i see. So the expectation here would be that you should devise methods to solve this then
Okay i can work with that
broken wraith
And I need to take a bathe 😭
So can we do it quickly
Or I can keep the room for myself while bathing?
limpid turret
So then i assume you have some familiarity with the idea quadratics, yes?
broken wraith
Yes
limpid turret
Or I can keep the room for myself while bathing?
You can keep it open. But if it closes, you can simply open a new channel once you return. No need to worry about losing this one
limpid turret
Sure. If I'm not available, then I'm sure someone else will be able to help you. I'll try to be around, but around this time i can get very busy
broken wraith
Ok cya
broken wraith
And I need to take a bathe 😭
ATTENTION
lone heartBOT
@broken wraith Has your question been resolved?
brave hazel
can someone help me with this? i have no progress yet
tender turtle
brave hazel
lil bro u in the wrong channel
brave hazel
5 is 180-47-52
brave hazel
go to the help channels with no name
tacit arch
can someone help me with this? i have no progress yet
Are you taking calculus
brave hazel
Are you taking calculus
nope
i forgot what's in add math
but so far we've learned polynomials, matrix, transformation
gauss jordan
raw pike
Does anyone one know how to pick a contour when integrating a contour integral
wheat ridge
Yo Gav
tacit arch
Does anyone one know how to pick a contour when integrating a contour integral
!occupied
lone heartBOT
Does anyone one know how to pick a contour when integrating a contour integral
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
wheat ridge
Go to a different channel
broken wraith
.reopen
tacit arch
is anyone gonna solve my question..
Just be patient
raw pike
can someone help me with this? i have no progress yet
f(3)=2,is that what the question is asking because there’s just a graph with coordinates
tacit arch
Maybe open a new help channel
brave hazel
Maybe open a new help channel
this is the new help channel haha
brave hazel
f(3)=2,is that what the question is asking because there’s just a graph with coo...
i have no idea that's just what my teacher gave me
tacit arch
You're just lucky people keep spamming their questions in your channels
brave hazel
maybe it is
raw pike
i have no idea that's just what my teacher gave me
I think the answer is f(3)=2 because there’s no other information
Is it algebra ?
lone heartBOT
@brave hazel Has your question been resolved?
brave hazel
I think the answer is f(3)=2 because there’s no other information
okay thanks
brave hazel
Is it algebra ?
if polynomials is algebra then maybe
lone heartBOT
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Available help channel!
quick igloo
Are there Any ways i can easily remember the Explicit and Implicit Formulas?
quick igloo
my brain has been broken
feral trellis
my brain has been broken
same
rich quiver
Are there Any ways i can easily remember the Explicit and Implicit Formulas?
What's that?
quick igloo
its like a Exponent thingy
raw jetty
Are there Any ways i can easily remember the Explicit and Implicit Formulas?
formulas?
quick igloo
yeah, and what all the letters mean
raw jetty
explicit is just a variable interms of the other
implicit is a relationship between variables without stating onr interms of the other
raw jetty
??
quick igloo
im gonna look at the notes agian ._.
reef wren
Are there Any ways i can easily remember the Explicit and Implicit Formulas?
could you elaborate more
quick igloo
well, i know that the formula, im just confused on how to apply it
raw jetty
its like "any ways i can easily remember the x and y formula" but even more vague
reef wren
the AN= A1 x R^N-1
oh geometric series ?
quick igloo
uhhhhhhhhhh yeah
raw jetty
thats so far from explicit implicit?? 😭
reef wren
the AN= A1 x R^N-1
so it says the nth term of a geometric series is the first term multiplied by the ratio to the power of n-1
reef wren
thats so far from explicit implicit?? 😭
fr
quick igloo
thats so far from explicit implicit?? 😭
I know :( they are both on my quiz tmrr and i have no idea.
so the N-1 is like, you have a bagle that doubles every day, how many bagles in 3 days, 3-1 is two?
quick igloo
https://tenor.com/view/bagel-bagels-cream-cheese-cheez-cheese-gif-65105117719584...
its me
i think i get it a little more, ima run over my homework agian!
.close
lone heartBOT
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sick vessel
hi, could someone explain this to me please? how am i supposed to solve this? where do i start?
winter bay
hi, could someone explain this to me please? how am i supposed to solve this? wh...
Use the periodicity again
Notice that 31pi/12 > 2pi
waxen flame
Perhaps an explanation about modularity. 🤔
sick vessel
Notice that 31pi/12 > 2pi
ok yes
winter bay
Perhaps an explanation about modularity. 🤔
Wdym?
sick vessel
do i do 7pi/12 - 24pi/12 because im subtracting 2pi, no i wouldnt bc its negative
also why did it even say that cos31pi/12 is whatever they wrote
waxen flame
7pi/12 is coterminal to 31pi/12 because 7pi/12 + 2pi = 31pi/12.
winter bay
2pi = 24pi/12
sick vessel
yes i get that
winter bay
7pi/12 + 24pi/12 = 31pi/12
sick vessel
OH WOAH i had to add the 24pi/12 not subtract it
ohh
but how do i know when i add it and when i subtract it
winter bay
Well you have to subtract 24pi/12 to get 7pi/12
winter bay
but how do i know when i add it and when i subtract it
It doesn't matter if you add or subtract 2pi in the trig stuff
You'll get the same answer regardless
winter bay
also why did it even say that cos31pi/12 is whatever they wrote
Also the answer to this is likely more complicated than ur ready for
You have to use double angle identities and power reduction i think
sick vessel
but i did 7pi/12 - 24pi/12 and i got a negative answer which was -17pi/12
even if i worked with that negative i wouldve gotten the same answer???
winter bay
but i did 7pi/12 - 24pi/12 and i got a negative answer which was -17pi/12
U have to subtract 24pi/12 from 31pi/12
You're given cosine of 31pi/12 and u gotta find cosine of 7pi/12
sick vessel
ok but why did they include the sqrt of 6 and 2
whatever comes after the = next to cos 31pi/12
winter bay
ok but why did they include the sqrt of 6 and 2
Bc that's genuinely what that's equal to
sick vessel
OH what cos 31pi/12 equals to
winter bay
Yes
sick vessel
crap ok
sick vessel
so then how would i determine the value of cos 7pi/12
winter bay
so then how would i determine the value of cos 7pi/12
Because you know cos 31pi/12
sick vessel
im so confused im so sorry
ocean sealBOT
hiidostuff
winter bay
right?
sick vessel
ok yes
winter bay
ok yes
alright now
do you agree that $\frac{31\pi}{12} - \frac{24\pi}{12} = \frac{7\pi}{12}$
ocean sealBOT
hiidostuff
winter bay
ur subtracting 2pi basically
cool
ok so would you now agree that $\cos{(\frac{31\pi}{12} - \frac{24\pi}{12})} = \cos{(\frac{7\pi}{12})}$
ocean sealBOT
hiidostuff
sick vessel
yes
sick vessel
yes
winter bay
then $\cos{(\frac{31\pi}{12} - \frac{24\pi}{12})} = \cos{(\frac{31\pi}{12})}$
ocean sealBOT
hiidostuff
sick vessel
wait why does it equal 31pi/12 again
winter bay
wait why does it equal 31pi/12 again
$\cos{(t - 2\pi)} = \cos{t}$
ocean sealBOT
hiidostuff
sick vessel
**hiidostuff**
oh wait
oh crap how does that happen
even when u subtract 2pi u get the same thing that t was
or is it bc 2pi is a full circle and its just returning back to its spot
winter bay
or is it bc 2pi is a full circle and its just returning back to its spot
this
when you subtract 2pi
its like going backwards on the circle by 2pi
which gets you to the same spot
sick vessel
ok i got it
sick vessel
but like doesnt 31pi/12 - 2pi is 7pi/12???
because its 24pi/12
WAIT ITS THE SAME THING, because its doing a full circle back to the same spot, even after subtracting 2pi
OHH
31pi/12 = 7pi/12 !?!!!
winter bay
its a dif problem
sure
sick vessel
could u explain what coterminal means again, i got part 1, that was easy, but then for part 2, i need to find an angle that is coterminal to -246?
and it has to be greater than -720??
winter bay
well what is 2pi in degrees
sick vessel
360
sick vessel
-246-360 is -606
like when it asks for a negative angle i subtract -360, but if it asked for positive i would have added 360
winter bay
like when it asks for a negative angle i subtract -360, but if it asked for posi...
yeah
and both of those are coterminal to -246
winter bay
i know ill be back here lol, but TY again!
no problem
sick vessel
.close
lone heartBOT
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Available help channel!
golden sparrow
Hi can someone help me with this please
lone heartBOT
Hi can someone help me with this please
reef wren
Should I be finding the third side of the triangle or do Pythagorean theorem
find the 3rd side using pythogrean then you can find all ratios
reef wren
Root 8 right
yea
lone heartBOT
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Available help channel!
torpid raven
i would like a second opinion on this question
lone heartBOT
i would like a second opinion on this question
inner haven
i would like a second opinion on this question
G(-1) = integral 4 -> -1 f(t)
Because the bounds on top is less than the one on the bottom ( a > b ) we will switch them
and it will become
torpid raven
so it's C right
inner haven
i didnt actually compute it lol but ill do that now
torpid raven
just making sure cus the answer key the textbook gave is making me trip
inner haven
Maybe I did this wrong
inner haven
maybe its finding the total area from -1 to 4?
buoyant saddle
and it will become
this is correct
inner haven
this is correct
would that not compute to 4 tho?
buoyant saddle
and it should be 4 yes
inner haven
im not sure cause he said the answer was.6
buoyant saddle
cus thats what the textbook says
because the textbook is wrong
textbooks are wrong all the time
check you’re reading the right section
lone heartBOT
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Available help channel!
arctic river
In the solution it says that I have to find three points and then find the vectors b/w them which is a linear combination of vectors for the equation of a plane to get the parametric equations
mortal magnet
The normal vector points directly away from the plane, that is in the wrong direction
It also doesn’t tell you any additional information that would already be included in the equation
little drum
and a point on a plane say (0, 0, 5)
(0,0,5) is not on plane ;-;
mortal magnet
The 3 points way as you showed it is already pretty good, you don’t really save much on effort or time by deviating from there
arctic river
Let me digest that for a sec
little drum
Also, the point slope form is given by $$\frac{x - 0}{2} = \frac{y - 0}{-3} = \frac{z - 2}{5} = k$$
ocean sealBOT
Arya
arctic river
Oh ok that makes sense since if u r given a general equation of the plane it isnt parallel to the plane and therefore the vector eq w/ the normal vector would just be perpendicular
to the plane
Ok my question is that why do u need two vectors as opposed to just one
mortal magnet
one vector would be a line
a plane is not a line and so requires two vectors to fully describe it
lone heartBOT
wanton kindle
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safe meadow
What can I do about this problem
lone heartBOT
What can I do about this problem
little drum
Show figure
little drum
BC = √3, BD = 2t, DC = 3t => √3AD = 5t
safe meadow
BC = √3, BD = 2t, DC = 3t => √3AD = 5t
How you get BD = 2t
t is a variable not the length right
little drum
Nvm that. Can you use sine law?
safe meadow
Nvm that. Can you use sine law?
Yeah quite
Where do I use it
Angle bdc is 60°
Right
little drum
2/3 = BD/DC = sin(BCD)/sin(CBD) = sin(BAD)/sin(CAD) = BT/CT
And BC = √3, so you can figure BT, CT and hence AT
safe meadow
Oh yeah
safe meadow
And BC = √3, so you can figure BT, CT and hence AT
Do I use cos rule or what?
I'm kinda confused
Do I use Stewart theorem bro
little drum
For AT stewart would do the trick
safe meadow
little drum
b²m + c²n = a(d² + mn)
lone heartBOT
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devout helm
Anyone know how to use a micrometer?
lone heartBOT
Anyone know how to use a micrometer?
prime badge
devout helm
So I have to use the bottom reading+ the top reading?
void nymph
a vernier scale is aka a micrometer lol?
prime badge
So I have to use the bottom reading+ the top reading?
sounds right, i don't know 100%
placid zinc
20.04 somethings
void nymph
yeah
devout helm
How to get 20?
placid zinc
I've g2g, hopefully someone else can help you with that
coral flower
How to get 20?
basically
main scale + vernier/circular scale * least count
the main scale coincides at 20
vernier scale is like 4
least count is 0.01 (usually)
20 + 4 * 0.01 = 20.04
devout helm
basically
main scale + vernier/circular scale * least count
Is the main scale the bigger scale?
coral flower
Is the main scale the bigger scale?
the fixed one , yeah
the one that rotates is circular/vernier scale
coral flower
in this gif , yellow scle is main scale and green is circular
this for ur screw gauge
devout helm
So when the circular touches the marking of the main, we take that reading right?
coral flower
So when the circular touches the marking of the main, we take that reading right...
ye
coral flower
yes
also ping me pls
u take the main scale reading (where main scale coincides with the 0 of the other thing) and the vernier scale reading (where the moveable scale coincides with one of the main scale (line/point/smthing))
and use the same calculation , main scale + (vernier scale * least count)
devout helm
@coral flower How do I read this?
coral flower
picture a bit fuzzy , main scale coincides with 4.8 what about the vernier scale?
and looks like the least count for this is 0.05 mm 👀
devout helm
So it'll be 4.8+0.05?
coral flower
no
vernier scale coincides with 1 (ima say)
so 4.8 + 1 * 0.05 (ok actually ur correct , my bad)
usually vernier scale isnt realy that accurate , and ppl would prefer screw gauge for the external diameter
devout helm
Like a micrometer?
devout helm
the thing u used before , i call it screw gauge
Oh I didn't use that because it doesn't fit
wind cloak
fermat:
devout helm
But we do we have to use screw gauge specifically
wind cloak
nerd joke sorry
coral flower
But we do we have to use screw gauge specifically
u can use whatever u feel is easier
devout helm
u can use whatever u feel is easier
But reading might not be accurate right?
coral flower
But reading might not be accurate right?
would be pretty neglible tbh
devout helm
would be pretty neglible tbh
Oh but which is better tho?
coral flower
<@691353193384509443> How do I read this?
like here it can be 4.85mm or 4.825mm , both seem to fit
coral flower
Oh but which is better tho?
id use screw gauge personally , easier to read
devout helm
It's measured in mm right?
coral flower
would be writen on the instrument
usually the least count is also written on the instrument
u need to be careful of the least count btw , not all screw gauge / vernier calliper have the same one
devout helm
Oh I guess it's in cm for Vernier and mm for screw gauge
coral flower
Oh I guess it's in cm for Vernier and mm for screw gauge
really?
coral flower
sometimes it can be cm , make sure to change ur measurements into SI units :d
devout helm
sometimes it can be cm , make sure to change ur measurements into SI units :d
Ok by the way can you recommend any Vernier calipers simulator or micrometer simulator?
lone heartBOT
If you are done with this channel, please mark your problem as solved by typing .close
coral flower
@devout helm if u dont have any more questions <3 ^^
devout helm
.close
lone heartBOT
devout helm
. reopen
devout helm
<@1017151697967124480> if u dont have any more questions <3 ^^
How they get 0.25?
@coral flower
Sorry for the ping
lone heartBOT
Available help channel!
outer steeple
How big is the angel A
lone heartBOT
How big is the angel A
median oar
Could it be any number
outer steeple
Idk this question is too complicated my brain is not braining right now
median oar
So you don’t know if A could be any angle
outer steeple
yeah I don't know
median oar
Then you should take a breather and look at this question with fresh eyes
median oar
Ok but my point is could be anything
Can it be 5 degrees? -10 degrees? 1000 degrees?
What are we working with here
glad root
How big is the angel A
you can find the exact measure if you apply some properties
crimson dawn
How big is the angel A
Uh theres a specific property they want you to apply here but I think we should do this the longer way
Firstly what is the sum of the angles of a triangle
lone heartBOT
@outer steeple Has your question been resolved?
tepid scroll
lone heartBOT
tepid scroll
Can someone guide me, where do I even start I dont get a thing, in either parts
mortal trellis
what is the def of a projection
lone heartBOT
@tepid scroll Has your question been resolved?
tepid scroll
π^2 = π o π = π
Basically a mapping which if you apply twice or apply once will give the same result
mortal trellis
so a) is asking you to prove that pi^2=pi iff (id-pi)^2=id-pi
mortal trellis
wdym get it
its the mapping that takes a vector and returns that vector
id(v)=v
tepid scroll
Does nothing
mortal trellis
it "does nothing"
mortal trellis
the sets Im(id-pi) and ker(id-pi) are somehow connected to the sets Im(pi) and ker(pi)
they are asking for what that connection is
for example a vector could be in one of the sets iff it is in one or both of the others or something
tepid scroll
right but how do I calculate Im(id-pi) and ker(id-pi) itself
tepid scroll
for example a vector could be in one of the sets iff it is in one or both of the...
yeah like a condition I got that
mortal trellis
use the def of Im and ker
tepid scroll
Okat well i get the kernal one I think it will only be {0}
but the image one
a vector - its projection
no its not 0 only
hmmmmm
a vector - its projeciton = 0 oh oh
its all the vectors
pi^2(idv) - pi(idv)
cuz they the same
an will give 0
mortal trellis
I meant direction of implication in the sense of A => B vs A <= B etc
forget bases
and perpendicularity
tepid scroll
dirctionnnn
well Ker of idv - pi would go to 0
like what sort of vectors in idv - pi would give 0 in the other space
and
the image of idv - pi is just the range like everywhere it can go
lone heartBOT
@tepid scroll Has your question been resolved?
tepid scroll
can you express that in terms of an equation
No ugh I don't know how I would do that
(sry I was gone to eat food)
@mortal trellis
mortal trellis
it means that there exists a vector w in V with v=(id-pi)(w)
what can you do with that equation?
tepid scroll
no idea
maybe uh
yeah no clue
I'll ask my uni proffesor nw
thank you so much @mortal trellis
:>
.close
lone heartBOT
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frigid elbow
Determine, justifying, the continuity domain of each of the functions f and g
frigid elbow
dont know what to do here
tardy stag
so clearly it's continuous on every space between integers
is it continuous at the integers? at only some integers?
frigid elbow
hmm I think its continuos to all integers
tardy stag
why?
frigid elbow
hmm
oh wait
because no matter what integer u insert it always give a number
cause the square works like a abs
tardy stag
feels to me like you're confusing a few things...
integers are {..., -3, -2, -1, 0, 1, 2, 3, ...}
frigid elbow
yea
tardy stag
because no matter what integer u insert it always give a number
this sounds like you're describing the integers being closed under g, which is interesting but not useful here i think?
we're talking about continuity
tardy stag
um, well, what is your definition of continuity?
frigid elbow
um, well, what is your definition of continuity?
basically for me continuity is when any object (x) has always a image (y)
tardy stag
basically for me continuity is when any object (x) has always a image (y)
that sounds like the definition of a function in general?
what's an example of a function that is not continuous?
frigid elbow
frigid elbow
what's an example of a function that is not continuous?
when in a certain interval there arent any objects or images
or in a certain point
tardy stag
but this would be continuous?
tardy stag
what's wrong with that
frigid elbow
tardy stag
the function is defined at that point, it just moves down
see the closed dot right below it
tardy stag
i think you might want to review your definition of continuity
frigid elbow
i think you might want to review your definition of continuity
yea I never knew very well the definition of continuity I just do the exercises
tardy stag
well you can do the one you're on right now just by sketching it
but to justify your answer you'll probably need to actually use the definitions
frigid elbow
like here I did the left one correctly just cant understand the right one
frigid elbow
but to justify your answer you'll probably need to actually use the definitions
hmm yea I think so
tardy stag
like here I did the left one correctly just cant understand the right one
what did you say for the left one?
frigid elbow
the limit for 0+, the limit for 0- and f(0)
and they all gave me 1
so the domain is R
tardy stag
a common definition for continuity is that $f$ is continuous at $t$ iff $\lim_{x\to t} f(x) = f(t)$
ocean sealBOT
hayley, who shakes the world
tardy stag
which it sounds like you used on the left one
tardy stag
and is equal to the value at that point
tardy stag
why not?
tardy stag
the set is composed of many points
frigid elbow
tardy stag
why didn't you look at x=1 for the left problem?
like why did you focus specifically on x=0?
frigid elbow
because 0 was the main number
I dont know how to explain
Im not english
in the above it tells me that the function comes from 0-
and in the bottom one it tells me that the function comes from 0+
tardy stag
(what language? italian?)
frigid elbow
portuguese
tardy stag
yes, so you know the function is continuous below 0 because it's made of other continuous functions,
and you know the function is continuous above 0 for similar reasons
so all you needed to check was the "seam" at 0
it's similar on the right, but there are "seams" at every integer
frigid elbow
hmm ok
tardy stag
can you sketch g(x)?
frigid elbow
ok
frigid elbow
can you sketch g(x)?
tardy stag
,rccw
ocean sealBOT
tardy stag
okay, those are the two components which is good. but remember that the line only applies on the integers, and the parabola only applies on the non-integers
frigid elbow
ohh ok no problem
tardy stag
the parabola is on the integers, and the line is on the nonintegers
frigid elbow
ok
frigid elbow
yea
tardy stag
why?
tardy stag
remember the stuff about limits
tardy stag
here's a more accurate sketch of your function
see how most of the time it's a line
but at every integer it's a part of a parabola
frigid elbow
Yea
tardy stag
so if we look at x=2, what's the limit of g as x -> 2?
frigid elbow
3
But only in the parabola
If we talking about x -> 2+ its different
Or x -> 2-
tardy stag
um, well yes we're talking about those things
$\lim_{x\to2} g(x) = \lim_{x\to2^-} g(x) = \lim_{x\to2^+}g(x)$
ocean sealBOT
hayley, who shakes the world
frigid elbow
Ohh ok
tardy stag
in fact, $\lim_{x\to2}g(x)$ only exists if the + and - limits agree
ocean sealBOT
hayley, who shakes the world
frigid elbow
Its not continuos
tardy stag
why not?
frigid elbow
Cause for example for 2+ I get -1
tardy stag
okay. why does that make it not continuous?
frigid elbow
Cause f(2) and lim x -> 2+ its different
tardy stag
g, not f
but yes, good, $\lim_{x\to2} g(x) = -1$ but $g(2) \neq -1$ so it's not continuous at $2$
frigid elbow
I was replacing in this one
ocean sealBOT
hayley, who shakes the world
frigid elbow
ok nice
tardy stag
okay. what about at other integers?
tardy stag
why not? can you make an argument for why it's not? you can write in portuguese if you want, i should be able to read it
frigid elbow
ohh ok
quando x tende para números inteiros a função não é contínua uma vez que f(n) é diferente de lim x -> n+
tardy stag
i see another instance as well, look at the graph
tardy stag
yes
see how your line and your parabola intersect twice
once is at 0, like you said
where's the other one?
tardy stag
ok. so is it continuous there?
frigid elbow
yea
tardy stag
ok. how do i know there aren't more?
(again you can write in portuguese here if you want)
frigid elbow
cause the parabola can only meet the linear function two times
tardy stag
ok yeah that's probably fine
i would have said something like -- if x < -1 then x^2 + 1 > 1 - x
which is basically what you said
frigid elbow
g is continuous in {1} and {0}
frigid elbow
wait I did 3/2 but 3.5 its 7/2
frigid elbow
why is g(3/2) equal to 13/4?
ohh its not integer
so I have to replace in the function bellow
right?
frigid elbow
its continuous for all the non integers
tardy stag
yes exactly
so where exactly is g continuous?
you can use words rather than {} notation
frigid elbow
g is continuous in x = -1, x = 0, and when x belongs to R\Z
tardy stag
yeah great
tardy stag
yes
frigid elbow
okk thx
tardy stag
i suppose
frigid elbow
here if I had to do the lim x -> +infinite g(x)
which one I choose
or do I do it for both?
tardy stag
it would have to be the same for both branches
since there are integers all the way out to infinity
frigid elbow
but in the top one I get +infinite and in the bellow one I get - infinite
frigid elbow
so it doesnt exists
tardy stag
so it doesnt exists
correct it does not exist
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compact hawk
I have the following Cauchy problem (differential equations):
$[
\begin{cases}
y' = \sqrt{y}, \
y(0) = 1.
\end{cases}
]$
ocean sealBOT
Quantum
Compile Error! Click the 
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compact hawk
And i have to find the general solution:
$2\sqrt{y} = x + c$
ocean sealBOT
Quantum
compact hawk
From there, i have to study the domain, so it's $\forall y > 0, \forall (x+c)/2 > 0$
ocean sealBOT
Quantum
compact hawk
And so i get $(x+c)/2 > 0$
ocean sealBOT
Quantum
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solemn breach
how to find lcm on casio-fx991ex classwiz for period of trigonometric functions
lone heartBOT
how to find lcm on casio-fx991ex classwiz for period of trigonometric functions
@solemn breach Has your question been resolved?
lone heartBOT
@solemn breach Has your question been resolved?
lone heartBOT
@solemn breach Has your question been resolved?
woeful reef
Is this infinite series calculable? Note that 0 < b < 1, x is a real number, and m is a positive real number #math-discussion message
exotic canopy
wdym by calculable
little drum
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
exotic canopy
$b^{(x-mn)^2} = \frac{b^{x^2 + (mn)^2}}{b^{2xmn}}$
woeful reef
wdym by calculable
We can obtain an analytical solution for this
ocean sealBOT
artemetra
exotic canopy
$= b^{x^2}\frac{b^{(mn)^2}}{b^{2xmn}}$
ocean sealBOT
artemetra
exotic canopy
the b^x^2 is a constant, so we can take it out
little drum
is equivalent to asking for $\sum_{n = -\infty}^{\infty} r^{\alpha^2 n^2 - \beta n}$
ocean sealBOT
Arya
woeful reef
is equivalent to asking for $\sum_{n = -\infty}^{\infty} r^{\alpha^2 n^2 - \beta...
Uhm… I don’t know how to solve this 😓
exotic canopy
Yikes.
woeful reef
Oh no... weird symbol
peak valve
hello
lone heartBOT
hello
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
exotic canopy
Oh no... weird symbol
theta function
exotic canopy
ocean sealBOT
little drum
this is what I was looking for ;-;
exotic canopy
wikipedia FTW 💪
quasi vector
so you wrote your series in terms of a function which is defined in terms of a very similar series
exotic canopy
yep
woeful reef
,w \sum_{n = -\infty}^{\infty} r^{n^2 - n}
Where's the alpha and beta 🥲
woeful reef
That looks… scary
little drum
hmm, was just consulting wolfram about what the function was called. I remembered seeing the function so plugged some alpha, beta
little drum
Where's the alpha and beta 🥲
are b, m, x real numbers?
woeful reef
Yeah? I said that in the question 🥲
exotic canopy
yeah no i doubt it can get simpler than that
it's super easy to come up with sums that have no closed form
little drum
comparing with the theta function's complex valued variables z, l, (I'm using l in place of \eta which is the half-period notation), the farthest it goes is to \theta( -mx ln(b) i /pi , -im² ln(b) /b) where ln(b) is negative, i is √-1
you can substitute your m, x, b in this but after this is your headache.
Check this out
woeful reef
So basically… another infinite series 🥲
Is there really no way to escape the infinite series?
tacit arch
jacobi theta function is a function
it's also equal to a power series yes
but so is sin(x)
woeful reef
comparing with the theta function's complex valued variables `z, l`, (I'm using ...
@little drum is this theta2?
little drum
<@706934233012371577> is this theta2?
no, that's theta
woeful reef
no, that's theta
There's an empty theta function as well?
little drum
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dawn quail
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dawn quail
can someone explain the property or rule that is being applied here?
tacit arch
,tex .abs def
dawn quail
i get that we are adding up two integrals, but why is the first integral written backwards?
ocean sealBOT
riemann
tacit arch
|5x - 2| = -(5x-2) if 5x-2 < 0 and ...
dawn quail
interesting, so we know that [2/5, 0] is where this y axis = 0
2/5 = 0.4
so everything to the left is negative
everything to the right is positive
@buoyant saddle what did I say wrong?
buoyant saddle
y axis = 0?
dawn quail
where the function evaluates to 0?
errr
the root of the function
getting my wording mixed up here
buoyant saddle
sure but that is by no means the same thing as y axis = 0
y axis = 0 makes literally zero sense
dawn quail
i should have said y=0?
buoyant saddle
sure
limpid turret
Or f=0
dawn quail
what's wrong with saying y axis = 0
buoyant saddle
what do you think the y axis is?
forest marsh
what's wrong with saying y axis = 0
y axis is a set
dawn quail
i thought the y axis is the entire line
forest marsh
So set = 0
buoyant saddle
i thought the y axis is the entire line
which line?
buoyant saddle
which line?
^
tacit arch
y axis is the vertical line x=0
dawn quail
ah
forest marsh
so many 🤔 emoji's, dunno where i am going wrong
We want you to explain what you mean
dawn quail
i got them mixed up i think
i can just say [2/5, 0] is the y-axis
but i think i mean the x-axis here
forest marsh
What is [2/5, 0] a segment ?
tacit arch
parentheses are used to indicate points (2/5, 0)
what do you think [2/5, 0] represents
dawn quail
oh, thank you, I thought (2/5, 0) doesn't include those values, but [2/5, 0] does include those values
tacit arch
interesting, so we know that [2/5, 0] is where this y axis = 0
the grey point is (2/5, 0)
what are you trying to say avid
buoyant saddle
you’re confusing intervals with points
dawn quail
the grey point on the graph is considered the root
dawn quail
you’re confusing intervals with points
yeah
buoyant saddle
i can just say [2/5, 0] is the y-axis
this is still wrong
i don’t think you understood riemann
dawn quail
(2/5, 0) is the point on the x-axis where y = 0
buoyant saddle
redundant
dawn quail
i can also just say (2/5, 0) is the point on the x-axis? it's implied that it's the root?
buoyant saddle
the x axis is y = 0
dawn quail
right
buoyant saddle
i can also just say (2/5, 0) is the point on the x-axis? it's implied that it's...
the point?
we don’t usually say that
just say root
or zero
dawn quail
alright so (2/5, 0) is the "zero" or "root" (but not "point") on the x-axis
since this function is absolute, I multiply everything to the left side of the root by (-1) and add that left side integral with the right side integral
buoyant saddle
no it is a point on the x axis it’s just that i think it’s better to say zero/root
dawn quail
reverse-uno, here we come full circle with the 🤔
buoyant saddle
alright so (2/5, 0) is the "zero" or "root" (but not "point") on the x-axis
sin...
yep
dawn quail
Thank you, that's a good way to look at absolute functions. Find the root, and break it into two parts. Multiply the left side by (-1) and add the results together. Much easier to solve.
Not sure if that's always possible to do, but I hope so
limpid turret
Not sure if that's always possible to do, but I hope so
It could always be positive, like $\abs{x^2+1}$
ocean sealBOT
SWR
limpid turret
Or always negative, like $\abs{-1-x^2}$
ocean sealBOT
SWR
dawn quail
It could always be positive, like $\abs{x^2+1}$
so what would you do here? if it asks to find the integral of |x^2 + 1|
let's say it's same interval, [4,0]
buoyant saddle
definition of absolute value
dawn quail
you see an even power, and +?
buoyant saddle
sure
buoyant saddle
well i mean what are you defining a and b as
are they constants
you’ll just have some constant function depending on what a and b are
dawn quail
sorry, wrong variables. meant to write x and y
we would have to do this?
(-x^2 + y^2) + (x^2 - y^2)?
oh but we didnt find the root yet
buoyant saddle
i mean this isn’t a function
dawn quail
why not?
buoyant saddle
did you mean for these to be absolute value?
dawn quail
yeah
buoyant saddle
well what is it equal to?
buoyant saddle
functions of two variables in the cartesian plane?
buoyant saddle
y = f(x,y)?
buoyant saddle
y = f(x,y)?
does this make any sense to you
dawn quail
no, i would probably wanna replace y with a different variable here
f(x,g) = |x^2 - g^2|
y = |x^2 - g^2|
buoyant saddle
ok but again you have two independent variables and one dependent variable
dawn quail
that's not allowed?
buoyant saddle
how are we going to interpret this in the cartesian plane
dawn quail
3D I guess? lol
buoyant saddle
3D I guess? lol
sure but then we are dealing with surfaces
dawn quail
dawn quail
and this integral you’re using no longer really means anything
maybe if we just wanna find the surface area of a 3d object?
buoyant saddle
no that’s not how that works
buoyant saddle
if the integral is designed for 2d, i am curious why it doensn't work in 3d
do you know what the integral really is?
dawn quail
area under the curve
tacit arch
knief about to teach a whole multivariable integral course
little drum
Are we still on this?
tacit arch
i do like the graphics
little drum
or did we diverge
dawn quail
yea avid sorry but i will not go over double integrals with you
would "volume integrals" be the correct term?
tacit arch
or did we diverge
your first avid channel?
buoyant saddle
area under the curve
we are no longer working with curves in 3d
buoyant saddle
would "volume integrals" be the correct term?
yea you can find volume with multiple integrals
you can think of it as using rectangular prisms below the surface rather than rectangles below the curve
tacit arch
you can think of rectangular prism as a fancy word for boxes
buoyant saddle
yep
dawn quail
your first avid channel?
buoyant saddle
bruh
tacit arch
clearly this is 32.8
buoyant saddle
sorry, i'm still here
if you want to get a visual of what we mean for 3d you should look up dr trefor multivariable calculus
he has a playlist with some videos on the topic
dawn quail
Are we still on this?
for now this is a good starter for me
i will keep this in mind for 2d integrals, very basic stuff with an actual root
the question kinda depends on the interval and how many roots are involved
as for absolute functions that don't have any roots...
hopefully i will not get an integral question on these... but if I do...
maybe they are actually easier to solve?
buoyant saddle
hopefully i will not get an integral question on these... but if I do...
no hopefully you do because it’s way easier
dawn quail
that's what i was thinking too.. no need to split it
buoyant saddle
if it has no roots then it’s either the same as integrating the function itself or the negation of the function
you don’t have to split the integral
dawn quail
let's say it's a function that is below the x-axis, with no roots
"area under the curve" now becomes "area above the curve"?
little drum
"Area above the curve" would give a +ve value, "Area under the curve" would give a negative
Integral computes "Area under the curve"
dawn quail
I feel like area above the curve, would be infinity here
the same if we flipped it
I feel like area under the curve, would be infinity here
let's say from [-1,1] with both to give boundaries
little drum
I feel like area under the curve, would be infinity here
Set up an integral for area under the curve here, roughly
Say between points a, b
little drum
the same if we flipped it
dawn quail
"area under the curve", wouldn't it refer to this? if it's from [-1,1] and below the x-axis
little drum
Would it be int_a^b f(x) dx
?
Is the value of f(x) = infinity? Cause that will be the length of the small rectangle with "dx" width that you're adding for each rectangle with f(x) length
Area under the curve = int_a^b f(x) dx is basically a partition of the curve into rectangles of length f(x) and width dx for each "x"
dawn quail
but why are you drawing a,b above the curve, if it's "area under the curve"? integrals must always be directed towards the x-axis?
we would have to say "find the area above the curve" for this?
little drum
Like I said, what is f(x) here?
dawn quail
area "under" the curve can refer to both versions here? it's like we are taking the integral upside down when we consider a curve under the x-axis?
little drum
Area under the curve = `int_a^b f(x) dx` is basically a partition of the curve i...
No. The gist is 
. Since we take f(x) to be the length of each rectanglular partition, the area under curve by definition computes the area bounded between the curve and x-axis
dawn quail
"the area bounded between the curve and x-axis"
ah OK
so the word "under" can be a bit misleading
little drum
May be so
dawn quail
it should perhaps be "area between the x-axis and curve" instead, but that's too wordy
i like "area bounded by the curve"
seems more universal
little drum
You'll be using that terminology pretty soon
dawn quail
we will stop using "area under the curve"?
little drum
For hydrodynamics as well
Yes, and you'll be finding area bounded by y-axis, x-axis or some random curve/s
dawn quail
lol, seems like confusing/misleading terminology to start with, i wonder why they even say "under" if "bounded by" is better
little drum
Because they always start with a graph that looks like this, even when explaining Riemann Sums
,w plot e^x
ocean sealBOT
little drum
And here, the integral indeed is area under the curve
dawn quail
And here, the integral indeed is area **under the curve**
next is -e^x
lol but anyways, I guess it's just something that you gotta figure out on your own sometimes, or by the good folks here on Discord
not too sound too harsh about the education system, but sometimes I can relate to this with some of the profs at university
anyways, I will close this now! 😛
tyvm
.close
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warm quarry
I still dont really understand epsilon delta proofs and would like some extra help trying to fully understand it cuz i think it is really important for a basis of limits
warm quarry
For example show with the precision definition that lim x-> 1 1/(x+1) = 1/2
forest marsh
Start from the right and deduce a delta value
warm quarry
could you explain this a little bit more
We get told to do this:
All e>0 There exists delta > 0 such that |1/(x+1) - 1/2 | < e : All x 0<|x-1|< delta
Let e> 0
1, |1/(x+1) - 1/2 | < e and now solve for | x-1 | < e?
forest marsh
warm quarry
oh wait
we get told to do it the other way around?
so from |f(x) - L | <e to a delta?
warm quarry
okay
forest marsh
Thats how i use to do
warm quarry
So normally I know what to do unless i get something like this:
(x+1)(x-3) < E or in this case it will be : |1-x| / |2(x+1)| < e cuz now we cant solve for |x-1| <
so now we must pick a delta but from that part i dont really understand why and how
lone heartBOT
@warm quarry Has your question been resolved?
wary fable
We get told to do this:
All e>0 There exists delta > 0 such that |1/(x+1) - 1/2 ...
@warm quarry whats ur question?
warm quarry
so now we must pick a delta but from that part i dont really understand why and ...
this
wary fable
whats the limit to prove?
warm quarry
For example show with the precision definition that lim x-> 1 1/(x+1) = 1/2
.
this one
wary fable
$|\frac{1}{x+1} - 1/2| < \varepsilon \iff |\frac{1-x}{2(1+x)}| < \varepsilon \iff \frac{|x-1|}{2|x+1|} < \varepsilon$ thus $$|x-1| < \varepsilon \cdot 2 |x+1|$$
warm quarry
yes
so normally
i could devide or multiply one side to get |x-1| < e
and then i found my delta
but in some cases i cant
ocean sealBOT
Goëtia
wary fable
you need to lower bound the RHS
wary fable
wym?
deft plover
warm quarry
we have to use this?
wary fable
$|x-1| < \delta = \varepsilon \cdot 2 |x+1|$
warm quarry
sup?
wary fable
huh?
warm quarry
ye we must pick a delta
wary fable
isnt that a delta the one i gave?
warm quarry
and then delta = min{1,2e}
warm quarry
isnt that a delta the one i gave?
idk what the sup(e.2|x+1|) means
wary fable
and then delta = min{1,2e}
where did 1 & 2e came from?
deft plover
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Goëtia
