it’s been maybe 10 years since i’ve done this sorry can’t help
#help-38
strong granite
radiant spindle
You could prime factorize 3024 to see if there are any simple values for x
Or use the rational root theorem to find roots of the cubic
Sorry I don't understand what you mean by this
strong granite
Sorry I don't understand what you mean by this
i believe there is some sort of formula for this
just can’t remember it
radiant spindle
I didnt understand the question at first but now I think I do
I'd start by looking at each component of each term
coarse meadow
I didnt understand the question at first but now I think I do
i got 3024=2^4x3^3x7
radiant spindle
For example, a seems to be increasing by one when n increases
coarse meadow
For example, a seems to be increasing by one when n increases
it would be really easy if the 4-6 was a 4-5 but
im not too sure now
radiant spindle
i got 3024=2^4x3^3x7
So you can try to find combinations of 3 numbers that fit the form x,x-2, and x+4
I just checked and yes there is a valid solution
coarse meadow
wouldnt that take a long time
radiant spindle
Yes it would
Idk i just guessed
Idk since the 3 numbers have to be sorta close it limits the combinations
radiant spindle
it would be really easy if the 4-6 was a 4-5 but
Are you sure the second term isnt 3(6-5)
coarse meadow
is x=14?
radiant spindle
Thats what I got
coarse meadow
Are you sure the second term isnt 3(6-5)
yeah i asked my teacher and he said its the original question
coarse meadow
Thats what I got
i just tried x=16 and it was too big so i went down by one each time lol
radiant spindle
yeah i asked my teacher and he said its the original question
Wdym
So is it 3(6-5)?
radiant spindle
Or 2(4-5)?
coarse meadow
the question i said is the original
radiant spindle
Huh
Well another thing is that b increases by 2 each time
c not so sure
You are only talking about arithmetic sequences right?
coarse meadow
im pretty sure
radiant spindle
i dont think 6,6,7,8 is part of an arithmetic sequenc
coarse meadow
yeah it makes no sense imo
radiant spindle
😭
coarse meadow
would there be 2 different equations one for higher and one for lower values of a
idk man
coarse meadow
2n+2
coarse meadow
algs
shy valley
trim joltBOT
shy valley
does this look tright
lone basin
(a / b)^n ✅
lone basin
(a / b)^(-n) ❌
lone basin
Neither ❌
youre missing some that belong
shy valley
Neither ❌
youre missing some that belong
so swap one of them?>
lone basin
so swap one of them?>
Not swap. You dont need to remove anything from the (a / b)^n or Neither columns
shy valley
Not swap. You dont need to remove anything from the `(a / b)^n` or `Neither` col...
this one?
shy valley
Not swap. You dont need to remove anything from the `(a / b)^n` or `Neither` col...
it says its not correct
lone basin
Shoot, the neither column has one that doesn’t belong
lone basin
Show all three so i can verify properly
shy valley
Show all three so i can verify properly
lone basin
lone basin
For which one
shy valley
lone basin
Yes, $b^n a^{-n} = b^n \cdot \frac 1{a^n}$
solid kilnBOT
King Leo
lone basin
so why is it wrong
Sry for late response, but you can combine b^ n / a^n, and then it conforms to one of the other columns
shy valley
Sry for late response, but you can combine b^ n / a^n, and then it conforms to o...
how would i dot aht
@lone basin
trim joltBOT
@shy valley Has your question been resolved?
trim joltBOT
@shy valley Has your question been resolved?
stoic turtle
how would i dot aht
basically $b^n a^{-n} = \frac{b^n}{a^n}$
solid kilnBOT
Ohm Shankar| 20240
stoic turtle
and that can also be written as
solid kilnBOT
Ohm Shankar| 20240
stoic turtle
and then you can factor out the -1 power from both exponents so it becomes
solid kilnBOT
Ohm Shankar| 20240
stoic turtle
which conforms to column 2
trim joltBOT
@shy valley Has your question been resolved?
wraith hinge
yo
wraith hinge
how do you find the derivative of absolute value?
example
f(x) = x |x|
I used chain rule and got x / |x|
but it says its wrong
ionic pendant
I used chain rule and got `x / |x|`
how exactly does the chain rule figure into this?
wraith hinge
|x| = sqrt(x^2)
ionic pendant
it is correct, just less common
trim lichen
we are definitely not
west sleet
I used chain rule and got `x / |x|`
If you chain rule this you get 2x/2sqrt(x^2)=x/abs(x) so you are correct kinda
But the function is not abs(x)
It is abs(x)*x
Use product rule
Did I kill chat
wraith hinge
👍
west sleet
Gah
west sleet
Use product rule
@wraith hinge does this clear things up for you?
wraith hinge
yea ill just use the piecewise one since its easier
west sleet
Fair
tight wind
$\sum_{n=1}^{\infty} arctan(\frac{n}{sin(n)})$
trim joltBOT
$\sum_{n=1}^{\infty} arctan(\frac{n}{sin(n)})$
solid kilnBOT
alwaysonce
tight wind
How do you prove that n/sin(n) is infinity
as n approaches inf
this is for a determine whether the series conv/div problem
hollow tangle
sin(n) belongs to [-1, 1]
so n/1 is inf if n is inf
(taking best case of sin(n) is 1)
red mountain
$\sum_{n=1}^\infty \atan(\frac{n}{\sin(n)})$
solid kilnBOT
Bonk
tight wind
(taking best case of sin(n) is 1)
but what if sin(n) is -1
hollow tangle
-inf
tight wind
wait so then doesthat mean the series diverges
because dpending on sin arctan will approach pi/2 or -pi/2
carmine spade
wait so then doesthat mean the series diverges
yes
carmine spade
because dpending on sin arctan will approach pi/2 or -pi/2
this is not quite right though
because it will oscillate between these
hollow tangle
tan(pi/2) is inf or -inf depending on where you approach from
tight wind
because it will oscillate between these
Oh
how would i express my answer in my work
Like im not sure how to articulate all of this
Because n/sin(n) oscillates between -inf and inf, arctan oscillates between -pi/2 and pi/2 thus its divergent?
carmine spade
the fact that you want to use is that for an infinite sum $\sum^\infty a_n$ to converge you must have $\lim_{n \to \infty} a_n = 0$
if this isnt a fact you have seen yet then its a good one to prove !
solid kilnBOT
Acman
tight wind
so then here lim n-> inf is oscillating betwen -pi/2 and pi/2 != 0 thus its not convergent?
also to be clear just because lim n-> inf = 0 doesnt mean that a infinite sum is convergent right
carmine spade
so then here lim n-> inf is oscillating betwen -pi/2 and pi/2 != 0 thus its not ...
yes, though you need to be careful with how you word it
carmine spade
also to be clear just because lim n-> inf = 0 doesnt mean that a infinite sum is...
yes consider $\sum_{n=1}^\infty \frac{1}{n}$
solid kilnBOT
Acman
tight wind
oh right harmonic
tight wind
yes, though you need to be careful with how you word it
how would you word it ?
dapper swift
**alwaysonce**
this problem is an application of if $a_n \nrightarrow 0$, then $\sum a_n$ diverges
solid kilnBOT
south
dapper swift
now because arctan is a continuous function, you have $\lim_{n \to \infty} \arctan(n/\sin(n)) = \arctan (\lim_{n \to \infty} n/\sin(n))$
solid kilnBOT
south
dapper swift
you can interchange the limit and arctan
tight wind
yes
dapper swift
yeah and then $\lim_{n \to \infty} \frac{n}{\sin(n)}$ doesn't exist
goes to both -infinity and infinity
solid kilnBOT
south
tight wind
wait so in my work i can write that lim n->inf of n/sin(n) oscillates between -inf and inf thus it doesnt exist?
dapper swift
I know I'm repeating other people's work
dapper swift
wait so in my work i can write that lim n->inf of n/sin(n) oscillates between -i...
yes
also arctan(infinity) -> pi/2 and arctan(-infinity) -> -pi/2
you don't need to write this down; just thought it would be nice to explain where the other helper was coming from
dapper swift
no worries!
tight wind
.close
trim joltBOT
trim joltBOT
Available help channel!
trim joltBOT
solid kilnBOT
lin.fei ‧₊˚❀༉‧₊˚.
red mountain
g=10 m/s^2 💀
you have 2 things happening here
the time it takes for the stone to hit the water
and the time it takes for the sound to go back up
the time it takes for the sound to go back up is simply t=d/v
with d the distance and v the speed of sound
but you got t=10s
thats correct
what about it?
the speed of sound does not change
you are acting like its an object that has an acceleration of 10m/s^2
however, its not
its speed is constant
so the take it takes to cover a distance is t=d/v
wdym?
the formula $v=u+at$ is taken from $\dv{a}{t}=v$
however, the a is 0 because the speed of sound is unaffected by gravity
thus v is just u
solid kilnBOT
Bonk
violet gust
what? no. Final velocity is not speed of sound
final velocity can be calculated with v = u+at
initial is 0, and t you calculated as 10 sec
use that and you find v = 100m/s downwards
red mountain
use that and you find v = 100m/s downwards
thats not the question thats being asked
violet gust
the stone is freefalling under the influence of gravity
red mountain
we dont care about the speed of the stone when it hits the water
violet gust
yea we dont
explain this then
No
Like, there is no point in calculating hte final velocity of the stone
unless it is asked for
!xy honestly. Can you tell what you are expected to calculate?
trim joltBOT
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.
red mountain
!xy honestly. Can you tell what you are expected to calculate?
cmon bro
its two unrelated parts
time it takes to hit the water
time it takes for the sound to travel up
thats all
violet gust
Yea, I know. I am asking coz she wants to find final velocity of the stone. I expected there would be something more that she wants to calculate it
So once you get the time to hit water, you can safely ignore everything about the stone
Yes. Coz there is no relation between velocity of sound and velocity of stone
trim joltBOT
trim joltBOT
Available help channel!
chilly crypt
guys is tehre something wrong w my notes bc im not sure if i wrote down the right formulas (especially the one where i have to add by total area) i have no one to ask abt this im sorry 😭
hollow tangle
why are you doing all your work on such a small paper?
red mountain
its think its a cheatsheet
chilly crypt
why are you doing all your work on such a small paper?
HAHAHA mbb i find it easy to memorize like that
chilly crypt
its think its a cheatsheet
nour its just my way of studyinggg
i put all formulas in one page
hollow tangle
that is a cheatsheet
chilly crypt
guys is tehre something wrong w my notes bc im not sure if i wrote down the righ...
but guys this is correct right
sweet terrace
Can someone help me with algebra?
red mountain
Can someone help me with algebra?
!help
trim joltBOT
Can someone help me with algebra?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
chilly crypt
guys is tehre something wrong w my notes bc im not sure if i wrote down the righ...
anyonee
trim joltBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
hollow tangle
(you can ping helpers)
trim joltBOT
@chilly crypt Has your question been resolved?
thorn copper
AB…HI regular 9-gon
AIJ=45
KIH=?
thorn copper
just help me show the circle is on the symmetry axis
red mountain
all these angles are the same
red mountain
from that you can find IAJ and IHJ
thus you can find IJA and so IJH
then you can find HIJ
with HIJ and AIJ you can find KIH
if AK is a straight line
trim joltBOT
@thorn copper Has your question been resolved?
thorn copper
yeah it isnt straight since the answer is 45
red mountain
then im also kinda stumped
thorn copper
how does that show the circle is on the symmetry axis
there must be a simple way to show this
or maybe i am blind and this requires complex analysis
red mountain
or maybe i am blind and this requires complex analysis
nah i doubt it
there has to be smth simple we're overlooking
thats why i hate geometry problems
its always drawing that one line or extra angle that makes it simple
prisma plover
how do you know the answer?
ripe valley
AB…HI regular 9-gon
AIJ=45
KIH=?
I got KHI=60
thorn copper
yeah it is
thorn copper
how do you know the answer?
geogebra
i mean i can solve it backwards but that means proof by contradiction
i dont wanna use the existence of backwards problem as a solution to this one
trim joltBOT
@thorn copper Has your question been resolved?
prisma plover
<@&286206848099549185>
frank inlet
?
red mountain
<@&286206848099549185>
this isnt your channel lol
prisma plover
but its still unsolved
zinc ginkgo
but its still unsolved
don't ping for other people. you don't know if OP is here or not
red mountain
but its still unsolved
doesnt matter, its not your channel, dont act in OPs behalf (unless asked)
thorn copper
i know helpers arent helpful on these kind of problems
so im waiting for a geo wizard to spawn
thorn copper
its always drawing that one line or extra angle that makes it simple
also this definetely isnt just that simple
thorn copper
house.
red mountain
santa house house
prisma plover
if you can prove that KL = IL then KIH = 45
thorn copper
lol
prisma plover
$KL = HL\sqrt{3}$
solid kilnBOT
General_Jacob
thorn copper
trust me this isnt that kind of question
red mountain
!original
trim joltBOT
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.
red mountain
yeah ik but im curious what the original is
thorn copper
the problem sounds really simple
the solution most definetely isnt
i was thinking inversion might be helpful
red mountain
wherre did you get it from?
thorn copper
wherre did you get it from?
a friend sent me
i’ll go sleep please ping me if you find a solution before channel dies
so i can take a look
prisma plover
@thorn copper
i solved it
you can mirror it
and then find the angle
here you would be looking for the angle KAI
i assumed that MI and AK are perpendicular and i think i shouldn't have done that
trim joltBOT
@thorn copper Has your question been resolved?
sick forum
can someone help me understand or with my work
trim joltBOT
can someone help me understand or with my work
trim joltBOT
can someone help me understand or with my work
Show your work, and if possible, explain where you are stuck.
empty orchid
Can you define slope intercept form?
empty orchid
Okay.
empty orchid
I get I have to solve for Y
Do you know the methods to isolate variables in an equation?
sick forum
not really
static bolt
Guys, I love math.
empty orchid
not really
Okay. You have:
- Subtracting something on both sides
- Dividing
- Multiplying
- Adding
Basically, the 4 arithmetic operations, except you do it on constants/variables.
sick forum
alright and if you subtract that you subtract it from itself and something similar on the other side of the equation right?
So you can remove that from it
empty orchid
alright and if you subtract that you subtract it from itself and something simil...
If the english is englishing, yes.
sick forum
hmm
so that means X is negative right so I’d guess you have to make X a positive value
empty orchid
so that means X is negative right so I’d guess you have to make X a positive val...
Well, if you want, but there's a faster way.
What can we do to make that -x a 0 on the left hand side?
empty orchid
I don’t fully know the steps
Okay. Do you know how to solve one-step equations?
sick forum
I think so
sick forum
is it 1?
sick forum
uhh
I feel like I know it but I’m not sure
because we were told there always an invisible coefficient infront of a variable that should be one
empty orchid
because we were told there always an invisible coefficient infront of a variable...
Yes.
empty orchid
so it should be -1x+1c=0?
Yes.
trim joltBOT
@sick forum Has your question been resolved?
thick pelican
Hello
limpid dawn
.close
azure dagger
help
azure dagger
i wanna
use remainder/factor thereom
to show that P(2) = 0
how to i do this with all the m
red mountain
long division
azure dagger
i dont wanna tho
red mountain
then find (z-2)(az^2+bz+c) find a,b,c
azure dagger
that also takes long but ig that works
red mountain
i mean, long divison is easier
and faster
and simpler
but if you dont wanna do it
red mountain
there arent many alternatives lol
red mountain
you can get m as a coefficient
try doing long division and show me where you get stuck
red mountain
I mean you can always do P(2) = 0
not for part 2 though
azure dagger
to try to find m
how does this show that 2 is a factor tho
red mountain
so youre gonna have to factor it out either way
jolly pebble
not for part 2 though
right thats true
red mountain
how does this show that 2 is a factor tho
you can write a polynomial as the product of its roots
P(x)=k(x-x1)(x-x2)...(x-xn)
with n roots
azure dagger
yeah
@red mountain im asking tho how could trying to find m through factor theoreom show that 2 is a root
for any m
red mountain
factor out (z-2)
red mountain
<@946543471668379678> im asking tho how could trying to find m through factor th...
!noping
trim joltBOT
<@946543471668379678> im asking tho how could trying to find m through factor th...
Please do not ping individual helpers unprompted.
red mountain
nope
azure dagger
ok sry
azure dagger
oh okay
azure dagger
yeah i understand
red mountain
so, you gonna do long division or keep stalling?
azure dagger
sry its just i dont like long division but if i must :(
ive been stalling this question for 4 hours its time
red mountain
its a useful technique, i recommend you learn it
azure dagger
the divisor is (z-2)
red mountain
yes
trim joltBOT
@azure dagger Has your question been resolved?
azure dagger
@red mountain so im doing long division
and
how do i subtract with the variablkes
.close
trim joltBOT
trim joltBOT
Available help channel!
real herald
Learning abstract algebra kelly tables, why is the axiom of closure satisfied when every element only appears once in a column or table?
real herald
like in this case, what would be wrong if Q was there multiple times in row 1
Spasificly how does it corralate with closure?
trim joltBOT
@real herald Has your question been resolved?
ionic pendant
that's to do with different properties (specifically cancellability)
if closure was an issue it would be because an element not in the group showed up on the table
limpid dawn
besides that if you assume all elements to be distinct you would quickly derive a contradiction
real herald
@ionic pendant ok so its not related to closure?
If you look at 6:55
thats kinda where im lost as to what the explanation is trying to say
trim joltBOT
limpid dawn
thats kinda where im lost as to what the explanation is trying to say
.reopen
trim joltBOT
✅
limpid dawn
I think what he's trying to say is that because of this latin square property (each element appears exactly once per row/column) it implies closure (the converse is not necessarily the case)
real herald
@limpid dawn so if each element appears exactly once per row/column it implies closure?
why is that the case?
limpid dawn
<@587715738484211754> so if each element appears exactly once per row/column it ...
how is closure defined
real herald
You cant get an element outside of the set if you complete an opperation with two elements within the set, ie and opperation on (S,.) with a,b being in s, a.b must also be in s
limpid dawn
yes the first part sums it up
for every a,b in some set say S with some operation o you want that a o b is also in S
limpid dawn
and well each element after the operation is still an element in that set
real herald
im still lost, are all elemets still in the set regardless? how does this related to having it once each row / column
amber python
limpid dawn
because the latin square property is necessary but not sufficient for a table to form a group basically
amber python
you are staring at the multiplication table
do you see any element outside of the set in the table?
trim joltBOT
@real herald Has your question been resolved?
real herald
do you see any element *outside* of the set in the table?
nope
but again, what does that have to do with rows and columns, i dont get the corralation for closure
real herald
because the latin square property is necessary but not sufficient for a table to...
ok
what does it imply? just closure?
amber python
but again, what does that have to do with rows and columns, i dont get the corra...
it doesn't
latin square property is too strong for closure
it implies closure but closure is a far weaker assumption
real herald
ok thats what im curious about, why does it imply closure"?
amber python
well what does the latin square property say about all rows
real herald
They only have one of each element
oh
you can also tell by just seeing there are no outside elements tho right
idk why he explained it as such lmaio
amber python
well yes
amber python
do you see any element *outside* of the set in the table?
that's why i said this
amber python
cool
trim joltBOT
trim joltBOT
Available help channel!
rustic drum
trim joltBOT
rustic drum
Increase obviously
maiden zinc
10 full periods
urban copper
nice
trim joltBOT
trim joltBOT
Available help channel!
boreal apex
[
T(N) = \sum_{0\le i< N}\sum_{0\le j < i^2} 1 \q (j,\operatorname{mod} , i = 0)
]
solid kilnBOT
Aero
boreal apex
Could someone explain to me how to go about computing this sum
trim lichen
the inner loop procs when j=0, then when j=i, then when j=2i, all the way up to j=i(i-1)
a total of i times
but also do you not want to start i at 1 not 0?
otherwise the time complexity will be O(1) because the code will exit with a division by 0 error.
boreal apex
the inner loop procs when j=0, then when j=i, then when j=2i, all the way up to ...
So it just reduces to [
T(N) = \sum_{i =1}^{N-1} i
]
Well I am starting from $i = 1$ to fix the error you mentioned
solid kilnBOT
Aero
boreal apex
So, O(N^2) pretty much
trim lichen
yep
boreal apex
Alright so i have a side question now
just found this result earlier and i was curious if you are able to prove this in general via induction
it seems like the sum of the first n bth powers is O(n^(b+1))
from just messing around with these problems
if you are summing first n natural numbers, thats gonna be O(n^2)
n^2 naturals, O(n^3)
and so on
is this actually something that holds in general however?
boreal apex
the inner loop procs when j=0, then when j=i, then when j=2i, all the way up to ...
also wait going back to this, i think our assumption was incorrect wasnt it
you still need to compute the modulo operation every iteration
trim lichen
it seems like the sum of the first n bth powers is O(n^(b+1))
that's correct
even when b isn't an integer
trim lichen
you still need to compute the modulo operation **every iteration**
oh yes that's true. the if check is not free
well then i guess it's O(sum[1,N] i^2)
which is O(N^3) technically
boreal apex
Hence, [
T(N) = \sum_{0\le i< N}\sum_{0\le j < i^2} 1 \in \OO(N^3)
]
solid kilnBOT
Aero
boreal apex
woah well that if statement was a devious little distraction lol
boreal apex
even when b isn't an integer
very interesting
anyways, thanks for you time. Have a great day!
.close
trim joltBOT
trim joltBOT
Available help channel!
drifting whale
what does this mean
trim joltBOT
what does this mean
tired frigate
FR is typing..
tired frigate
what does this mean
Js insert the x into the function val
drifting whale
ok so for a i) y=2
drifting whale
Js insert the x into the function val
whats the function val
drifting whale
y is 1 innit
what?
tired frigate
whats the function val
f(2) the function val is 2
idk i made that up i meant the value inside the function
drifting whale
what does the function val do
tired frigate
Idk if its an actual term
drifting whale
1
tired frigate
Yessir
trim joltBOT
tired frigate
No problem
trim joltBOT
Available help channel!
next vapor
i need to study the convergence of sequence an+1=1-(1/4an) where a1=1 for n>=1s
limpid dawn
You can try to see if it's bounded by considering the limit, and also write down a few terms to see how it behaves monotonically
trim lichen
i need to study the convergence of sequence an+1=1-(1/4an) where a1=1 for n>=1s
$a_{n+1} = 1-\frac{1}{4} a_n$?
solid kilnBOT
ann.in.a.teacup
trim lichen
$a_{n+1} = 1-\frac{1}{4a_n}$
solid kilnBOT
ann.in.a.teacup
trim lichen
like this?
next vapor
yes
slim temple
i need to study the convergence of sequence an+1=1-(1/4an) where a1=1 for n>=1s
the fractions are always decreasing in their ending value but converging to 1/2
next vapor
yes i replaced an+1 and an with L and solved the quadratic equacion
i found out L=1/2 is that all i need to do?
slim temple
yeah
next vapor
what if when i am solving a problem like this i find out that L can have 2 different values
slim temple
probably choose the one that makes the most sense
both are algebraically right and hold some form of importance, but usually one is the obvious answer
next vapor
are you sure you know know what you are talking about?😭
slim temple
i think so, anyways
trim joltBOT
slim temple
are you sure you know know what you are talking about?😭
on an example (while not directly the same, the method is quite similar) $\sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12+...}}}} = -3, 4$
because $x=\sqrt{12+x} \Rightarrow x^2-x-12 = 0$ has those two solutions
4 seems logical, -3 is related to how you operate with roots in complex realm
solid kilnBOT
zzz0nnn
next vapor
yeah i know this type of problems
slim temple
well, happy to help ig
next vapor
lol
trim joltBOT
Available help channel!
shell kindle
I don't really understand the last part of this question:
shell kindle
shell kindle
yeaa idk what the last part means
trim lichen
does your textbook ever define this notation
cause i highkey have no clue what they mean by it either, despite knowing my way around complex number stuff
shell kindle
ohh yea it doesn't defin the C ever
like i was thinking it had something to do with the first part, like seketching S and T but idk what the link is
wait i found something
This is the solution they gave but im so confusedd
Like do i just substitute the Cartesian equation of T into the one for S, which also happens to be the same as R?
shell kindle
ohh i think they want me to find T = S, but its worded really badly
like the set of points that satisfy both S and T, but idk why they said C
thankk you for helpingg
i think ill close it, its probably just a bad question
.close
trim joltBOT
trim joltBOT
Available help channel!
drifting whale
rq the domain for this should be {X E R | X cant be equal to 2 } right
trim lichen
if you cannot type ∈ the best substitute is in not E
drifting whale
how did u type that
trim lichen
i have an AutoHotkey script set up to produce some math symbols with shortcuts
but that doesnt matter for my point
trim lichen
and likewise for ≠ you should write it as != if you can't do the symbol
also lowercase x not uppercase X
but yes {x in R | x != 2} is correct.
drifting whale
and for range its { y ∈ R | y != -1 }
trim lichen
yes
drifting whale
where should i start for this
do i need to use the U sign
i forgot whats it called
union
for range i was thinking of maybe { x ∈ R | ( - inf , -1] U (0, inf) }
or just R = ( - inf , -1] U (0, inf)
trim lichen
uh wait
drifting whale
okay
trim lichen
do you want it in set builder notation or in interval notation
drifting whale
uhhh
trim lichen
you can't really mix the two like that
drifting whale
ok my teacher wants it in the form of either
trim lichen
either one is good?
trim lichen
in that case (-∞, -1] ∪ (0, +∞) is just fine
drifting whale
{ x ∈ r ( x , x ) }
trim lichen
but if you wanted to write it in setbuilder: {y ∈ R | y ≤ -1 or y > 0}
drifting whale
smth like these he said is both fine
drifting whale
but if you wanted to write it in setbuilder: {y ∈ R | y ≤ -1 _or_ y > 0}
do we use or
trim lichen
like the word "or"? yes
trim lichen
the U means union, the flipped U means intersection. those two are pretty fucking different.
but neither one would go inside set builder notation usually
drifting whale
oh
drifting whale
or just R = ( - inf , -1] U (0, inf)
wait for this u can write it as this right using the union
oh ye u said
mb
drifting whale
but if you wanted to write it in setbuilder: {y ∈ R | y ≤ -1 _or_ y > 0}
rq how did u get the 2nd part
drifting whale
oh does the "or" mean its split up
trim lichen
the or means it's a union of two intervals
drifting whale
ic
trim lichen
one described by y ≤ -1 (that's your (-∞, -1] ) and the other by y > 0 (that's your (0, +∞) )
drifting whale
for domain is it then
hmm
wait how would u do it
hmm
(- inf , -2) U (-2,2) U ( 2, inf)
how do u write with < >
empty orchid
Hm?
drifting whale
one described by y ≤ -1 (that's your (-∞, -1] ) and the other by y > 0 (that's y...
like what they did here
empty orchid
Oh.
empty orchid
Well, there’s an upside down arrow symbol for stuff like that, symbolic wise
drifting whale
-2<x<2 for the middle bit
why do we need to add the x
empty orchid
Forgot how to render it using LaTeX
drifting whale
Well, there’s an upside down arrow symbol for stuff like that, symbolic wise
upside down?
hmm i dont think ive learnt that yet
trim lichen
why do we need to add the x
so that it becomes a condition placed on x, rather than the true but pointless statement "the number -2 is below the number 2"
empty orchid
upside down?
Kinda like 
trim lichen
Well, there’s an upside down arrow symbol for stuff like that, symbolic wise
???
bruh you are just confusing op
drifting whale
so that it becomes a condition placed on x, rather than the true but pointless s...
ohh
trim lichen
Kinda like <:thisnt:863858059398742086>
im gonna respectfully ask you to
trim lichen
and, not or
drifting whale
oh
trim lichen
it is good practice to write the "in R" bit
but it's not that big of a deal if you forget it here, since it can be inferred from context
drifting whale
if i do it everytime i wouldnt loose marks would i
trim lichen
no, you wouldn't.
trim joltBOT
trim joltBOT
Available help channel!
wooden hamlet
For the question in the left corner why does the answer key say we are subtracting and not adding even though we are going towards the left
trim joltBOT
For the question in the left corner why does the answer key say we are subtracti...
@wooden hamlet Has your question been resolved?
haughty nest
For the question in the left corner why does the answer key say we are subtracti...
substraction is the same as adding
trim joltBOT
@wooden hamlet Has your question been resolved?
wooden hamlet
substraction is the same as adding
I thought when you go to the left on the graph you add and to the right you subtract
haughty nest
as substracting or adding they're equivalent
as for your question that depends on whether u're adding a negative thing or adding a positive thing
lone basin
substraction is the same as adding
Bro what
@wooden hamlet subtracting from the input of a function moves the function to the right
haughty nest
do you even study algebra ? xD
haughty nest
<@695456015805710337> subtracting from the input of a function moves the functio...
substracting a positive number be specific
lone basin
substracting a positive number be specific
This is the reason you think I haven’t studied algebra?
haughty nest
Bro what
u said what as if you're pointing out that i said something wrong?
well u're preuni so u obviously haven't studied it
lone basin
u said what as if you're pointing out that i said something wrong?
Because you’re implying a - b = a + b
haughty nest
yeah u didn't study algebra yet so its okay
trim joltBOT
@wooden hamlet Has your question been resolved?
pure fiber
guys when the limit of $n \to +\infty$ goes to $+\infty$ or $-\infty$ is divergent, if it goes to $L \in \mathbb{R}$ is convergent, escpecially if L = 0 is infinitesimal
solid kilnBOT
nico.alesi
pure fiber
but what if the limit doesn't exist? is it just indeterminate or is there a name?
so I should classify it as divergent
thank you
yeah that makes sense
thank you once again
.close
trim joltBOT
zinc ginkgo
<@&268886789983436800> spam
lime moth
need some help for multivariable calculus. I need to check if a function is continuous.
red mountain
!da2a
trim joltBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
red mountain
yesi can read it
and you want to fibure out if its continuous
for that you need to take the limit
lime moth
yes
I did, I just want to make sure that it is correct. I figure out that the limit (of the cos stuff) is 0. Since cos is multiplied by x (approaching 0)
meaning that the function is continous.
supple copper
can you show that is actually true?
lime moth
Proof, aw didnt think of it.I mean it is intuitive.
lime moth
No, no we didnt cover that.
red mountain
hint: take y=0
supple copper
squeeze theorem?
lime moth
yes.
supple copper
squeeze theorem is a 1D theorem
it applies to functions from R to R
we have a function from R^2 to R here
lime moth
ah, sure.
lime moth
hint: take y=0
Can you explain?
supple copper
im sure you can make a 2d version of the squeeze theorem but i dont think you have that here
supple copper
it'll be 1 everywhere except for x = 0
red mountain
the limits for every single paths to (0,0) needs to be equal
lime moth
So function is continous. got it.
Not ***
supple copper
Proof, aw didnt think of it.I mean it is intuitive.
that's why i say it's not quite intuitive in this sense
red mountain
thus if you can show two paths that give different limits, its not continuous
supple copper
So function is continous. got it.
i just showed you it's not continuous
it's 1 everywhere except at x = 0 it is 0
lime moth
thus if you can show two paths that give different limits, its not continuous
Got it. Understandable.
supple copper
the paths need not even be straight
lime moth
i just showed you it's not continuous
typo
supple copper
that's where the polar coordinates come in when you get to it
trim joltBOT
trim joltBOT
Available help channel!
velvet parrot
We have a U Magnet with a scale. Given the system, the switch is turned on(current starts to flow), the reading of the scale increases. Find the direction of the magnetic field(X-> Y or Y -> X)
trim joltBOT
We have a U Magnet with a scale. Given the system, the switch is turned on(curre...
@velvet parrot Has your question been resolved?
trim joltBOT
@velvet parrot Has your question been resolved?
edgy willow
We have a U Magnet with a scale. Given the system, the switch is turned on(curre...
use the right hand rule to see if the beam and magnet attract or repel. current goes out of the + end and field goes from north to south on the magnet
leaden nebula
Help
leaden nebula
where did the bounds 0 to 3pi come from? did my prof make a mistake or smth
yeah he did nvm. I'll change the bounds for t to 3pi lol
.close
trim joltBOT
trim joltBOT
Available help channel!
twilit birch
I forgot how to do these, Ik ln(e) = 1
trim joltBOT
I forgot how to do these, Ik ln(e) = 1
twilit birch
what have you trieed
???
trim joltBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
6
drifting vortex
!done
trim joltBOT
If you are done with this channel, please mark your problem as solved by typing .close
@twilit birch Has your question been resolved?
hybrid mauve
Guys how do I approach the 2.5.9 stuff?
trim joltBOT
Guys how do I approach the 2.5.9 stuff?
nova spire
Guys how do I approach the 2.5.9 stuff?
so what we want to do in the end is create explicitly that subsequence
it's a good idea to understand how we're gonna create it first
First of all, is it clear that S is an interval?
hybrid mauve
It's clear that it's from minus infinity to the lowest number on the sequence, whatever that is.
And I think that this sup S will be the lim inf of the sequence
hybrid mauve
How so? isn't it less than a_n for infinitely many of em?
nova spire
How so? isn't it less than a_n for infinitely many of em?
we never asserted that sup S is in S itself
in fact in many cases, sup S is not in S
if you want to think about easy examples, think about a_n = (-1)^n
hybrid mauve
sup S would be 0 in this case, no?
nova spire
no
a_n oscillates indefinitely between -1 and 1
there's an infinite amount of each
so S is in that case all x < 1
hybrid mauve
oh right right, for some reason added a 1/n as a brain fart
nova spire
sup(S) = 1 is not in S
but what we do find is that it's the lim sup
we're not gonna try to prove sup(S) is the lim sup here in general
we're only interested in showing it's a limit point
hybrid mauve
Ok I think I see what you mean, basically that the subsequence with the biggest limit will converge to s, which is sup S. that's how the gist of it is, right?
nova spire
weellll kinda
we can try to show afterwards (after the initial proof is done) that sup(S) = limsup(a_n) if you want
but right now let's try and prove what's asserted in the exercise
one thing to start checking is to see if "sup S" does exist
how can we be sure?
hybrid mauve
by the completeness of the real numbers
nova spire
so what do we need to apply axiom of completeness
hybrid mauve
Okay so It's like any nonempty set of real numbers that's bounded above has a supremum
hybrid mauve
Since the sequence is bounded then it def has real number values from start to finish
nova spire
Since the sequence is bounded then it def has real number values from start to f...
we never doubted that every a_n is real, even without boundedness hypothesis
but you can guess that boundedness comes a lot into play
nova spire
so S needs to be a
> nonempty set of real numbers that's bounded above
to get that S verifies those
so maybe first, why is S non-empty?
hybrid mauve
I think boundedness def comes into play here, if it was unbounded negative S will be empty, no?
sand parcel
nova spire
I think boundedness def comes into play here, if it was unbounded negative S wil...
so yes lower bounded will come into play here
can you perhaps be more specific as to why (a_n) lower bounded -> S is not empty?
maybe come up with an explicit element of S?
stable crescent
what did you try @hybrid mauve
hybrid mauve
Let's say bounds of the sequence are (m,n) then S has elements from (-infinity, m) no?
hybrid mauve
what did you try <@115539876052467712>
Dunno mate I just saw this and feel like a headless chicken
nova spire
Let's say bounds of the sequence are (m,n) then S has elements from (-infinity, ...
yes any number below m will definitely be in S
so great we have that S is nonempty
why is S upper bounded?
stable crescent
To construct the subsequence, we exploit the fact that s=supS ensures that infinitely many terms of (a_n) are arbitrarily close to s.
hybrid mauve
why is S upper bounded?
Since every element above m will have an element in the sequence below it, right?
nova spire
Since every element above m will have an element in the sequence below it, right...
I'm assuming in that case you explicitly have m = inf(a_n)
but that's not enough
even if for x > m there will be some elements in the sequence below it
it doesn't prove/disprove that there could be infinitely many a_n above x
so no it's not about the lower bound of (a_n)
and if it's not about lower boundedness...
hybrid mauve
I'm hella lost, think I should slow down and solve more of the questions in the previous chapters.
nova spire
oh xd
we're not even in the subsequence creation part yet
take your time to deepen your understanding of sets and set theory
hybrid mauve
Yeah it's just, don't think I really understand real numbers
nova spire
it takes a huge part in everything around BW and real numbers
hybrid mauve
Yeah I'll get back to this one later, thanks though, really appreciate taking your time with me
.close
trim joltBOT
trim joltBOT
Available help channel!
shrewd summit
Prove that a 4-digit number is divisible by 3 if and only if the sum of its digits is divisible by 3.
i labelled the number as abcd and split it into 1000a + 100b + 10c + d but not sure where to go from there
bright quarry
well you have to pick a direction first
which direction of the proof do you want to do first
@shrewd summit
shrewd summit
no idea
bright quarry
well it’s an iff statement
there’s the if part
and the only if part
you need to assume it’s divisible by 3 then show the sum of its digits are
then do the reverse
shrewd summit
oh
bright quarry
assume the sum of its digits are divisible by 3 then deduce that the number is divisible by 3
bright quarry
so i assume a + b + c +d is div by 3
you can do this direction first yes
do you need help?
or can you do it from here
shrewd summit
uh idk where to go further w the algebra
bright quarry
well see if you can split up the 4 digit number into something + a + b + c + d
since the sum of the digits is divisible by 3 you then need to show that something is divisible by 3
which would complete that direction
shrewd summit
yeh i did a + b + c + d = 3m
bright quarry
well see if you can split up the 4 digit number into something + a + b + c + d
did you understand what i said here
shrewd summit
idk where the something came from
bright quarry
you have to find what it is
1000a + 100b + 10c + d = (some shit) + a + b + c + d
find (some shit)
shrewd summit
wait so
bright quarry
what?
shrewd summit
then sub into