fucntion one it took some time but did that as well
#help-0
turbid narwhal
your prep is going too well man from where you are studying
lusty laurel
your prep is going too well man from where you are studying
pw
it doesnt matter from where im studying
consistency matters
turbid narwhal
you did adv question i'm asking about mains
turbid narwhal
consistency matters
yep thats the main key
lusty laurel
my school also does mocks and their paper is damn good
turbid narwhal
of what i was able to
you are preparing well man i didn't able to do mains questions also they fells difficult for me
turbid narwhal
my school also does mocks and their paper is damn good
from where you belongs to
turbid narwhal
you are preparing well man i didn't able to do mains questions also they fells d...
like yesterday i tried Quadratic questions of mains 10 questions but i got answer of only 6 of these
lusty laurel
like yesterday i tried Quadratic questions of mains 10 questions but i got answe...
revise the topic which you werent able to do
here, do this
worthy lichen
H_max from the ground will be 30m for that case?
lusty laurel
qaudratic
turbid narwhal
revise the topic which you werent able to do
topics are revised but the thing is problem to staring question or thinking about it
lusty laurel
H_max from the ground will be 30m for that case?
calculate it up then as well
lusty laurel
I am giving you calculated h max
im lazy
worthy lichen
v² = u² + 2ax
turbid narwhal
calculate it up then as well
i take ss of this because i didn't have pen and paper
lusty laurel
It gives x = 5
bro
lone heartBOT
Available help channel!
lusty laurel
its 25 then
lone heartBOT
its 25 then
lusty laurel
why 5+5
worthy lichen
The distance
lusty laurel
The distance
you want hmax
so height of building + height it reached
20 + 5
why you adding the length it fell down as well
turbid narwhal
you want hmax
okay if you are preparing from PW you know RJ sir gives us a formula of Hmax do you remember because i forgot it
turbid narwhal
so height of building + height it reached
are you an author man
lone heartBOT
@lusty laurel Has your question been resolved?
jade sierra
wsg chat
raw jetty
how many ways are there for A,B,C, and 7 other people to sit around a round table if A,B,C dont sit adjacent with eachother
nimble sleet
how many ways are there for A,B,C, and 7 other people to sit around a round tabl...
seems like a classic inclusion-exclusion principle question. If you let $A_1$ be that A and B are adjacent, $A_2$, B and C are adjacent, $A_3,$ A and C are adjacent
\medskip
then you need to calculate the "bad" cases for you to count off. Those being [
\text{Bad} = |A_1 \cup A_2 \cup A_3|
= |A_1| + |A_2| + |A_3| - |A_1 \cap A_2| - |A_1 \cap A_3| - |A_2 \cap A_3| + |A_1 \cap A_2 \cap A_3|
]
ocean sealBOT
nimble sleet
isnt A1 cap A2 cap A3 impossible <:pandathink:524885344995508235>
yes
nimble sleet
so 9!-(3×2×8!-3×2×7!)?
let me verify
also i think you should be doing 9! - blah, because the permutations for a circular arrangement is that much
raw jetty
ah right
nimble sleet
ok at face value that seems correct yes
lone heartBOT
lone heartBOT
Available help channel!
static saffron
Lets say i have the following system of differential equations:
$$\frac{db}{dt} = \chi b^$$
$$\frac{db^}{dt} = \chi b$$
How would i solve this?
The matrix for this seems $((0, \chi),(\chi,0))$ and i guess i will just do the normal approach of solving a system like this?
ocean sealBOT
derdotte
static saffron
Just for some more context. b is actually the complex number representation of an operator $\hat b$ in a base where $\hat b$ has a defined eigenvalue. And this equation arises from parametric downversion in quantum optics. Gotta solve it for figuring out correlations
ocean sealBOT
derdotte
lone heartBOT
@static saffron Has your question been resolved?
static saffron
found a way that doesnt revolve around solving this awkward system of conjugates.
Differentiate first equation, insert second, solve second order instead. Much easier
.close
lone heartBOT
lone heartBOT
Available help channel!
tender aspen
In Q-10, what does the question mean by bounded by y axis? I mean, the other equation is a circle and the y-axis goes right through the middle of it
So which side would be bounded by y-axis?
coral flower
gray isle
this isn't a full circle
tender aspen
Ohh
But even after that, I wasn't getting the right answer
I mean lamda= (-1, infinity) because of y axis
gray isle
how are you getting that lambda could be negative
tender aspen
That's not what I'm getting
It's in the answer
I'm getting lamda > 0
Option A is the answer given
Why do we have to take
(lamda + 1) >0
instead of
lamda > 0?
I mean, y axis is x=0, right?
Why are we taking y-coordinate?
true phoenix
Prove that there exist no integers a and b such that a³ + (a+1)³ + (a+2)³ ..... (a+6)³ = b⁴ + (b+1)⁴
true phoenix
My idea was to try every mod 6 case as I am unable to find any alternate method for solving it
true phoenix
I tried mod 6 because when cubed the remainder remains the same so i thought that might be related to the question
vale wigeon
do it mod 7 and the left hand side is always zero
thick beacon
pretty simple proof here but my problem is in the marking scheme the contradiction they used was that there exists positive numbers a, b such that a+b<2sqrt(ab)
thick beacon
however my question is why can you use a contradiction like there exists negative numbers a, b such that a+b=>2sqrt(ab)
iron roost
proving there's a negative number such that a+b>=2sqrt(ab) doesn't prove that for all real positive numbers a,b, it applies
lone heartBOT
@thick beacon Has your question been resolved?
thick beacon
proving there's a negative number such that a+b>=2sqrt(ab) doesn't prove that fo...
oh ic
im sorry but isn't tht how contradiction works ?
iron roost
the contradiction in this case would be that a and b are both positive real numbers and there exists a,b such that the inequality isn't true
thick beacon
i proved that negative numbers doesn't exist to satisfy the equation, wouldn't it follow that a positive number will ?
iron roost
you don't want to prove that a positive exists
you want to prove that it is true for all positives
take x=x+1, obviously not the case for numbers less than 0, but also not the case for numbers greater than 0
verbal elbow
How do I do question 34 part b? (Sorry for the poor lighting)
lethal belfry
,rccw
ocean sealBOT
lavish cave
did you do 34a?
verbal elbow
Yep
lavish cave
okay, what did you get for that?
verbal elbow
Just not sure how to simplify the expression
lavish cave
ah
lethal belfry
Let $f(x) : \R \to \R$ , where $f(x)=e^{3x+2}$ and let $g(0,\infty) \to \R$ where $g(x) = \ln(x)$
\
find the value of k such that $f(g(2))=ke^x$
lavish cave
right then you can write it as $e^2 \cdot e^{\log_e (x) \cdot 3}$
ocean sealBOT
wai
verbal elbow
e^(3ln(x)+2)
ocean sealBOT
south
lone heartBOT
Available help channel!
glad terrace
lone heartBOT
glad terrace
can someone tell me where I went wrong here?
I was checking my answer (top right) and I got close but not exactly what I started with
twin nimbus
@glad terrace what is exactly different between the two? They look identical to me, but I also just woke up
Oh, 47 vs 3
10 is multiplied by both (x+1) and (x+2), similar error with 11
twin nimbus
glad terrace
10 is multiplied by both (x+1) and (x+2), similar error with 11
I hate this bruh
I have little to no clue how to multiply them when it’s 3 fractions
like what goes where
ts so buns
twin nimbus
Are you aware of the term "least common multiple?"
Honestly, I think the way fractions are taught are a little bit bleh, like they don't bother to teach GCD and LCM to 4th graders learning how to add fractions, because they're number theory, but they really should. A little discussion about prime numbers is probably not beyond children, and it sets you up for actually understanding how fraction addition works.
glad terrace
Are you aware of the term "least common multiple?"
yeah I know of that
but like could I apply it here?
nope
should I just be multiply each thing by every other denominator or something?
twin nimbus
@glad terrace figure out what the common denominator is, then multiply each fraction so that they have a common denominator
lone heartBOT
@glad terrace Has your question been resolved?
latent hazel
can anyone help me with my revision for school, im in grade 8
vale wigeon
you need to send specific questions here that you're using to revise
latent hazel
imma send the stuff
vale wigeon
one at a time preferably
vale wigeon
mmmm
latent hazel
I kinda forgot abt gradient
vale wigeon
that's quite a lot. you need to come here with the questions you struggle with and get them resolved one by one
latent hazel
and slope intercept form
vale wigeon
an entire Google doc of them is kind of a big ask
latent hazel
an entire Google doc of them is kind of a big ask
Can u help me explain the gradent about all the formulas?
vale wigeon
i can send you some videos or tell you to look up the channel known as The Organic Chemistry Tutor yourself
on YT
hushed shale
guys what are your all qualifications?
lone heartBOT
guys what are your all qualifications?
hushed shale
n=24 ...?
potent mirage
guys what are your all qualifications?
lmao what
buoyant saddle
guys what are your all qualifications?
lone heartBOT
@hushed shale Has your question been resolved?
hushed shale
https://tenor.com/view/squidward-spare-change-spare-some-change-begging-poor-gif...
?
potent mirage
<@&268886789983436800>
gray isle
like i want to know whts age of you all tbh😆
Please stop being creepy and don't probe people for personal info.
.close
hushed shale
.close
lone heartBOT
lone heartBOT
Available help channel!
mortal junco
I've accidentally proven some big math equation that hasn't been proven for a long time and I am trying to write a valid math proof in math words and terms [I understand my proof but it isnt in "math language" if you know what I mean] and I have nobody around me to help me with learning how to properly write math proofs and reviewing what I wrote and give me feedback after.
to put it short, how do you write math proofs and what are all the basics I need to know before writing one and how should I organize it? I have some examples on what I've written which the image linked to this message is that example [remember I've never dealt with math proofs advanced math, I've just excelled and dealt with extracurricular mathematics in highschool and I am in 12th grade right now]
slate vortex
what are you trying to prove
Also your statements don't really make sense
$\exists n \in Z, n/2 \in Z \implies n$ is even
ocean sealBOT
Ari
slate vortex
You should remove the "there exists n in Z"
mortal junco
ahh
slate vortex
Also we usually use $\mathbb{N}$ or $\mathbb{Z}^+$ for positive integers, not $Z$
ocean sealBOT
Ari
slate vortex
some people consider N to have 0 though so maybe Z+ is better
mortal junco
yeah at the time of writing that part didn't know about mthbb
i forgot to change it
I just felt like defining it more specifically cuz
the actual thing im trying to prove depends on positive integers
a lot
the entire thing is positive integers
mortal junco
some people consider N to have 0 though so maybe Z+ is better
yeah i've come across that and i was very confused Z+ is usually what I use anyways
slate vortex
the actual thing im trying to prove depends on positive integers
what are you trying to prove
mortal junco
You should remove the "there exists n in Z"
you mean the "if we have" at the beginning??
mortal junco
what are you trying to prove
not trying to prove its more like trying to learn how to express what i proved in math
collatz conjecture
ocean sealBOT
Ari
slate vortex
collatz conjecture
u did not prove the collatz conjecture 💀
mortal junco
u did not prove the collatz conjecture 💀
ive been told this constantly for the past 3 days
i dont know what to tell you
i see it working
sharp thorn
cant we just say $\forall \frac{n}{2} \in \mathbb{Z}^{+} \implies n$ is even?
slate vortex
i dont know what to tell you
Explain the proof
ocean sealBOT
Bettim
mortal junco
Explain the proof
I don't want to give it away
thats why i didnt even say
what im trying to prove
at the beginning
slate vortex
well explain the general idea then
mortal junco
i can also just do
actually now that i think ab it how does it make sense to say
something like for all n in Z while trying to define what is even or odd
specifically the for all / exists
oh
is that what you're saying
Ahh
makes sense
mortal junco
well explain the general idea then
I divided all natural numbers into some specific grouping where they all follow a certain pattern without repeating and therefore every number does not grow till infinity and there are no other loops other than 4-2-1-4
and no, i didnt do this for some arbitrary number sets where i attempt
it is general
i dont know how to write math proofs
but i spent the last 3 days
small fog
are you trying to prove the collatz conjecture
mortal junco
I divided all natural numbers into some specific grouping where they all follow ...
^^^
small fog
okay, what is the specific grouping and the patetrn
slate vortex
Son, there's no way your proof is correct if you're not even in university yet
There's a reason this problem is unsolved
small fog
mortal junco
i've seen this often
patent dirge
cuz then you find it
it was proposed nearly a century ago
mortal junco
I hope I never said it I guess
small fog
if you think people are gonna "steal" your proof
mortal junco
I didn't want to brew this "suspicion"
small fog
you are not making anything worthawhile
mortal junco
if you think people are gonna "steal" your proof
I don't know anything ab people
small fog
no like
mortal junco
I don't know what it means to be proving something and owning that proof
small fog
the concept of stealing proofs
slate vortex
There's nothing to plagiarize here because your proof isn't correct.
small fog
in general
mortal junco
<@321693448115716096> whats ur background
okay ill put it this way
small fog
I don't know what it means to be proving something and owning that proof
you dont "own" a proof
patent dirge
okay ill put it this way
js say it outright
slate vortex
I don't know what it means to be proving something and owning that proof
So if you don't know what it means to have proven something, do you really thing your "proof" of one of the most notoriously difficult unsolved problems is really going be correct?
solemn sparrow
mortal junco
js say it outright
2 years ago I didn't even know how to do basic arithmetic and anything ab math other than numbers and the equals plus minus signs
patent dirge
So if you don't know what it means to have proven something, do you really thing...
^, it was proposed nearly a century ago
patent dirge
2 years ago I didn't even know how to do basic arithmetic and anything ab math o...
dude
mortal junco
suddenly i was inlove with math
small fog
2 years ago I didn't even know how to do basic arithmetic and anything ab math o...
if you actually explained your proof we could explain what the logical error is
patent dirge
mathematicians dedicate their entire life
mortal junco
excluding sleep etc.
patent dirge
to solve problems like collatz
slate vortex
LMAO
small fog
this is a learning moment
mortal junco
mathematicians dedicate their entire life
I've read something that said
don't let it discourage you that you didn't study math your whole life or something like that
I just liked math
small fog
@mortal junco you can learn a lot from what went wrong with your proposed proof
just like
mortal junco
and tried to solve whatever I didn't think I could
patent dirge
don't let it discourage you that you didn't study math your whole life or someth...
yes but there is a line between that and delusion 💀
how old are u
mortal junco
<@321693448115716096> you can learn a lot from what went wrong with your propose...
I mean at this point
slate vortex
I just liked math
And that's great. But a part of math is learning from your mistakes
solid saffron
i just solved the Collatz Conjecture
patent dirge
what classes havs u taken
small fog
he genuinely thinks he proved it
mortal junco
outright obliterate me
patent dirge
what classes havs u taken
@mortal junco
patent dirge
outright obliterate me
💔
mortal junco
<@321693448115716096>
i live in turkey
small fog
hear out his mistaken proof
mortal junco
youre forced to take
slate vortex
Yes this is a learning moment
mortal junco
the same math lessons
patent dirge
i live in turkey
that doesnt answer my question
small fog
what classes havs u taken
this is not productive
patent dirge
what is your mathenaticla bacjground
mortal junco
ill just say the proof
small fog
it doesnt fucking matter let him say his false proof and we can learn from it
patent dirge
it doesnt fucking matter let him say his false proof and we can learn from it
well he doesnt really want to "expose" it
mortal junco
I've heard from somewhere that every number can be written by adding powers of 2 and that meant every positive integer can be written with 2 groups, dividing them into 50% of all integer numbers
patent dirge
might as well
mortal junco
2n and 2n-1
small fog
he just said he can
small fog
I've heard from somewhere that every number can be written by adding powers of 2...
yes
exactly
mortal junco
and when I thought about it
patent dirge
I've heard from somewhere that every number can be written by adding powers of 2...
ye
small fog
odd and even numbers
mortal junco
I said, why not expand this to 3?
and when I was messing around with 3 came across 3n+1
and I realized that
small fog
yep you can write everything as either 3n, 3n+1, or 3n+2
small fog
yep
small fog
wym
mortal junco
okay so
patent dirge
has no odd leading to it
wdym
small fog
like it is not expressible as 3n+1
small fog
yep
mortal junco
every number is
either led by 2 numbers
or 1 number
1 of those is always avaliable for every single integer
small fog
wym
mortal junco
which is
multiplying it by 2
remember
im thinking reverse
for me
collatz is
(n-1)/3
and 2n
right now
im trying to find
leading numbers to numbers
what are the leading numbers to 5
small fog
10
small fog
yes
mortal junco
theres even leading
10
and i realized
10 can be expressed as odd and even
then 20 is only even
leading to it
40 has odd and even
patent dirge
yea
mortal junco
80 has even
160 has odd and even
and I realized
66% of all integers
show this property
while 33% being powers of 3
small fog
ok so the problem with this is that its a heuristic argument.
Your argument is basically "on average, every number will lead to 1".
mortal junco
powers of 3 are never expressible by 3n+1
solid saffron
what if he actually proved it and we're all witnessing math history
small fog
but this doesnt rule out that theres like
mortal junco
it isnt just
that
there is
so much more
this is like
definitions
this is understanding
what i did
small fog
show this property
wym
solid saffron
make a youtube video
mortal junco
if i just tell you
E3N E3N+1 E3N+2 O3N O3N+1 O3N+2 groups
youre not gonna understand that much
i mean
you could
cuz its obvious
solid saffron
make a youtube vid
patent dirge
explain it
patent dirge
alr continue
mortal junco
i am explaining the core idea
reverse collatz
2n and n+1/3
so what I noticed is
66% of numbers as I said
shows the same property likewise 5
if you reverse it
mortal junco
well wrong
positive
small fog
as odd and even
mortal junco
integers
small fog
take 7
mortal junco
thats
not what i meant
okay
yk ill just wait
imma send to my whatsapp my paper
small fog
no wait
mortal junco
and ill send from whatsapp
small fog
im trying to understand
mortal junco
yes
mortal junco
also id like to vc if its possible sometime now or later
small fog
and 33% do
mortal junco
yes
exactly
but
thats not
true
its actually
33% of numbers have odd leading to them
and i said 66% have
not 33%
its just the process of realization
small fog
yes but 33 is the right number
mortal junco
at first im wrong and i deduce something right
its like contradiction proof
im first saying smtn wrong and stating whats wrong and getting something out of it
solid saffron
bro jus publish ur video
mortal junco
legit
for 3 days
i couldnt study
for my uni exam
cuz of this
and i have 22 days left
solid saffron
can you shut up
what i do
mortal junco
let me explain
solid saffron
if he says it here and hes right you could prolly just steal it
if he makes a video its kinda hard to steal
solid saffron
ye you gotta publish it
small fog
@mortal junco just explain the proof
what do you mean 66% of numbers
have an odd leading to them
they dont its 33%
right
mortal junco
its
small fog
unless i misunderstood
mortal junco
33% of numbers having odd leads cuz
66% was assuming from the 5 tower
one second
imma do smtn rq
my mom
is telling me
small fog
yes 33% of numbers have odd leads
mortal junco
ill be back in 3-5 mins
small fog
ok
solemn sparrow
Imagine the next Fields medalists is being prepared in one of these channels ah hell nah lmao 😭
mortal junco
Imagine the next Fields medalists is being prepared in one of these channels ah ...
if i didnt take this serious id just write what i found and publish that but that wont satisfy anybody
and also this would just make me
"who found the idea that lead to collatz being proven by someone else"
i guess id rather take that now
geniunely
solemn sparrow
Keep cooking brother
small fog
also
you can publish your current paper in https://vixra.org/
and then like when its wrong nothing happens
mortal junco
i found these type of websites
and i DONT understand them either
like geniunely
i dont
idk how to publish
what it means
am i missing smtn
solid saffron
it means you are stating you are the first person to think of this new theory or proof
mortal junco
okay so
lemme put it there
how do i put my
real life papers
in there
my phone doesnt have google btw
small fog
upload a pdf
mortal junco
i deleted google cuz it is a distraction
solid saffron
idk you figured out the Collatz Conjecture u could figure this out
small fog
i deleted google cuz it is a distraction
thats a horrible idea in my opinion but your choice
small fog
ok so
mortal junco
i cant express it
mortal junco
its
small fog
or a physical paper
mortal junco
real life
paper
of scribbles
listen
i wasnt able to
express my idea
in general algebra form
solid saffron
ye you gotta digitize that
small fog
ok you can like
mortal junco
its true
i see it
but i cant
write it
therefore i technically
havent proved it yet
mortal junco
collatz conjecture was 3 steps for me and im stuck on the 3rd step
could we vc
im tired of typing
i can also camera share
in vc
small fog
alright
lone heartBOT
@mortal junco Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
hardy arch
Hey, so I'm basically learning trignometry for Right angled triangles. and i'm just not sure when to either use multiplication or division to find the specific length of a triangle.
short vapor
which length?
hardy arch
yeah
short vapor
so, each of soh, cah, and toa connects two sides and an angle
(sorry if im being a bit simplistic i dont know how much you know)
whne you're solving a problem like this, what you need to figure out is which two sides you know
oh no you got that
sorry
it's basically just some algebra from here....
how far have you gotten? or just up to the pictures you got
hardy arch
Well I've gotten assignments on both using multiplication/dividing to get the specific length. but when I start by finding out whether if its soh cah toa, I always seem to get the sin cos tan wrong. For example I said it was sin32, while the answer key says cos32
short vapor
for... which question
short vapor
sohcahtoa gives us 3 rules
sin(θ) = O/H
cos(θ) = A/H
tan(θ) = O/A
these rules each connect two sides and an angle
so depending on which sides you know, and which sides you are trying to figure out, you use different rules
for image two, you know the opposite side, and want to know the hypotenuse
so you would use sin(θ) = O/H
hardy arch
mhm
short vapor
that's how you know which one to use. it would be sin(32) because if we used cos(32) or tan(32) we wouldn't be able to get the answer
hardy arch
what happens if we used cos32 or tan32, would the answers be obvious that it's wrong?
short vapor
lets say we tried to use cos(32)
we get cos(θ) = A/H right
but we dont know the adjacent side
right?
short vapor
didn't you write down opposite?
hardy arch
i wrote adj on the right side
short vapor
oh you thought 32 was a side length?
hardy arch
yeah
hardy arch
yep
short vapor
okay
well yeah figuring out which formula to use is really just a case of which sides do i know / want to solve
hardy arch
Great, is it possible if you could maybe do a bullet point of this so I can maybe screenshot for another time?
Just in case if I forget
short vapor
okay yeah
SOHCAHTOA
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
pick the identity that connects a side you know with a side you want to find out, and then solve for the side you are trying to figure out
hardy arch
thanks!
short vapor
np!
lone heartBOT
Available help channel!
worldly sleet
Guys, I need your help
lone heartBOT
Guys, I need your help
worldly sleet
How do I find something that’s undefined
zinc bolt
!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.
zinc bolt
@worldly sleet
worldly sleet
I see it
The problem is that the one on the right is undefined
Basically, meaning that it ruined any equation that’s in
zinc bolt
Yea because 0 doesn't equal 1
hushed locust
desmos apparently returns 1 for true inputs and undefined for false inputs
worldly sleet
Basically thinking if i equal one then i(1+1)+1=3
And i = nothing should =1
Do you know how I can fix this problem?
hushed locust
And i = nothing should =1
what does this mean?
tidal lintel
=3
tawdry lily
And i = nothing should =1
What does "i" represent?
worldly sleet
Basically imagine it like a switch
{i = 1}= on
{i= undefined} = off
And I thought this would work
hushed locust
just because two things are undefined doesn't mean they're equal, because "undefined" isn't a number
worldly sleet
So there’s no way I can make this work
tacit arch
That's usually how undefined works yes
worldly sleet
But how can I code :(
tacit arch
Don't code undefined things
tawdry lily
So there’s no way I can make this work
What exactly are you trying to do?
Here Desmos says i = undefined because it only works in a cartesian plane diagram
Desmos does not compute anything in the Argand's diagram
worldly sleet
Making on and off switch
worldly sleet
Desmos does not compute anything in the Argand's diagram
Argand?
tawdry lily
Argand?
Argand's diagram is a diagram with an imaginary axis as the y-axis
Usually coordinates are writen in the form of a + bi
worldly sleet
Insert happy noises
alpine mural
Klaas Creek is on a bearing of 314° from Hampervale and the distance between them is
158 km. Badgerton is 325 km from Hampervale and its bearing from Klaas Creek is 044°.
Find the bearing of Badgerton from Hampervale.
How do I draw this, I have no clue
lunar saddle
Remember bearing is from north clockwise
alpine mural
Remember bearing is from north clockwise
Yeah, I know, but I just can't seem to draw it properly
lone heartBOT
@alpine mural Has your question been resolved?
alpine mural
Aren't bearings clock-wise not counterclockwise
hushed scroll
Aren't bearings clock-wise not counterclockwise
It doesn't matter, if you rotate the figure 90° counter clockwise and then mirror it along y axis, it will give the exact image of the situation.
If you want to find angle between them, either draw exact figure or a figure like this, this won't change the angles or distance or anything, the answer will be same
If you want exact figure then draw what you think is correct
You can try
Are you up to something?
alpine mural
.close
lone heartBOT
hushed scroll
Do you think you can find angle between H and B from here
lone heartBOT
Available help channel!
desert raptor
Hi, how do I proceed further?
desert raptor
<@&286206848099549185>
dire plover
ok
so what you do is exand the H's into summations
you mutiply boths sides by -n
and you convert the iterated sums into sums over sets
then they will turn identical
for example look at the number of terms of the type 1/a*1/b*1/c where a =\=b=\=c=\=a for particular abc, in the RHS, this is 6 ( 6 from H_n^3, 0 from 3H_nH_n^(2), 0 from 2H_n^(3)) and in the RHS it is also 6 (6 from 3 (H_k^2)/k, 0 from 3H_k^(2)/k)
do the same for
a=b=\=c and a=b=c
and you will find they all match
does this make sense?
desert raptor
and you convert the iterated sums into sums over sets
how do i do this
dire plover
how do i do this
ok ill just do it for the first one
desert raptor
do it for this one
dire plover
do it for this one
i mean for the LHS
dire plover
does this step make sense to you?
desert raptor
lemme see
aren't the first and the third terms the same @dire plover
or did you mean to write a > b
oh nvm
yes go on @dire plover
dire plover
dire plover
or did you mean to write a > b
either would work
dire plover
they both give same thing due to symmetry
dire plover
i see the logic
so you can do a similar thing for the case that you gave
dire plover
yup
desert raptor
okayy
now exploiting that in the third case seems tricky
dude harmonic sums are interesting asf
dire plover
dude harmonic sums are interesting asf
the method i gave doesnt rlly require it to be harmonic, the same is true if instead of multiplying by 1/i you multiplied by a_i and you did H_n^(k) = sum j = 1 to n (a_j)^k, for an arbitrary sequence a
desert raptor
the method i gave doesnt rlly require it to be harmonic, the same is true if ins...
ic
so now u want me to do smth similiar but with sum 1/abc
dire plover
so now u want me to do smth similiar but with sum 1/abc
yup
lone heartBOT
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Available help channel!
tepid scroll
claim
lone heartBOT
@tepid scroll Has your question been resolved?
lone heartBOT
@tepid scroll Has your question been resolved?
lone heartBOT
@tepid scroll Has your question been resolved?
red fractal
i cant find to figure it out?
lone heartBOT
@tepid scroll Has your question been resolved?
tepid scroll
i cant find to figure it out?
What dude
tepid scroll
<@&286206848099549185>
alpine sable
tepid scroll
Yee
lone heartBOT
@tepid scroll Has your question been resolved?
lone heartBOT
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desert raptor
How do I prove the following result?
lone heartBOT
How do I prove the following result?
desert raptor
,w sum i = 1 to inf H_i/i^2
ocean sealBOT
desert raptor
Abel's summation is not working well
ivory fern
What is H_i?
vast harbor
harmonic number ig
desert raptor
What is H_i?
desert raptor
Abel's summation is not working well
Tried it with a_k = k^-2 and b_k = H_k
<@&286206848099549185>
thick lynx
Tried it with a_k = k^-2 and b_k = H_k
Check out https://math.stackexchange.com/a/1591372
desert raptor
Check out <https://math.stackexchange.com/a/1591372>
Thanks
A second question
Au-Yeung's quadratic series
,w sum i = 1 to inf (H_i/i)^2
ocean sealBOT
thick lynx
Looks like that one is famous too
Check out https://math.stackexchange.com/a/2162424 @desert raptor
desert raptor
Check out <https://math.stackexchange.com/a/2162424> <@851774318727397396>
Time to introduce myself to polylogarithms
Since both proofs require them
Suggest a resource please @thick lynx
thick lynx
Where did you find these?
desert raptor
Where did you find these?
Oh I was solving an integral
thick lynx
Suggest a resource please <@332561465405865985>
Idk, probably some analysis book of which I only have German ones
thick lynx
Oh I was solving an integral
seems like you were doing some pretty long integral problems lol
desert raptor
seems like you were doing some pretty long integral problems lol
My connection is bad rn so it's taking a while to send the picture
desert raptor
Idk, probably some analysis book of which I only have German ones
I'll look around
desert raptor
This reduces to that
thick lynx
is that integration bee?
desert raptor
is that integration bee?
Nah, Valean
thick lynx
Ah, that integration book
desert raptor
Ah, that integration book
Yes, it's quite notorious
But it's fun
When you attack the integral correctly it just falls apart into a known result
Anyways, thank you
.close
lone heartBOT
desert raptor
Ah, page 14 on the sample I found
I didn't read the preface, so I was quite pleased to find a problem there :p
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Available help channel!
tepid barn
lone heartBOT
tepid barn
Is the first exercise a definite integral
And is the second exercise the lenght of Arc lenght of curve
If thats the case then how can i solve the second exercise
sacred tundra
does anyone do a level maths??
tepid barn
Wym
lone heartBOT
@tepid barn Has your question been resolved?
lone heartBOT
@tepid barn Has your question been resolved?
proven leaf
the arc length of a parametric curve (\mathbf{r}(t)=\langle x(t),y(t)\rangle) over ([t_0,t_1]) is given by:
[L=\int_{t_0}^{t_1}\sqrt{\qty(\frac{dx(t)}{dt})^2+\qty(\frac{dy(t)}{dt})^2}dt]
ocean sealBOT
PajamaMamaLlama
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opaque shard
I think i have the not continuious and not differientiable correct, but to make sure im just gonna ask anyways.
My main question is how the heck do i graph f'() of this thing
leaden bobcat
you are correct on continuous - differentiable
for graphing the derivative, can you do it for 2 < x < 3?
opaque shard
for graphing the derivative, can you do it for 2 < x < 3?
i dont think so?
opaque shard
no 😦
leaden bobcat
Do you know what the derivative of a function is?
opaque shard
i know how to get a derivative from a problem but not from a graph or the definetion
leaden bobcat
Can you write down what the derivative of a function at a point is for you?
So we can go from there
opaque shard
is this what ur asking?
3x^2 = 6
leaden bobcat
this looks like an equation
did you mean to write “the derivative of 3x² is 6x”?
leaden bobcat
yes sorry i forgot the x
not only that, that equal sign is inadequate for what we are saying
you wrote 3x² = 6x, which is a completely different thing from saying “the derivative of 3x² is 6x”
leaden bobcat
how did u do the superscript/?
hotkeys in my keyboard, Altgr+numbers
you can write in LaTeX here
The derivative of $3x^2$ is $6x$. Like this
ocean sealBOT
Luigi
opaque shard
oh thats cool
leaden bobcat
dollar signs for whatever you want to format in a “mathematical way” so to speak
anyway, this is only operational, but doesn't really tell us what the derivative of a function is
where did you learn about derivatives?
opaque shard
i had to self teach myself
opaque shard
no
leaden bobcat
okay, do you know what the slope of a line is?
opaque shard
yes
leaden bobcat
great
now, tangents in geometry, no clue what they are?
Something like “a line tangent to a circle”
opaque shard
i remember learning it but it was a while while back
opaque shard
secant intercets through the circle twice tangent only once
leaden bobcat
okay, now for a graph of a function
if you take a point on a graph, and start drawing lines from there, most of them will touch the graph in many points
opaque shard
got it
leaden bobcat
but (if the graph if nice enough) you will find a special line that “touches” the graph only once (if you restrict yourself close enough to the point)
This is a colloquial introduction to what we call the “tangent line” of a function a specific point
The derivative of a function is defined as the slope of this line (if it exists)
opaque shard
so a tangent line is a point where a line only touches it once?
leaden bobcat
so a tangent line is a point where a line only touches it once?
a line is a line, not a point
the black line is a tangent line for the blue graph because it touches it only at 1 point
opaque shard
got it thats a better definition
leaden bobcat
Mind this is very colloquially
because there are a lot of pathological examples where what we just said doesn't really make sense
but for “nice enough” graphs, this is true
left wharf
what kind of pathological examples?
leaden bobcat
what kind of pathological examples?
I told him “a tangent line touches the graph ones”, this requires many asterisks since to start, it may touch a lot of times again outside of a neighbourhood of the point (just extend the graph outside to do so)
secondly, it may touch infinitely many times even in a neighbourhood of the point (for ex. x²sin(1/x) at x = 0 extended as 0)
looks like this
leaden bobcat
got it thats a better definition
to get an even better definition we can think of a tangent line as the “best” line that approximates that of the graph at the point of intersection
opaque shard
got it so how do we graph this f'()
leaden bobcat
got it so how do we graph this f'()
now, for 2<x<3 the graph of f is already a line, don't you agree?
left wharf
I told him “a tangent line touches the graph ones”, this requires many asterisks...
For which x does the slope intersect the graph at an infinite number of points?
opaque shard
now, for 2<x<3 the graph of f is already a line, don't you agree?
seems to be a line yes
leaden bobcat
For which x does the slope intersect the graph at an infinite number of points?
the tangent line at x=0 of x²sin(1/x) is the line y=0, which touches the graph infinitely many times, even when restricted arbitrarily close to x=0
left wharf
I don't think that function is differentiable at x=0?
left wharf
oh yeah nevermind
leaden bobcat
seems to be a line yes
so, what would you say is “the best line that approximates the function” when the function is itself a line?
opaque shard
would it not be 2 because of the curve
leaden bobcat
What is the subject of what you wrote?
I'm talking specifically about the function for 2 < x < 3
left wharf
the tangent line at x=0 of x²sin(1/x) is the line y=0, which touches the graph i...
good function very nice
opaque shard
What is the subject of what you wrote?
I'm talking specifically about the functi...
im confused what ur asking
opaque shard
got it
leaden bobcat
it's already a line (segment)
we said the “tangent line” of a graph is the best line that approximates the graph
but for 2<x<3 our graph is already a line, so what would you say its tangent line is?
opaque shard
maybe x=-1 because its flat or x=3
leaden bobcat
I think you are confused about what I am asking
x=-1 or x=3 are numerical values for some x
I am asking about what the tangent line is (a geometrical object)
opaque shard
im saying would you not put a tan line there?
leaden bobcat
you are looking at a different part of the graph
I wanted your attention for 2<x<3
here
opaque shard
but if that a segment there cant be a tangent line though i thought
leaden bobcat
the “better” definition I gave you of tangent line is “the best line that approximates the graph”
if the graph is already a line, then it is its own tangent line
Maybe you want a few mins to think about it?
opaque shard
i think i might just take the L on this problem
leaden bobcat
you said you are self-teaching
on what bases do you start?
As in, do you know elementary algebra, etc.
opaque shard
honeslty i was looking for the answer then i would look at the answer for a while and determine how you got the answer
leaden bobcat
I'm confused by what you just said
you're saying you want me to give you the answer so you can think about it?
opaque shard
so i can see how you got the answer and determine how to do it, I did the othe problems i just cant figure this one out
leaden bobcat
Did you solve the other problems?
opaque shard
yes
leaden bobcat
then you understand how to draw the graph of the derivative when the function is a line
left wharf
Have you tried using desmos.com/graph to graph f(x)=-x^2 and f'(x)
leaden bobcat
same for when the graph is a parabola
opaque shard
yes but this has a jump a curve all this
leaden bobcat
Then I'm not sure of what's stopping you in this one
for x < 2 your graph is a parabola, so in there you do it exactly like B.
leaden bobcat
yes but this has a jump a curve all this
you draw the graphs separately
as you said at x=1 the graph is “flat” so there derivative is 0
you eyball another value (tangent line looks like has sloop 1 for x = -4)
since, just like for B., you know you will get a line, you can just draw the line passing though these points
you will have to stop once reaching x = 2 when the jump occurs
opaque shard
so y = 0 until 2 then its a line with the slope of 5 then a slope of 1
leaden bobcat
are you sure the slope of the first line is 5? It's going down, it cannot be positive
leaden bobcat
not 1/5
(1/5 is still positive)
if anything you should wonder about whether it is -5 or -1/5
which one is it?
opaque shard
-5
leaden bobcat
yes
leaden bobcat
so what should your drawing look like?
opaque shard
?
leaden bobcat
That looks like the graph of the original function
We said that for 2<x<3 the slope is -5 and for x > 3 the slope is 1
Look at how you did C.
opaque shard
wait are the lines always straight (left to right) when graphing f'
opaque shard
yeah
leaden bobcat
not always, just when the original function is a line
which is what I was trying to explain to you before
opaque shard
so 2 <x<3 should be horizontal as well as x>3
leaden bobcat
which is what I was trying to explain to you before
if the original function is a line, the tangent line is the function itself and it is the same at every point, so the slope of the tangent line is always the same value, this is why you get horizontal graphs for f' in that case
leaden bobcat
so 2 <x<3 should be horizontal as well as x>3
yes