Use complex
#help-41
nova briar
wdym?
pure heron
To verify your answer
wraith violet
What happened to cos a x cos b
wraith violet
Not sure I understand
indigo cairn
huh?
wraith violet
So sin was being multiplied by cos then it turns into sin + cos
The last term disappears as well
amber waspBOT
@wraith violet Has your question been resolved?
kindred plover
1- one to one
2- not
3- not
4- one to one
right?
amber waspBOT
1- one to one
2- not
3- not
4- one to one
right?
split sail
yes
wheat grotto
1- one to one
2- not
3- not
4- one to one
right?
yes
amber waspBOT
amber waspBOT
Available help channel!
frigid mountain
This is not making any sense
amber waspBOT
This is not making any sense
frigid mountain
Like why does it say "r-1" then it proceeds to write "r+1"
spiral scarab
This is not making any sense
this calculus or nah?
spiral scarab
wha grade you in rn
frigid mountain
This is 11th grade course
spiral scarab
👍
frigid mountain
This is not making any sense
<@&286206848099549185>
amber waspBOT
@frigid mountain Has your question been resolved?
frigid mountain
No 😭
amber waspBOT
@frigid mountain Has your question been resolved?
amber waspBOT
frigid mountain
Help
Why does it say "r-1" but then it uses "r+1" in the equation
amber waspBOT
Available help channel!
honest orchid
need help
honest orchid
celest cove
what do you think
celest cove
what do domain and range mean
honest orchid
x and y
celest cove
too vague
quick ridge
why do all high school teachers do that
every person in high school would always say domain is x and range is y
honest orchid
So whats the answer
honest orchid
x and y is better
celest cove
thats one specific case, for functions of the form y=f(x) where our range is the set of y values and domain is the set of x values
it is not a general concept of domain and range
honest orchid
quick ridge
in simple terms the domain is the set of input values which would commonly be denoted by x yes, but as this illustration shows a function is a mapping between two sets, the domain and the codomain, each element in the domain is mapped to an element in the codomain. the range is the set of values the function takes on, or in other words the set of values in the codomain that have a pre image (arrow pointing to them)
honest orchid
blud said in simple terms and gave a confusing paragraph😂
nah thats acutally funny
😂
quick ridge
what was confusing?
quick ridge
💀💀
quick ridge
i cant be more clear than this
quick ridge
in simple terms the domain is the set of input values which would commonly be de...
^
do you need it in fortnite terms or something
quick ridge
yea it’s jelly’s channel
celest cove
no
honest orchid
what
quick ridge
you linked jelly’s channel
quick ridge
blud
honest orchid
font buggin
honest orchid
so the answer not 3
quick ridge
are you in 6th grade
quick ridge
so the answer not 3
nah boss
honest orchid
has to be in 2
celest cove
time?
quick ridge
ahh it’s a quiz
celest cove
oh dear oh dear oh dear
honest orchid
Nah
celest cove
open a book
honest orchid
I gotta sleep soon
quick ridge
open a book
probably allergic
quick ridge
yea and the time of the assignment is running out huh
honest orchid
nah
quick ridge
show the full screen blud
celest cove
times running out
honest orchid
yall crazy
honest orchid
I asked for the answer not an explanation on domain and range
quick ridge
!nosols
amber waspBOT
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.
honest orchid
i know that already
celest cove
we gave you enough information to know what to do
quick ridge
we aren’t here to give you the answers
celest cove
we told you
honest orchid
lets do vc
celest cove
nah
quick ridge
I asked for the answer not an explanation on domain and range
and we’re not giving you the answer
honest orchid
its easier
celest cove
tick tock chap
quick ridge
lets do vc
no one wants to man sorry
celest cove
quit yapping and do your test
quick ridge
at least tell me how to solve
i did
honest orchid
test?
quick ridge
question 9 (1 point)
celest cove
submit it then
quick ridge
it’s not number 3
💀
nah it is
you’re right
photomath is right
our mistake man
😂😂😂
honest orchid
say on bro
quick ridge
we were just messing with you
hollow temple
amber waspBOT
hollow temple
How does 2sinxcosx become 1 + sinx
cobalt vigil
How do I do #6?
4x + y + x(dy/dx) - 2y(dy/dx) = 0
x(dy/dx) - 2y(dy/dx) = -4x - y
dy/dx (x-2y) = -4x - y
dy/dx = (-4x - y) / (x - 2y)
amber waspBOT
@hollow temple Has your question been resolved?
normal dove
what does it mean that happening of one event confirms non occurence of her in mutually exhaustive set of events?
amber waspBOT
what does it mean that happening of one event confirms non occurence of her in m...
@normal dove Has your question been resolved?
amber waspBOT
@normal dove Has your question been resolved?
patent slate
We know that the limit
(→1)^→inf is Euler's number
amber waspBOT
We know that the limit
(→1)^→inf is Euler's number
patent slate
Does the limit
(→inf)^→0 also has a value??
shadow stump
We know that the limit
(→1)^→inf is Euler's number
it's actually indeterminate, which means it can have any value depending on the specific functions. Some specific functions will make it e, but not others
shadow stump
Does the limit
(→inf)^→0 also has a value??
this one is also indeterminate
patent slate
it's actually indeterminate, which means it can have any value depending on the ...
Any example
Okay I know what you mean
Another question
(1+x)^1/x is e where x tends to 0
So does the limit
1/x ^ (1+x) where x tends to 0 has a value too
Or 1/x^(x)
I imagine it as a very big number raised to a very small number →0
Can it tend to a new constant too?
shadow stump
something in the form 1/0 will tend to either +infinity or -infinity depending on the sign. something in the form 0^0 is also indeterminate
if you want to find the limit of 1/x^x, you can use the fact that x = e^(ln x)
cloud niche
amber waspBOT
shadow stump
so each elementary row operation corresponds to a particular elementary matrix
shadow stump
so if you multiply C by a particular sequence of elementary matrices, you get the identity matrix (this is how you row reduced it)
if we call those elementary matrices $E_1, E_2, \ldots E_k$ then we have [ E_k \cdots E_2 E_1 C = I ]
grizzled pagodaBOT
cloud
shadow stump
what does that tell us about the matrix $E_k \cdots E_2 E_1$?
grizzled pagodaBOT
cloud
cloud niche
uhmm
tells us that C can be written as the product of the inverses of those elementary matrices??
shadow stump
we have (some matrix)*C = I
cloud niche
oh ok
and the inverse of that
and that inverse of that (some matrox) is basically the factor C of a product of elementary matricies?
shadow stump
yes
the inverse of that matrix is C, and you can use the properties of inverses to distribute the inverse
shadow stump
well you still need to work out what E_1, E_2, (and their inverses!) are
cloud niche
but isnt that given?
cloud niche
this
shadow stump
you are given the row operations, but you still need to write out the elementary matrices corresponding to those row operations (and since you are inverting them, also write their inverses out)
amber waspBOT
@cloud niche Has your question been resolved?
shadow stump
yes, you can confirm by multiplying them all out
amber waspBOT
@cloud niche Has your question been resolved?
cloud niche
yes, you can confirm by multiplying them all out
okok. thank you so much!
amber waspBOT
okok. thank you so much!
@cloud niche Has your question been resolved?
Available help channel!
carmine tusk
amber waspBOT
carmine tusk
I don’t get the answer at all?
stiff jetty
I don’t get the answer at all?
what do you not get about it
stiff jetty
I don’t get the answer at all?
!status
amber waspBOT
I don’t get the answer at all?
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
@carmine tusk Has your question been resolved?
cloud niche
can someone check my work please
amber waspBOT
can someone check my work please
cloud niche
amber waspBOT
@cloud niche Has your question been resolved?
amber waspBOT
@cloud niche Has your question been resolved?
safe jackal
Looks good to me and to Wolfram
crisp stratus
Prove $a_n \to A \implies \sqrt{a_n} \to \sqrt{A}$
amber waspBOT
Prove $a_n \to A \implies \sqrt{a_n} \to \sqrt{A}$
grizzled pagodaBOT
artemetra
crisp stratus
let $B = \lim_{n\to \infty} \sqrt{a_n}$\
$\implies A = \lim_{n\to\infty} a_n = (\lim_{n\to\infty} \sqrt{a_n}) (\lim_{n\to\infty} \sqrt{a_n}) = B^2$\
$\implies A = B^2$\
$\implies B = \sqrt{A}$
grizzled pagodaBOT
artemetra
crisp stratus
@stuck vapor sorry for the ping, it's the problem i was doing yesterday. my friend just showed me this proof -- is it any good or is there some flaw here?
i guess there is nothing that shows B actually exists - but is it necessary?
indigo cloud
i guess there is nothing that shows B actually exists - but is it necessary?
yes
you can only split up limits if the limits you get actually exist
amber waspBOT
@crisp stratus Has your question been resolved?
crisp stratus
you can only split up limits if the limits you get actually exist
how does one show that in this case
crisp stratus
**artemetra**
also suppose $A, a_n \geq 0$
grizzled pagodaBOT
artemetra
stuck vapor
how does one show that in this case
Not exactly more easily, since as you saw if the limit exists it's clearly sqrt(A)
crisp stratus
right so the only problem is me saying ``let $B = \lim_{n\to\infty} \sqrt{a_n}$''
grizzled pagodaBOT
artemetra
indigo cloud
"only"
crisp stratus
well..
that's the mistake right
everything else follows fine it's just that i am making an assumption
indigo cloud
didnt you nearly have it last time? you only needed to bound sqrt(a_n)+sqrt(A). that should be doable
crisp stratus
i had it last time but Bezier said i needed to show that my formula for another epsilon was surjective
which i think is fine but i felt like there would be an easier/nicer way around this
indigo cloud
wdym surjective
you mean you wanted to choose bla = f(eps) or something?
it would probably be enough to have bla > or < f(eps)
crisp stratus
wdym surjective
crisp stratus
okay thanks
crisp stratus
**artemetra**
and this is not good enough right
indigo cloud
I dont think there is something simpler than those simple steps
crisp stratus
okay
indigo cloud
no, it doesnt show existence
amber waspBOT
stuck vapor
i had it last time but Bezier said i needed to show that my formula for another ...
Maybe I wasn't clear
But you had a wording issue, not actually following the order of things in the definition of the limit
And the way to get the correct ordering basically required a bit of extra work, but not as in "prove smt more", just write it the right way round and the way to do so would be obvious then
crisp stratus
.reopen
amber waspBOT
✅
crisp stratus
Maybe I wasn't clear
But you had a wording issue, not actually following the or...
ah i see
i'll write it nicely and send it
stuck vapor
Just a nice e-N proof
stuck vapor
You don't need to ask
Look at what you need to prove, figure it out
amber waspBOT
@crisp stratus Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
fervent oasis
how can I solve this using "mod arithmetic"?
amber waspBOT
how can I solve this using "mod arithmetic"?
warped sage
since we're in mod 7, we want a number thats equivalent to -3
still pecan
Yes
amber waspBOT
amber waspBOT
Available help channel!
umbral epoch
need help
amber waspBOT
@umbral epoch Has your question been resolved?
cloud niche
can someone check my work
amber waspBOT
Available help channel!
split sail
amber waspBOT
split sail
Yes
subtle viper
reversing start and end points of a line segment negates the vector
And note that AB + BC = AC
a + b = AC
split sail
Wait how is AB+BC=AC
subtle viper
If you go from A to B
and then from B to C
That's the same as if you went from A to C
start and end points are the same
XY + YZ = XZ is a crucial property
subtle viper
sry am only partially available, if you're stuck on other vectors just write here
And other passengers will help voluntarily :]
amber waspBOT
amber waspBOT
Available help channel!
bleak mason
amber waspBOT
inland pulsar
yup
bleak mason
-2^4 is 16
inland pulsar
yup
amber waspBOT
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.
inland pulsar
-432
go read #helpers-info
bleak mason
So it’s -27x^3 • 16x^4
split sail
go read <#1164751389034041374>
alright my bad
inland pulsar
Im stuck there I tried solving it and got -11x^7
btw you are supposed to multiply the coeff not substract
inland pulsar
Wait where
leave that
bleak mason
Ohhh so -27x times 16x
inland pulsar
yupp
bleak mason
That’s
-432x^2?
Cause it’s x times x and I assume it will become ^2
Okay so what do I do now
Is that the answer
bleak mason
Ohh
inland pulsar
x isnt
bleak mason
Why
inland pulsar
So it’s -27x^3 • 16x^4
this is correct
bleak mason
How
bleak mason
this is correct
How do I continue from there
bleak mason
Ohhh so -432^7
inland pulsar
forgot x lol
inland pulsar
yupp
inland pulsar
legoo
bleak mason
I literally just started this chapter of math today so it’s all new to me
inland pulsar
ohh nice
you were one of the easier ones for me today
not in terms of ques
but how you understood
bleak mason
I can’t imagine doing anything harder than this I was so confused today in class about it
But then again collage boys are really a piece of work and scream like hoolagans so it was hard to hear or understand any
Anything
amber waspBOT
If you are done with this channel, please mark your problem as solved by typing .close
amber waspBOT
@bleak mason Has your question been resolved?
bleak mason
.close
amber waspBOT
amber waspBOT
Available help channel!
tribal stone
do you know how they got the pathlength of 2.4%
amber waspBOT
do you know how they got the pathlength of 2.4%
shadow stump
looks like it comes from reading the graph on the right
amber waspBOT
@tribal stone Has your question been resolved?
tribal stone
<@&286206848099549185>
amber waspBOT
@tribal stone Has your question been resolved?
pallid canopy
do you know how they got the pathlength of 2.4%
Says to refer to Figure 8.1, not 8.11
amber waspBOT
amber waspBOT
Available help channel!
minor night
amber waspBOT
minor night
this is the answer for it
i dont think its right
because it says "for -5/4 < x < 1, f(x) < 0", i.e. y is negative, but y doesnt become negative until x > 1
they might have meant f'(x)
but am i wrong or are they?
shadow stump
i think they meant to say f'(x) rather than f(x) for conditions 2 and 3
that does make the solution incorrect for the problem as presented, though
sharp depot
i think they meant to say f'(x) rather than f(x) for conditions 2 and 3
if this is the case
the nthe answer is fine
amber waspBOT
@minor night Has your question been resolved?
abstract arch
Can someone help me with this question?
amber waspBOT
Can someone help me with this question?
@abstract arch Has your question been resolved?
abstract arch
.close
amber waspBOT
amber waspBOT
Available help channel!
cloud niche
amber waspBOT
amber waspBOT
Available help channel!
thorn harness
whats the difference between this and taylor expansion
amber waspBOT
whats the difference between this and taylor expansion
thorn harness
can i just use taylor expansion for this?
restive orchid
effectively, yeah, although I suppose it kind of depends on how you define the binomial expansion
for non integer exponents it ends up working out that it matches the binomial coefficients, although the strict definition in terms of factorials won't quite work for you
thorn harness
for non integer exponents it ends up working out that it matches the binomial co...
does it always work for rational exponents?
cuz if it works ill just keep using it
restive orchid
does it always work for rational exponents?
depends on what "it" is
what I sorta vaguely described might not be the same thing you got
restive orchid
what I'm picturing is $$\sqrt[3]{8+4x} = 2 (1+\frac{x}{2})^{1/3} = 2\sum_{n=0}^\infty \binom{1/3}{n} (\frac{x}{2})^n$$
grizzled pagodaBOT
Merosity
restive orchid
idk if that lines up with how you did it or not
thorn harness
i did both and it aligns
restive orchid
how do you evaluate 1/3 choose 2
thorn harness
💀
restive orchid
i did both and it aligns
how did you do both
1/3 choose 2 should be the third term
well, part of it
restive orchid
what's the coefficient formula
thorn harness
idk how to type it out like that
restive orchid
are you talking about the taylor series or the binomial
thorn harness
binomial?
restive orchid
I'm going to leave now
crystal cloak
How do we do this?
amber waspBOT
How do we do this?
amber waspBOT
@crystal cloak Has your question been resolved?
vestal hatch
In that case, solving for limits directly doesn't work because you get infinity*0, right
pale shell
You can probably do sandwhich on f(x)g(x)
vestal hatch
Maybe try finding lim f(x)/h(x), where h is a simple function that you think grows around the same speed as f as x→0
visual wren
How many simplified fractions are there in 100
amber waspBOT
How many simplified fractions are there in 100
visual wren
pls help from this question
tulip tapir
what?
amber waspBOT
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.
visual wren
i thought your saying is a joke
grizzled plume
seriously
visual wren
that question doesn't even make sense
hahahahah
idk even know what does it mean
what next?
tulip tapir
no clue
visual wren
what is the connection from euler totient
rancid raven
what next?
Chat gpt is giving a nice answer
Although I have never studied this Euler totient
grizzled plume
Although I have never studied this Euler totient
the wikipedia or aops would help
rancid raven
the wikipedia or aops would help
If it's easy for you, you should help them
I don't know about it , else I would have helped
amber waspBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
@visual wren Has your question been resolved?
visual wren
!noans
amber waspBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
visual wren
.close
amber waspBOT
tulip tapir
tf 
solar gust
Lmao
tulip tapir
hi yaku long time no see
solar gust
Hi ren howdy ?
tulip tapir
good, wbu
solar gust
Doing good, exam soon
tulip tapir
oh
amber waspBOT
Available help channel!
worn vault
I have the following pair of equations:
[ x_k\sin\theta + y_k\cos\theta = \sin(\phi_k - \phi_c)] and
[x_k\cos\theta - y_0\sin\theta = \cos(\phi_k - \phi_c)\sin(\lambda_k-\lambda_c)]
worn vault
I have two sets of points where $(x_k, y_k, \phi_k, \lambda_k)$ satisfy the equations
grizzled pagodaBOT
The د
worn vault
this leads to four equations
how can I solve for the constants $\theta, \phi_c$ and $\lambda_c$?
worn vault
.close
amber waspBOT
amber waspBOT
Available help channel!
split sail
can someone explain what the lecturer means when he says this ?
What exactly does he imply when he says "weird sets"
prime cipher
Hi 🙂
This is linked to a quite advanced concept in measure theory
Basicaly
When you do probability you measure sets
Like on this example, a random point on a square
If the distribution is uniform, then to find the probability of the random point going to the left half, you just need to measure the left half and compare it with the measure of the square right
BUT
This word "measure" is just not easy to formulate
split sail
If the distribution is uniform, then to find the probability of the random point...
wdym by if distribution is uniform?
prime cipher
wdym by if distribution is uniform?
Every place is as likely to be chosen
split sail
as in if its drawn on an axis, the unit length is defined as 1 unit and cant be broken down further?
prime cipher
So, like I said, there is a formal definiton to a measure
we say that a measure is just three things
split sail
go on
prime cipher
A set $\Omega$ of the thigs you want to measure For the square, you say just the points in the square
grizzled pagodaBOT
LucienF
split sail
wait so the word measure in measure theory quite literally stands for measuring things?
prime cipher
A set of subsets of $\Omega$ that that the sets you can measure
grizzled pagodaBOT
LucienF
prime cipher
And a map $\mu$ from this set of subsets to $\mathbb R$, that is your actual measure
grizzled pagodaBOT
LucienF
prime cipher
wait so the word measure in measure theory quite literally stands for measuring ...
Yes
Like defining measure
split sail
okay so
prime cipher
properly
prime cipher
Don't worry I were too and I'm a Phd student now ahahahah
split sail
i was never really told what a set is
like literally, mathematically
it was always a list or a bunch of like stuff
split sail
Don't worry I were too and I'm a Phd student now ahahahah
damn
all the best for your thesis or research
prime cipher
The problem lies in the second object, this set of meassurable sets
prime cipher
all the best for your thesis or research
❤️
split sail
The problem lies in the second object, this set of meassurable sets
no the thing is, i already lost you at the definition of measure 😭
what is your field/branch of study btw? if you dont mind me asking
prime cipher
You cannot find a good map that will both fit the axioms of an actual measure; and be able to measure every sets you can possibly imagine
Measure : (Set of things, sets of those things you want to measure, the map that measures the sets)
The measure you know on, well everything
Thats called the Lebesgue measure
split sail
i have never felt this dumb in my entire life
prime cipher
To have a proper meaning, it can only measure what we call Borelian sets
prime cipher
i have never felt this dumb in my entire life
Thats ok thats an advanced stuff
And you can create non borelian sets
So sets that you cannot actualy measure
split sail
but what is a borelian set...
prime cipher
Complicated
prime cipher
Just a consequence of the axioms of a measure and this tribe, the set of measurable subsets
split sail
will stick to probability for kids
prime cipher
will stick to probability for kids
Soon soon you'll do it for grown up
split sail
https://youtu.be/j9WZyLZCBzs?list=PLUl4u3cNGP61MdtwGTqZA0MreSaDybji8&t=2188
whats the mathematical "level" of this lecture series ?
prime cipher
I'll finish by just giving you the link to an actual non measurable subsets
prime cipher
whats the mathematical "level" of this lecture series ?
Waait a sec
split sail
that will be intereseting
prime cipher
Ok I was wrong, there is actually a bigger set of measurable sets than just the Borelians but no one knows yet if this is every subsets of the real numbers.
ahahah
The name of this non-borelian set I mentionned you is the triadic set of Cantor
Its a wierd as fuck set that does not fit in this first definition i gave you
prime cipher
Aahahah dont worry, to sum up, a set can have a measure if it fits a precise definition, and some sets does not, so have no measure attached to it, thus no probability
split sail
is this even maths..
split sail
Aahahah dont worry, to sum up, a set can have a measure if it fits a precise def...
ahhhhh
see now i get it
prime cipher
Yes, if you continue to infinity
split sail
you dont define something, you dont get a probability for the subset of a function present in the "something"
prime cipher
I*ll look at the lecture
split sail
you dont define something, you dont get a probability for the subset of a functi...
is that good enough at this level?
prime cipher
you dont define something, you dont get a probability for the subset of a functi...
Yo need to define things to do math with it ahah
split sail
Yo need to define things to do math with it ahah
yes that makes sense ofc
split sail
is this even maths..
and one of the many(?) examples is this stuff?
split sail
is this even maths..
what even is this, seems more out of quantum mechanics than maths
prime cipher
I'd say the level of the lecture is Year2 of college
split sail
electron probability stuff
prime cipher
end of year one
split sail
I'd say the level of the lecture is Year2 of college
college as in uni right?
after grade 12?
prime cipher
yes
split sail
Im french ahaha
different systems
i will enjoy probability, i like combinatorics
even tho i do suck at it
prime cipher
Your welcome, take care, and don't worry, math is so big that no ones understand everything 🙂 You don't have to feel ashamed if you dont understand something
split sail
Your welcome, take care, and don't worry, math is so big that no ones understand...
:D
thank you
have a good day
.close
amber waspBOT
prime cipher
you too bye
amber waspBOT
Available help channel!
amber waspBOT
amber waspBOT
@quasi pagoda Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
split sail
amber waspBOT
split sail
amber waspBOT
split sail
Does it make sense to say $\lim_{x\to\infty}\frac{2(\infty)^3-(\infty)^2}{2-\infty-(\infty)^4}\to\frac{\infty}{\infty}$?
grizzled pagodaBOT
forMaths
keen topaz
Divide by highest power
split sail
What do you mean?
split sail
Divide by highest power
?
tender cipher
A nice thing to do if u hate the infinities is to just express it in terms of 1/x instead of x
tender cipher
Because when x-> infinity, 1/x-> 0
keen topaz
Because when x-> infinity, 1/x-> 0
Yeah
split sail
A nice thing to do if u hate the infinities is to just express it in terms of 1/...
So divide numerator and denominator by x?
keen topaz
So divide numerator and denominator by `x`?
No x^4
split sail
oh, because that is the biggest power
keen topaz
oh, because that is the biggest power
Yes
tender cipher
There's a lot of ways to do this
Dividing by highest power is one, expressing in 1/x's is another, and also u can always do the repeated lopital here
split sail
i'd rather not repeat the L'Hopital
tender cipher
I have used lopital more times than Eminem says fuck
split sail
lol
well then im screwed
because L'Hopital is sooooooooooo boring
Actually, limits in general is boring
I miss ODEs and homogenous DEs.
tender cipher
Also, could you elaborate more on the second method? Expressing in 1/x's
Basically write z = 1/x and express the expression in terms of z
keen topaz
I have used lopital more times than Eminem says fuck
LMAO
tender cipher
With z-> 0
tender cipher
Basically write z = 1/x and express the expression in terms of z
Makes things much simpler to think about, that's all
split sail
Basically write z = 1/x and express the expression in terms of z
So in this case, all xs would be replaced with z^-1?
Because otherwise I am confused lol
tender cipher
It converts ur infinities into nice zeros
tender cipher
So in this case, all `x`s would be replaced with `z^-1`?
Yea
split sail
Ah
tender cipher
Basically if u have x-> inf then write it in terms of z=1/x-> 0
split sail
Aha, that makes sense
tender cipher
I miss ODEs and homogenous DEs.
Wait u have done ODEs
tender cipher
Wait r u doing this as a part of RA course?
split sail
I have no idea what RA course is
tender cipher
How did u skip to ODEs before limits
split sail
lol well
i take a private tutor
the way it was introduced to us in school was limits first and then ODEs
but my private tutor made us do ODEs before limits
So things are reversed lol
tender cipher
Damn that's crazy
keen topaz
How did u skip to ODEs before limits
tender cipher
but dividing by the greatest power isn't really L'Hopital's rule now, is it?
No, it's just simplification
tender cipher
split sail
AAAAAAAAA IM GONNA DIE
ykw, i will just tell my private tutor that i couldnt solve it
tender cipher
Tbh simplifying the expression before using lopital should be valid
split sail
true
tender cipher
No child should suffer repeated lopitals
tender cipher
What's cyclical integration 
split sail
I'd rather find $\int,x\ln((x))^2$ then do L'Hopital's
grizzled pagodaBOT
forMaths
split sail
What's cyclical integration <:hmmcat:831508801646755850>
It's like a cheeky integration by parts
quick spoke
weird question but u can just differentiate top and bottom like n times lol
split sail
When you integrate by parts but you end up getting the same thing
And then you go, "haha you cheeky bastard"
split sail
weird question but u can just differentiate top and bottom like n times lol
UGH! i'd rather BURN my house
tender cipher
That's not integration then, that's just Sisyphus' punishment
amber waspBOT
amber waspBOT
Available help channel!
keen pawn
I'm trying to prove that if $a,b\in \Z$, then $lcm(a,b)$ exists
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen pawn
So I'm defining $lcm(a,b)=l$ to be that natural number that has the following properties
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen pawn
$a \mid l \land b \mid l$
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
keen pawn
and if $a \mid e \land b \mid e \implies e \mid l$
vast spade
**Mr bean is not $\\R \\setminus \\Q$**
is it lcm(a,b) being unique or just the existence of lcm(a,b)?
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
lethal steppe
Maybe you could use the fact that $\leq$ is a well-ordering on $\mathbb{N}$?
grizzled pagodaBOT
FirstNameLastName
lethal steppe
What is your question then?
keen pawn
so $ab$ atleast is an element
grizzled pagodaBOT
Mr bean is not $\R \setminus \Q$
lethal steppe
Yeah that seems like the right approach to me
The set of positive multiples is a nonempty subset of the natural numbers, therefore it has a least element
And verifying that it has |ab| as an element should be enough then
earnest sinew
amber waspBOT
earnest sinew
Consider C as a constant in the next qestions , we have the y is implictly defined as a function of t by the corresponding equations. In each exercise determine an Differencial equation where y is a solution
dapper phoenix
Yea Izzy is right
earnest sinew
my work
its the exercice 2
i differenciate both sides with respect to t
and i think thats it
earnest sinew
But in the last exercice
my english is not the best i am sorry btw
i put the ODE in a solver
and it gave me y = C1/(t^2 +4)
and then i did a substituion of that expression in the original expression and i didnt get an equal thing from both sides
so that means i did something wrong right ?
The other ODE didnt have an "easy" solution the solution was written with non elementary fucntions so i couldnt test it
<@&286206848099549185>
.close
shadow swift
does anyone know how f(x) = $\frac{1}{h}\cdotln(1+sin2h)$ = $2\cdot\frac{sin2h}{2h}\cdot\frac{ln(1+sin2h)}{sin2h}$
grizzled pagodaBOT
Quantie
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
shadow swift
h = 1/x
its from the proposed solution
$\lim_{x\to\infty} \left(\ln\left(1+\sin\left(\frac{2}{x}\right)\right)\right)^x$
grizzled pagodaBOT
Quantie
shadow swift
is the problem
ruby dome
Hi
shadow swift
yo
brisk nexus
Hi
shadow swift
alr i got it by small angle approximating, but its a much less elegant solution
.close
split sail
ok so
split sail
this is straightforward
f(x) = +-root(r^2-x^2)
Find the integral of f(x) from -r to r
it's pir^2
I mean
.close
amber waspBOT
split sail
its just a circle
f^2(x) + x^2 = r^2, and what you are trying to find is equivalent to finding the area of a circle of radius r
although i think you gotta assume r > 0 as a restriction
ok
amber waspBOT
Available help channel!
slate gale
Guys. If sin x/cos x = tan x,
Does that mean sin^2x/cos^2x = tan^2x?
pallid canopy
Yes
slate gale
Ohhhh i see
amber waspBOT
amber waspBOT
Available help channel!
leaden carbon
I have two questions for this.
-
Where is the -1/2 exponent coming from?
-
When do we “stop” with the chain rule? My expectation is that since we need to take the derivative of the stuff inside the root, we’d end up with more terms.
Meaning, why does (t-3)^2 not become 2(t-3) * t? Shouldn’t we have to apply the chain rule again?
Perhaps I missed it.
pallid canopy
√a = a^(1/2)
And power rule for derivatives
What else would there be for the derivative past chain rule?
They did multiply by the derivative of the "inside" function
leaden carbon
I agree with that, but I’m not sure why it’s negative.
And maybe I’m just misunderstanding the inner function, then.
I cannot see why we do not multiply by an additional t.
They have the 2*60^2(t-3) that I expect. But taking the derivative of that requires us to also take the derivative of t-3, no?
Because it in itself is a function.
craggy sundial
I agree with that, but I’m not sure why it’s negative.
And maybe I’m just misu...
and what's the derivative of t-3?
craggy sundial
yea it's just 1 so they omitted it
amber waspBOT
craggy sundial
Thank you again!
did you figure out where the -1/2 comes from?
leaden carbon
I did not, but figured I’d look harder at it now that I wasn’t confused about the 1
Could you explain it?
.reopen
amber waspBOT
✅
craggy sundial
yea, so how do we do the power rule on x^a?
leaden carbon
Ahhhh, the 1/2-1 is where it’s coming from, right?
craggy sundial
yup, mhm
leaden carbon
Well, that settles both of them, then lol. Thanks again.
craggy sundial
no problem
leaden carbon
.close
junior vale
amber waspBOT
junior vale
its will be 2m?
solemn escarp
no
spare belfry
no, why?
solemn escarp
factorize m
amber waspBOT
split kraken
amber waspBOT
Available help channel!
calm pewter
amber waspBOT
inland pulsar
!status
amber waspBOT
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
1
inland pulsar
if you have 10 chocolates
and want to give it to 2 children
how many choco per child?
calm pewter
5
calm pewter
3.3333333333333333
calm pewter
kk
inland pulsar
what does convert mean?
calm pewter
turn 1 unit to another
calm pewter
16000 devide 17?
inland pulsar
nope
inland pulsar
np
calm pewter
1600 by 17
calm pewter
94.12
inland pulsar
because 0.333... isnt possible
now do this ^
inland pulsar
but wait wouldnt it be 95 bc we need more of it
lets say you have 10 chocolates
and you wanna give to 3 children
you give each 3 or 4?
calm pewter
3 but i gotta give some guy bits of other guys chocolate or smth
inland pulsar
thats the ans imo
inland pulsar
1600 by 17
bro why you dividing by 17?
calm pewter
1600 by 17
i think this was wrong aswell bru
inland pulsar
yeah me too
calm pewter
u had to do 1600/65
inland pulsar
why 25?
calm pewter
sry