how do i continue from here
#help-10
oak scroll
royal basin
try proving f(b)-f(a) = g(b)-g(a) instead of the stated goal
inland spruce
@royal basin thanks for helping me eventhough you were busy, that channel closed by mistake
oak scroll
try proving f(b)-f(a) = g(b)-g(a) instead of the stated goal
and does this have to do with limits or continuity?
royal basin
not directly no
i was going to suggest that you use the fundamental theorem of calculus
versed cave
That's such a good idea
oak scroll
would you please state it mathematically ? I take maths in Arabic so it's a bit hard for me to understand English maths terms
versed cave
The fundamental theorem of calculus is this
warm shaleBOT
Nonna
versed cave
F(x) is the antiderivative of f(x)
oak scroll
so i have to use integrals
strange stump
What two irrational number add up to 2?
strange stump
Oops sorry
oak scroll
I'm not sure I can use this type of maths on this question because this question is on the 1st unit which is all about differentiation
I took integrals last year but yeh i dont think i can use that theorem on the question
mental solstice
I'm not sure I can use this type of maths on this question because this question...
then maybe try Cauchy's mean value theorem
it's the one that says there exists $c$ such that $f'(c)(g(b) - g(a)) = g'(c)(f(b)-f(a))$, under some very general assumptions
warm shaleBOT
Camilleone
obtuse pebbleBOT
@oak scroll Has your question been resolved?
languid bone
obtuse pebbleBOT
<#488120190538743810>
languid bone
help
timid silo
ask
obtuse pebbleBOT
@languid bone Has your question been resolved?
lethal grail
I have no idea how to solve this: What is the common solution for both functions?
y = x + 1
y = 4 − 3x
x =
y =
obtuse pebbleBOT
I have no idea how to solve this: What is the common solution for both functions...
lethal grail
Yeah it kinda messes up my head and i got no idea how to solve this
and i like just dont want the answer i wanna know how to get the answer.
heady plover
I have no idea how to solve this: What is the common solution for both functions...
This problem belongs to simulataneous equation
Rewrite as y-x=1 and y+3x = 4
Subtract the equation to eliminate one variable... then you will be left with x.
-4x= -3 thus x= 3/4
Now take this x value and substitute in one of the equation to get y value
@lethal grail Hope this helps 👍
lethal grail
well no not really
i am supposed to write a graph
thoose are the cordinates or something
like theese stuff yeah
<@&286206848099549185>
heady plover
https://www.youtube.com/watch?v=6pCUvw6tF4A @lethal grail check out this
lethal grail
ill check
heady plover
Sure
lethal grail
well i know more now so i think i can do it. I just have to make a chart and a graph and i would be good?
.close
inland spruce
I think you didn't send full question
frigid phoenix
frigid phoenix
I think you didn't send full question
u got what I mean?
inland spruce
u got what I mean?
??
frigid phoenix
Did you get my question?
inland spruce
Did you get my question?
no
frigid phoenix
I just want to know how does f(t-a)= f(t-4) = t - 4 then became f(t) = t
look at the right part of the soln
inland spruce
oh ok
obtuse pebbleBOT
frigid phoenix
oops
inland spruce
oops
frigid phoenix
anyway how
inland spruce
@frigid phoenix make new one
inland spruce
anyway how
wait a min
frigid phoenix
okayy
obtuse pebbleBOT
Available help channel!
dull crypt
hi
inland spruce
hi manu
dull crypt
i'm trying to solve this
to no avail, i should add!
inland spruce
to no avail, i should add!
put f (x) in the x of g(x) and try to equate
obtuse pebbleBOT
@dull crypt Has your question been resolved?
dull crypt
I did try, though wasn't sure what to dowith that :x
inland spruce
lemme ask
dull crypt
5sqrt(4x^2 + a^2 + 4xa) - 4a = 31a
inland spruce
g(f(x))=5(|2x+a|+3a) - 4a
inland spruce
yep, not sure where to go from there though
oh
5(2x+a+3a)-4a =31
also 5(-(2x+a)+3a)-4a =31
inland spruce
i don't understand
|2x+a| = 2x+a or - (2x+a)
dull crypt
oh wack
wouldn't it be sqrt 4x^2 + a^2 + 4xa? or is that just equal to 2x _ a
2x + a*
inland spruce
|5| is +5 or - 5
dull crypt
ah i got you
inland spruce
modulus is the two lines called
dull crypt
i see
inland spruce
|-5| =5
dull crypt
yep
dull crypt
i'm overcomplicating it because i forgot what magnitude was in essence haha
dull crypt
thank you
ah, still confused somehow. you either have [ 15a + 5(2x + a) - 4a = 31a] which you can rearange to find x as being equal to 1.5a, or you have [15a - 5(2x + a) - 4a = 31a] which again can be rearranged, this time resulting in x = -2.5a. what am i doing wrong haha
<@&286206848099549185>
dull crypt
unfortunately not
I believe it wants the answer in terms of an integer number
or at least a number as opposed to an amount of a constant
obtuse pebbleBOT
@dull crypt Has your question been resolved?
rich sparrow
You've got lhopital down wrong
It's g'(x) can't go to 0
Or more correctly, if the new limit thatlhopital creates exist
(sometimes you can use lhopital multiple times in a row)
That's not really lhopital
That's "the algebraic limit theorem"
I suspect lhopital will be a bit lower on your page
Yep
You should take a fresh look on the problem noe
hollow epoch
whats the difference between local and global min/maxes
obtuse pebbleBOT
whats the difference between local and global min/maxes
nocturne minnow
whats the difference between local and global min/maxes
A maximum or minimum is said to be local if it is the largest or smallest value of the function, respectively, within a given range.
However, a maximum or minimum is said to be global if it is the largest or smallest value of the function, respectively, on the entire domain of a function.
nocturne minnow
drifting wraith
"global" is the usual meaning of maximum
local is just the Λ shape anywhere of any size
hollow epoch
so minimums usually local?
nocturne minnow
That would be considered as the global max of the function since it's the highest peak of this graph
nocturne minnow
It's not excluded but normally if it is the highest peak in the graph, it's considered as the global max
scarlet locust
a point x=a is local maxima if $f(a) > f(x) \forall x \in [a-h, a+h], h \to 0^{+}$
nocturne minnow
a point x=a is local maxima if $f(a) > f(x) \forall x \in [a-h, a+h], h \to 0^{+...
That's getting way too much into notation in which the OP might not understand
scarlet locust
a local maxima can be global maxima
I mean this definition was the clearest for me 
rather than
nocturne minnow
I mean this definition was the clearest for me <:lol:758678995541295162>
I mean, you know set notation, like for all, but the OP might not
scarlet locust
True, mb
nocturne minnow
It doesn't matter if it makes sense to you, you're trying to teach the OP so you should use terms they understand, if they know the notation you gave, that's fine but you should put it in layman terms
nocturne minnow
whats the difference between local and global min/maxes
Overall, for your understanding, what I think you should know is that global max/min is the highest or lowest point of the overall graph, while local max/min are the other highest/lowest points that isn't the global
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
muted bear
obtuse pebbleBOT
muted bear
is this done using the squeeze theorem?
i forgot and idk how to start
<@&286206848099549185> can someone help pls
kind hawk
I would use partial fractions
inland spruce
same
muted bear
I would use partial fractions
how would that help computing the limit?
kind hawk
well first compute the integral before worrying about the limit
muted bear
ok ill do it and see what i get
kind hawk
oh you can also do something interesting using the substitution u=1/t
I think that's nicer than partial fractions
muted bear
i did that at another point
this one
i managed that
i tried splitting the parts to get that
but didnt seem to amount to much
kind hawk
unless I've made a mistake, we have $\int_{1/x}^x f(t) dt = \int_{1/x}^x t^3 f(t) dt$, yes?
warm shaleBOT
Denascite
muted bear
uh no
its for 1/x to 1
so like you have to change the parts for it to work
i think so atleast
kind hawk
I don't think so
for 1 to x you should get the same
or just do the whole interval at once
I mean maybe I did a mistake, check my work if you want
assuming I didnt, what happens if we add those two integrals
muted bear
assuming I didnt, what happens if we add those two integrals
thats exactly where i left off
i added them
kind hawk
and then?
muted bear
i didnt know what to do
kind hawk
I'm gonna call the integral $I$. so we have $$I=\int_{1/x}^x f(t) dt = \int_{1/x}^x t^3 f(t) dt$$
therefore $$2I = I+I = \int_{1/x}^x f(t)+t^3f(t) dt = \int_{1/x}^x (1+t^3)f(t) dt$$
warm shaleBOT
Denascite
kind hawk
what can we do now
kind hawk
and then?
kind hawk
well now we want to compute the limit
kind hawk
what is the definition of arctan?
kind hawk
yes
muted bear
it was simple i just gave up too early lmao
kind hawk
yes you did
obtuse pebbleBOT
kind hawk
no need to be sorry. just don't give up as easily next time
obtuse pebbleBOT
Available help channel!
copper crater
Help please
obtuse pebbleBOT
Help please
copper crater
Help
quick vault
What help do you need?
copper crater
What is the formula for this?
N+1 on one side and 2(n + 1) on the other? And you subtract one?
But it doesn’t work for all…
<@&286206848099549185>
fickle turret
!15min
obtuse pebbleBOT
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.
fickle turret
Are you actually doing this in school?
fickle turret
It's very odd to sent a photo like that
copper crater
I really need help tho
fickle turret
So you want a formula for the number of squares in the n-th step?
fickle turret
2n+1
copper crater
Ok
fickle turret
2(n+1) = 2n+2
copper crater
So what would the full formula be?
fickle turret
So what would the full formula be?
What do you think it would be?
copper crater
Isn’t one part n+1?
fickle turret
Yes
fickle turret
So (2n+1)(n+1)-1
fickle turret
.close
final girder
Hi
final girder
My question is to do with right angle triangles. It's worded
"A 4m ladder leans against a vertical wire fence, the foot of the ladder is 2m from the base of the fence, Fang the lion can jump 3m vertically, can he Jump over the fence?"
I think no, as if Feng can only jump 3m vertically if the ladder is higher than his vertical jump, which it is by a metre, he cannot jump over the fence.
random ocean
your reasoning is wrong but answer is right
final girder
What would be the right reasoning
random ocean
u need to calc height by pythagorus and show that its more than 3m
final girder
The fence?
random ocean
what fence
final girder
A 4m ladder leans against a vertical wire fence
random ocean
vertical wire fence=sqrt(4^2 - 2^2 )
final girder
So I need to prove he can't jump over the fence by calculating its height using the info they gave me
Aite
fickle turret
vertical wire fence=sqrt(4^2 - 2^2 )
Don't "spoon feed" out answers
final girder
"Feng cannot jump over the fence, as he can only jump 4m, and if you use Pythagoras to calculate the height of the fence by doing 4^2 - 2^2 = height of fence^2, then square rooting it, you'll be left with 3.46m, which is higher thanpl Fangs vertical jump meaning he cannot jump over it"
random ocean
Don't "spoon feed" out answers
i thought he could understand it after i wrote
u need to calc height by pythagorus and show that its more than 3m
but he had doubts so i solved it for him
random ocean
"Feng cannot jump over the fence, as he can only jump 4m, and if you use Pythago...
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stable river
hi, i have a very basic word problem to solve and i solved it to a fraction but i think it was too easy that maybe i just did it wrong? can i get someone's opinion please
obtuse pebbleBOT
hi, i have a very basic word problem to solve and i solved it to a fraction but ...
stable river
obtuse pebbleBOT
@stable river Has your question been resolved?
obtuse pebbleBOT
@stable river Has your question been resolved?
mint mauve
Whenever I try this question my y^2 keeps getting cancelled out; and am now unsure of how to solve this question
obtuse pebbleBOT
Whenever I try this question my y^2 keeps getting cancelled out; and am now unsu...
mint mauve
This is what I've been doing so far, it's my second time trying this which is why it's not yet done before I realized I was getting the same answer as before
mint mauve
oh my God
AGHHHHHHHHHHH
CALCULUS
okay
signs are my worst enemy but thats why i defeat them
robust sleet
$\frac{1}{2}x^2 - xy + \frac{3}{4}xy - \frac{3}{2}y^2 - ( \frac{2}{3}x^2 - xy - xy + \frac{3}{2}y^2 )$
warm shaleBOT
Fucktalogist
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tawny tree
Im having issues with an induction proof, i have to prove that if cosx=p/q is an integer then q^ncos(nx) is also an integer. How do i proceed?
obtuse pebbleBOT
Im having issues with an induction proof, i have to prove that if cosx=p/q is an...
@tawny tree Has your question been resolved?
tender cypress
Im having issues with an induction proof, i have to prove that if cosx=p/q is an...
p/q is integer?
mint tendon
i think the base case here would actually be n = 2, cant hurt to prove that anyway
tawny tree
yes p/q is an integer
mint tendon
or wait no what am i saying
wild swallow
yes p/q is an integer
surely you mean p/q is rational
wild swallow
wild swallow
oh
no but
thats still
you also need q integer
otherwise you can just use any q
tawny tree
Ah yes yes
tender cypress
you also need q integer
it is obviously
tawny tree
q integer p integer
wild swallow
so p/q rational
tawny tree
yes
wild swallow
im sure you can write cos(nx) as a polynomial in cos(x)
tender cypress
im sure you can write cos(nx) as a polynomial in cos(x)
not needed in this proof
tawny tree
.close
timid silo
obtuse pebbleBOT
timid silo
Hey
could someone help me out with this
I thought nearest ten thousand would be 5 significant numbers
so I got 4347800
wild swallow
what is ten thousand
timid silo
10000
wild swallow
4347849
10000
huh
wild swallow
which ten thousand is nearest
shut plover
obtuse pebbleBOT
shut plover
I'm stuck how do I get rid of the f(x) after I find the value of f(4)?
warm shaleBOT
hardy widget
I'm stuck how do I get rid of the f(x) after I find the value of f(4)?
Substitute in $f(x)=\frac{x+6}{x+1}$, then you can simplify?
warm shaleBOT
messy circle creation
hardy widget
idk if that's what you want but that's my response ig lol
shut plover
Alright then thank you. I was gonna get a better picture of the work but that was fast lol
shut plover
Wait by substitute in f(x) do you mean just try and solve the equation in as is?
Or should I plug in x+6/x+1 into the second equation?
Like this
warm shaleBOT
hardy widget
yeah that
btw it's an expression, not an equation
since there's no equality
just thought I'd point that out
cuz why not
shut plover
Expression sorry
hardy widget
but yeah you can just simply the complex fraction here now
thick oracle
You dont need the brackets
hardy widget
^ But if it helps you keep track of things, there's no reason not to keep them
shut plover
Can get rid of the x's since they are dividing each other and keep the 6/1?
hardy widget
You can only "cancel" terms in the numerator and denominator if they're common factors
Instead, I would ||multiply the numerator and denominator by x+1||
shut plover
Oh yeah I forgot that you could do that☠️
I'm sorry I'm just getting back to math
hardy widget
🤷♂️ I don't mind tbh
shut plover
hardy widget
hardy widget
❌
shut plover
No wait. It's wrong from the get go because I was suppose to multiply x+1 with -2
hardy widget
should be $\frac{x+6-2(x+1)}{(x+1)(x-4)}$
warm shaleBOT
messy circle creation
warm shaleBOT
Flamindog12
hardy widget
**messy circle creation**
yeah, that's what you get after using distributive on the numerator here.
shut plover
That x-4 should be below
hardy widget
btw, you should have the entire denominator in the second set of squiggly brackets
just for future note
hardy widget
,rotate
warm shaleBOT
hardy widget
✅
drowsy girder
$$11ab \leq a^3 - b^3 \leq 12ab$$
obtuse pebbleBOT
$$11ab \leq a^3 - b^3 \leq 12ab$$
warm shaleBOT
Pluton
drowsy girder
Q: solve for natural solutions
obtuse pebbleBOT
@drowsy girder Has your question been resolved?
drowsy girder
<@&286206848099549185>
This is the third time im sending this question without a single response 
obtuse pebbleBOT
@drowsy girder Has your question been resolved?
mint tendon
u know the answer, ur just looking for an "elegant" way of showing it
drowsy girder
Basically. I feel the way im doing it isnt elegant
It requires you to use a calculator
Or estimate roots
Its a problem from some competition so im expecting an elegant solution
But idk what im missing
bold bane
I'm not saying that there are two solutions online if you Google the inequality, but there just might be if you click on the second link of the search results.
obtuse pebbleBOT
@drowsy girder Has your question been resolved?
mint tendon
the official solution is literally your method
i dont think there exists an elegant way of showing it
terse plover
whats the answer here?
obtuse pebbleBOT
whats the answer here?
upbeat blade
what would a combinatorial proof even look like?
obtuse pebbleBOT
what would a combinatorial proof even look like?
@upbeat blade Has your question been resolved?
obtuse pebbleBOT
@upbeat blade Has your question been resolved?
dusk island
i dont get the 4
obtuse pebbleBOT
i dont get the 4
dusk island
if its linear, why does it keep repeating the same number?
scarlet gale
It doesn't. It alternates between -1 and 1.
lost stirrup
(-1)^n
scarlet gale
(-1)^n
Please don't just give answers. Instead, help people to understand how to solve them.
lost stirrup
Sure, sorry
dusk island
It doesn't. It alternates between -1 and 1.
m can change -1 and 1????
scarlet gale
Yes.
lost stirrup
Since even powers make the negatives inside them positive, every even power makes answer positive
scarlet gale
If you look at problem 4 from the previous section, they have 3ⁿ.
That multiplies the previous result by 3 each time, right?
Like you get 3, 9, 27, 81, 243, ….
That's useful here.
Does that make sense so far?
scarlet gale
Yes, this isn't linear.
dusk island
Yes, this isn't linear.
x can also not be linear? how?
scarlet gale
You can tell because if you jump up and down on the graph of the thing, it makes a zigzag rather than a line.
It jumps between -1 and 1, so it can't be linear.
Does it make sense why it's not linear?
lost stirrup
m can change -1 and 1????
You can use Newton Gregory interpolation to find it out too
dusk island
It jumps between -1 and 1, so it can't be linear.
so like, the x is just -1, 1, -1, 1 and not 1,2,3,4,5
lost stirrup
Yes
scarlet gale
Right, see how 1, 2, 3, 4, 5 keeps going up at the same rate each time?
It adds 1 each time, right?
That's how linear things work.
But this one doesn't do that.
It adds 2, subtracts 2, forever.
lost stirrup
so like, the x is just -1, 1, -1, 1 and not 1,2,3,4,5
Remember sin(x)? It alternated from -1 to 1
scarlet gale
So, it's not a line.
scarlet gale
I'm not sure what you mean by the x.
Linear means it is a straight line.
Does that make sense?
dusk island
so what do you think is the answer?
warm shaleBOT
scarlet gale
See how that 1, 2, 3, 4, 5 makes a straight line?
dusk island
OOOOHH
dusk island
See how that 1, 2, 3, 4, 5 makes a straight line?
so pretty much, the x starts with -2???
scarlet gale
Sorry?
scarlet gale
Do you see how it starts at the y axis with 1, then goes up to 2, 3, 4, and so on?
dusk island
i mean like, generally i always see x as starting with 1, 2, 3, 4, 5
but it can aslo start with -2, -1, 1?
dusk island
Do you see how it starts at the y axis with 1, then goes up to 2, 3, 4, and so o...
yes?
dusk island
Do you see how it starts at the y axis with 1, then goes up to 2, 3, 4, and so o...
i think it starts with -1?
im still in question why it keeps repeating
i found this answer, is this really the answer?
we havent had this lesson yet
obtuse pebbleBOT
@dusk island Has your question been resolved?
obtuse pebbleBOT
@dusk island Has your question been resolved?
timid pivot
can someone help me wit this question
obtuse pebbleBOT
can someone help me wit this question
timid silo
,rotate
warm shaleBOT
kindred oasis
What have you tried?
timid pivot
What have you tried?
idk im kinda lost on what to do
i tried converting the revolutions per minute for the larger pully into angular speed
kindred oasis
Think about what the two pulleys have in common
timid pivot
probably linear speed
timid pivot
u onto something
kindred oasis
So you should equate their linear speeds to find the angular speeds
desert sinew
Since the two pulleys are in touch with each other, their “travelling distance” must be the same per minute.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lean ember
Help
daring rock
@lean ember Do you have a specific question about this?
When they say "check that this is an equivalence class", does that mean prove it rigorously?
lean ember
I think it is better if we prove it as well
To have a better understanding on the concept
lean ember
<@412234227958939648> Do you have a specific question about this?
This is the complete question.
daring rock
Are you comfortable with the idea of equivalence relations?
lean ember
Ya
But sometimes, I get really confused.
All I know about Relation on a set is that it a set as well.
lean ember
All I know about Relation on a set is that it a set as well.
A subset.
daring rock
A relation is a set of ordered pairs
lean ember
Yup
daring rock
In this case, a set of ordered pairs of real numbers
daring rock
Yeah that's true
lean ember
And an equivalences relation is a special kind of Relation which follows some rules.
Transitivity
Symmetry
Reflexivity
daring rock
Since they specified 'points in the plane', I'd interpret that to mean a subset of R^2
meaning real numbers
lean ember
Hm....
But I don't think so.
The question is saying,
"define two points to be equivalent"
Does this mean that I have to take an ordered pair of points?
Like,
((x1,y1),(x0,y0))?
daring rock
Yes, technically, but I don't think that's the best way to visualize it
daring rock
Instead of thinking of the relation as an ordered pair, we could just think of it as a symbol like <, >, or =
daring rock
Yes but those are just examples, our relation doesn't have to specify order
We could call our symbol $R$, and say that $(x_0,y_0) R (x_1,y_1)$ if and only if $y_0-x_0^2 = y_1 - x_1^2$
lean ember
hm....
warm shaleBOT
tatpoj
daring rock
Sorry, forgot some underscores lol
lean ember
No problem
daring rock
**tatpoj**
This does define a set of ordered pairs of ordered pairs, but thinking of it that way is confusing, like you said
lean ember
Yeah!
So we have a set of real numbers.
Lets say S(because we are using R for relation).
So S×S is a new set.
Then we have to cross S×S with S×S.
Which will give us a new set.
And our relation R would be the subset of this new (S×S)×(S×S)?
daring rock
Yes.
lean ember
Damn...
daring rock
That is technically true but I think you're focusing too much on that interpretation
lean ember
Okay..... 🤔
daring rock
The relation > can be thought of as a set of all ordered pairs (x,y) of two real numbers where x is greater than y.
But that's a massive set
And > is actually not that complicated, right?
daring rock
You can understand it intuitively without envisioning the entire set
lean ember
hmm.....
daring rock
So, I'd say no
lean ember
Okay.... 🤔
But isn't it necessary for a relation to be a subset of some A×A
If we even got a single element from R which doesn't belong to A×A, what then?
daring rock
A relation is a subset of A×B, but A does not have to equal B
This is my understanding anyway
lean ember
Woah really?
daring rock
Sure
daring rock
Of course. The floor function is a relation between the real numbers and the integers, for example
floor(pi) = 3
can be expressed as
pi F 3
if we want
We are way off track from your original problem lol
lean ember
Of course. The floor function is a relation between the real numbers and the int...
Wait ....
lean ember
We are *way* off track from your original problem lol
If u look at this thing called, floor relation, as you said, it is a subset if R×Z right?
lean ember
We are *way* off track from your original problem lol
Sorry, just a bit more time plz
daring rock
Oh, yes. It's a subset of R × Z
lean ember
But R×Z is a subset of R×R aswell.
daring rock
That's true
daring rock
Every A×B is a subset of U×U if you choose a big enough U 🤷♂️
lean ember
Do u have some example of two disjoint sets?
daring rock
hm
lean ember
Do u have some example of two disjoint sets?
Like, two totally different sets
lean ember
we Just ignore
A relation with a set crossing itself.
daring rock
Let A be the set of all polynomials with integer coefficients.
lean ember
Every A×B is a subset of U×U if you choose a big enough U 🤷♂️
So the A×A is holding
lean ember
Let A be the set of all polynomials with integer coefficients.
Hmm....okay
daring rock
You could define a relation S from A to N (naturals) such that aSb if and only if the sum of the coefficients of a is equal to b
In other words
Every polynomial corresponds to a natural number, by summing its coefficients
Thats a relation from A to N
lean ember
You could define a relation S from A to N (naturals) such that aSb if and only i...
u mean aSn?
daring rock
well I meant a is an element of A and b is an element of N
I could have been more clear lol
lean ember
Now lets come back to the main question
warm shaleBOT
tatpoj
daring rock
We could let $y_i-x_i^2 = c_i$ and say that $(x_0,y_0)$ and $(x_1,y_1)$ are in the same equivalence class iff $c_0=c_1$.
warm shaleBOT
tatpoj
daring rock
So, $R$ is definitely a relation from $\R^2$ to $\R^2$
We just need to show that it's reflexive, symmetric, and transitive
Huh, guess the tex bot is dead
Reflexive is easiest
We have to prove that (x_0,y_0) R (x_0,y_0)
Any ordered pair relates to itself
daring rock
sure thing, take care
obtuse pebbleBOT
@lean ember Has your question been resolved?
lean ember
No
alpine crown
how do i find limit as x goes to 4^- of 5/(x-4)
obtuse pebbleBOT
how do i find limit as x goes to 4^- of 5/(x-4)
@alpine crown Has your question been resolved?
alpine crown
also what do I have to search on youtube to learn more about this?
obtuse pebbleBOT
@alpine crown Has your question been resolved?
sacred bolt
Hi can i have some help I am doing Linear equations and i need to solve them. I need to know is there any formulas for this or no?
obtuse pebbleBOT
Hi can i have some help I am doing Linear equations and i need to solve them. I ...
royal basin
it will take more effort to memorize a formula than it would to actually learn how to solve linear equations
obtuse pebbleBOT
@sacred bolt Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
strange stump
Sorry it is a science question. The question is even experts can't tell the difference between a plant with less magnesium and less protein and why is that so?
obtuse pebbleBOT
Sorry it is a science question. The question is even experts can't tell the diff...
random ocean
this isnt even physics 😔 biology i suppose
strange stump
I said science question for your information
random ocean
isnt even related to maths
random ocean
strange stump
<#406129911992942593>
Ik
warm canopy
you're very unlikely to get an answer here in a reasonable timeframe, if at all
strange stump
you're very unlikely to get an answer here in a reasonable timeframe, if at all
Okay
let's just hope someone answers
obtuse pebbleBOT
@strange stump Has your question been resolved?
strange stump
<@&286206848099549185>
obtuse pebbleBOT
@strange stump Has your question been resolved?
dusk estuary
yow
dusk estuary
how can i graph this function using desmos w/ an infinity
[-3,infinity) cant graph in desmos
.close
stable rain
whats the notation for residue? R(z)? Res(z)?
obtuse pebbleBOT
whats the notation for residue? R(z)? Res(z)?
kind hawk
I've only seen Res(z)
kind hawk
well I haven't seen it. generally people would be too lazy to write that out
tall tusk
ok
tall tusk
so the squeeze theorem
is there another theorem
i forgot name
that only requires An>=Bn
like squeeze theorem requires three numbers to compare
@wild swallow
@mint tendon
so if An>Bn, and An has a llimit
then Bn too
if Bn is divergent
An is divergent too
kind hawk
dominated convergence? something like that?
but that only gives you convergence, it doesn't tell you the limit
so it's weaker
tall tusk
which one tells you convergence?
kind hawk
also for this you need that Bn is positive or something similar, so in the end you are also comparing three numbers
wild swallow
dominated convergence is such overkill for this
tall tusk
what
wild swallow
i cant read
tall tusk
bro can u explain
kind hawk
I assume you want a theorem of the form:
If $0\leq B_n\leq A_n$ and $\lim A_n$ exists, then $\lim B_n$ also exists
warm shaleBOT
Denascite
wild swallow
its the same theorem
wild swallow
just replace c with 0
kind hawk
but you need the assumption that 0 <= B_n
tall tusk
wait
kind hawk
otherwise this is false
kind hawk
B_n could just go to negative infinity
minor cedar
obtuse pebbleBOT
high lily
what have you tried?
minor cedar
Plugging it into a calculator 😭
wild swallow
you might find it helpful to know the change of base formula
minor cedar
Which is?
warm shaleBOT
warm shaleBOT
strange fern
Oh ok, i didnt see properly
minor cedar
So how do I solve it with the “…”
wild swallow
then read the rules before you post
strange fern
👍
minor cedar
So that’s the answer is log 2022! (2022!)^2
wild swallow
well since the cats out of the bag yes
wild swallow
you use this formula to bring the logs up to the top
and they end up having the same base of 2022!
then you use the sum to product log law
minor cedar
Which is?
warm shaleBOT
minor cedar
So the answer is 2
wild swallow
so it seems
minor cedar
Thank you so much
minor cedar
I see
ruby path
that was a joke
minor cedar
So if we really only used the last part of the problem what was the point of the first parts
Like 1/log4 2022!
obtuse pebbleBOT
@minor cedar Has your question been resolved?
stable rain
hi its me again pizza boy, being confused about laurent series
obtuse pebbleBOT
hi its me again pizza boy, being confused about laurent series
stable rain
so there are 3 different laurent series for a function and they are obtained by assuming each of the different shaded regions are holomorphic and thus we can use ... idk how i continue this
also so how do i intepret these results? why are there negative terms of the laurent series for the first n second and not the last? im guessing its as the values of the 2 poles cancel out? idk
residues of the pole at z=1 and z=1 are both 1 and -1 so adds to 0? idk if thats what u do, add
wild swallow
so there are 3 different laurent series for a function and they are obtained by ...
they are obtained by expanding the series in each of the different regions
you require a different expansion to get convergence
wild swallow
also so how do i intepret these results? why are there negative terms of the lau...
there are negative powers of z in both the second last and last series
the annulus and the complex plane with a disc removed
there are no negative powers of z in the first series because its the expansion inside the disc
we require convergence within the disc in that case
so there cant be negative powers of z
stable rain
they are obtained by expanding the series in each of the different regions
what does it mean, expanding the series in a region? like for taylor series, we find an estimate about some point, this is similar but about a region?
in that these regions in this case would satisfy the conditions of convergence for the geometric series we apply
stable rain
there are negative powers of z in both the second last and last series
oh yea i read it the wrong way around 1/z^n is the principle part oops
stable rain
we require convergence within the disc in that case
what does this mean
OH
WAIT THERES NO SINGULARITY AT 0
oops
if there was a singularity at 0 would it be different?
eg 1/(z(z-1)(z-2))
if we took the annul of 0<|z|<1
is that even an annulus?
also just to confirm these annulus regions exclude the boundary right
obtuse pebbleBOT
@stable rain Has your question been resolved?
fading sigil
hi
fading sigil
can anyone help here
fading sigil
coral cloak
you need to figure out some angle stuff first
well alternatively
you can calculate the hypotenuse of the ABD triangle
and then have a system of equations with two related unknowns for the sides
angle stuff might be easier if you can use a calculator to calculate arcosines etc
coral cloak
yes
think about what unsolveds you have here
DC
and BC
and think about how you can relate them
fading sigil
similar triangles?
coral cloak
think about this
(AD+DC)^2=(AB)^2 + (BC)^2
(BC)^2=(BD)^2 +(DC)^2
this is just the pythagorean theorem
obtuse pebbleBOT
@fading sigil Has your question been resolved?
strange fern
Find the number of integral points on the line segment joining points (1,2) and (2000,2100)
obtuse pebbleBOT
Find the number of integral points on the line segment joining points (1,2) and ...
@strange fern Has your question been resolved?
strange fern
<@&286206848099549185>
wild swallow
,w equation of the line joining (1, 2) and (2000, 2100)
warm shaleBOT
wild swallow
see what you make of it
obtuse pebbleBOT
@strange fern Has your question been resolved?
real quest
Need help!!
obtuse pebbleBOT
Need help!!
lean sigil
well, there are more than a single n that its true for
fickle turret
Make a table of the first values of both functions
lean sigil
And then if you need to prove it, try to do it using induction
real quest
2^(n+1) = 2^n * 2
2^n > 2n
so : 2^(n+1) > 2 * 2n
real quest
2*2n = 4n
lean sigil
why did you multiply it by 2 tho
real quest
cause 2^(n+1) = 2*2^n
lean sigil
in induction, we are assuming for n and proving for n+1
real quest
ok
lean sigil
So you need to write (n+1) instead of n in both sides and then try to prove that its true (when assuming that its true for n)
lean sigil
what can we do now?
real quest
divide by 2?
lean sigil
its possible, but I don't see how it helps us
fickle turret
Isn't helpful
real quest
replace 2^(n+1) by 2*2^n ?
lean sigil
note that 2^(n+1) = 2 * 2^n
lean sigil
replace 2^(n+1) by 2*2^n ?
yes
real quest
so :
2*2^n > 2n + 2
lean sigil
yes
lean sigil
2*2^n = 2^n + 2^n
real quest
yes
lean sigil
and from the induction we know that: 2^n > 2n
real quest
so :
real quest
yes
fickle turret
for every n, right?
No, only for n > 1
lean sigil
No, only for n > 1
yea true
real quest
so this characteristic can be transmitted but what is the first n to work?
fickle turret
It doesn't have an impact on the proof as we're starting induction after 2
lean sigil
so this characteristic can be transmitted but what is the first n to work?
you get this from the table you created earlier
lean sigil
1, 2, 4, 8 and 0, 2, 4, 6
.
real quest
ok ok so for n in [3; + infinity[
lean sigil
yes
royal compass
ok ok so for n in [3; + infinity[
Cimer j’ai le même exo pour demain 🙂
real quest
quel lycee?
royal compass
Ah oui mdr
real quest
bonne chance en tout cas bg XD
royal compass
Ouais pareil pour toi
real quest
.close
subtle adder
what is the formula for number if squares in an m * n grid
obtuse pebbleBOT
what is the formula for number if squares in an m * n grid
subtle adder
for example, in this 4x3 grid, there are 12 + 6 + 2 = 20
timid silo
why the last +1?
subtle adder
why the last +1?
never mind, that was just a small overlooking
timid silo
hmm, but yes we could start looking at how many squares with fixed size there are, and then sum them all together until reaching min(n, m)
how about you count the ways a square can fit horizontally (while being fixed vertically) and how many ways it can fit vertically (while being fixed horizontally), and multiply that together?
subtle adder
how about you count the ways a square can fit horizontally (while being fixed ve...
I don't understand
timid silo
like for size 2, we have 3 different x coordinates we can put a square to and 2 different y coordinates
past fog
m*n grid
The amount of squares is exactly that
m • n
How many squares across, or m, times the amount going down, n
4 by 5 grid has 20 squares
4 • 5 = 20
subtle adder
that is not what i meant by that question
timid silo
we are counting larger squares too
subtle adder
we are counting the squares formed by the smaller unit squares
timid silo
ahh i cant explain it rn
timid silo
like for size 1 its m*n, for size 2 its (m-1)*(n-1) squares
then make a sum formula out of that, and simplify until it has an easier closed form
timid silo
exactly, maybe i would change the upper bound to min(n, m)
subtle adder
like for size 2, we have 3 different x coordinates we can put a square to and 2 ...
i tried doing this
like move a "larger" square a step down
and let the length be the same
and then just pulled the formula from intuition
and it works
@past fog that's the answer
thanks rbit
timid silo
according to wolfram alpha this can be expressed without a sum but .. more complicated
subtle adder
according to wolfram alpha this can be expressed without a sum but .. more compl...
i prefer the above
anyway i'm closing this channel
.close
solid frigate
obtuse pebbleBOT
ruby path
Group the like terms
obtuse pebbleBOT
@solid frigate Has your question been resolved?
obtuse pebbleBOT
@solid frigate Has your question been resolved?
obtuse pebbleBOT
@solid frigate Has your question been resolved?
velvet socket