okay, i'll walk you through them, then.
#help-27
woven locust
its concave down?
eager agate
no.
eager agate
yes! good job!
devout snowBOT
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Available help channel!
little helm
Good morning, I have a quick question about the delta here and in what context does “for everyone” mean. I know that f(x)-f(x0) means that it has to apply to all epxilon but it can with delta Somehow I can't really imagine it."For all ε > 0 and all δ > 0 we have |f(x) − f(x0)| < ε for all x ∈]a, b[ with |x − x0|. < δ."
devout snowBOT
Good morning, I have a quick question about the delta here and in what context d...
devout snowBOT
@little helm Has your question been resolved?
graceful cosmos
Usually it's "for all ε > 0, there exists a δ > 0"
Other than that, maybe can you give an example of something that's tripping you up?
little helm
idk how i should put it we already did this one at uni
but the meaning of that what you just said is that every epsilon has one delta
does that mean that you have the same epsilon for example f(x)-f(x0)=f(y)-f(y0)
little helm
Good morning, I have a quick question about the delta here and in what context d...
but that was for an constant function that was the conclusion from yesterday
graceful cosmos
You choose the variables in the order their presented, from left to right.
That means an ε is chosen, and then with the knowledge of the ε that was chosen, a δ is chosen.
The definition of the limit says that you should be able to choose any ε, and then should be able to choose some δ
The guaranteed existence of a δ, no matter which ε you pick, is the existence of a limit
Note it doesn't actually matter what δ is
little helm
ah so it depends on epsilon
little helm
The guaranteed existence of a δ, no matter which ε you pick, is the existence of...
what do you mean by that
graceful cosmos
Yeah you will need to change your δ depending on which ε was chosen
little helm
or with it doesnt what delta is
graceful cosmos
And many δ tend to work
little helm
Yeah you will need to change your δ depending on which ε was chosen
but is that for the normal definition or for the task that i sended
graceful cosmos
Okay so you do specifically want the altered definition
That is, "for all ε, and for all δ"
That makes it pretty different from the definition of the limit, since you should be able to choose any ε and any δ. Not many functions this would work for
graceful cosmos
Is there a full question, or some definition, this is linked to?
little helm
That makes it pretty different from the definition of the limit, since you shoul...
to that you said that it wouldnt work for many function
but i lack to to understand that
graceful cosmos
So with the normal definition of the limit, we are putting a box around the limit point. I am free to choose any height for the box, and you have to choose a length for the box. You have to choose such that the function doesn't leave the top/bottom of the box. If you can do that, the limit is proven.
In your new version, I get to choose the height of the box, and the length of the box. If, no matter which height and length I choose, the function doesn't leave the top/bottom of the box, then your definition works
I'm pretty sure that only constant functions can fit your definition
little helm
with length you mean the x-axis or notr
little helm
So with the normal definition of the limit, we are putting a box around the limi...
ok i understand
so if im right you take a point and you put an epsilon around it now you have to pick an delta so that the box doesnt leave it
which means you have to pick an delta that is suited to the epsilon right?
graceful cosmos
Graphics like this are pretty useful
little helm
In your new version, I get to choose the height of the box, and the length of th...
and here im choosing any delta or any epsilon doesnt matter what it will still define the criteria
graceful cosmos
For this picture, the limit point is (2, f(2))
An ε is forced upon us, and we must choose a δ such that the box created will contain the function
graceful cosmos
For this picture, the limit point is (2, f(2))
An ε is forced upon us, and we m...
This is for the traditional definition, of course
graceful cosmos
and here im choosing any delta or any epsilon doesnt matter what it will still d...
Yeah that's a good way to say that
little helm
ah
and in that case if i just take the function x
then the alternated wont fit because it doesnt count for every delta
because if i take a higher x then it would leave epsilon#
little helm
Yeah that's a good way to say that
but thank you very much for your explanation
devout snowBOT
@little helm Has your question been resolved?
dry oak
if you have a bag of blue and red squares, the chance of you pulling a red square from the bag is 10%, if you try 10 more times, will the chance increase?
devout snowBOT
if you have a bag of blue and red squares, the chance of you pulling a red squar...
dry oak
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void knot
Here I know we can't, but how to explain the reason behind?
devout snowBOT
Here I know we can't, but how to explain the reason behind?
tall stirrup
The limit of reciprocal is the reciprocal of the limit, so we can write like that as well
void knot
Ok then can we get the f'(0) and f"(0) by this limit?
feral agate
Here I know we can't, but how to explain the reason behind?
you should be able to say this
because you know it's continuous
devout snowBOT
@void knot Has your question been resolved?
crystal obsidian
remainder of g(x), when divided by 10x^2-13x-3 is 5x-7, remainder of f(x), when divided by 2x^2+11x-21 is 3x-4. find a linear factor of the polynomial f(x)-g(x)
devout snowBOT
remainder of g(x), when divided by 10x^2-13x-3 is 5x-7, remainder of f(x), when ...
urban spindle
!status
devout snowBOT
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
i know that g(x)= (10x^2-13x-3).h(x)+5x-7
and f(x)=(2x^2+11x-21).q(x)+3x-4
but how do i get a common factor without knowing h(x) and q(x)
fossil locust
i know that g(x)= (10x^2-13x-3).h(x)+5x-7
and f(x)=(2x^2+11x-21).q(x)+3x-4
10x^2 - 13x - 3 = (5x + 1)(2x - 3)
now try subbing x = -1/5 and x = 3/2 in, to get the remainders of the two linear factors
urban spindle
then I suggest writing f(x)-g(x), cutting some of the possible terms, and factoring those 2 polynomials (hope it's right work).
crystal obsidian
then I suggest writing f(x)-g(x), cutting some of the possible terms, and factor...
can cut that remainder
crystal obsidian
then I suggest writing f(x)-g(x), cutting some of the possible terms, and factor...
and i get -2x+3
crystal obsidian
10x^2 - 13x - 3 = (5x + 1)(2x - 3)
now try subbing x = -1/5 and x = 3/2 in, to...
should i sub to both f(x) and g(x)?
fossil locust
should i sub to both f(x) and g(x)?
yeah
fossil locust
10x^2 - 13x - 3 = (5x + 1)(2x - 3)
now try subbing x = -1/5 and x = 3/2 in, to...
wait sorry this factorisation isn't correct
that is weird
,w factorise 10x^2-13x-3
crystal obsidian
yeah
woven radishBOT
crystal obsidian
um
fossil locust
fixed
crystal obsidian
-1/5 and 3/2
urban spindle
factorise the other too; I think it will be pretty visible what the common factor is. (or the problem works different than I have in mind)
crystal obsidian
factorise the other too; I think it will be pretty visible what the common facto...
f(x)?
,w factorise 2x^2+11x-21
urban spindle
well yes...meaning, 2x^2+11x-21
woven radishBOT
crystal obsidian
2x-3
but we've asked to find a linear factor of the polynomial f(x)-g(x)
does that mean a common factor to both fx and gx?
urban spindle
but we've asked to find a linear factor of the polynomial f(x)-g(x)
try rewriting f(x)-g(x) using the factorisation
crystal obsidian
try rewriting f(x)-g(x) using the factorisation
(2x^2+11x-21).q(x)+3x-4- (10x^2-13x-3).h(x)+5x-7
= -2x+3
what about hx and qx
urban spindle
won't need to know them; but need to write the 2 polynomials using the factorisation
instead of 2x^2+11x-21, we write the product of 2 linear factors
that we just saw earlier
crystal obsidian
uh wait
urban spindle
same for 10x^2-...
urban spindle
(2x^2+11x-21).q(x)+3x-4- (10x^2-13x-3).h(x)+5x-7
= -2x+3
also this is not quite correct. that whole thing is not equal to -2x+3.
crystal obsidian
so its (2x-3)(x+7).q(x)+3x-4 - (5x+1)(2x-3).h(x)+5x-7
crystal obsidian
(2x-3)(x+7).q(x)- (5x+1)(2x-3).h(x)-2x+3
urban spindle
can you see a common factor?
urban spindle
listen...if you write f(x)-g(x)=(6x+20)(something), you already found what you're looking for (this is an example).
the remainder plays a role in this
but q(x) and h(x) don't
urban spindle
**(2x-3)(x+7).q(x)- (5x+1)(2x-3).h(x)-2x+3**
what's a common factor you see here
crystal obsidian
(2x-3) it is
urban spindle
so f(x)-g(x)=(2x-3)(....?
crystal obsidian
(2x-3){(x+7).q(x)- (5x+1)}-2x+3
urban spindle
If we write it like that, we didn't find a factor of f(x)-g(x). isn't the remainder divisible by 2x-3 too?
crystal obsidian
If we write it like that, we didn't find a factor of f(x)-g(x). isn't the remain...
hmmmm
urban spindle
(-2x+3)/(2x-3) =?
crystal obsidian
so remainder also should be common
urban spindle
and it is. we just have to find out that division
crystal obsidian
(2x-3){(x+7).q(x)- (5x+1)h(x)-1}
crystal obsidian
yhyh
haha
nvm got it, tysmm for the guidance
btw
i hav a trig q too
c)
devout snowBOT
@crystal obsidian Has your question been resolved?
lament cradle
hi
lament cradle
when i multiply fractions do i multiply the whole number also
like for this x/2 +7
since i am multipyling by 2
Do i multiply the 7 also
or only the x to get rid of the fraction
tall stirrup
yeah multiply the seven as well
vestal bay
or only the x to get rid of the fraction
Which fraction are you multiplying 3 to?
lament cradle
The x/5 + 2
vestal bay
Then do i also multiply the other fraction
it says (x/2 +7) = 3(x/5 +2)
lament cradle
Yes
So 3x/5
But i am not sure do i multiply the x/2 to the 3x
So it becomes 6x
vestal bay
But i am not sure do i multiply the x/2 to the 3x
What do you mean?
lament cradle
vestal bay
I think you need to find the common denominator for the left and right sides.
lament cradle
Oh
So if there’s two fractions I find common denominator and not do it separately?
devout snowBOT
@lament cradle Has your question been resolved?
oblique rover
devout snowBOT
mystic scarab
should i try lhopital
Absolutely not 🚫
Think of first order approximations of tan, arctan, sin (near 0)
oblique rover
Think of first order approximations of tan, arctan, sin (near 0)
Yes I’ve did this and it works
frozen aurora
recognize that x^2 has basically no effect and arctan has no effect either
oblique rover
But how can I see I shouldn’t use lhopital
static raft
sin(2x)=2x when x is very small
frozen aurora
recognize that x^2 has basically no effect and arctan has no effect either
because of how massive the powers are
oblique rover
Think of first order approximations of tan, arctan, sin (near 0)
But is this rigorous enough
frozen aurora
But how can I see I shouldn’t use lhopital
when it will become something much more complicated that you probably won't be able to simplify
oblique rover
I’ve solved it using Taylor’s
mystic scarab
But is this rigorous enough
Of course
mystic scarab
I’ve solved it using Taylor’s
Yeah I meant that
devout snowBOT
@oblique rover Has your question been resolved?
primal elbow
anyone can help me on this?
devout snowBOT
@primal elbow Has your question been resolved?
gaunt hatch
devout snowBOT
delicate fossil
yep
gaunt hatch
the second term i got is when i did v*u'
gaunt hatch
nah my handwriting is messy nw
delicate fossil
set that to 0, yes
@gaunt hatch what'd you get?
delicate fossil
i checked the working for it and im so lost
lmao
I think after you equate to 0 you should get
$\frac{x\cos x}{2\sqrt{\sin x}}+\sqrt{\sin x}=0$
right?
woven radishBOT
@delicate fossil
devout snowBOT
@gaunt hatch Has your question been resolved?
gaunt hatch
can you simplify
ok i got smthing
i got it, but i wanna understand what they did in the answer scheme
what did they do here
delicate fossil
what did they do here
ah they just brought 1/2 sqrt(sinx) as common factor
basically
$\frac{x\cos x}{2\sqrt{\sin x}}+\sqrt{\sin x}=0$
$\implies\frac{x\cos x}{2\sqrt{\sin x}}+\frac{2\sin x}{2\sqrt{\sin x}}=0$
$\implies\frac{1}{2\sqrt{\sin x}}\left(x\cos x+2\sin x}\right)=0$
woven radishBOT
@delicate fossil
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
delicate fossil
pretty wacky way to do it but i guess
gaunt hatch
<@951897314333700186>
Compile Error! Click the <:errors:504266556054962196> reac...
bruh 😭
tysm bro 🙏🏾
got it now
.close
terse granite
devout snowBOT
tall stirrup
Calculator shows it to be 14
devout snowBOT
@terse granite Has your question been resolved?
terse granite
Calculator shows it to be 14
how tho
ocean tartan
pl tell me what the heck is t1
devout snowBOT
pl tell me what the heck is t1
ocean tartan
😭
ocean tartan
yeah what's that
quaint citrus
significance level/2 for both tails
ocean tartan
critical value
rocky carbon
i think its t_{1- alpha/2}
bro do you know how to do physics?
quaint citrus
1-significance level/2 for the rest under the curve
so like dependent on alpha, generally for 95% C.I>, ur critical value will be 1.96
ocean tartan
alpha is 0.02 in our case
quaint citrus
oh ok
ocean tartan
so like dependent on alpha, generally for 95% C.I>, ur critical value will be 1....
ah ok i think i read that off a table last example
is there a formula for this critical value?
1-alpha/2 then what?
quaint citrus
u need to use the table
ocean tartan
u need to use the table
can you show me how to read it
the 1- alpha/ 2 how do i look that up in the table to find our needed value
before i used this formula
and he already said z = 1.96 for 5%
but i dunno how you find it in the table
quaint citrus
whats ur df
quaint citrus
yea i think so
table doesnt go up to 160 so u would use the value all the way at the bottom for alpha = 0.02
though i feel like im missing something if ur doing 1 tailed versus 2 tailed
ocean tartan
yeah sec lemme try and then check with python
hmm a little bit off i guess
by 0.01
ohh nvm i used the one for infinity
restive river
i dont get this
devout snowBOT
i dont get this
quaint citrus
just factored out n! from numerator
lets call u = n!
ku + (n -k +1)*u = u(k + (n-k+1)) = u(k + n - k + 1)
restive river
just factored out n! from numerator
didnt know this but I get it now, thank you!
.close
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Available help channel!
red helm
Does the expected shortfall/value at risk Q~_X(u) evaluated with u = 1 always equal E(X) ?
devout snowBOT
Does the expected shortfall/value at risk Q~_X(u) evaluated with u = 1 always eq...
red helm
olive snow
Oh les probas de zinzin
red helm
J’ai juré hahaha
olive snow
J'ai lu deux trois trucs sur markov mais j'ai pas vraiment fais d'application dessus
Essaye de poser la question là bas aussi
Tu auras plus de chance de tomber sur un crack
olive snow
Ah att
olive snow
Non
C'est pas ca
Faut que tu ailles tout en haut des trucs de salons
Et que tu cliques sur rôles et salons
Puis tu prend le rôle undergraduate ou postgraduate
Et puis normalement tu pourras écrire
sand dove
mmmmh
sand dove
Oui il faut prendre undergraduate math au minimum pour poster sur ces salons avancés
olive snow
Coeur sur toi <@432085903196815361> ❤️
Ya un poto en jaune qui est prêt à aider je crois
red helm
Rafiiii
olive snow
Kekw
magic thicket
punaise maintenant je passe plus inaperçu
bah voyons
@red helm postgrad math? T'es sûr? En vrai tout le monde l'a de nos jours ils sont pas très regardant, mais bon, tu fais pas beaucoup de maths de master quand même
devout snowBOT
@red helm Has your question been resolved?
devout snowBOT
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Available help channel!
coral lotus
How to solve standard deviation
devout snowBOT
How to solve standard deviation
eager nova
Do you really believe inside your heart that repeating the same question without adding more information will make people answer it?
coral lotus
🧍♀️
molten scroll
Your question doesn't make sense, can you please elaborate
coral lotus
static raft
do u know the formula?
coral lotus
do u know the formula?
No
static raft
[
z = \frac{x - \mu}{\sigma}
]
woven radishBOT
Mary
devout snowBOT
@coral lotus Has your question been resolved?
rapid cosmos
Do u need central limit theorem
digital crescent
<@&286206848099549185> I have no clue how to find 1/2 and why this limit is not 0
devout snowBOT
<@&286206848099549185> I have no clue how to find 1/2 and why this limit is not ...
tender cobalt
<@&286206848099549185> I have no clue how to find 1/2 and why this limit is not ...
do you know that $\lim_{x\to0}\frac{\sin x}{x}=1$
woven radishBOT
mtt
digital crescent
$
tender cobalt
its a yes or no question, you dont need to repeat it
digital crescent
yes i do
but, i forgot about its demonstration
and they say in the question that they use derivative
tender cobalt
they did not
woven radishBOT
mtt
digital crescent
between paranthesis there is (nombre dérivé) (derived number) i don't know why
apart from that i understand
tender cobalt
"derive" is an everyday word that means "to figure out"
from $\lim_{x\to0}\frac{\sin x}x=1$ you can figure out or `derive' that $\lim_{x\to0}\frac{\sin x}{2x}=\frac12$
woven radishBOT
mtt
digital crescent
Thank you.
But nombre dérivé (dérivée en un point) is the derivative in a given point usually so I am still unsure why it is mentionned
tender cobalt
well it doesnt say dérivée en un point does it
tender cobalt
**mtt**
and this fits the description of "number which is derived from something else"...
tender cobalt
derive has two separate definitions, you have to get used to both
the other one is the verb form of "derivative" (at least in english)
you can derive x to get 1
digital crescent
thank you
tender cobalt
np
digital crescent
one last quick question
i can't remember if sinx/x was among the limits that we don't need to demonstrate
is it?
tender cobalt
i can't remember if sinx/x was among the limits that we don't need to demonstrat...
it should be one of those memorized limits
if you forget about the limit, you can use L'Hôpital to show that the limit is 1
digital crescent
this is what was initially confusing me
-1 ≤ sin(x) ≤ 1
that gives me a limit of 0 for sin(x)/x
maybe i do it wrong
tender cobalt
that doesnt
the graph of sin x / x is here:
you may have used squeeze theorem incorrectly
digital crescent
-1 ≤ sin(x) ≤ 1
-1/x ≤ sin(x)/x ≤ 1/x
-1/x -> 0
1/x -> 0
oh wait
this is encradement not hopital
tender cobalt
what youve shown there is that $\lim_{x\to\infty}\frac{\sin x}x=0$
which is correct but not what is being looked for
woven radishBOT
mtt
tender cobalt
a minor variation would also show that lim x -> -∞ leads to 0 as well
digital crescent
I just found out that i never learned to use hopital.
I just heard of it a lot but we didn't learn it in high school.
Well, my issue is solved.
thanks
tender cobalt
np
keep in mind if they didnt tell you to use hopital, it may not be a good idea to use it
it is good enough to solve otherwise unsolvable or tedious limits
neon oxide
Heres a possible chain of thought on how to get the substiution:
- Gosh, that fraction inside is disgusting. Can I transform it to something nice?
- Well, if I write x = 1- a(t) for some function a(t), the bottom of the fraction will just be a(t).
- When I do the substitution, I will get a'(t) at the top... can I pick this function a(t) such that this will cancel with the bottom?
- Oh I can! by picking a(t)=t^2, since square root will reduce the bottom to just a t term, which is also the form of the derivative! Let's try that!
void knot
Why do we want the bottom of the fraction be a(t)
neon oxide
Alternatively (and equivalently), realizing that $d(\sqrt{1-x})= -\frac{dx}{2\sqrt{1-x}}$ can give you a hint.
void knot
If they didn't tell us the answer, we wouldn't know that
woven radishBOT
Lemmanade
neon oxide
Why do we want the bottom of the fraction be a(t)
I'm using a(t) to signify some unknown part that I haven't decided what I want to be yet.
The first explanation is running through a thought process of coming up with the substitution of $x=1- t^2$
woven radishBOT
Lemmanade
void knot
Normally ppl won't think of making the bottom of the fraction be a(t) i think.. It's more usual to just let the whole fraction be a(t) or whatever
misty crest
writing it as $\frac{\sqrt{x}}{\sqrt{1-x}}$ might make it more clear
woven radishBOT
knief
neon oxide
I think your getting stuck on me using actual functions here? Replace a(t) in my explanation with (something that involves t). I want to get rid of the bottom part of the fraction and I know that once I do substitution I'll have something like (derivative of something that involves t)/(sqrt of something that involves t) which I want to cancel each other out. So the thing that fits here is if (something that involves t) is t^2.
void knot
What I mean is, I understand how he solved it using this substitution, but I don’t understand why he would want to do it this way. The usual way of thinking is to directly set everything inside the square root equal to t
@neon oxide Did I make my confusion clear now😭
misty crest
What I mean is, I understand how he solved it using this substitution, but I don...
i mean where does this get you though
misty crest
**knief**
the trick is really apparent when you write it like this and noticing that we have the sqrt(1-x) in the denominator which appears in the derivative of sqrt(1-x)
neon oxide
Oh ok. So I would say the "usual way" isn't quite to set everything inside the square root to t. This is just what it turns out to be for easy questions. Instead, the usual way is to "set t to something such that the derivative also appears". Consider the integral $\int x\sqrt{1-x^2}dx$. The substitution is $t=1-x^2$ not because it's inside the sqrt, but because it's derivative (upto a scalar) appears as a factor.
woven radishBOT
Lemmanade
void knot
My fixed way of thinking is: if the integral contains only one square root with some expression inside, I will set everything inside the square root equal to the t, But this shouldn’t necessarily be the common way of thinking. The common approach is still to manipulate the expression to match a derivative, is that what you mean?
neon oxide
Yeah it sounds like your on the right track. A lot of this stuff is also just doing a crazy number of examples, and you'll start to intuitively understand which substitution you need to do.
void knot
Like this one, how can we think of its substitution?
I would only think of making t＝（x-a)(b-x)
But i think it's wrong
neon oxide
Instead, can you think of a substitution that would make (x-a)(b-x) a square?
i.e., x=?
void knot
So we let x-a=b-x? If we want them to be a square
neon oxide
The idea being, "yuck, I hate sqrts. If I can make the bottom not a sqrt that would be great"
No, you need to use a new variable
neon oxide
Almost, x=(something with t) such that after plugging it x-a= b-x
Wait hold on, let me double check this is the correct way to do this first.
Ok, the substitution I was thinking about gives me an imaginary number... So I'm assuming not the method we want to use here.
Instead, do yo know of any common integrals with sqrt and -x^2 in the bottom?
void knot
Hmm wdym🤔
neon oxide
I'm unsure of what you have covered in class yet, but do you know any integrals of functions that look something like $\int \frac{dx}{\sqrt{\text{something}-x^2}}$
woven radishBOT
Lemmanade
neon oxide
Yes, arcsin has that form. So for this one, one idea is "can I do a substitution to get the stuff inside the sqrt in the form to use the arcsin integral?"
void knot
bx-x^2-ab+ax
(a+b)x-ab-x^2
Let (a+b)x-x^2=-t^2 ?
Idk
We can't get rid of the x term
neon oxide
Hint: You can turn a quadratic expression into one of the form x^2-c^2 with perfect squares
void knot
neon oxide
I have to go now. Feel free to message me about this if you stay stuck.
void knot
Ok thank you!
plush sigil
I’m stuck
devout snowBOT
@plush sigil Has your question been resolved?
arctic pendant
Hii guys
arctic pendant
I want my proof to be verified since I am not a math student so there’s no one help me checking these little proofs for me😭😭😭
Here’s the question: Prove that every bounded infinite set has a limit point.
And here’s my work!
Bcs I am studying Econ so basically I am dumb at mathematics
solar goblet
I want my proof to be verified since I am not a math student so there’s no one h...
i think you will have better chance asking in #real-complex-analysis
devout snowBOT
@arctic pendant Has your question been resolved?
alpine python
there's topology channels too
arctic pendant
<@&286206848099549185>
narrow bloom
And here’s my work!
Your proof is correct, there's only minor issues in
*wording/grammar and that you should define y_l before you define the neighborhoods O_l
arctic pendant
.close
devout snowBOT
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median depot
On a whale-watching trip, the SS Dolphin sailed 15 miles from port on a heading of 40∘
, then 8 miles on a heading of 320∘
, and then 4 miles on a heading of 250∘
. What is the current position of the SS Dolphin relative to port? can someone help me sketch this out
devout snowBOT
On a whale-watching trip, the SS Dolphin sailed 15 miles from port on a heading ...
nova glen
On a whale-watching trip, the SS Dolphin sailed 15 miles from port on a heading ...
Can you show what you've tried?
nova glen
Looks correct
devout snowBOT
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Available help channel!
round talon
I thought Z+ was positive
devout snowBOT
I thought Z+ was positive
vague spoke
Hey can someone help me with this
sonic parrot
Hey can someone help me with this
Create a different help
vague spoke
oh new to this how to do it ?
supple knot
Z^+ is positive integers normally yes. Maybe typo
Unclear without the original question
round talon
Unclear without the original question
what?
why didnt they include -5, -4, -3, -2, -1, 0
if -9 ≤ -6 ≤ 0
is this another typo?
or maybe they just didnt include ≤ 0
sonic parrot
why didnt they include -5, -4, -3, -2, -1, 0
Because they don't satisfy the equation
The second line
devout snowBOT
proud gull
maybe (a³+b³) = (a+b)(a²-ab+b²) can help
void knot
Ooh ty!!
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restive river
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restive river
The polar function is r=cos(theta/2)
I have trouble understanding how to solve this question
The period of the function is 4pi but how do I know which thetas correspond to each portion of the graph
We have R=1 when theta is 0 because cos(0/2) = 1
But when you get to R=-1
Isn't theta pi, which should give cos(pi/2) but that's not -1, it's 0
So clearly I'm having trouble knowing which region corresponds to which theta
devout snowBOT
@restive river Has your question been resolved?
restive river
<@&286206848099549185>
devout snowBOT
@restive river Has your question been resolved?
tame palm
So clearly I'm having trouble knowing which region corresponds to which theta
You're going to have some intersections that overlap because the angle and radius value will have the same rectangular coordinate value but not the same polar coordinate value.
restive river
You're going to have some intersections that overlap because the angle and radiu...
I get what you mean
tame palm
restive river
If so how can I understand where the interval 0 to pi ends
tame palm
Calculate it's value. It can be beneficial to just calculate every npi/2 point on the curve.
restive river
Calculate it's value. It can be beneficial to just calculate every npi/2 point ...
I did just that
But I had problems because, like you said, cartesian coordinates would overlap
And I wouldn't know what specific pi/2 I would be solving for
This would be the answer to the thetas which correspond to the dashes
tame palm
Ok, you aren't sure of the correct intervals.
restive river
Yeah I don't know how to get the answer above
I tried following along with it
But I couldn't verify anything
tame palm
You at least recognize that endpoints of the intervals will be at n pi/2, right?
restive river
You at least recognize that endpoints of the intervals will be at **n pi/2**, ri...
I don't get why that is
tame palm
Two of the intersections lie at (0, y). You can infer that it is some form of 90 degrees times n.
restive river
Yes, these intersections happen at "pi/2"
And the answers do show n times pi/2
Ok, I can assume that
My problem was just I don't know if that's pi/2
Because I didn't know how thetas worked
tame palm
vs 3pi/2 or some other pi/2?
restive river
And if they worked like that for every graph
restive river
vs 3pi/2 or some other pi/2?
No
Just if it was pi/2 at all
Is it correct to say each quadrant is k times pi/2
starting from zero
Does it work like that for all polar graphs
tame palm
As in will any point at x=0 will be at n pi/2?
restive river
As in will any point at **x=0** will be at **n pi/2**?
Hmm
cos(pi/2/2) is cos(pi/4) which is not 0
Which is my problem
cos(pi/2) is obviously 0 however.
r=cos(theta/2)
Isn't any point on the graph
supposed to be r distance from the origin
The first intersection at the top is a little more than 0.5
and less than 1
which means r is like 0.7ish which I don't understand because cos(pi/2/2) is around -0.25
tame palm
One moment, let me make another graph for you.
Change the value of n and the points of n pi/2 will be plotted.
You will notice that the points always like in some direction that is n pi/2.
Regardless of how you change the graph.
restive river
I see
But now
How do I relate the points that I see at n pi/2
to the intervals
How do I isolate the dashed portion from the solid
tame palm
Plot the points in order in terms of r and theta.
restive river
And how do I go in order
tame palm
Start from 0, pi/2, pi, 3pi/2, etc.
It's something you would typically have to plot out.
restive river
r=1 when theta = 0
r=cos(pi/4) when theta = pi/2
r=cos(pi/2) when theta = pi
r=cos(3pi/4) when theta = 3pi/2
Cosine for each
r
r=sqrt2/2,0,-sqrt2/2
tame palm
And that's when you see that r equal 1, sqrt(2)/2, 0, -sqrt(2)/2, etc. in the relative directions.
restive river
yep
tame palm
And that x =r cos(theta) which you can use to find which points like on the y-axis.
restive river
why can't I find the r's on the y and x axis
tame palm
You can. Just use the polar equation that you were given. r =cos(theta/2).
restive river
what is r at the top intersection
tame palm
,calc cos(pi/4)
woven radishBOT
Result:
0.70710678118655
Honestly, you will need to make a graph most of the time and plot points.
restive river
I kind of don't know how the polar curves work in the sense of separating half from the other half
some say you use -r
tame palm
Refer to the previous graph I sent you. The green line is positive r and the red line is negative r.
restive river
I don't see it
I mean I do know any r below the x axis
is negative
but this is a left vs right sort of thing
tame palm
No, don't think of r as below the x-axis.
tame palm
Think of a line that is pointing in the direction of theta. Any point away from the origin that goes in that direction is a positive radius. Any point in the opposite direction is in the negative direction.
restive river
Think of a line that is pointing in the direction of theta. Any point away from...
So do we say the right side (solid line) is r
tame palm
You just have to be able to visualize in your head that if theta is 270 degrees and r is negative then it is above the origin.
restive river
You just have to be able to visualize in your head that if theta is 270 degrees ...
makes sense
add 180
tame palm
Basically in direction in Q3 and Q3 with a negative radius will be plotted in Q1 and Q2 respectively.
tame palm
This is one of those areas that you really just have to do it. There's no "trick" that will make it make sense. 🙂
It just clicks one day.
restive river
yeah but like this question
which should be like the most common question ever
Talks about particle motion
tame palm
The best thing you can do is just start plotting polar graphs on paper.
Come up with different polar equations are start making plots.
tame palm
I'm going to chalk this up to you skipping the step of making plots of polar equations.
It's one of those things that you just gotta do.
restive river
I'm going to chalk this up to you skipping the step of making plots of polar equ...
While it is necessary
To learn and get a better understanding of polar curves
This question isn't worth much surprisingly
And is meant to be more of an algebraic one
Which is why it's confusing the hell out of me
And I just want to be able to get it
Because it's 5 am
tame palm
You want to be able to mathematically solve this problem without graphing it.
tame palm
I don't think that's going to happen with polar curves.
There are perhaps others who are more versed in polar equations who may have a useful tip, but just by pure math, you won't be able to show that a curve doesn't wrap around itself in some weird way without mathematically writing many points between two points on a curve.
eg.
restive river
Alright even if I do graph
what am I supposed to get
How does that help me isolate the left portion or know the intervals which the particle goes through
tame palm
Plot the candidate points in order. Plot a point in between the candidate points to determine which part of the curve the interval is on.
tame palm
This is all about understanding how polar equations work. You won't need to do this all of the time.
tame palm
I feel for you. We've all been there.
devout snowBOT
@restive river Has your question been resolved?
white lava
how does one do this?
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Available help channel!
bronze dust
Problem: Find all integer solutions to the equation
𝑥
3
−
𝑦
3
𝑧
3
+
5
x
3
−y
3
😒
3
+5
bronze dust
Problem: Find all integer solutions to the equation
x^3 - y^3 = z^3 + 5
cold bough
$x^3-y^3=(x-y)(x^2+xy+y^2)$
woven radishBOT
everg
devout snowBOT
@bronze dust Has your question been resolved?
bronze dust
.close i will do it later
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short hare
what do you call f(x) if f(-x) = -f(x)
note: this is not my main question, but i need to know the phrasing so i can ask the question
static ember
well, y = -y, can you solve for y?
short hare
f(-x) = -f(x)
this is a type of function and it has a name in english which idk
odd function?
google translation is letting me down
static ember
it's odd yeah
short hare
its asking me about the type of this function, i understand why its odd, but i dont understand why its not odd nor even
like not odd not even type of function
ik this sounds weird
static ember
try to rotate this function around the origin by 180° in your head
short hare
but i dont see it being symmetrical around (0.0)
static ember
if that thing doesn't perfectly match the original, it's not odd
there's an easy way to see it for this function though
if f(-x) = -f(x), then what if x = 0?
short hare
i dont understand your question 😭 im sorry
short hare
then f(0) = -f(0) right=
aha aha
short hare
then f(0) = -f(0) right=
oh and then- the function should pass thru (0 , 0)
and it doesnt
static ember
right, any odd functio must pass the origin (at least if 0 is in the domain)
,w graph x^3-x
woven radishBOT
short hare
its asking me about the type of this function, i understand why its odd, but i d...
but wait- this didnt pass>..
static ember
like this one is odd, and rotating it by 180° around the origin you get a perfect copy
static ember
but wait- this didnt pass>..
yeah it's not odd then
short hare
like this one is odd, and rotating it by 180° around the origin you get a perfec...
i understand
short hare
yeah it's not odd then
the teacher said its odd?!?!??
the original question stated that this function is consistantly... decreasing or going down ig, then teacher said "if its consistantly going up or consistantly going down then the function is odd"
static ember
huh that makes no sense
short hare
thats what he said!
altho i believe you bc you actually gave a reason and proper application
but he just- gave it off as a side note
smth to memorize, imagine memorizing math
static ember
its asking me about the type of this function, i understand why its odd, but i d...
I can see if you shift the graph a bit it may become odd
but this way it's not odd
short hare
this teacher is actually one of the most popular/best arabic math teachers
so i really dont know
static ember
I would ask your teacher again
devout snowBOT
short hare
.reopen
devout snowBOT
✅
short hare
@static ember sorry for pinging you, but this function doesnt pass thru (0,0) and 0 is a part of its domain, but its still odd
(this is 2x-3)
feral agate
it's not odd
misty crest
he just said it is?!?!?!?
where did they say this
oh
you meant your teacher
i thought you meant rbit
misty crest
well your teacher should be fired then
stone fjord
well your teacher should be fired then
Lmao but very real
misty crest
f(x) = 2x - 3 -> f(-x) = -2x - 3 ≠ -f(x)
short hare
(this is 2x-3)
i just realized that f(-x) is not = to -f(x). what is that guy on about
misty crest
yep
short hare
this is the second time goddamn it
misty crest
dude probably saw an odd exponent and went yea it must be odd
short hare
dude probably saw an odd exponent and went yea it must be odd
his video
got
over 100k views
he is the king of youtube math in my country
literally the best!?!?!?!?
misty crest
he is the king of youtube math in my country
who
short hare
its in arabic
misty crest
oh nevermind
short hare
this is how he proved that 2x-3 is odd, he said we're gonna assume that f(a) = f(b), then we solve, if a = b then its odd and if a is not equal to b then its not odd
idk how the image will help you
but ig its there
f(a) = f(b) (f(x) = 2x -3)
2a-3 = 2b-3
a=b
and thus f(x) is odd
winter patrol
that's not the test for whether a function is odd
short hare
that's not the test for whether a function is odd
first image shows [ odd , not odd]
second image shows (after solving)
odd
👏 for the teacher
3-x^2 now for this function its not odd bc when you put f(a) = f(b) a = +-b
and thus its not odd
i dont understand the logic or the method
cinder nova
sounds like a mistranslation, all of this is a test of 1 to 1 functions
cinder nova
the original question stated that this function is consistantly... decreasing or...
that would make sense too
short hare
sounds like a mistranslation, all of this is a test of 1 to 1 functions
what are 1 to 1 functions
winter patrol
a function being 1 to 1 doesn't necessarily mean its odd
short hare
what do you call f(x) if f(-x) = -f(x)
note: this is not my main question, but ...
do you call this type of function "odd"?
if so, there is no mistranslation
winter patrol
yes. that's their property by definition
short hare
there is no mistranslation.
bc- thats the point of the lesson
to find weither the function is odd even or not even not odd
winter patrol
they havent applied any of that in the image above and thus should not be making any conclusions/comments about whether the function is odd
short hare
and the choices here translate to "odd , not odd"
short hare
they havent applied any of that in the image above and thus should not be making...
so the logic works but not on all odd functions, then he used it on a non-odd function and concluded its odd
well this makes sense but how could he even do such mistake
this man is like 57 which more than half were dedicated to math 😭
short hare
f(a) = f(b) (f(x) = 2x -3)
2a-3 = 2b-3
a=b
and thus f(x) is odd
this, but inconsistant
welp
ig ill- ignore his method and go with you guys
let me get a recap on how to determine weither a function is odd or not
cinder nova
does he have an example of a function that not "odd"
winter patrol
the point is its not a test for whether a function is odd/even
so its not logical
actually not even that
as there are odd functions that aren't one to one
short hare
does he have an example of a function that not "odd"
i mean yeah? there is another method he taught us, which he said "draw a line like this (red line) and if it only intercepts the function in 1 point at every part of the function, its odd. if it intercepts on more than 1, its even.
winter patrol
no
short hare
xd
cinder nova
as there are odd functions that aren't one to one
yea those 2 properties don't really relate
that's why I feel like this is a mistranslation/miscommunication
short hare
im dying
winter patrol
feels like this is a mistranslation
cinder nova
i mean yeah? there is another method he taught us, which he said "draw a line li...
that is definitely for 1 to 1, not odd
short hare
well here, the drawing on the right is odd and the drawing on the left is not odd
winter patrol
definitely mistranslation
this is about whether a function is injective (one to one)
not odd/even
short hare
"horizontal line test"
if passed thru 1 point: odd
if passed thru 2 points: not odd
short hare
this is the start of the lesson stating where f(-x) = f(x) the function is even, and where f(-x) = -f(x) its odd, and neither equations are true its not odd or even.
i think yall can figure it out with the negative signs
د(-س) is f(-x)
winter patrol
i dunno where, but it seems somewhere along the line, he mixed them up
short hare
then he solves some questions where he tells us to get f(-x) and compare with the original function to figure out its type.
this is the biggest proof that its not a mistranslation
notice how the arabic in both images is the same?
but his handwriting is a bit squiggly thats all
short hare
this is the biggest proof that its not a mistranslation
google translation got it right
so yes, the ENTIERTY of this, is to find out weither the function is odd, even, not even not odd.
so this guy is literally tweaking. he's gonna make 106k students fail their exams
static ember
can you show the arabic wikipedia page for this term?
it really does talk about injective functions
short hare
short hare
"odd function" is the first text, then it shows the definination
short hare
https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9_%D9%85%D8%AA%D8%A8%D8%A7%...
الدالة المتباينة injective
this is what it says
الدالة المتباينة
however, odd function is الداله الفرديه
you see how they're very different
first is pronounced "mota-bay-na" and second is pronounced "far-de-ya"
static ember
you see how they're very different
no tbh
winter patrol
anyway from what you're describing,
your teacher is mixing them up
short hare
short hare
anyway from what you're describing,
your teacher is mixing them up
okay
what do ido
the lesson is called "odd and even functions"
and the questions ask us to determine their type
winter patrol
raise the issue with him
static ember
what does he define as even
winter patrol
to see wtf is going on
short hare
so how do i determine if a function is odd (not neccesarily injective)
winter patrol
to clarify whether you're actually dealing with actual odd/even functions
or injective functions
short hare
what does he define as even
f(-x) = f(x)
static ember
that really is even
and f(-x) =-f(x) is odd
but f(a) = f(b) => a = b is injective
short hare
to clarify whether you're actually dealing with actual odd/even functions
or inj...
well, in my currcilum, iam NOT dealing with injective functions.
idk what they are tbh
short hare
الدالة المتباينة
never heard this word before
static ember
what you described before, if you draw any horizontal line and it never hits two points
then it's injective
two or more
static ember
yeah very confusing
short hare
how does he start the lesson with f(-x) =-f(x) then end it with if a = b then f(x) is injective
i cant even believe it
are injective functions complex?
maybe in my currcilum we just
dont assume odd functions are not injective
static ember
these terms dont really have much in common
short hare
or perhaps since we only take even/not even not odd/odd functions and even/not odd not even functions are NEVER injective, thus every function that is injective is also odd
is there a fourth type of function?
that i perhaps didnt learn
winter patrol
don't bother with trying to find a general way to link these
static ember
is there a fourth type of function?
surjective
a function could be any combination of these things though (almost, if it's even and odd at the same time then it's just the 0 function, which is neither injective nor surjective (depending on domain and stuff))
short hare
don't bother with trying to find a general way to link these
okay
now
what i need help in
is
how to determine if a function is 100% odd (not necessarily injective)
like a general way that generally works
on graphs.
the perfect 180 rotation and how it passes thru (0,0)?
(if x=0 is a part of its domain ofc)
.close
harsh ravine
how to solve?
devout snowBOT
how to solve?
eager nova
What have you tried?
harsh ravine
well, I have -5 and 1
Upon further inspection of my trash notes, I am starting to understand the equation
eager nova
Did yoi factor the polynomial?
harsh ravine
yes
eager nova
What is the factored form?
harsh ravine
I started with the Big X method then I got 2(x + 5)(x - 1) = 0
I see so you start by splitting the middle, then you factor, then you solve for the two x valuse
eager nova
What is your question then? You solved it
harsh ravine
I was stuck at it so I asked for help here, and then as we were discussing it, it started to make sence
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
devout snowBOT
zenith jacinth
yes
devout snowBOT
zenith jacinth
its not done yet tho if you need x
devout snowBOT
✅
zenith jacinth
yes
zenith jacinth
i know that you are right
no need to ping me 2 times
oh my god...
its correct
near sluice
The question translated to english is, "A melting ice sculpture in the shape of a sphere maintains its spherical shape as it melts. The volume of the sphere decreases at a constant rate of 2 𝜋 cubic meters per hour. At what rate is the surface area of the sphere changing at the moment when the radius of the sphere is 5 meters?"
I got an answer but i have no answers sheet, can somebody calculate it and tell me if im correct? i got dA/dt = -4 𝜋 /5 m^2/h
devout snowBOT
The question translated to english is, "A melting ice sculpture in the shape of ...
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Available help channel!
umbral ivy
I've got the first one right, but the second one is wrong
I'm confused abut the definite integral for (b), -4 to 4 f(x)dx.
I know we have the definite integral of -4 to 2 f(x)dx = -6
and the definite integral for 2 to 4 f(x)dx = 11
umbral ivy
I tried t work it out myself by saying
the definite integral of -4 to 4 f(x)dx would be equal to the integral of -4 to 2 f(x)dx + the integral of 2 to 4 f(x)dx
I am also not good enough with LaTeX to do something like this in that, so im sorry if it's awkward
Here's a photo of my attempt to work it out
oh, it's just 5
it's just -6+11 = 5
I see, I dont have to plug it back in
.close
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thorny ferry
can someone dumb this down a little
devout snowBOT
can someone dumb this down a little
hexed fractal
can someone dumb this down a little
If you only want a tldr you can use chatgpt or other ai services for this.
thorny ferry
If you only want a tldr you can use chatgpt or other ai services for this.
specifically what does it mean by x being negatively large y becomes positively large when it says x^4 becomes positively larger?
cinder nova
if you imagine the graph of x^4, as you go to the left by a lot (x negatively large) it goes up by a lot more (x^4 becomes positively larger)
thorny ferry
if you imagine the graph of x^4, as you go to the left by a lot (x negatively la...
so I dont image x^4 as base value but imagine (x^4) going to the left and its value (x^4) just gets bigger?
cinder nova
so I dont image x^4 as base value but imagine (x^4) going to the left and its va...
yea, and because it's an even power and there's no negative sign, it gets bigger positively
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stuck ravine
Could someone explain this
devout snowBOT
Could someone explain this
spare zealot
Are you in calculus or algebra?
stuck ravine
calculus
spare zealot
What do you know about relative extrema?
stuck ravine
not much
spare zealot
What do you think a relative extreme is on a graph?
stuck ravine
I don't know. maybe the highest point ?
spare zealot
Yeah exactly, a relative extreme is any high or low point within a certain interval
Notably, it's where the sign (positive or negative) of the slope of the graph changes. Know any ways we could analyze the slope of the function at a point?
stuck ravine
Notably, it's where the sign (positive or negative) of the slope of the graph ch...
Find the Derivative and compare it with zero ?????
spare zealot
Precisely
Any point that the derivative function is equal to 0 within the given interval is a relative extreme of the function you started with
stuck ravine
Any point that the derivative function is equal to 0 within the given interval i...
do you have a youtube video or anything that explain this topic?
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