help-49

[cerulean oyster]

The method with deviation of the averages is the basic idea behind what we just explained

A weigthed average is a completely different thing

[worldly pine]

i will do it manually if this question come in exam

that's all i would say

thank you

bye

[cerulean oyster]

!done

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[worldly pine]

.close

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[craggy owl]

hello i would like some clarification between one sheet and 2 sheets

[craggy owl]

i am a bit confused when it comes to the negative

for instance if there are any 2 negatives that would be a 2 sheet?

[astral canyon]

yup, and the 2 sheet would be on the axis of the variable that's not negative

like if you had y as the nonnegative one, you would have a 2-sheet that's through the y axis

[craggy owl]

i see

and that would be the case for any plane

[astral canyon]

by any plane you mean?

[craggy owl]

like z or x as the non negative one

[astral canyon]

yeah

[craggy owl]

gotcha

thank you

.close

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[viral dagger]

what is this even asking, could someone explain it?

[lethal path]

I bet they mean $a \cos^2 x + b \cos x + c = 0$

[grand pond]

south

[lethal path]

anyways just use the double-angle formula on cos 2x, then solve for cos^2 x

[viral dagger]

what?

[lethal path]

cause they talk about the 'analogous quadratic equation'

so the equation before must also be a quadratic

[viral dagger]

i still dont get what you mean

like what is it asking? does it want a quadratic equation interms of a,b,c,cos(2x) thats equivalent to the original quadratic?

[lethal path]

yes, you want to turn this into a quadratic equation with $a, b, c, \cos 2x, \cos x$

[grand pond]

south

[midnight plank]

@viral dagger Has your question been resolved?

[waxen musk]

Its a quadratic in terms of cos(x)

Well in terms of cos(2x)?

Thats a little weird

Cause youd lose the quadratic like that, and also im not sure how it wants you to deal with the cos(x) term

[midnight plank]

@viral dagger Has your question been resolved?

[viral dagger]

exactly

ok i think im gonna skip this question, i dont even think i understand it properly

.close

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[misty wagon]

hi chat my friend asked me this question

Let $f(x)$ be a function, such that

[6f((x+1)^2) -(f(x))^2 \ge 9]

for all $x$ in $\mathbb R$

Prove that no inverse exists for $f$

[misty wagon]

so i tried to prove it

[spiral rock]

Prove what

[grand pond]

魔法の💫kitty!

[misty wagon]

sorrysnfsfo bit of a mess rn

thats what i did

but then i found a counterexample on desmos LMAO

so i believe the proposition is wrong

[misty wagon]

My question is, since the proposition was wrong (my friend fully made up the question himself)

What did I do incorrect in my proof?

[spiral rock]

Why do you think its a counterexample?

[misty wagon]

because the red line is completely above the x-axis, and yet my choice of f(x) is not one-to-one

[spiral rock]

Thats exactly what you want

[misty wagon]

but i want to prove that f has no inverse

[spiral rock]

Yeah, its not injective

So no global inverse

[misty wagon]

wait what whats a global inverse

[spiral rock]

Like an inverse everywhere

[quiet parcel]

its an inverse over it's entire domain

[spiral rock]

You can have inverses if you restrict your function to a small interval

[misty wagon]

but arent i looking to prove that the if the red line is above the x-axis, then f(x) must be injective for all x?

[spiral rock]

The red line being above the x axis is equivalent to the inequality being satisfied

[misty wagon]

the inequality is satisfied and yet i have a choice of f(x) that is not injective, thus contradicting the if then statement

[spiral rock]

You want f to not be injective

Read the question

[misty wagon]

FUCK

IM SO SORRY

YEAH I JUS HAD A MASSIVE BRAINFART

[misty wagon]

IM VERY SORRY TY FOR UR PATIENCE 😭

.close

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[midnight plank]

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[sand flume]

han can pi be -1? 2+cos(pi) is 1

[lyric charm]

$\cos(\pi)=-1$ does not mean $\pi$ itself is equal to $-1$.

[grand pond]

Ann

[sharp gull]

pi is basically 180 degrees

Not sure though

[graceful drum]

that only means that the polar graph will have radius 1 at theta = pi.

so the coords are (pi,1) which lands on -1 in the x axis

[sand flume]

I see my misunderstanding I was confusing the endpoint and its length

thx guys

[graceful drum]

welcome

[sand flume]

.solved

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[open dew]

I might have done this wrong

[silent dock]

Why do you think that it’s wrong?

[open dew]

i got a decimal from it

.09486

[silent dock]

How did you get that?

Did you use a calculator?

[open dew]

i just took cube root

yeah i used a calc

[silent dock]

,w cube root of 0.001

[grand pond]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by puresudlor

[open dew]

OHH wait

how do i do cube root on a graphinc calc do you know

i just put a 3 in front i cant find how to do it

[silent dock]

Can you take a picture of it and send it here?

[open dew]

yes

[near cliff]

-# casio better

[silent dock]

Sorry, I don't know the direct function for the cube root on this particular calculator. Usually, the cube root shares a key with the square root. For what it's worth, you may calculate it by entering (0.001)^(1/3); this achieves the exact same result.

[open dew]

oof alright

well its .1 let me try the answer

[near cliff]

shift + x^2?

[golden comet]

I always just input a ^1/3 for cube root

[silent dock]

I think that will output a square root.

[golden comet]

yeah that is a square root

[open dew]

yeah

its okay ill figure it out some other time

i can always just use desmos

thank youf for helping me i appreciate it

.close

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[silent dock]

Any time

[midnight plank]

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[cold pulsar]

what is the meaning of the c that I marked red?

[cold pulsar]

thanks in advanced

[nimble copper]

complement

[fallow scarab]

you look nice today steak

[silent dock]

I only see blue markings here

[cold pulsar]

sorryy

[nimble copper]

^c means complement

[cold pulsar]

what is complement

[nimble copper]

https://en.wikipedia.org/wiki/Complement_(set_theory)

[cold pulsar]

thanks

.close

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Channel closed

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[urban sentinel]

This is what I tried

It was wrong

[tulip oar]

16*2=32 not 36

[urban sentinel]

Oop

I’m so dumb

[chrome arch]

Lol

[tulip oar]

happens dw

[urban sentinel]

I feel like the tiredness is getting to me now

[tulip oar]

these are easy probs they dont take much brain

[chrome arch]

Pov when u do too much maths

[chrome arch]

Yeah ngl i agree

[urban sentinel]

Literally

[tulip oar]

i am like jee asp😭

[urban sentinel]

Yeah this is just lv 2/5

[tulip oar]

cry ass maths

[chrome arch]

Haha

[tulip oar]

whats 5on5 looks like?

[urban sentinel]

It’s either the computer messing with me or mee being blind

[urban sentinel]

I’ll show

[chrome arch]

Which grade r u in

[tulip oar]

eager

[urban sentinel]

I’m not gonna attempt that.

[chrome arch]

Easy stuff

[tulip oar]

11th but studied like half of 12th and olympiad lvl maths

[chrome arch]

Damn crazy

Got some advice for 10th?

[tulip oar]

use a^2-b^2=(a-b)(a+b)

[urban sentinel]

Ohhhh

[tulip oar]

yeah just follow your class notes and 10th is too easy tbh

[tulip oar]

lmk if you get it

[chrome arch]

Boards kinda eating me up kinda stressed for it ngl

[urban sentinel]

I’ll attempt it

[exotic atlas]

that was a short sleep aryan…

[exotic atlas]

fr

[chrome arch]

Well

[tulip oar]

hey boards are easy man i would recommend you to study less but smart

[tulip oar]

sure thing

[chrome arch]

Ik got the same advices frm seniors but still kinda worried

[tulip oar]

study all day and night for you would be my tip

[exotic atlas]

guys kick aryan from the server he’s lying he said he was gonna go to sleep and he couldn’t help me anymore but here he is chatting away

[chrome arch]

Thts not an offense here

[tulip oar]

i dont think so you are worried about maths

[chrome arch]

No not rlly

Mostly sst

[tulip oar]

zylez why are you still stuck on that

[tulip oar]

i scored 95/100 my tip is make short notes

[exotic atlas]

GUIDELINES:

● #help channels are for homework type questions/problems. Topical channels prioritise open-ended discussion about particular topics.
●

SOCIAL CHANNEL GUIDELINES:
● Keep it civil in the #chill channel. Treat it as a channel for friendly banter with your classmates or possibly your teacher/professor/advisor.

[viral dagger]

helpers here are voluneers, they are not oblogated to help people and have the right to stop helping somebody. but still, lying and saying you cant help isnt very nice either :(

[exotic atlas]

FAX

[chrome arch]

Sure thing thanks for it!

[chrome arch]

She was cheating on her test bud

[viral dagger]

oh wait what

[chrome arch]

N i had to go but then i decided to staylater on

[viral dagger]

do you have proof of it?

[exotic atlas]

TECHNICALLY IF WERE GONNA ACCUSE ME

i did not say a thing about answers

U started giving me answers

[tulip oar]

hey how do i get that tag

[exotic atlas]

i just sent th eproblem

[chrome arch]

She was asking ans to her hw qs

[exotic atlas]

no i wasn’t

i just sent u the problem

[viral dagger]

what tag?

[chrome arch]

Tho i feel it was her assessment

[exotic atlas]

?

ok?

[urban sentinel]

I might give up

[tulip oar]

helper

[chrome arch]

Wht happened

[exotic atlas]

so we’re just gonna move on from this convo

[viral dagger]

oh yea right

!redir whoops

[midnight plank]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[tulip oar]

just use the identity i gave u let first parenthesis be a and second be b

[viral dagger]

you mean helpful?

[exotic atlas]

yeah aryan

[tulip oar]

helper is the tag so far ik

[urban sentinel]

He’s helping me

[chrome arch]

?

[tulip oar]

or helpful whats the diff

[exotic atlas]

keep convos to #chill

[chrome arch]

U can go there then

[exotic atlas]

or maybe go ti bed like u said u were going to do

[urban sentinel]

They are still helping me I was juys attempting alone first before asking for directions

[viral dagger]

some other people (including me actually) arent really helping and having unrelated conversations with the problem

[exotic atlas]

why don’t we go there together

except i’m not going with u cause basically i need help with my hw

[tulip oar]

did you get it

[chrome arch]

Go do ur hw bruh

[urban sentinel]

the division is confusing me

[exotic atlas]

i am

[tulip oar]

okleme do it

[urban sentinel]

I’m really bad with division when it’s included with other stuff

[chrome arch]

Thts pretty normal ngl just keep practicing ull get good

[urban sentinel]

acc took me up till 5th grade to understand it while others had already got it

[urban sentinel]

I needed to finish this lil chapter before tmr cus my teacher is gonna go through a new chapter

[urban sentinel]

Factorising im pretty sure its alld

[tulip oar]

can you proceed now?

[urban sentinel]

Ohhhh so that’s what you do

They share the same /2

[tulip oar]

yeah since a/2+b/2=(a+b)/2

when denominators are same you can add them or subtract them straight up

[urban sentinel]

Ohhh

Can I save that pic

[tulip oar]

sure

[urban sentinel]

Let me try to go from that point

Is there a multiplication between the two

Or is it still -

[tulip oar]

calculation part is not imp just remember this identity i told you its very useful i still use it in daily maths a^2-b^2=(a+b)(a-b)

[tulip oar]

yeah simplify and multiply

[chrome arch]

The ans is p

[urban sentinel]

Just p?

[chrome arch]

Yep

[tulip oar]

hey aryan you're not allowed to tell that

[chrome arch]

After simplifying this

[urban sentinel]

I’ll try it wait

[chrome arch]

Sorry my bad

U guys can continue

Ill leave

Bye

Cya

[tulip oar]

have a good day aryan

[chrome arch]

U too dexter

[urban sentinel]

I got ittttt

[tulip oar]

cool

[urban sentinel]

Excuse my handwriting

I’m so tired

[tulip oar]

good job well you tried but this shouldnt take that long

[urban sentinel]

It wasn’t that hard at all

[tulip oar]

and write that identity somewhere in your notebook

[urban sentinel]

I haven’t worked with that specific formula yet

I’ll note it down

[tulip oar]

write it as a standard result

[urban sentinel]

Illl write it down

Tysm

I didn’t think I would be able to do it cus the divisions is terrifying

[exotic atlas]

DEXTER MORGAN THIS IS THE THIRD PERSON THATS GIVEN UP IN HELPING ME

[urban sentinel]

Girl

[tulip oar]

nw ask if you're stuck up somewhere i'll follow up

[urban sentinel]

Seriously ur annoying atp

Go to ur own channel

[exotic atlas]

i don’t have one anymire

[urban sentinel]

<@&268886789983436800>

[exotic atlas]

he quit

[urban sentinel]

Can I add you

[exotic atlas]

ngl i don’t know how to make one

[tulip oar]

girl you ruined my occupied doubt

[modest heart]

Please leave this channel

[exotic atlas]

i promise idk how to make one

[urban sentinel]

Shes done this the past hour

[exotic atlas]

i read the thing

[tulip oar]

sure thing

[modest heart]

See #❓how-to-get-help

[urban sentinel]

It’s so annoying

[exotic atlas]

i read it it’s not working

[modest heart]

Go to like #help-30 and send a question you need help with

[urban sentinel]

She has an opened channel

[modest heart]

oh

[modest heart]

go to #help-29

[urban sentinel]

She keep coming here though

[exotic atlas]

i’m closing it

forgot

[modest heart]

Cool well don't post in this channel any further at all.

[tribal temple]

(also, may I ask for why you think this?)

[urban sentinel]

She said it

Anyway I’ll close this now so it becomes available

Tysm @tulip oar @chrome arch

[tulip oar]

have you done lvl 5?

[tulip oar]

nw

[chrome arch]

See the address bar it says assessment so i feel it might be a test

[urban sentinel]

Yesss that last one I can do it has no divisions

[chrome arch]

Npp

[chrome arch]

@tribal temple

[urban sentinel]

Yeah I’m gonna leave this cus ur talking

[tulip oar]

great go ahead and practice more division probs!

[urban sentinel]

I willll

.close

[midnight plank]

Channel closed

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Use .reopen if this was a mistake.

[chrome arch]

Had a great time with yall

[tribal temple]

.(TBF I have seen some homeworks that appear similar, it may be the way the site is set up that it says that but it's nonetheless homework, but thank you for letting me know )

[chrome arch]

Oh okay

Npp

[tulip oar]

dm me or aryan if youre stuck we'll follow up

[chrome arch]

Yes

[tulip oar]

why is it occupied yet

[midnight plank]

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[south mountain]

Hey, I'm having a little bit of trouble with something regarding linear algebra for computer rendering, and I'm not sure if it's a bug in the rendering library, or a conceptualization issue on my part.
I'd like to pan a camera represented by two points (position, target) and by an upwards vector in world space.

We've started learning some transformation matrices for affine transformations, but haven't covered the entire topic yet.
At the moment, I know that I can compute this by defining a vector cam_motion = (x, y, z) and then computing the new position as a linear combination of the camera's basis vectors (upwards, forwards, and right) in world space.

To calculate those basis vectors, I can use target - position = forwards. I can also use the cross product as so: forwards x upwards = right. After normalizing these vectors, I can now move the camera any direction by adding an offset to position and to target as so: position += x * right + y * upwards + z * forwards.

So then, here's where the code seems to pan incorrectly -- I am trying to represent this operation using a transformation matrix and the motion seems to be incorrect when using the matrix library provided.

I define the matrix operation like so: [ right_1, upwards_1, forwards_1 ] [ x ] [ right_2, upwards_2, forwards_2 ] [ y ] + position = new_position [ right_3, upwards_3, forwards_3 ] [ z ]

Is there an error in the assumptions and calculations on my part?

[south mountain]

On an unrelated note, my instructor has me a bit lost on what frame to canonical transformation is for. They just kinda dumped the definition onto a powerpoint slide and didn't elaborate. I'll ask them, but I was wondering if there's any recommended resource I could look to first?

[ancient ridge]

Are you not normalizing your basis vectors

[south mountain]

They are normalized, though the matrix library that provides a vector type does have a NaN bug when normalizing some values

So I'm just aiming to make sure the conceptual foundation is correct before I poke around deeper in that

[midnight plank]

@south mountain Has your question been resolved?

[midnight plank]

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[leaden seal]

Is 4 in rREF?

[carmine sigil]

no,

[wet pollen]

It is in REF, but not RREF.

[carmine sigil]

you need to have 0s above the leading digit in each row

(and the leading digits all need to be 1.)

[midnight plank]

@leaden seal Has your question been resolved?

[midnight plank]

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[vital marten]

is it okay to use a small angle approximation in this for sin(x) and cos(x) after differentiating top and bottom?

[subtle blaze]

What does it look like after you differentiate

[vital marten]

I believe this

[visual tiger]

you were allowed to do that from the beginning btw, and it works because you're working with a product and/or quotient

what I mean by "from the beginning" is "replace sin^2(x) by x^2"

[vital marten]

should i have just done it from the beginning then?

[visual tiger]

well it doesn't matter once you already did all of that

you approximated 2sin(x)cos(x) into 2x

[vital marten]

yeah just for future reference

[visual tiger]

which is the same as if you had first approximated sin^2(x) as x^2

and so derivation giving us 2x

[vital marten]

yeah makes sense

alright thanks guys

always appreciate the help

.close

[midnight plank]

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[fierce canyon]

,rccw

[fierce canyon]

.close

[midnight plank]

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[quaint crag]

I AM GOING TO CRASH OUT, I HAVE TRIED EERYTHING AND IT KEEPS SAYING IM WRONG

[quaint crag]

like I have tried putting a negative argument, but also positive (argument was -1/6 pi, made it 5/6 pi and it still didn't work)

[small jasper]

where is 29 coming from

,w 8192/78125 sqrt 3

[grand pond]

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[quaint crag]

i found 7theta = -pi/6 hence i took it as 5pi/6, divided by 7 to get theta and then added 2pi/7

[small jasper]

actually the rest of your arguments are fucked after $z_2$

[grand pond]

Civil Service Pigeon

[small jasper]

what

-pi/6 and 5pi/6 are not coterminal

$e^{-i\frac{\pi}{6}}=e^{i \left(2\pi-\frac{\pi}{6} \right)}=e^{\frac{11\pi}{6}i}$ though

[grand pond]

Civil Service Pigeon

[quaint crag]

omg

im so dumb

ffs

THANK U im acc too tired for this 😭

[small jasper]

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[quaint crag]

.close

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[sullen hollow]

Need help with C

Idk about the scaling facotr

[untold tree]

have you tried drawing the picture out?

I recommend drawing the new triangle for part C

[modern sapphire]

do you even need that here?

[midnight plank]

@sullen hollow Has your question been resolved?

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[viral dagger]

how did they get the blue part

[midnight plank]

@viral dagger Has your question been resolved?

[midnight plank]

@viral dagger Has your question been resolved?

[midnight plank]

@viral dagger Has your question been resolved?

[midnight plank]

@viral dagger Has your question been resolved?

[midnight plank]

@viral dagger Has your question been resolved?

[vague seal]

this probably won't help but it kinda looks like the 2g(a+b/2) = g(a) + g(b)

[small jasper]

||Set a=b=0.15 and then set a=x, b=0.3-x||

[urban needle]

Which topic is it

[midnight plank]

@viral dagger Has your question been resolved?

[viral dagger]

ohh

[viral dagger]

functional equations

[midnight plank]

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[open dew]

what the flip is this bro

idek if im on the rigth truck I was following along with a video I dont understand it at all

[lavish venture]

what happened in (1) and (2)??

why did you multiply by b^-3 in (1)

[open dew]

the video i was following told me to dude i have no clue

[lavish venture]

and then after multiplying the rhs became b??

[open dew]

idk i need help please lol

[lavish venture]

$a \cdot b^{-3} = \frac{3}{64}, \quad ab^2 = 48$

[grand pond]

knief

[open dew]

my teacher gave a bad video or somehting

[lavish venture]

divide the first equation by the second to get b^5 = 48 * 64/3

[stiff bison]

second by first*

[lavish venture]

you're really smart

[open dew]

divide it by? how would i do that with the b^-3 and the b ^2?

[stiff bison]

also i believe that would be 48/(3/64) which becomes 48*64/3

[lavish venture]

you're still going on with this?

i'll let you figure it out yourself

[open dew]

is it 1st by second or second by first

[lavish venture]

yes this is what i said

[lavish venture]

if its confusing just do a substitution method

$ab^{-3} = \frac{3}{64} \implies a = \frac{3b^3}{64}$

[grand pond]

knief

[open dew]

you guys said 2 different things i dont know what to do

[stiff bison]

just follow his he was first

[open dew]

okay

[open dew]

is the substitution method what you just posted?

[lavish venture]

it would be this

then you put that in for the second equation

$\frac{3b^3}{64} \cdot b^2 = 48$

[grand pond]

knief

[lavish venture]

solve for b

[open dew]

how did you do that i dont understand?

[lavish venture]

how did i do what

[open dew]

the 1st part

[open dew]

.

[lavish venture]

$ab^{-3} = \frac{3}{64} \iff \frac{a}{b^3} = \frac{3}{64}$

[grand pond]

knief

[lavish venture]

multiply both sides by b^3

[open dew]

why by b^3 ? does it change from a b^-3 to a positive?

[open dew]

?

[lavish venture]

b^3 is in the denominator here

its just isolating a

if you had $\frac{a}{69} = 420$ you'd solve for $a$ by multiplying both sides by $69$

[grand pond]

knief

[open dew]

yeah i get that but why does it go from being a -3 to a positvive 3?

that what i dont understand

[lavish venture]

definition of negative exponent?

$x^{-n} = \frac{1}{x^n}$

[grand pond]

knief

[open dew]

yes

[lavish venture]

so what is confusing

[open dew]

i get to switch it to the other side the signs flip but the b is still on the saem side so wouldnt the sign not flip

[open dew]

.

[lavish venture]

what?

$ab^{-3} = a \cdot \frac{1}{b^3} = \frac{a}{b^3}$

[grand pond]

knief

[lavish venture]

multiplying both sides by b^3 clears the denominator on the left

[lavish venture]

and you get this

[open dew]

so you put b^3 under 1 and by doign that it changes b^-3 ot a positive 3

[lavish venture]

you literally agreed with this

take x = b and n = 3

[open dew]

okay

.close

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[buoyant fjord]

ok suppose we have $f: \mathbb{R} \rightarrow \mathbb{R}$

[grand pond]

Julian

[buoyant fjord]

such that

$f'(x)=f(x), f(0)=1$

[grand pond]

Julian

[buoyant fjord]

ok then

consider for some $a \in \mathbb{R}$, $f(a) \cdot \sum_{j=0}^{\infty} \frac{(-a)^j}{j!}$

[grand pond]

Julian

[buoyant fjord]

im having issues proving it equals 1

[scarlet snow]

what have you learnt so far

[buoyant fjord]

im in analysis

but i dont know much

basically i proved

[scarlet snow]

okay can you find f first

[buoyant fjord]

well im trying to prove f equals its taylor polynomial

and this is part of the process

[scarlet snow]

do you know the representation of f though?

[buoyant fjord]

wdym

i know its the exponential function

[scarlet snow]

okay cool

so f(a) is what

its easiest to try and find what you are working towards

[buoyant fjord]

well its f'(a) as well

[scarlet snow]

yes but expand it

using the definition of f

[buoyant fjord]

do you mean $f^n(a)$

[grand pond]

Julian

[scarlet snow]

no

what did you say f was

f(x) = ?

[buoyant fjord]

its the exponential function

[scarlet snow]

yes

[buoyant fjord]

but that doesnt help cuz

[scarlet snow]

so f(a) = ?

[buoyant fjord]

i cant assume anything

[scarlet snow]

what cant you assume

[buoyant fjord]

i cant assume anything all i have is f'(x)=f(x) and f(0)=1

[scarlet snow]

have you done differential equations?

[buoyant fjord]

no but this is an analysis class

[scarlet snow]

does that mean you cant use the fact that its the exponential function 🤔

[buoyant fjord]

yea i cant

lol

[scarlet snow]

oh okay interesting

[buoyant fjord]

i could eaisly prove everything tho if

[scarlet snow]

can you expand f(a)

using a series

[buoyant fjord]

i mean i can write it as its taylor polynomial plus the error factor

i cant assume the error factor is 0

[scarlet snow]

cant you write is as an infinite sum

it

[buoyant fjord]

i mean like this yes

but that leads to needing to prove this equals 1

[scarlet snow]

I see, so you cant use the series without showing the remainder approaches zero as n approaches infinity?

[buoyant fjord]

yea exactly

[scarlet snow]

okay I see the problem lol

I've never taken analysis so ill let someone else help you

[buoyant fjord]

lol ok

thanks for tryna help

[scarlet snow]

<@&286206848099549185>

[buoyant fjord]

i might have figured it out cuz some guy who didnt know told me just use exponential laws and then i realized that the taylor(x) times taylor(-x) is constant because of some stuff i proved earlier

.close

[midnight plank]

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[buoyant fjord]

how do we prove this given this definition

[buoyant fjord]

and i already proved f equals its taylor series

so we can use that too

oh wait this is trivial im a lil slow

.close

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[last slate]

hi

[last slate]

For question 15, how do i choose arbitrarily vectors in P?

[nova yoke]

if f(7) = 0, you know that (x-7) is a factor

[lyric charm]

this makes me want to cry

[nova yoke]

smartass answer: that's not even a set

[exotic stratus]

You missed these

[nova yoke]

also, "plynomial"

[exotic stratus]

lol

[exotic stratus]

!showyourwork

[midnight plank]

Show your work, and if possible, explain where you are stuck.

[last slate]

😂😂😂

[last slate]

i dont even have any bc.. idk how to choose my arbitrary vectors

[solid iris]

"proof it"

[nova yoke]

^ this was a hint

[exotic stratus]

... arbitrarily?

[nova yoke]

IF yes

[solid iris]

also violates instead of violate

[lost abyss]

What's a subspace?

[last slate]

this channel turned into roasting the questions 💀

[last slate]

brrruh 😂

[last slate]

i need to pick u and v

to test the subspace axioms

[solid iris]

one can argue thats just for emphasis but in that case its not even consistent with the other "if"

[exotic stratus]

just in case i need to clarify, arbitrary means random. Just take any two polynomials and they'll belong to P, and for S, you can take the most basic ass thing ever, since the procedure requires any two arbitrary vectors, you should be good to go

[last slate]

right, idk how to pick it

like is the set any polynomial?

[nova yoke]

yea, i'm going with occam's razor on this one

[last slate]

the set is what

i don’t understand the question

[nova yoke]

taake two polynomials, say p(x) and q(x), that satisfy p(7) = 0 and q(7) = 0

show that their sum has the same property, and that any scalar multiple of one of them also has the property

[last slate]

this is the part i dont get

[nova yoke]

what's unclear?

[lyric charm]

both of y'all have default-discord grey pfps

[nova yoke]

best pfp

[last slate]

fr

[last slate]

the polynomials are in which format

for example im used to p(x) = a + bx +cx^2

[nova yoke]

you can just leave them in generic form p(x) and q(x)

[last slate]

I dont get it

[nova yoke]

that fact that they're even polynomials is kind of irrelevant here

if you take two functions p(x) and q(x) which both have value zero when x = 7

then what can you say about their sum?

i.e. what is (p+q)(7)?

[last slate]

their sum is 0 if the input is 7

[nova yoke]

yes

and how about cp(7) where c is a scalar?

[last slate]

0

but

i just dont get the formatting still at all

[nova yoke]

which formatting

[last slate]

the set

[last slate]

.

thats a vector in P_2

[nova yoke]

well that's a quadratic polynomial

[last slate]

right

[nova yoke]

here your polynomials can have any degree

you could laboriously write out some generic form for each

[last slate]

but it must be 2 or more to be a vector space right

[nova yoke]

but it's easier to just reason abstractly

[last slate]

can a vector set of degree 1 polynomials be a vector space???

i don’t believe so

[nova yoke]

the set of polynomials with degree <= n is a vector space for any positive integer n

including n = 1

for n = 1, this is the set of all degree 1 polynomials and all constant functions

i.e. anything of the form ax + b

[last slate]

wait this is what i meant mb

Not degree 1 but 2

[nova yoke]

right, if it was degree <= 2 then it would be a vector space

but degree exactly equal to 2, no

because you could have for example two polynomials with leading coefficients 1 and -1, then their sum has smaller degree

[last slate]

≤ 2 still includes = 2 though

[nova yoke]

yep

polynomials with degree 0, 1, or 2, along with the zero polynomial

that's a vector space

[last slate]

oh like all together in 1 set with these different degrees?

ohh

yeah i get it now

[nova yoke]

yes you need all of them

[last slate]

a polynomial isnt not a vector space is the degree is only =n?

[nova yoke]

because for example (x^2 + 1) + (-x^2 + 1) = 2, which has degree smaller than 2

[last slate]

right

But if you considered all lesser degrees, 2 would be enclosed

because its part of the zero degree polynomials

[nova yoke]

yep

[last slate]

?

[nova yoke]

the set of all polynomials with degree n is not a vector space

[last slate]

i see

[nova yoke]

the set of all polynomials with degree <= n is

[last slate]

but bruh whats up with this question i don’t understand the format still 😂

okay

so its any polynomials

[nova yoke]

just reason with generic polynomials p(x) and q(x)

don't worry about writing out coefficients

[last slate]

i can pick any random polynomial??

[nova yoke]

(in fact the same argument works with any functions)

[last slate]

i dont have to have the form theyre in?

[lyric charm]

don't even bother trying to pick out a form

[nova yoke]

you can, but you don't need to

[last slate]

to like, see how the addition and scalar multiplication works

[lyric charm]

keep p as p and q as q that's it

you should know what adding two functions does

[last slate]

but youre tryna prove its enclosed

[nova yoke]

all you need to know are the following facts:
the sum of p(x) and q(x) is p(x) + q(x)
and the product of the scalar c with the polynomial p(x) is cp(x)

[last slate]

Any two functions added gives you a third function.. but how do you show here that that 3rd function is enclosed

or not

[lyric charm]

"enclosed"...

that's the wrong word

[last slate]

Oh wait, since its any degree, it doesn’t matter right

[lyric charm]

lnrd you're really trying your hardest rn to overthink and overcomplicate this problem

[last slate]

Bc we know its gonna be a polynomial of some sort nonetheless

[nova yoke]

you know that the sum of two polynomials is a polynomial
you know that the product of a scalar and a polynomial is a polynomial
so just show that the sum and product have value 0 at x = 7 if the original polynomials do

[last slate]

which will have any degree

right

[last slate]

closed?

[lyric charm]

you're trying to show that if p(7) = 0 and q(7) = 0 then (p+q)(7) = 0 also

for this you need to know what (p+q)(x) is, like its definition

[last slate]

all i know is the output for 7

which is 0

if i choose any othet random ones itll be something that still is in that vec space though right

[lyric charm]

so what you are saying is, you do not know what it means to add two functions.

[last slate]

so i don’t necessarily need to use the fact that f(7)=0

[last slate]

no

I know

[lyric charm]

ok then tell me

forget this question forget subspaces forget linalg

[last slate]

you add two functions you get a third function

[lyric charm]

if you've got two functions named p and q

what does it MEAN when we speak about the function p+q

how do we calculate the value of p+q at any point x

[last slate]

we get a new function lets call it r

[lyric charm]

given that we have access to p and q individually

ok sure, call it r if you want. what is r(x) equal to

[last slate]

you plug for both, get the output then add it

[lyric charm]

as an equation

r(x) = ...

[last slate]

p(x) + q(x)

[lyric charm]

right.

so (p+q)(x) by definition equals p(x)+q(x)

[last slate]

yes

[lyric charm]

this is what i was pulling out of you

[last slate]

im not disagreeing

[lyric charm]

so then the proof goes rather straightforward

[last slate]

but do i need to deal with f(7)

[lyric charm]

if p(7)=0 and q(7)=0, then
(p+q)(7) = p(7)+q(7) = 0 + 0 = 0

[last slate]

true

must I use f(7) tho?

[lyric charm]

there's no f

there are two functions which you assume to lie in your set

[last slate]

No I mean must i use this information

[lyric charm]

doesnt matter what you call them

bungo seems to have suggested p and q

[last slate]

must i use p(7) and q(7)

[lyric charm]

the act of writing out p(7)=0 and q(7)=0 is using this information

[last slate]

yes

[lyric charm]

obviously yes, unless you are ok with the justified criticism of "you didnt prove shit"

[last slate]

in that case it’s convenient to do so

[lyric charm]

it's convenient to accept the criticism of "question not actually done"?

[last slate]

no to use the given info

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[austere heart]

.close

[midnight plank]

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[last slate]

can someone remind me of that theorem

[last slate]

that has like the Characteristic equation of a sequence

[late rover]

second-order linear recurrence

[last slate]

yes this!

.close

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[last slate]

does reccurence work here?

didn't work for me

[midnight plank]

@last slate Has your question been resolved?

[spiral rock]

Each I_k is a subset of [0,1]

So you only need to show every x in [0,1] is an element of some I_k

[midnight plover]

Wach akhay drk

[midnight plover]

Khdm bl inclusion double rah sahla

Obach doz mn [0,1[ l reunion dyal I_k khdm ble principe de tiroire

[midnight plover]

Masmithach reccurence blanglais smitha induction

[midnight plank]

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[last slate]

i know double inclusion works

[last slate]

i'm trying to do it with induction

[midnight plover]

Induction*

[last slate]

👍

[midnight plover]

Here if you use induction the I itself will change to k/n+1 , k+1/n+1

Thats why i guess it cant work here

[last slate]

yeah and K will be in {0...n}

but wait

i think it still works

[midnight plover]

How

[last slate]

I_n is in [1-1/n, 1[

inclue

[midnight plover]

So? Whats next

[last slate]

hadi inclue f [0,1[

its union with the union till n-1 is 0,1

maybe i'm dumb

[midnight plover]

Db nta mafhmtich lconcept dyal reccurence m3a lreccurence rah definition dyal l’ensemble I_k ghatbedel ghatwli mn k/(n+1) ; (k+1)/(n+1) ya3ni rah ila knti nawi nchd lhypothese de reccurence otzid 3liha I_n bunion rah ghalat

[last slate]

ah bon

l ensemble ghadi ytbedel

yeah yeah

you're right

double inclusion it is

chokran

[midnight plover]

I_k li flhypothese P(n) de reccurence machi nfsha I_k li f P(n+1)

[midnight plover]

Hny

[last slate]

yupp

.close

[midnight plank]

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[night gyro]

how do i substract this

[latent wadi]

Factor out 1/6 pi

Then substract 36-4

[night gyro]

wdm

[latent wadi]

1/6 pi • ( 36-4)

[night gyro]

1/6 pi -1/6 pi?

[latent wadi]

Use distributive law to see how this is equal to the first form

[night gyro]

wht if i keep the pi on 36 and 4?

[rare maple]

?

[night gyro]

like this

[latent wadi]

Yeah that's okay too

Theres many ways to do it

[night gyro]

how do i do it then

[latent wadi]

In any way you want

[night gyro]

whts my next steps if i keep pi on 36 and 4

[latent wadi]

It can be 1/6 (36pi - 4pi)

[latent wadi]

= 1/6(32pi)

[night gyro]

then

[latent wadi]

= 5,3333 pi

Get it?

[night gyro]

thats the ans right?

[latent wadi]

Supposedly

Well, do you understand how the substraction worked?

[night gyro]

ill keep it as 32/6 pi

since is non calkc

[night gyro]

yes

u factr out 1/6

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[midnight plank]

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[night gyro]

tysm

[midnight plank]

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[ionic thicket]

may i ask what does the right side mean mathematically

[languid mica]

Its an integral over a closed path

[ionic thicket]

if u = xyi + yzj + zxk how do i do the integral on the right?

[languid mica]

You mean u is a vector function??

Like i,j,k are unit vectors

[ionic thicket]

yep

[languid mica]

Actually over a closed surface S

Well this theorem helps you calculate it

[ionic thicket]

this is the question

[languid mica]

So you use the formula on the left which its equal to

[ionic thicket]

is my closed surface the cube side with L?

[languid mica]

Ig

Well you have

0<= x,y,z <= L

Alr first compute the dot product divergence • u

[ionic thicket]

LHS?

3L^4/2

[languid mica]

The thing in the parenthesis

[languid mica]

Ah alr

You already did that

[ionic thicket]

integrate x+y+z from 0 to L 3 times dx dy dz = 3L^4/2

but idk how to do the right side

[dawn dagger]

I think you'd have to consider the faces of surface cube

[languid mica]

Well you have 6 faces

[dawn dagger]

which you have 6 of them

[languid mica]

Yea this

[ionic thicket]

yep

and then?

[dawn dagger]

try to find a parameterization

,, \oint_S \bm{u} , d\bm{S} = \sum_{\text{faces}} \iint_{\text{face}} \bm{u} \dotproduct \bm{n} , dS

[ionic thicket]

oh my god whati s that

[dawn dagger]

for example, let's pick the bottom meaning z=0, then n could be -k

then u. k = zx which is 0 because z=0

so one face falls off

you have something like this

[ionic thicket]

wait how do i know this is first octant

[dawn dagger]

first octant is where x,y,z are all positive

[ionic thicket]

okay

[dawn dagger]

you could realize that the faces where x=0, y=0 or z=0 are falling off

[ionic thicket]

sorry im a bit stupid, could you please elaborate on this?

[ionic thicket]

why are they falling off?

[dawn dagger]

ok look at (vi)

[ionic thicket]

when z = 0 u = xyi right

[dawn dagger]

no

i am talking about the region

the bottom region we have z=0 ground level

[ionic thicket]

yes

[dawn dagger]

and we can also take -k as a vector which is normal to that region

facing downwards

[ionic thicket]

yes

[dawn dagger]

and then (xy,yz,zx).(0,0,-1)=-zx

and since z=0 the dotproduct evaluates to 0, so the whole integral evaluates to 0

so the face "falls off"

[ionic thicket]

mmm true

what about the faces that dont?

[dawn dagger]

we would have to evaluate these integrals and sum the up

[ionic thicket]

which face doesnt fall off

how do i know?

[dawn dagger]

well you have to do it

there is also a lot of symmetry involved

[ionic thicket]

are the NON falling off faces the ones that are perpendicular to x y z axis? namely v and iii

wait

or i iii v?

[dawn dagger]

yes

these are also the cases, where either x=L, or y=L or z=L

[ionic thicket]

yep

what do i do next?

[dawn dagger]

ok let's pick for example the top face

[ionic thicket]

yes

[dawn dagger]

How would you describe the region

like constraint wise, for x,y, and z

[ionic thicket]

x from 0 to L, y from 0 to L

z at z=L?

[dawn dagger]

ye

normal vector u could pick?

facing outwards

[ionic thicket]

k

[dawn dagger]

ya

[ionic thicket]

and then?

[dawn dagger]

can you set up the integral?

$\iint_{[0,L]^2} (xy,yz,zx)^t \dotproduct (0,0,1)^t , dydx$

[ionic thicket]

hold on

is this what u.dS means

[dawn dagger]

ye

[ionic thicket]

S means surface?

and i need to sum up all the dot products of surfaces

?

[dawn dagger]

S generally means surface ye

[ionic thicket]

I think i am kind of getting this lol

what if its a sphere

[dawn dagger]

the thing with a cube is that there is no one nice parameterization for it, so we split it into faces

[ionic thicket]

i seee

what about a sphere though

[dawn dagger]

well we can parameterize it easily

would need only one double integral

[ionic thicket]

is this = double integral of zx dy dx

[dawn dagger]

yea

we also know that z=L

it reduces to $L\int_0^L \int_0^L x , dydx$

[dawn dagger]

which is just L^4/2

and then we evaluate the other 2 two integrals as well and sum the up

[ionic thicket]

OHHH

I GET IT NOW

[dawn dagger]

though i am pretty sure there is some nice symmetry here but i can't prove it

[ionic thicket]

don't we just picks the faces where either x,y,z =/= 0

[dawn dagger]

yea

[dawn dagger]

Let's see for (i) we would have 0<y,z<L and x=L, and we may pick n=i

,, \iint_{[0,L]^2} (xy,yz,zx)^t \dotproduct (1,0,0)^t , dzdy

[dawn dagger]

So Ly dzdy which is similar to Lx dydx as before

so it's again L^2/4

[ionic thicket]

the sum = 3L^2/4 hence the divergence theorem is proved

[dawn dagger]

so yea the first 3 and last 3 integrals seem to evaluate to the same result because of symmetry, so there might be a way to do this way quicker, but the general rule of thumb is to count all "faces" of your surface together, if you cannot parameterize it in one way

[ionic thicket]

i seee

thank you so much for taking your time and going through this with me i understand it now

[midnight plank]

@ionic thicket Has your question been resolved?

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[twilit field]

I don't get this

[twilit field]

isn't it basically this

[humble torrent]

How so?

[twilit field]

[I'm usinger axler as halmos is even more confusing]

[humble torrent]

I mean they have similar properties

[twilit field]

Aren't they the same essentially via risez

[runic hamlet]

up to iso they are pretty similar but those definitions are obviously very different

[humble torrent]

Yes there’s a correspondence, i think there was something more to it though

[runic hamlet]

well for starters riesz/the first def only applies in an inner product space

the second is more general

[twilit field]

Got it

tq

I'll close this now if it's fine?

.close

[midnight plank]

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[midnight plank]

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[jade magnet]

i did everything except the last part

im confused on how to get tan(11pi/24)

from tan(pi/8)

pi/8 = 3pi/24

oh wait

nvm

.solved

[midnight plank]

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[midnight plank]

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[midnight plank]

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[orchid saddle]

Is this good enough?

crazy

[desert pewter]

I am stuck in a concept anyone plz?

[orchid saddle]

who was that guy 💀

[spiral rock]

!occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[desert pewter]

Where seat is blank?

[orchid saddle]

take it to another help channel bro

wait i see my issue

.close

[midnight plank]

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