help-19

[faint charm]

yes interval

x€<c,d> , in every point in this interval

this means that?

[woven plaza]

No. That's what the square brackets mean. If they mean that with angle brackets they're using nonstandard notation

[-1, 2.5] is the interval from -1 to 2.5 including -1 and 2.5.

(-1, 2.5) is the interval from -1 to 2.5 excluding -1 and 2.5.

[-1, 2.5) is the interval from -1 to 2.5 including -1 but excluding 2.5

[faint charm]

👍 👆

[dusky pulsar]

generally it is denoted by ()

[woven plaza]

But in general the notation
f : A -> B says that f is a function which maps values from the set A into values from the set B.

You can replace A and B with any notation for a set

[faint charm]

ye

so interval <a,b> from set A

[woven plaza]

Right, and R there is most likely referring to the set of real numbers

[clever fjord]

Robert

[faint charm]

gotta learn 500 math definitions

for college test

[woven plaza]

What is the context that you saw these angle brackets?

[faint charm]

For example definition of a differential of real function with one variable in point x=a€(c,d)

f: <c,d> -> R is differentiable in point (idk point translation ) x=a€<c,d> if there is a limit lim x->h

and so on

[woven plaza]

You're translating to english, yes?

[faint charm]

from croatian

[woven plaza]

Okay I'm 95% sure then, given the context, that your source material means either [] or () when it writes <>. Probably () given that you've seen [] in the context but (I'm assuming) not ().

My best guess is that it's using:
<a,b> to be the interval from a to b excluding a and b.

[faint charm]

maybe its

ye synonimous

the question had (), answer had <>

in same expressions

[woven plaza]

Hmmmmm

Can you show me the whole context?

Like a picture or screenshot

[faint charm]

ok

1st differential of a real function of 1 variable in point x=a€(c,d)

definition then below is answer

f:<c,d>->R is differentiable ...

[woven plaza]

Yes, I can tell you with certainty that <> must mean the exclusive interval (<a, b> means from a to b excluding a and b). Because that's what's necessary for the definition of the derivative,

<> is being used as a nonstandard notation for () here

Btw when you said this:

1st differential of a real function of 1 variable in point x=a€(c,d)
In English we would say "1st derivative of a real function...". The word differential in English means something related but different.

Great penmanship and notes btw 🙂

[odd edge]

@faint charm Has your question been resolved?

[odd edge]

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[dry orchid]

Hello

[ornate knoll]

hi

[dry orchid]

I am supposed to write w in coordinate form but I don't even know what coordinate form is

[ornate knoll]

kan someone help me with finding the equetion for this graf

[stark kettle]

!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).

[stark kettle]

coordinate form is just (4,5) where we have an x and a y

given are vectors u and v

so we first need to get them in vector form

[dry orchid]

see I am already lost

explain it to me like I am five

I understand vectors have a direction

I know what coordinates are

but these are just coordinates I see, how can I determine direction from coordinates

[stark kettle]

$\vec u=\begin{pmatrix}2\3\end{pmatrix}$

[dry orchid]

u = (2, 3)

[clever fjord]

pixel

[dry orchid]

yes so just assume I know nothing

ok sry not nothing but very little

[stark kettle]

gimme a sec ill make it visual

[dry orchid]

thank you it is very much appreciated

I would like to be able to do this without visualisation later

[dry orchid]

The vector is assumed to go from (0, 0)?

[stark kettle]

yes

[dry orchid]

Is that how direction is detemrined?

Okay that makes sense

Now I know how to determine direction

[stark kettle]

so a point is basically the same as a vector

so if we want to add vector u and v

we first need to have them in vector form

[dry orchid]

Okay, and I don'

t know what that is either

Vector form, what would that be

[stark kettle]

(2,3) would be $\vec u=\begin{pmatrix}2\3\end{pmatrix}$

[clever fjord]

pixel

[stark kettle]

we have the x on top

and the y on the bottom

[dry orchid]

The right part is vector form?

[stark kettle]

yes

[dry orchid]

Left coordinate?

Okay

This is very helpful I just want to let you know that

[stark kettle]

and to make it clear that it's a vector we add that arrow on top

[dry orchid]

Right

[stark kettle]

what would be the vector form of v then?

just name the elements you don't have to do it in latex like i did

[dry orchid]

yes sry i was trying to figure out the syntax by looking at what you did

[stark kettle]

take ur time

[dry orchid]

x would be on "top" and y would be on "bottom", so 1 on top, 2 on bottom?

[stark kettle]

correct

[dry orchid]

Okay

To add them, is it so simple that I literally just add the top part together

and the bottom part together

[stark kettle]

yes

[dry orchid]

seperately

[stark kettle]

add the top

and add the bottom

[dry orchid]

So for the vector w it would be 3 on top and 5 on bottom?

[stark kettle]

yess

and now we need to go back to coordinate form right?

i believe that was the question

[dry orchid]

Right

so the vector w is (3, 5)

[stark kettle]

very good

[dry orchid]

in coordinate form

Okay thank you for treating me like a 5 year old

[stark kettle]

nah you're good

[dry orchid]

If I instead multiplied the vector u with the vector w

[stark kettle]

we can't multiply vectors

[dry orchid]

Okay

[stark kettle]

there are certain operations

like dot product

and cross products

you'll learn that later

[dry orchid]

You say that but I am in Uni now

I should actually update my roles

I am cooked brother

I am still in denial

[stark kettle]

you're taking linear algebra?

[dry orchid]

well I started the 26th and

right now people are just being welcomed

and partying

I can tell I am way behind in the math department

Every department if I am being honest

I am 22 and there are so many 19 year olds who are just brilliant, they have taken more math courses than I have and all in succession

My education has been all over the place with many gaps between courses

I am just full of dread right now tbh

I am going over old tests from each math course to see what I am missing

I worry there are too many for me to learn before they become relevant

[dry orchid]

To answer your question, I will be taking linear algebra, at least I assume so

Anyway thank you, adding vectors and switching from coordinate to vector form shouldn't be a mystery anymore

.close

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[opal temple]

the problem is to prove that

[opal temple]

such that m_n -> infinity and its a series of whole numbers

the proof is this:

[lethal spoke]

Is ?

[opal temple]

sorry one sec lol

that

so i dont understand why this proof wouldnt work for any series sequence that converges to infinity?

why did they restrict m_n to only be whole numbers?

[lethal spoke]

This is just the limit definition

But with e in place of L

[opal temple]

i get that but why is m_n restricted to only be whole numbers?

[lethal spoke]

What

[opal temple]

.

[lethal spoke]

If you want to prove this you can use an approximation

[opal temple]

this is a proof

i understand this proof

i just dont understand why it wouldnt work for any series that converges to infinity

[lethal spoke]

What do you mean converge to infinity

[opal temple]

its limit is (positive) infinitiy

[lethal spoke]

If its limit is infinity the series doesn't converge to a finite value

[opal temple]

i know

[lethal spoke]

now then what will be the finite upper bound for the sum to infinity of the series

[opal temple]

the sum?

oh

oops

sorry

my bad

anytime i said series i meant sequence

haha sorry english isnt my first lang

[lethal spoke]

If a series is convergent and increasing it means that there exists M such that the nth partial sum is always less than M

But if the limit of the series approaches infinity then there is no M such that the nth partial sum ≤ M

Which means it is not convergent to begin with

[opal temple]

whats a partial sum?

[lethal spoke]

The sum of the First n terms of a series

[opal temple]

i didnt get to that yet

again sorry if i confused you

i meant sequences not series

and when i say converges to infinity i mean the limit is infinity, not that it converges to a finite limit

the only thing im trying to understand is why that proof only works for a sequence thats only of whole numbers

[lethal spoke]

If the limit L is infinity it is not convergent to begin with.

If the limit L is finite then it might be convergent

[opal temple]

sure but some books use a different terminology that says "converge to infinity"

anyway thats not what im asking about

[lethal spoke]

https://www.sciencedirect.com/topics/mathematics/convergent-series

[opal temple]

ah

sorry like i said i dont know series' yet

<@&286206848099549185>

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[opal temple]

.close

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[magic dome]

I factored out x^2+x-90

That gave me (x+10)(x-9)

So X cannot be -10 nor 9

Did I do the notation wrong?

Left infinity needs to be negative :|

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[barren coral]

Chad just became his own helper damn

Good on you for recognizing that lmfao

[magic dome]

i just had to graph it then my brain realized XD

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[rustic sail]

Hey, I need to prove that gcd(a,b)=gcd(|a|,|b|)

[rustic sail]

This is extremely intuitive but I can't find a way to prove it mathematically

[mystic saffron]

What definition of gcd are you using?

[fossil hawk]

Isn't this trivial
Since if a|-b implies a|b

[rustic sail]

If a,b are integers and they are not both zero, then the largest number in the set of common divisors of a and b is the gcd

[mystic saffron]

Maybe you can see that x and -x always have the same set of divisors

[rustic sail]

Does that prove that their gcd are the same?

[rustic sail]

Good point - is that rigorous enough though?

[mystic saffron]

It is rigorous if you prove it

[fossil hawk]

Assume a and b have a gcd d
Then we have a = dx and b = dy where x and y are coprime
So - a = -dx and -b = -dy
So d|-a and d|-b
Giving -x and -y which are coprime so it must be there gcd

correct me if I said smthng stupid

[rustic sail]

How would you go about proving that? I can only think of a statement like if any pair of divisors of x is (a,b), there is also a pair (-a,-b) which also works and therefore if a is a divisor of x, so is -a

[rustic sail]

Yeah I think that works, thanks!

[fossil hawk]

yw : )

[mystic saffron]

a divides x means there is y such that ay=x. But then a(-y)=-x. So a divides -x too

[fossil hawk]

Sorry for the space in the smile my autocorrect converts it into a smile emoji which I don't want

[mystic saffron]

And the set of common divisors of x and y is the intersection of the set of divisors of x with the set of divisors of y

[rustic sail]

Right

[odd edge]

@rustic sail Has your question been resolved?

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[young sedge]

is it not -n/x^n-1

1 * x^-n

thats -n * x^(-n-1)

or alternatively -n/x^(n-1)

[true musk]

So we have $x^{-n}$ now

[clever fjord]

MetuMortis

[true musk]

So answer should be $-n*x^{-n-1}$

[clever fjord]

MetuMortis

[royal herald]

brody is spilling the beans

[true musk]

Which is equal to $\frac{-n}{x^{-1*(-n-1)}}$

[young sedge]

oh so ultimately you end up doing n+1

[clever fjord]

MetuMortis

[fossil hawk]

Yup correct

[fossil hawk]

bro is sigma or rather summation

[pulsar elbow]

stop doing that

[lethal spoke]

No its
#help-19 message

[young sedge]

oh ty

.close

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[fossil hawk]

Oh mb

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[stable pier]

Is the one step subgroup test appropriate to show that H is a subgroup here? Sorry for the messy handwriting. I just want to make sure I understand this and what the one step test does (& where its needed). But since the determinant isn't equal to 0 I'm not really sure I need a one step?

[brittle beacon]

The "one step" being showing that $a, b$ being in the "subgroup" implies that $ab^{-1}$ is in the subgroup?

[clever fjord]

@brittle beacon

[stable pier]

Yeah, if we show ab^-1 then the subset is a subgroup

or closed under multiplication while showing the inverse of b exists in the set

I think?

[brittle beacon]

I mean, you can use that to show anything is a subgroup really, that's a quicker way to show you have closure under the "larger group" operations (so as long as you're nonempty, you have the identity, and then are closed under inverses and multiplication)

[stable pier]

ohh okay. Okay just wanted to confirm. I think I know whats going on. This is just a confusing subject for me 😭

So if it had specifically stated that xy =/ 0, then I could technically just show that it is closed under multiplication right?

to prove subgroup

[brittle beacon]

I mean, at least in general, if you proved closure under multiplication, you'd still need to show that you contain inverses, which checking just closure under multiplication doesn't really do

As above, the "one step" does both for you provided you're nonempty

[stable pier]

Okay I think I got it :) thank you very much

[brittle beacon]

[stable pier]

.close

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[drifting pine]

i need help with this, i dont know what im supposed to do

[drifting pine]

i need to find the measure of each angle

[warped sigil]

is the (9x+12) degree angle an interior angle or an exterior angle?

@drifting pine

[drifting pine]

exterior

[frosty pewter]

to find the angles first do 180 - 9x + 12

then you will have all the interior angles

[warped sigil]

well the interior angle and 9x + 12 would be supplementary, so yeah 180 - (9x + 12) is the interior angle

so their sum would be 180 degree

you can find x from that

[drifting pine]

so for the interior angle next to the exterior one, it would be 192 - 9x?

[frosty pewter]

wait no

180 - (9x+12)

[warped sigil]

itd be 168

-9x

[drifting pine]

oh

[frosty pewter]

forgot the brackets

[drifting pine]

ohhhh

im see if that works, thanks

[warped sigil]

just sum up the angles and equate it to 180

[drifting pine]

so, i do 180 - (9x + 12) get 180 - 9x - 12, 168 - 9x

what do i do with that

[warped sigil]

now you have 3 interior angles

168 - 9x

6x + 3

4x - 3

their sum would be 180 degrees

[drifting pine]

so x + 168 = 180

[warped sigil]

triangle angle property

[drifting pine]

x = 12

[warped sigil]

yeah

now substitute the value of x in the angles

[drifting pine]

got it, i was so confused for a second because i did 9x + 12 + 168 - 9x = 180

[warped sigil]

oh lol

[drifting pine]

thanks again

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[boreal jewel]

This isn't necessarily help with a problem but can you guys who passed precalc give me some stuff I should study on, I'm in 10th grade and taking honors algebra 2 and precalculus at the same time but I have no knowledge of either and want to be prepared for precalculus, can anybody give me a video or parts of precalculus I need to study on

[river brook]

aops book might be goodd

[boreal jewel]

I wish but I got it tommorow 😔

[boreal jewel]

What's the first part of precalc that you had to do, I'll probably get it to

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[signal oar]

U^(°°) = U

Maybe that helps

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[potent jasper]

Did I properly setup desmos for graphing this limit?

[potent jasper]

Limit in question

Table in question

[mystic saffron]

sorry, my head isnt designed to turn as much as 90 degrees

[potent jasper]

Sorry about that. Here is the question rotated.

[mystic saffron]

its ok

i think youre supposed to (just) substitute the values of x into the equation?

[potent jasper]

Yeah that’s what I’m trying to do here

[mystic saffron]

if thats the case i think youre going on the right track

[potent jasper]

I wanted to do it on a graph though I was not sure I did it correctly on Desmos

Is how I imputed the values correct to outputting the correct values of the limit on Desmos?

[fringe bough]

Yes those are correct

[potent jasper]

Ok sick, I was pretty sure but wanted to double check I did not make any silly mistakes. Also I’ve not been able to find it but does Desmos have a builtin limit function instead of having to handle it like how I am?

[fringe bough]

I don't think it does, but it's not too hard to just plug in numbers very close to 0 or whatever

[potent jasper]

Yeah that’s fair

[fringe bough]

The table they gave you is a little misleading. It makes it look like you're going to always get -1 for negative values of x, and 1 for positive values for x

but that's not actually the case

not that it probably matters for this question

[potent jasper]

Yeah I know there is actually two tables the other gives wildly different values than the second I show here.

[fringe bough]

oh okay, that makes sense

[potent jasper]

But thanks everyone for the help ^^

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[fringe bough]

np 👍

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[elder vault]

.close

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[viscid flint]

please stop opening channels with things completely unrelated to math.

[elder vault]

I noticed it, so I close it immediately

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[vagrant talon]

So I am in the 8th grade

I need help with algebra 1

Or at least practice

We are currently on Solving Multi-Step Equations and Inequalities

I just need a good site of place to find practice that I can print our

the harder it is the better or more I prefer it

Thank You!

[mystic saffron]

by "nulti"-step equations do you mean multi-step equations

[vagrant talon]

yes sorry for the misunderstanding

[mystic saffron]

its ok

do you mean simultaneous equations

like equations in a system

like 2 equations being system-ed together

and you need to solve them

[vagrant talon]

Something similar

[mystic saffron]

ah those

[vagrant talon]

but it is only 1 equation

[mystic saffron]

oh

i think you can go to some websites like studocu and course hero et cetera

and in the search bar just type what you need

[vagrant talon]

something like -4l + 2(5k - 6) = -3k - 39

[mystic saffron]

oh these

@vagrant talon i found a bit of these on the internet and they are printable pdfs with answers

[vagrant talon]

oh thank you

[mystic saffron]

hope they help

[vagrant talon]

I appreciate it

[mystic saffron]

yw

[vagrant talon]

god bless

[mystic saffron]

my pleasure

remember to close the channel if you have no more enquiries at the moment

[vagrant talon]

oh okay

[vagrant talon]

btw how do I close the channel

[mystic saffron]

.close

^ this command

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[mystic saffron]

need help with KT conditions

[mystic saffron]

for maximisation with inequality constraints

Lambda >=0

but minis

minimisation is the same, or lambda <=0?

because i have these solutions

which satisfy the Kuhn Tucker

BUT, the solution set says its wrong

and somehow my tightness assumption is wrong

[odd edge]

@mystic saffron Has your question been resolved?

[quasi sparrow]

What "solution" is this sentence

[quasi sparrow]

And how does it differ from this sentence

[mystic saffron]

the solution i calculated

is x* = 1.12

y*=1.16

near the bottom of the page

and the correct solutions from the textbook is x=1 y=1

[quasi sparrow]

Where did you get a=8 from?

Or was that given

[mystic saffron]

sorry yes

was given

and the objective function is concave and the constraint is quasiconvex. (for extra info)

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

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[pale breach]

so would f be 4?

and then then how do i find g

or would g just be 4 as well?

[pallid tinsel]

What does f approach when x approaches 4 from the negative side

What does g approach

Hence what does the sum approach

[pale breach]

well x -> 4- so i start from the left make my way toward the right it would be (4,3) right?

and g being (4,20)?

[odd edge]

@pale breach Has your question been resolved?

[mystic saffron]

23

[odd edge]

@pale breach Has your question been resolved?

[pale breach]

wait what about 23

[odd edge]

@pale breach Has your question been resolved?

[odd edge]

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[cunning dust]

$\frac{(1+i)(1+i)}{(1-i)(1+i)} = i \ \
r = 1 \
\theta = tan^{-1}(\frac{1}{0})$

[clever fjord]

pixel

[cunning dust]

have i done anything wrong

[uneven osprey]

no

[cunning dust]

so there is no theta

its undefined

[uneven osprey]

just the division by 0 thing is not good

[uneven osprey]

use limits to be more clear

[cunning dust]

but that's what its supposed to be, no?

[cunning dust]

wdym

[uneven osprey]

1/0 approaches infty

arctan(infty).

think it like that

[cunning dust]

mmm okay okay

.close

[odd edge]

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[timber socket]

solution is 12i-3j+32k?

[ancient patrol]

ok u know cross and dot product well right?

[dense moth]

Scalar triple product

[dense moth]

Vector •Vector = Scalar

So that can't be solution

[fossil hawk]

Tru

[odd edge]

@timber socket Has your question been resolved?

[odd edge]

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[scenic quiver]

help, so 1st img is the original question and 2nd img is how me and my tutor solved it yesterday, and last img is how i solved it again today jsut to review the rule. anyway
my question is about the -2, why is it that in the 2nd img when me and my tutor solved it, the - went to -3n? where should the minus go? should it go to 3n or 2?

[scenic quiver]

also my 2nd question is that at the end of our solving (the 2nd image) why did he make it so that it was + there?
thats why when i write my solving again, im asking how/why is it +? how do you know to change it to plus? we are dividing right? so it should be minus

<@&286206848099549185>

[plush rose]

negative × negative is positive, right?

[scenic quiver]

yeah thats true in that case, but im also asking about theeee

[scenic quiver]

1st pic here

same thing shouldnt apply since the numerators at the top are both positive its the denominators that are positive x negative

it was -3 before btw he just changed it to +

[plush rose]

$$ 1/-2 = -1/2, right? So if you have -(1/-2), it would be -(-1/2) = +1/2 $$

[clever fjord]

Blue Gaming

[scenic quiver]

ok wait i get the 2nd half that youre saying i know that two negatives make a positive, but howd the - from the -2 go to -1 or are you saying it looks like this

[plush rose]

yes

My TeXit skills are not very good, sorry about that

[scenic quiver]

npnp its ok

but

now would the - go to the 3n or the 2?

[plush rose]

In the exponent it is on the 2, right?

[scenic quiver]

since where the minus is would change the answer of the question completely

[scenic quiver]

yeah its on the 2 in the original question

but when me and my tutor solved it yesterday (i didnt notice i forgot to put -) he put - on the 3n

[plush rose]

He also does not have the -2 on the exponent?

[scenic quiver]

im not sure what you mean

exponent is the power i know that but why would the power need it?

[plush rose]

I mean this

[scenic quiver]

huh im not too sure about that actually but he treated it as -3n during our meeting

actually

hold on

so

in that part

the exponent, it gets flipped (idk the rule is just like that)

so instead of -2 would it become -3n then?

huh but that doesnt explain the outside exponent

[plush rose]

It looks like that's what your tutor did

[scenic quiver]

the n^4*2/-3n

[scenic quiver]

yeah we were in a bit of a rush since it was the end of the lesson, but my main question is what would be the correct way to write it now

[plush rose]

Assuming your tutor got it right (it looks like it), you should put the - on the 3n like your tutor.

[scenic quiver]

hmm, okay

[scenic quiver]

is it due to that flip flopping thing then ?

and then it stays like that

since either way whatevers inside that bracket becomes e and then only the outside exponents are what matters

[plush rose]

I haven't got the part about e myself, so I don't know whether that's true.

[scenic quiver]

ah its some kind of rule like

wait

something like this

oh wait

yeah this one was the one i was taught yesterday

[plush rose]

I'll have to leave for class now, but to conclude I think you should put it on the 3n like your tutor.

[scenic quiver]

ah sorry about that then, goodbye

[plush rose]

don't worry

bye

[odd edge]

@scenic quiver Has your question been resolved?

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[tawny notch]

Hi, need help with this question

^statistics

[odd edge]

@tawny notch Has your question been resolved?

[odd edge]

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[paper moth]

someone help me im confused

[sand horizon]

You know that cos(a) = -21/29 and sin(a) = 20/29

[paper moth]

yes

OH WAIT

[ancient rampart]

try connecting p to the y axis

[paper moth]

wait so is x=cos and y=sin?

is that a rule?

[sand horizon]

On the unit circle

[ancient rampart]

tbh here they dont teach much about this unit circle where im from

[sand horizon]

Dommage, its cool

Many things to do with unit circle

So what about tan ? @paper moth

[paper moth]

sin/cos

[sand horizon]

What do you think about this .

[paper moth]

help me bro

i have a test tmrw on trig functions, trig identities, unit circle and two way tables

[paper moth]

move 1 to other side??😭

[sand horizon]

There is only one trick to know here

[paper moth]

ik there is formulas for this but i dunno what one to use

[sand horizon]

Let u = sin(x)

[paper moth]

u?

[sand horizon]

Yeah

[paper moth]

what is u

[sand horizon]

Or X as you want

y

Z

The letter you want

[paper moth]

yeah do y

[round lynx]

is it not literally just the x and y coords as your solution lol

[round lynx]

then tan is just sin / cos

[paper moth]

yeah th

[sand horizon]

Let y = sin(x) and see what happen

Fr

[paper moth]

2 sin^2 x -3y +1

[round lynx]

so what are you tryna do

[sand horizon]

Not quite

You have to change the sin^2 too

Becareful

[paper moth]

If y = sin(x)

then is sin^2 x = ?

[sand horizon]

= ?

[paper moth]

idk whatit is

sorry

[sand horizon]

$\sin^2(x) = (\sin(x))^2$

[clever fjord]

YakuBros

[sand horizon]

Do you see it ?

[paper moth]

sin and x become one and ^2 goes to both of them?

so y^2?

[sand horizon]

So what does it gives now ?

[paper moth]

2y^2-3y+1?

oh quadratic equation

[sand horizon]

Exact

Solve it for y

[paper moth]

y=1, y=1/2

@sand horizon

[sand horizon]

Yeah

So now

Go back to y = sin(x)

And change y by sinx

And solve for x

[paper moth]

Ok

so do i put y=1 or y =1/2

[sand horizon]

You put sin(x) instead of y for each of the equations and solve thoses separetely

[paper moth]

I'm sorry I don't get it

[sand horizon]

You have y = 1 and y=1/2

But you have to solve for x, knowing that y = sin(x)

So you replace

It gives sin(x) = 1 on first hand, and on second hand you have sin(x) = 1/2

[paper moth]

ohhhhh

so 1/sin = x

1/2/sin = x

@sand horizon

[sand horizon]

???

No

Sin(x) isin't a multiplication

Its a function

Sinus of x

So you use the method to solve trig equations

Sin(x) = sin(a) <=> x = a +2npi or x = (pi-a) +2npi

[paper moth]

what is 2npi

sorry

@sand horizon

my laptop switched off mb

[sand horizon]

You know that sin is 2pi periodic ?

And cos aswell

[paper moth]

nope

periodic?

oh ok

but what is 2npi

Bro

Where did u go?

bro thanks for the help appreciate it

imma just leave

.close

[odd edge]

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[sand horizon]

I advice you to read some courses about trig functions and how to solve the teig equations

[paper moth]

can you send me one please

[sand horizon]

Go check on khan academy thats free and well explained

[paper moth]

just send the link bro please with the specific course

🙏

[sand horizon]

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func

[paper moth]

ok tysm

[odd edge]

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[honest sluice]

Hey, i need some help on this one !

[honest sluice]

So my idea is C2+iS2 so I can get exponantuol form

Already did this but its just awful lol

[pastel dew]

I think you cannot do much with sum of exponentials

[honest sluice]

Mhhh, I thought about a geometric « suite » (idk the English word)

[pastel dew]

ooh right

[honest sluice]

Then i return to a trigonometric form of my complexe, then i split it to have the reel part and the imaginary one, but maybe there is like a better way to do it

[uneven osprey]

what are you exactly supposed to find?

[honest sluice]

I jsut need to calculate it

[uneven osprey]

like some single expression involving n

?

[honest sluice]

yep

[uneven osprey]

separately?

what does et mean?

[honest sluice]

C2 and S2 separately yes

[uneven osprey]

okok

[honest sluice]

I got an anserw but maybe there are other ways of thinking idk

[uneven osprey]

there's a formula for the sum of cosines and sines with their angles being in an Arithmetic progression

are you aware of it?

[honest sluice]

cos(a+b) exetera ?

[uneven osprey]

erm no

wait

[honest sluice]

ok so tell me more

[uneven osprey]

there's also for sine too

[honest sluice]

oh, i wasnt aware of that

[uneven osprey]

here we have an Arithmetic progression too

[uneven osprey]

so we can use the similar derivation like this

[uneven osprey]

btw, it is derived by some telescoping method

[honest sluice]

oh, its way simpler indeed, ill try to get like a pdf on this in french so i can understand it better

thx !

.close

[odd edge]

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[bitter robin]

im facing a problem when i try to solve through my calculator it keeps saying syntax error

[meager juniper]

What is the thing you're putting into your calculator?

[bitter robin]

an equation even though i did it on a online calc it worked there but on my physical calc it keeps saying syntax error

[meager juniper]

What is the equation?

And also what model calculator?

[bitter robin]

On the app it worked but on my calculator it keeps saying syntax error

[proper solstice]

lmao who uses calculator

[bitter robin]

In my uni we do

Lmao

[proper solstice]

what was the input for the syntax error?

[bitter robin]

Wdym

[proper solstice]

i mean what did you type that the syntax error came

[bitter robin]

I sent it

[bitter robin]

.

[round lynx]

I have that 😓

No one uses it

[bitter robin]

What do u mean

[round lynx]

There’s better calcs

[proper solstice]

are*

[bitter robin]

Our professor asked for a scientific one so i bought this

[round lynx]

Fair enough

[bitter robin]

Idk what to get

[round lynx]

There’s a rlly good one i forgot the name but it’s expensive

[bitter robin]

Ugh if I can fix this I wouldn’t need to buy a new one but it’s annoying me

[round lynx]

Cas calcs are actual menaces

[bitter robin]

I literally bought it yesterday everything works but some equations keep erroring

[proper solstice]

try different methods to solve this issue

[round lynx]

Even teachers hate them

[bitter robin]

Omg really

Most people here use Casio

[round lynx]

Same here

But they suck

[proper solstice]

Ok

[round lynx]

They malfunction a lot

[bitter robin]

It’s first time this has happened to me that’s why I’m confused

[proper solstice]

congratulations at mastering the art of stating the obvious!

[bitter robin]

Is this a bot

Whatever

[proper solstice]

Me?

😦

[bitter robin]

Yea lmao

🤣🤣🤣

[proper solstice]

Yes I have no personality

[round lynx]

Who me

[proper solstice]

I think I should get myself a pfp

[bitter robin]

Omg bro I need help how can I fix this YouTube cant help me

[bitter robin]

Maybe

[round lynx]

Here’s how you do the question btw

You dont need a calc for this lol

[proper solstice]

that way people would instantly assume I have a personality

[round lynx]

Oh shit

[bitter robin]

The professor said to depend on it so easier for me 🤣🤣

[round lynx]

I meant -2 not 2

[proper solstice]

Wrong

No wnder you'r ea scammer

[bitter robin]

I’m literally bad at math

[proper solstice]

I mean spammer

[round lynx]

Im aware ._.

[proper solstice]

How did you get this role?

[round lynx]

Fixed it

[proper solstice]

?

[round lynx]

I spam invited for an inv contest and discord flagged me

[proper solstice]

Now people will treat you with disdain and contempt

[round lynx]

I emailed discord to fix it and they said they wld but clearly they never did

[round lynx]

Happens on the daily

[serene axle]

;-;

[proper solstice]

OOps

no way

i Was wrong

It should be -2 correct

[bitter robin]

yea ill see if i can get a new calc this is annoying

.close

[odd edge]

Channel closed

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[serene axle]

Yea

[round lynx]

Or just learn algebra baha

[odd edge]

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[desert drum]

Lost in question 3, need help

[desert drum]

.close

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[brazen raptor]

for lim x -> pi/6 cot(x), y is the limit sqrt(3) and not sqrt(3)/2?

[uneven osprey]

cot(pi/6) is sqrt3

[brazen raptor]

o

k

[nimble blaze]

you may be confusing cot with cos

[brazen raptor]

oh

yeah

ok I get it

thx

.close

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[solar cave]

Hello

[solar cave]

Am I doing this right?

Hello?

[round lynx]

No

You need to translate it down 4 units and left 2 units

[solar cave]

ohh ok

Is that it?

[round lynx]

Well you need to find ur x and y intercepts, turning point and then graph

[barren coral]

why are you a likely spammer 😭

[round lynx]

Atp i shld put the story in my bio to stop ppl from asking

I spam invited for an inv contest, discord flagged me as a spammer

[barren coral]

damn

[odd edge]

@solar cave Has your question been resolved?

[odd edge]

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[odd edge]

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[mystic saffron]

This might seem a stupid question, but how do i do this?

[fringe spruce]

what are the red brackets for?

[mystic saffron]

Err the problem

[fringe spruce]

(2x+3)^2= 4x^2 + 12x+ 9

then we multiply that by 5

so it becomes 20x^2+ 60x+45

i think this is what u need?

or am i wrong?

[mystic saffron]

Yeah, excuse me, where does the 12x came from?

[fringe spruce]

2 multiplied by the 2 x then muplited by 3

so 2 .2x.3 that equals 12x

[mystic saffron]

Ohhhhhhh

[fringe spruce]

a is the 2x and the b is 3

is everything understandable?

[mystic saffron]

Yup

[fringe spruce]

glad to help

[mystic saffron]

.close

[odd edge]

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[mystic saffron]

.reopen

[odd edge]

✅

[mystic saffron]

How do i do this?

[fringe spruce]

what does the questiuon want

[mystic saffron]

To simplify ig?

[fringe spruce]

i mean u simplify it then what?

[mystic saffron]

Oh wait no

Um

[fringe spruce]

yeah i was aboutta say'

hehhehe

[mystic saffron]

Finding the composite function

so there's f(x) and g(x), fg, gf

[fringe spruce]

what do u want

and whats given

[mystic saffron]

Or do i just

Leave it like that?

[fringe spruce]

u can leavce it like that

[mystic saffron]

Oh sweet

[fringe spruce]

it wont make a difference

[mystic saffron]

Oke

.close

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[odd edge]

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[errant vapor]

Given f(x,y)=(O+Xx+Yy-Q) squared find (P,Q) where P subscript x equals Q subscript y equals gradient of f(x,y), find gradient f(x,y) and (P,Q). f(x,y) is for one dimension. Each dimension has its own constants. All but x and y are constant. I can make f(x,y) be more than one dimension added, plus+, together if needed. X E.

[errant vapor]

https://www.whitman.edu/mathematics/calculus_online/section16.03.html A source for this. X E.

https://sites.science.oregonstate.edu/math/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/grad/grad.html Another source. X E.

[soft terrace]

Can you elaborate on your question more. The formulas you've provided don't make sense for the question.

[errant vapor]

I don't know Latex, [O is Origin of 2d in 3d, X is x direction vector in 3d, Y is like X for y, and Q is a point in 3d] That in [] is for one dimension only, like Oz, Xz etc. What is unclear? X E.

derivative of P for x is equal to derivative of Q for y and either of those is equal to gradient of f(x,y). X E.

Like Px=Qy=Grad f(x,y). X E.

Like I have (Ox,Oy,Oz), X, Y and Q like that and in each dimension sub in for only one dimension like [Ox,Xx,Yx,Qx]. X E.

@soft terrace have I elaborated enough?

Thus in total this is to be applied to a planar polygon finding average of all distances from a point to polygon parts, it returns distance squared when applied to a whole polygon. X E.

P and Q are functions of x and y so there is P(x,y) and Q(x,y). X E.

Anyway, it all comes down to find gradient f(x,y). X E.

Well this seems simple but maybe it isn't, any <@&286206848099549185> got an answer?

[odd edge]

@errant vapor Has your question been resolved?

[errant vapor]

Please tell me if I need to explain better. X E.

[odd edge]

@errant vapor Has your question been resolved?

[errant vapor]

Can someone say why I am getting nothing here?

I guess ping me if there is a solution. X E.

[errant vapor]

https://zzzcode.ai/answer-question?id=be35267a-d8a1-4e1f-afb6-210111ce0867 Easy solution, anyone want to check this?

And yes I know, no A.I. but this is to like my own thing. X E.

It says partial derivative of f over partial derivative of x is M. f over y like that for N. Results being 2X(O+Xx+Yy-Q) and 2Y(O+Xx+Yy-Q), is that correct? X E.

[errant vapor]

.close

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[paper cape]

Hello guys, is there a difference between
$\lim \limits_{n \to \infty} \sum^n_{k=1} a_k$ and $\sum^\infty_{n=1} a_n$?

[clever fjord]

Akkaman

[paper moth]

Wtf

What is this

Lim?

Isn't that sigma symbol?

[paper cape]

The limit.

[paper cape]

Yes.

It's a series but I'm unsure if both mean the same or if there is a difference.

[brittle beacon]

The latter is defined by the former

[paper cape]

What do you mean?

So it pretty much means the same?

[brittle beacon]

As in, $\sum_{k = 1}^\infty a_k$ is \emph{defined as} $\lim_{n\to\infty} \sum_{k = 1}^n a_k$, they mean the same

[clever fjord]

@brittle beacon

[paper cape]

So it has nothing to do with the convergence of $a_k$, right? ^^

[clever fjord]

Akkaman

[forest sky]

they are the same, so they either both converge or both diverge

[paper cape]

Thank you. 🙂

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[paper moth]

w

w

w

w

w

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[brittle beacon]

.(well, ignoring e.g. that if a_k doesn't converge to zero then there's no way the series converges, not really)

[paper cape]

Thank you. 🙂

[paper cape]

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[stone blade]

Show that the span of any non-empty subset is a vector subspace. I do not know how to start this

[fickle silo]

you have the definition of a span?

[stone blade]

I do not actually, my lecture did not define that today

[fickle silo]

ugh ok weird

hmm maybe you already have the upcoming notes though?

[stone blade]

Yeah I do have the upcoming notes!

[fickle silo]

otherwise we can go with the wikipedia definition

[stone blade]

And what it seemed is that the span was kind of like, a basis times your vector spaces coordinates?

It doesnt do a good job at explaining it, it just shows an example lol

[low locust]

this is something that will depend heavily on how you define a span. because you can quite literally define it as the smallest subspace containing your set, so by that def it is automatically a subspace

[fickle silo]

it's the "smallest" vector subspace that contains all the vectors of the input set is what I like to imagine the most

[stone blade]

So would a span be like, the set of all vectors that come from some sort of linear combination?

[odd veldt]

The span of a set of vectors is the set of all vectors that can be made with those original vectors

[fickle silo]

you just take the input vectors and add and combine the however you like to

[stone blade]

So if I have like, two vectors v and w, the span would just be A_1 v + A_2 w where A_1 and A_2 are both real numbers?

[odd veldt]

Yup! It would be the set of all vectors of the form A_1 v + A_2 w

[sleek moth]

If you have a vector space that contains v and w, it is obvious that every vector of the form you outlined must belong to that vector space because the operations must be well-defined

What's not obvious is that the set of vectors of the form you outlined forms a vector space, but it does

[stone blade]

So the linear combination of V and W form a vector space?

[fickle silo]

this is the general definition according to wikipedia \
$span(S) = {\sum_{i=1}^k \lambda_i v_i: k \in \mathbb{N}, v_i \in S, \lambda_i \in K}$

really just all the possible linear combinations of the input vectors

[clever fjord]

rbit

[stone blade]

Alright so its literally just adding all the possible vectors scaled by some arbitrary scalar?

[odd veldt]

Pretty much!

[stone blade]

Well where each vector has its own scalar value

[sleek moth]

also this is a super funny coincidence but this is what I'm writing for my thesis rn 😂

[odd veldt]

Any vector that can be made with the input vectors

[fickle silo]

also one important note is that you can also input infinite sets, but all linear combinations have to be of finitely many vectors

[odd veldt]

Like, (0 0 1) isn't in span{(1 0 0), (0 1 0)} but (5 2 0) and (4 111 0) are

[fickle silo]

so the linear combination doesnt have to make use of all vectors

[stone blade]

Huh that's really interesting! I appreciate the help on defining a span lol this makes a lot more sense

[odd veldt]

Yup, the scalar multiple of some of them can be 0

[fickle silo]

also you said non-empty set, but the span of an empty set is just the null space, which is a subspace too

[stone blade]

So then my question is that I would have to show that the span of some non-empty subset is a vector space right? So I would I just use some arbitrary vectors to show that it outputs some sort of basis?

Like take A_1 v + A_2 w = e_1? or something like that?

[fickle silo]

you go by the definition of a vector subspace

[odd veldt]

Do you have a list of axioms you need to satisfy for a set to be a vector space?

[stone blade]

Yes! There has to be a defined scalar multiplication and Vector addition right?

With the identitive axiom and the distributive and ssociative property as well?

[odd veldt]

Yup that sounds right

[stone blade]

Okay so the subspace has to follow all of those axioms as well yes?

[odd veldt]

Yup, though you might have a shorter list of axioms you need to check for the subspace

[fickle silo]

you have the 3 properties that define a subspace, somewhere in your notes?

[odd veldt]

Like, if you start with a vector space you already know you have associativity, so there's no need to check with the subspace right?

[stone blade]

I do not sorry, I was sick for that lecture and no one was willing to send me any notes

[odd veldt]

There might be something in your textbook?

[fickle silo]

damn

[stone blade]

but if I were guessing, it would probably be like, theres closure under addition and closure under scalar multiplication

lol I got those two right

[odd veldt]

If you're using "Linear Algebra Done Right" then this is on page 18

[stone blade]

I remember hearing something about closure lol

Would you reccomend that as a textbook for linear alg?

[odd veldt]

It's a good textbook for abstract linear algebra, though maybe not for more applied linear algebra

[stone blade]

I'm in this weird scholars section of Calculus 3 which starts off with a course in linear algebra, then goes to Calc 3, then to Diff Eq's

[fickle silo]

doesn't it need to be closed under negation to or am I missing something

or wait scalar -1 of course

[odd veldt]

Yeah I was about to say

[stone blade]

Okay so, we have a defined vector space and subspace right?

Would we just have to show that hey, A_1 v + A_2 w = some basis which is a subspace of the vector space?

[odd veldt]

Yeah you should be starting with a vector space, and taking the span of some of the vectors

Hmm, that would probably work but idk if it's the answer your prof would be looking for

[stone blade]

I just wanted to get started with the question

I am going in to ask him tomorrow but I wanted to try to get a frame work for it

[odd veldt]

Do you have a textbook for that class? If so I'd recommend looking through it to find how subspace is defined there

Well I think if you're feeling alright about how span works then you shouldn't have too much of an issue

[stone blade]

And I think I understand what you guys are saying, then I can definately use my textbook to more rigorously answer the question

I think I was just missing the information as to what I needed to know to answer the question from the beginning! So thank you so much!

I hope you have a great rest of your day @odd veldt !

[odd veldt]

Yeah you too man!

[stone blade]

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[paper cape]

Hello guys, how do I prove that $\sum^\infty_{n=0} \frac{1}{(n+x)^2}$ is convergent for $0 < x \leq \frac{1}{2}$? I can use that $\sum^\infty_{n=0} \frac{1}{(n+\frac{1}{2})^2}$ and $\sum^\infty_{n=1} \frac{1}{n^2}$ are convergent.

[clever fjord]

Akkaman

[brittle beacon]

What do you know about series convergence, and how you can show/disprove convergence?

[paper cape]

I only know the monotone convergence theorem tbh.

[fickle silo]

index shift n -> n-1 and you get a majorant just like yesterday

[paper cape]

I tried that but the problem is that I can't "mathematically correct" show an inequality that $\sum^\infty_{n=0} \frac{1}{(n+x)^2}$ is bounded.

[clever fjord]

Akkaman

[fickle silo]

although, no, no index shift it already is

do you know how if a_n and b_n are sequences, then

$a_n \leq b_n \Longrightarrow \lim_{n \to \infty} a_n \leq \lim_{n \to \infty} b_n$

[paper cape]

Suppose $u_n$ is the partial sum of $\sum^N_{n=0} \frac{1}{(n+x)^2}$, then saying
$\sum^N_{n=0} \frac{1}{(n+x)^2} \leq \sum^N_{n=1} \frac{1}{n^2}$ would be wrong.

[clever fjord]

rbit

[paper cape]

No.

[fickle silo]

what about $\sum_{n=1}^N \frac{1}{(n+x)^2} \leq \sum_{n=1}^N \frac{1}{n^2}$, why would that be wrong? Like the inequality itself?

[clever fjord]

rbit

[paper cape]

It would be correct for n = 1 but wrong if the left one has index n = 0.

That is my problem.

[clever fjord]

Akkaman

[fickle silo]

yeah, but if it's bounded for n=1, then it's also bounded for n=0 (just take the bound for the n=1 case and add the very first summand of n=0 to it)

[paper cape]

How do I write that correctly? As an inequality?

[fickle silo]

$\sum_{n=1}^N \frac{1}{(n+x)^2} \leq \sum_{n=1}^N \frac{1}{n^2} \leq \sum_{n=1}^{\infty} \frac{1}{n^2} = L$ I would start with this

[clever fjord]

rbit

[fickle silo]

you get $\sum_{n=1}^N \frac{1}{(n+x)^2} \leq L$ and adding $1/x^2$ on both sides we arrive at $\sum_{n=0}^N \frac{1}{(n+x)^2} \leq L + \frac{1}{x^2}$

[paper cape]

And let's say x = 1/10, then the very first summand of n=0 would be 100 and since $1/n^2$ converges to $\frac{\pi^2}{6}$, how does that work?

[clever fjord]

Akkaman

[fickle silo]

then the bound becomes pi²/6 + 100

[clever fjord]

rbit

[fickle silo]

our bound is allowed to depend on x, that doesn't matter for its convergence

[paper cape]

That is actually very smart.

[fickle silo]

as we let x be a constant and then analyze the convergence

[paper cape]

Yeah I think that should work.