help-13

[undone sage]

You just ask your doubt

[drowsy glen]

man you are exposing

[undone sage]

No need to bother about such things

[drowsy glen]

its not doubt its a help

umm

my exams are gonna appear in few days

[undone sage]

Just tell already

[drowsy glen]

i am very tensed for exam bcuz in last semester i got degraded performance in math

can you help me out?

[undone sage]

Yes

[drowsy glen]

any tips?

[undone sage]

Go and study properly

Solve more and more questions

Don't panic

Be calm

Think logically

That's it

[hollow kiln]

drink water and sleep 8h

[drowsy glen]

i am not able to solve questions ine exam but when i take a look at paper at home and i can solve them!

[drowsy glen]

what?

[sand meadow]

don't study new topics

[hollow kiln]

that's 80% of the work

[undone sage]

Your heartbeat normal when you give exam?

[hollow kiln]

20% is you putting that work in

[undone sage]

Maybe due to panic

Don't overthink

While giving exam

[hollow kiln]

"dont panic" sometimes doesnt just work, so i would recommend you meditating for 5 mins before the exam

[undone sage]

Wether u will pass fail score good marks etc.

[hollow kiln]

just close your eyes and try to focus as much on your breath as possible

[sand meadow]

what exam is it

[crimson sedge]

also do mock tests

[sand meadow]

like University or school?

[undone sage]

breath slowly and calmly for 2 mins when you start to panic

[crimson sedge]

if school

[drowsy glen]

math

[drowsy glen]

okay

[drowsy glen]

school

[undone sage]

And drink water too

[drowsy glen]

🙂

[drowsy glen]

plenty?

[undone sage]

Yes

[drowsy glen]

is there a square for 28?

[undone sage]

How much you feel like drinking

[crimson sedge]

root?

[drowsy glen]

not like 2*2=4 like this

[undone sage]

Demn this lag

Battery 8%

[crimson sedge]

root 28 = 5.29150262213

[hollow kiln]

,tex 28² ?

[wraith dagger]

haygiya

[drowsy glen]

nope

[drowsy glen]

bruh

[hollow kiln]

,tex \sqrt{28} ?

[drowsy glen]

got it

[hollow kiln]

:sadge:

[drowsy glen]

@hollow kiln

why is there a pink diamond beside you?

[hollow kiln]

woman

[drowsy glen]

oh gender mar?

mark

[hollow kiln]

ye

im also a man

and non binary

and ask pronouns

thanos basically

i have all the crystals

[drowsy glen]

oh

it has a history behind that?

[hollow kiln]

lol

no

[drowsy glen]

if i become good at math can i also become a helper here?

[hollow kiln]

you select the helper role

idk anything about maths

[undone sage]

Yes boi you can even become now

[hollow kiln]

joined yesterday

[drowsy glen]

im not good in math so i wont help out people lol

[undone sage]

You will one day

Just keep on practicing

And avoid rote learning

[hollow kiln]

im kinda good at latex thats why i help people out

[sand meadow]

how can i learn latex?

[undone sage]

.close

[cedar kiln]

Channel closed

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Use .reopen if this was a mistake.

[hollow kiln]

idk i just started typing and learned it

[sand meadow]

.reopen

[undone sage]

lol

[hollow kiln]

maybe try ,help if you want to learn faster

[sand meadow]

i dont know a thing

[hollow kiln]

type whatever you want to type between $ symbols

[sand meadow]

i am currently preparing for exam... i will learn latex in june

[hollow kiln]

$hi$

[cedar kiln]

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[wraith dagger]

haygiya

[short dome]

cuz f(x) = f(-x)

[short dome]

aint 6 supposed to be even
cuz f(x) = f(-x)

[earnest socket]

looks like it

[short dome]

so the answer key is wrong?

[crimson sedge]

yeah

though it might also be a typo in the question, because there are two constant terms

maybe it should be -5x, in which case the answer would be right

[short dome]

oh ok thanks

.close

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[lavish jolt]

why did they add that term below

isn't Γ (p+u+1) enough to desribe whats in the denomenator up there

[mighty drift]

There's no reason for the product to stop at 1+mu

[lavish jolt]

so we want it to stop at 1

so we multiplied then devided by Γ(u+1)

if thats right than that equality isn't correct

wait i'll write what i understood

wait no

it did stop at 1+mu

[wraith dagger]

Mehdi_Moulati

[lavish jolt]

i don't understand the bounds

we didn't learn gamma function using the product so im not very familiar with it

[mighty drift]

Write it with factorials then

If that's more natural for you

[lavish jolt]

yeah i know

[soft owl]

(p+u)! = (p+u) * (p-1+u) * (p-2 + u) * ...* 3 * 2 * 1

[lavish jolt]

wouldn't it only end to 1 if we add u!

[soft owl]

but you made a mistake in the numerator

[lavish jolt]

i forgot the first term

[wraith dagger]

Mehdi_Moulati

[lavish jolt]

yes

this is what we got

so in order to write (p+u)! as Γ(p+ u+1)

it must end at 1

[soft owl]

yeah , Γ(p+ u+1) is the product of numbers from 1 to p+u

[lavish jolt]

alright i think i get it

Thank you a lot

[soft owl]

anytime

[lavish jolt]

.close

[cedar kiln]

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[autumn notch]

given these

[autumn notch]

are the vectors orthagonal, also is the family ortonormal

[crimson delta]

What is the definition of orthogonal

What is the definition of orthonormal

[autumn notch]

A set of vectors S is orthonormal if every vector in S has magnitude 1 and the set of vectors are mutually orthogonal.?

and i just realized that is is orthogonal, so disregard that question.

my book, says that it is orthonormal if the set of vectors are orthogonal with regards to the inner product and consists of unity vectors with regards to the inner product

[crimson delta]

Same thing, just more general

Unit vectors = vectors with magnitude 1

[autumn notch]

okay

and then how do i check for my two vectors

[crimson delta]

Well what are their magnitudes

[autumn notch]

oh so if <u,u> = 1 and <v,v>=1 then it is orthonormal?

i did this

[crimson delta]

Remember that norm(x)^2=<x,x>

So yes if that is 1, then the magnitude is 1

[autumn notch]

ah awesome

btw how do i find the norm of a single vector?

[crimson delta]

.

Then sqrt

[autumn notch]

i see

thanks man

.close

[cedar kiln]

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[crimson delta]

With the usual dot product this is just the standard formula for length of a vector

[cedar kiln]

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[crimson delta]

I.e. sqrt(sum of squares of entries)

[bright agate]

wow

*claps

[crimson delta]

Shitty inet takes too long to send

.close

[cedar kiln]

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[abstract abyss]

need help idk

[abstract abyss]

i'm sure it's not difficult but i'm new to vectors

[limpid agate]

I think the question is incomplete

Find the direction and magnitude of... What exactly

[lyric jungle]

u + v... maybe?

[abstract abyss]

of the vector maybe

[cosmic steppe]

What vector

u+v?

u-v?

[cosmic steppe]

That doesn't help

It's missing info

[abstract abyss]

wat it needs

[cosmic steppe]

I think your teacher forgot to put down the resultant vector lol

[empty pike]

Lol

[abstract abyss]

yeah i'm sure it's resultant vector

[cosmic steppe]

I mean your teacher's gotta specify the resultant vector

It could be u+v, v-u, u-v, 2u + 627272v

Etc etc

[abstract abyss]

oh it's u+v

now can u help

[upbeat lotus]

Use parallelogram law

$|{R}|=\sqrt{A²+B²+2AB cos\theta}$

[wraith dagger]

Arnab Pal

[cedar kiln]

@abstract abyss Has your question been resolved?

[abstract abyss]

wat from here

[upbeat lotus]

Put the values in

[abstract abyss]

y i need the equation here

isn't it pythagoras theorem

[upbeat lotus]

You need equation to find v+u

[abstract abyss]

but it's the parallelogram law

not triangle

[upbeat lotus]

Nah

Pythagoras theorem was a²+b²=c²

$|{R}|=\sqrt{A²+B²+2AB cos\theta}$

[wraith dagger]

Arnab Pal

[upbeat lotus]

It dosen't include 2ABcos theta

It is parallelogram law

Your diagonal is u+v

[abstract abyss]

wat u got there is the law of cosines

[upbeat lotus]

$C=\sqrt{A²+B²-2AB cosC°}$

[wraith dagger]

Arnab Pal

[upbeat lotus]

Law of cosine is this

[abstract abyss]

so wat equation is here

i need to know the point so i can work it out again

[upbeat lotus]

https://youtu.be/Mep0foZMOCg

You should watch it

Duration of the video is 2 min

[abstract abyss]

alright

[upbeat lotus]

https://youtu.be/LrwYAC_4ThY

You could also watch this

You would know everything about parallelogram law

That you need to know

[abstract abyss]

it's got the magnitude but not the length 😦

[upbeat lotus]

What length?

[abstract abyss]

my bad the direction

and btw y he made it a triangle from a parallelogram

[upbeat lotus]

Yupp

[abstract abyss]

wat is the point

there's a triangle law

[upbeat lotus]

To make the thing easy

You could use triangle law

I have to go for dinner

Ask anyone else for help

[abstract abyss]

ok eat well

[cedar kiln]

@abstract abyss Has your question been resolved?

[abstract abyss]

still confused

y is it law of cosines

[upbeat lotus]

@abstract abyss

It is not law cosine

[abstract abyss]

my teacher said it is

[upbeat lotus]

https://byjus.com/question-answer/derivation-of-triangle-law-of-vector-addition-and-parallelogram-law-of-vector-addition/

[upbeat lotus]

Should watch this derivation

Wait

[abstract abyss]

idk abt a and b for the law of sines

y is it not 10 and 6

[upbeat lotus]

,w √(6²+10²+2×6×10×cos(50))

[abstract abyss]

i know i need help w the law of sines now pls

so wat are big a and small a

[upbeat lotus]

Ok

Law of sine is

$\frac{sin (a°)}{a}=\frac{sin (b°)}{b}=\frac{sin (c°)}{c}$

[wraith dagger]

Arnab Pal

[upbeat lotus]

In this type of triangle

[upbeat lotus]

This is law of sine

[upbeat lotus]

Yeah you could use law of cosine for angles

[upbeat lotus]

No no no

You couldn't use exterior angles

You have to use int angles

[abstract abyss]

i wanna know y it's 15 and 130 degrees and 6 and 50 degrees

oh ok

but the side is fine

but y is the 130 degrees not the angle of b or c idk

[upbeat lotus]

You know what I was thinking

[abstract abyss]

wat

[upbeat lotus]

In your question v=6 and u=10

[abstract abyss]

yeah

[upbeat lotus]

And in this question one side is 1 and the other is 6

[abstract abyss]

maybe it's a 10 just mistake

[upbeat lotus]

yeah I saw in the law of cosine

Anyways

[abstract abyss]

bro y is sinA/a = sin130/15

[wraith dagger]

Results provided by WolframAlpha

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Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[upbeat lotus]

Yeah

[upbeat lotus]

If you use parallelogram law you will end up with same ans

[abstract abyss]

dunno wat one is a b or c

i need help to know

[upbeat lotus]

Watch this

And think

[upbeat lotus]

You have to assume it in your mind

[abstract abyss]

but i don't know

[upbeat lotus]

If you take a side then you have to take opposite angle

[abstract abyss]

cause corresponding angles

[upbeat lotus]

Not really

[abstract abyss]

all i needed to know ty

[upbeat lotus]

Yeah

[abstract abyss]

i'm just a bit confused here as well

to inverse it

and 6/5(sin130) isn't 18 degrees anyway

[abstract abyss]

ah ok

[upbeat lotus]

,w sin^-1(6/5×sin130°)

[abstract abyss]

yeah and my teacher said it's 18 wat

[upbeat lotus]

Wait

[wraith dagger]

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Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[abstract abyss]

see ugh

[upbeat lotus]

Result in radian

[abstract abyss]

wat is he on

[upbeat lotus]

It is not in degree

I have to use my calculator

[abstract abyss]

nah bro radian is -0.372

[abstract abyss]

not 18 again

[upbeat lotus]

Yeah

Maybe he is wrong

I know what he did wrong

[abstract abyss]

wat

[upbeat lotus]

I was confused too

[abstract abyss]

AH RIGHT

he is just full of mistakes

[upbeat lotus]

Everybody makes mistakes

[upbeat lotus]

18 is right

[abstract abyss]

i don't know wat i need to inverse it for

[upbeat lotus]

You need to inverse it for theta

Like suppose

x=6/15×sin 130°

AND

[abstract abyss]

um 6/15

[upbeat lotus]

$c=\theta$

[wraith dagger]

Arnab Pal

[upbeat lotus]

Oh yeah

So

Sin c=x right

[abstract abyss]

yes

[upbeat lotus]

Here

And if you want to take out the c

so you have to move the sin to the RHS

RHS = right hand side

When you will do that

[abstract abyss]

alright so x/c

[upbeat lotus]

No no you don't have to move the c

[abstract abyss]

c = sin/x sry

[upbeat lotus]

You have to move sin

[abstract abyss]

x/sin

[upbeat lotus]

Not sin/x

[upbeat lotus]

Yeah but we don't write sine function like this

We use ^-1

For sin

Or any other Trigonometric functions

So

$sin^{-1}(x)$

[wraith dagger]

Arnab Pal

[upbeat lotus]

Inverse Trigonometry is another level of thing

[abstract abyss]

right so to got sin u just need to divide by theta

[upbeat lotus]

You got inverse sin you got theta

And you don't need anything else

[abstract abyss]

so theta is sin^-1(x) ?

trigonometry is well confusing

[upbeat lotus]

Yeah

[upbeat lotus]

Maybe

[upbeat lotus]

But not more than "her"

[abstract abyss]

so true my friend

[upbeat lotus]

🥲

[abstract abyss]

ty so much bye

[upbeat lotus]

Bye

,w plot x^2 + {y -3/4(x^2)^(1/3)}^2 < 1×1

[wraith dagger]

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[abstract abyss]

.close

[cedar kiln]

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[zenith fiber]

Hey, so I had more of a quick question. This isn't specifically to this picture but whenever a set is defined like this I don't really get why it's written in this format. Could someone explain it?

[zenith fiber]

Another example would be

A = {x | x is every positive integer}

don't really get the x | x

part

[crimson sedge]

the line means "such that"

so "all x such that x is in A or x is in B"

[zenith fiber]

What does all x mean?

[crimson sedge]

https://en.wikipedia.org/wiki/Set-builder_notation#Sets_defined_by_a_predicate

[crimson sedge]

its a placeholder variable

here its an element of either A or B

[zenith fiber]

Ah

Okay

Thanks

[crimson sedge]

np

[zenith fiber]

.close

[cedar kiln]

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[cedar kiln]

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[royal river]

i need to solve this differential equation with substitution, i feel like i’ve solved it properly but my answer is wrong, i can’t spot my error, can someone please help? i’m lost and exhausted

[royal river]

initial conditions are y(0)=1

p.s. i know it’s seperable but the question asks to solve it with substitution

[hollow kiln]

elalem nelerle ugrasiyo allahim

[cedar kiln]

@royal river Has your question been resolved?

[royal river]

eyv.

[cedar kiln]

@royal river Has your question been resolved?

[cedar kiln]

@royal river Has your question been resolved?

[cedar kiln]

@royal river Has your question been resolved?

[soft owl]

what's the equation ?

[vernal shell]

Hello, do you have the correct answer?

[royal river]

nope

[vernal shell]

Oh I wanted to check my answer, nvm

Substitution method to solve differential equations is what you do in i). Then in ii) you don't have to just use substitution all the time, that's substitution for solving integrals which is not what they mean

Well that's what I think

Otherwise the solution is too tedious, sorry I couldn't follow it 😵‍💫

[cedar kiln]

@royal river Has your question been resolved?

[royal river]

yes, i end up with an annoying integral so i have to do lots of u substitutions, but i’m still using substitution to solve the differential equation

[vernal shell]

I forgot to add that the integral in the fifth line can be solve by partial fractions

I've already checked my answer with wolfram alpha 🤔

[shadow kite]

.reopen

Hi there

I need some guidance on this problem

[dire geode]

Not how this works.

Read #❓how-to-get-help

[cedar kiln]

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[tulip river]

It's asking me to find the value of x for which i have the min and max of the function

[tulip river]

If i do the derivative of the function i find x > -24 as

yet when my teacher does the same he finds x < -24

why is that?

[mental trail]

can you show your work?

[tulip river]

Sure, give me a second

[mental trail]

Be careful, as the derivative of |(x+3)(x-4)| has discontinuity points

[tulip river]

x= -3 and x= +4?

[mental trail]

There are three cases you need to distinguish:
x < -3
-3 < x < 4
4 < x

[tulip river]

Okay, how should i do so?

This is the answer i got from my teacher, i don't understand what he does either

[mental trail]

so, by intuition, since f(x) >= 0, the only minimums you can ever hope to find are f(x) = 0

since f(x) = g(x) for x>4 and x<-3, (and f(x) = -g(x) for -3<x<4), you study g(x) instead

since g(-3) = 0 = g(4), those are the only global minimums you can find

[tulip river]

I see, now its much more clear thank you

[mental trail]

finally, since g'(-24) = 0, -24 is either a local minimum or maximum of g

so in any case, it's gonna be a local maximum for f

[tulip river]

Got it, thank you a lot for the explanation : )

.close

[cedar kiln]

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[cedar kiln]

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[low wagon]

can i show someone in vocal a few analysis 1 exercises i made for training? there's some tricky stuff my teacher put i think i didn't get right

[low wagon]

i have a laptop im using to write exercises on with my pen that's y i'd rather screenshare than send the pics here

to give context it's about the convergence of some series, continuity and derivability

and a limit that i have to do with either taylor or de l'Hopital

im in the 384kbps channel waiting if anyone is up

<@&286206848099549185>

also one thing i just found out is can't screenshare in any voice channel so if u could help me with that tho that'd be awesome

italian real analysis (that's y i wanted to do voice call)

[wraith dagger]

♡LexQa♡

[sacred grail]

i only use log

[sacred grail]

yeah i think we can just use L'H

[sacred grail]

oh the limit doesnt exist?

oh it doesnt

i see

[sacred grail]

actually you dont need the >0

[sacred grail]

oh

ig not equality

[sacred grail]

[ a \textqq{text} b ]

[sacred grail]

[ a \textQQ{text} b ]

[sacred grail]

[ a \textlq{text} b ]

[sacred grail]

[ a \textqr{text} b ]

[low wagon]

.close

[cedar kiln]

Channel closed

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[sacred grail]

[low wagon]

[crimson sedge]

(i swear snow wasnt talking to herself)

[sacred grail]

[cedar kiln]

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[raven sandal]

Directional derivatives - In understand the entire initial solution for the first example, but in the second example, where and why do you need the unit vector in the direction of A

[raven sandal]

Like in this example, we do not use the unit vector

[crimson sedge]

It's because

It already is a unit vector

,w calculate sqrt(1/4 + 3/4)

[wraith dagger]

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[raven sandal]

ohhhhhhhhhhhhhh

right

that makes so much sense

Ok thank you @crimson sedge

[crimson sedge]

Anytime

[raven sandal]

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[toxic flame]

please can I get some help finishing this proof?

[toxic flame]

(Proof: √3 is Irrational)

[wraith dagger]

Max..

[toxic flame]

so suppose m and n are odd?

[random shale]

Your next step is then correct but from there I think there is an easier route.

Our goal is to show both m and n are multiples of 3. Which contradicts that the gcd(m,n)=1

Can you show that m is a multiple of 3?

[toxic flame]

Something using this?

or something like: m has to be a multiple of 3 because of the factor 3^x

[toxic flame]

something like this^?

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[grim lantern]

can someone explain to me how the 5 disappeared in the first line and where did the +1 come from in the second line

[tropic oxide]

t^2 - 5t - 6 = (t+1)(t-6)

it's just factorization

[grim lantern]

aah ok i've never seen it before with logs

thanks

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[marble ermine]

Hello, if $n \geqslant 2$ integer, $f: [1, + \infty[ \mapsto \mathbb{R}$ such as $f_n (x) = x^n - x - 1$; $a_n$ is the solution to $f_n(x) = 0$; what is the limit of $(a_n)_{n}$ ?

[patent cape]

the limit as what approaches what

and wdym (an)n

(a_n)n maybe

[marble ermine]

approach infinity

[wraith dagger]

Max..

[patent cape]

yeah ik that

[random shale]

and yea as n approaches infinity

[crystal raptor]

Probably useful to note that $a_n^n = a_n + 1$

[wraith dagger]

ΣAC

[marble ermine]

really, how so?

[marble ermine]

yes

[crystal raptor]

Why is it true?

[wraith dagger]

lilisworld

[crystal raptor]

Or why is it useful? (I don't know)

[marble ermine]

why is it useful

[crystal raptor]

No idea, but it's the only info you have about an

[marble ermine]

i also know that $(a_n)_n$ is a decreasing sequnce srry i forgot

[wraith dagger]

lilisworld

[marble ermine]

and f_n(x) is an increasing function

(a_n)>1

[crystal raptor]

Well then it's almost certain the limit is 1

[marble ermine]

whyy

[crystal raptor]

Your sequence is decreasing and bounded below by 1

A good guess is 1

Happens to be correct

[marble ermine]

it's bounded by 1 but is it enough to assume

that lim is 1?

[crystal raptor]

Try show 1 is the inf or smth

No needs more work

[marble ermine]

ok so a_n is never 1 for sure

so it's not the min(a_n)

@crystal raptor could u give me a hint

<@&286206848099549185>

[crystal raptor]

.

[marble ermine]

how do i do that

[crystal raptor]

No idea, give it a try

[gleaming cloud]

There can be multiple solutions to f_n(x)=0

[marble ermine]

yes and now we need to prova that these solutions are never smaller than 1

no wait

of course it is but why 1 and not 1.2 for example that's my problem

[crystal raptor]

Domain of fn is restricted

[marble ermine]

i dont get it

<@&286206848099549185>

in order to find the solution of x^n - x - 1 = 0 when n is very big;

that slution is bigger than 1

not bigger than 1.61...

1 < a_n <= 1.61

<@&286206848099549185>

<@&286206848099549185>

[cedar kiln]

@marble ermine Has your question been resolved?

[marble ermine]

@crystal raptor what's the link with this: a_n ^n = a_n + 1 ??

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[oblique lynx]

when i have vectors v,w and metric tensor G, does the metric tensor also applies while calculating the norm such that:

$$\langle\vec{v}|\vec{v}\rangle=\vec{v}^TG\vec{v}$$

[wraith dagger]

marejak023

[oblique lynx]

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[steady fossil]

How would I calculate the cartesian equation of a plane through the point (2,3,1), when the plane is equidistant/the same distance from the 3 points (1,3,5) (1,1,1) and (3,1,3)?

[cedar kiln]

@steady fossil Has your question been resolved?

[dull oxide]

Do you know vectors at all?

[steady fossil]

yes

Its the last exercise of my chapter, I just cant find the solution

[dull oxide]

If the plane is equidistant from 3 points, then the plane is parallel to the plane described by those 3 points

[steady fossil]

ah, I get it now ty

it means they have the same direction vector right @dull oxide ?

[dull oxide]

the two planes?

[steady fossil]

ye

[dull oxide]

They have the same normal vector

(or antiparallel)

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[cedar kiln]

@plucky holly Has your question been resolved?

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[sand cradle]

When we want the Taylor expansion of $\ln(1 + \frac{1}{x})$, we can substitute $u = \frac{1}{x}$, then take the Taylor expansion of $\ln(1 + u) = u - u²/2 + u³/3 - ...$ and substitute back $\frac{1}{x}$.

Why are we allowed to do that? We are taking derivatives to get the Taylor expansion, and

$f(x) = \frac{1}{x} + \frac{1}{x^2} = u + u^2$ for $u = \frac{1}{x}$, then $f'(x) = 1 + 2u = 1 + \frac{2}{x}$, but that is not correct

[sacred grail]

that's not a taylor expansion ...

that's a laurent expansion

[sand cradle]

It's the Taylor expansion at a = 0, so the Maclaurin series

[sacred grail]

there isn't one for ln(1 + 1/x)

it's a singularity

[sand cradle]

There is no Maclaurin series for that, yes, there are Taylor series for it though, where a is not equal to 0

[sacred grail]

then why are you saying a = 0

[sand cradle]

For ln(1 + u) = u - u²/2 + u³/3 - ..., that is the Maclaurin series, so the Taylor expansion at a = 0

[sand cradle]

By substituting 1/x = u, we can get the Taylor series of ln(1 + 1/x) at a = infinity, but my question is, why is that allowed?

$f(x) = \frac{1}{x} + \frac{1}{x^2} = u + u^2$ for $u = \frac{1}{x}$, then $f'(x) = 1 + 2u = 1 + \frac{2}{x}$, but that is not correct

When finding the Maclaurin series of ln(1 + u), we are taking derivatives too

And substituting back in the end is still valid, but why?

[sacred grail]

it should read f'(u) not f'(x)

the expansions for these functions are usually unique

so you can find them in whatever fashion you'd like

you're guaranteed by uniqueness to get the same result

[sand cradle]

Thanks

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[crimson sedge]

Need a bit of help with d

Don't know where to start

[ionic finch]

The first step is to understand your function f and g

[crimson sedge]

Okay

[ionic finch]

given here is f and g as a set of ordered pairs

where the ordered pair (a,b) can be viewed as an input, output pair

so, if you want to evaluate f(18), by definition of the function it's f(18)=-12

because (18,-12) is an element of the set f

[crimson sedge]

Right

[ionic finch]

so when you have an inverse function by definition, you have the output of the function f and you are tracing back to it's input

i'm wording it in a way that it gives intuition first

or say f(18)=-12

f^-1(12) means, for what output of f does the input is 12

so clearly we can refer the ordered pair for it's mapping

[crimson sedge]

Yeah

[ionic finch]

if f(18)=-12 then f^-1(12)=18

[crimson sedge]

Yeah that's the inverse

[ionic finch]

inverse function is the mapping from the set of outputs of function f to it's input

[crimson sedge]

Oh right now I see what your saying

[ionic finch]

Great, so I think you have a start now

[crimson sedge]

77 is a pair

And 1 is a pair too

[ionic finch]

so clearly now you can figure out f^-1(77)

[crimson sedge]

It's 23

[ionic finch]

right

so for the other one?

[crimson sedge]

1 has 2 yvalues

Oh wait nvm

[ionic finch]

Think about it

[crimson sedge]

It's 3

So 26 would be the answer

[ionic finch]

Just a point, if you have two inputs mapping to single output, then the inverse will not exist

because it breaks the condition of being a function when considering f^-1

the first condition is that all the inputs must have distinct, unique ouput

[crimson sedge]

Yeah, i first thought I'd have to sub in 77 for every x value and solve

[ionic finch]

or for inverse to exist for f, f must be a bijection

[crimson sedge]

But I figured that wouldn't make sense

[ionic finch]

Great

[crimson sedge]

I guess there's a way for everything

Thank you

[ionic finch]

Good job.

[crimson sedge]

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[dull dawn]

,rotate

[dull dawn]

you can use the Pythagorean theorem to find the hypotenuse of the triangle

and to find the distance, you can add up the two streets

[wraith dagger]

FinnaganFox

[dull dawn]

this is for helping, instead of doing the work for you

[cerulean sail]

In particular, how comes the friend can't make the post here themselves?

[obsidian coral]

No

[obsidian coral]

.

Right there

Have you ever seen that equation?

That's a geometry related equation

So you're saying you haven't done geometry?

No one is here to do work for others

Also, why are you asking for help for another person? If it's their work, they should be the one to do it

you can use the Pythagorean theorem to find the hypotenuse of the triangle
and to find the distance, you can add up the two streets

That's what you need

With that

[obsidian coral]

If you don't recall Pythagorean theorem, then two things, either look up videos or don't do the work for other people and let them do it on their own

They are going to learn if you do their work

[dull dawn]

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

[obsidian coral]

Then the real question is, how can you teach it to someone else if you don't know it yourself?

[dull dawn]

this video can teach it to you, these channels are more for helping with specific problems

[dire geode]

Sounds like you teaching but with extra steps

[obsidian coral]

Then look up other videos

We're not google

[dire geode]

You watched the entire video in 2 minutes?

[obsidian coral]

You have fingers and a wifi, you can look up Pythagorean theorem

[dire geode]

Explain why then

Just saying you don't understand doesn't explain anything

[obsidian coral]

That's other videos, key word other. Maybe this video will help

[dire geode]

If you can't explain why you're lost then how do you expect people to help

Did you tho

[obsidian coral]

It's a 10 minute video, I literally just scrolled through it and it explains it really well

And is not complicated at all

And pretty neat

It's "complicated" due to the fact you don't know what Pythagorean theorem is in the first place

[crystal raptor]

Just get your friend to ask on here themself

[obsidian coral]

So if you, yourself, can't recognize those terms, then you're going to have trouble yourself

Hence why the video would help you understand it

You don't understand it due to the fact you don't know what Pythagorean theorem is in the first place

So back to this statement

If you don't recall Pythagorean theorem, then two things, either look up videos or don't do the work for other people and let them do it on their own

The video explains it

[dull dawn]

^

[obsidian coral]

.

No

Then look up other videos
We're not google

You didn't look hard enough

https://www.mathsisfun.com/pythagoras.html

https://www.khanacademy.org/math/algebra-basics/alg-basics-equations-and-geometry/alg-basics-pythagorean-theorem/v/pythagorean-theorem

https://www.youtube.com/watch?v=d8EA5TxGzcY&ab_channel=TheOrganicChemistryTutor

https://www.youtube.com/watch?v=OHRT7YfoemI&ab_channel=2MinuteClassroom

Literally multiple resources I just provide using google

[dull dawn]

what

pftt if your going to harrass me im going to block you

im sorry, but I cannot help you any further, please dont contact me further.

[obsidian coral]

<@&268886789983436800>

[peak relic]

ty!

b&

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[dull dawn]

thank you!

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[dire geode]

Don't use help channels for this

.close

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[lusty grotto]

,rotate

[crystal raptor]

.reopen

[cedar kiln]

✅

[crystal raptor]

Are you the other guys friend?

9A, most likely you're them again

Well you've just sent the exact same question so don't feign ignorance

Unlikely

[dire geode]

Wow such insight

[lusty grotto]

u didnt have to repost the quesion then

[crystal raptor]

<@&268886789983436800> possibly ban evasion?

[peak relic]

Lol

[peak relic]

it's actually the same question, huh?

cute

[dire geode]

"just cuz I'm black"

[peak relic]

let's not even get into that one

[dire geode]

Ty ryc

[crystal raptor]

Ty ty

They'll be back I'm sure

[peak relic]

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[blissful pagoda]

Hi guys. I'm a bit unsure about eigenvectors and how to determine them.

[signal yoke]

So for your matrix A, an eigenvector v will be a vector such that Av = λv for some scalar λ

From this definition & what the question's asking, would you have ideas about how to proceed?

[blissful pagoda]

Would we substitute what we know into the formula and solve for the Scalar?

[signal yoke]

Well the idea is you test whether for each of these vectors v, Av returns a scalar multiple of v

So you'd try A times each of these vectors and see which outputs a scalar multiple of the vector in question

[blissful pagoda]

I see

Should we know what the scalar multiple is?

Or would any constant it spits out work?

(Constant which is a multiple of the vector)

Or should I find λ given a vector

Oh hang on I've worked it out

Using the characteristic polynomial, it says it on the bottom there

Thank you for the kickstart tho!!

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[vivid cargo]

i dont really understand why she shaded the left, like what was the reason to do so, and what does it mean to “shade above” or to “shade below”

[crimson sedge]

You want the region where y≥7x+4, so you take the line y=7x+4 and shade the region above that line (you could get confused if you say right/left, it's better to say above/below) since you have to find where the y is greater than or equal to that expression

Every point that is above that line satisfies the condition

Because taking a point above that line is like taking a point which has the same x as one of the points of that line, but has a greater y

[vivid cargo]

So being “above the line” would mean to shade where though

Thats what I dont get

because its not really “above” the line

[crimson sedge]

If the line was less steep you would get it

Try imagining a line that's almost horizontal, there you can distinguish better between above and below

[vivid cargo]

ohhh okay, i see

[crimson sedge]

Here the line is steeper but the concept is the same

[vivid cargo]

?

if so, yeah, that does make more sense

[fast sundial]

mx = gradient, b = initial value

all you need to know

[vivid cargo]

oh no, im not confused about the graphing

[fast sundial]

initial meaning when the line touches the y coordinate when x is 0

[vivid cargo]

just the above and below part

[fast sundial]

wym

[vivid cargo]

she said to shade either “above” the line

or “below” the line

[fast sundial]

yea so according to English above = up

so yes, your annotations are correct

[vivid cargo]

Okay, Thank you ❤️

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[hollow sleet]

hel

[hollow sleet]

mensuration problem

pls help me with this

[tropic oxide]

,rccw

[tropic oxide]

1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

which stage are you on?

||this problem, taken at face value, contradicts itself. if MNOPQR really was a regular hexagon, then NQ would be exactly twice as long as OP, but it is explicitly stated not to!||

@hollow sleet

[hollow sleet]

I am not on any stage

[hollow sleet]

chapter is about trapeziums

[tropic oxide]

by "stage" i mean "one of the 6 items on the list i just posted"

i.e. how far along you are with solving the problem

[hollow sleet]

1

[tropic oxide]

okay

right

yeah, then the first step would be to point out the self-contradiction in this problem.

i'd skip it outright and tell your teacher that the problem is screwed up.

[hollow sleet]

I have bought a book to practice so i am teacher 😂

[clear berry]

I think the point of regularity was that the two triangles were supposed to have equal sides and hence equal area

[tropic oxide]

well, then you should have no qualms with skipping the problem @hollow sleet

[tropic oxide]

i don't think a hexagon that isn't regular should ever be called regular.

if triangles MNO and RQP were supposed to be congruent, then the problem should've stated that outright, or provided us with the data necessary to conclude it.

[clear berry]

True, ture they could have explicitly mentioned if this were the case

[fast sundial]

Alright.. so evidently the problem is messed up

[cedar kiln]

@hollow sleet Has your question been resolved?

[hollow sleet]

it is 8th class problem

[slow sphinx]

Well according to the contradiction you are right an NQ should be 26 cm instead of 23 cm. Then whatever you can correct it since you are a teacher and at sometimes people do make mistakes when typing

[undone sage]

The given question is correct

And easy

[wraith crypt]

And some questions are just wrong, like this one

Take it from us and change the question so it has accurate phrasing if you're giving it to students

[undone sage]

What is wrong here please make some effort to explain

[wraith crypt]

A regular hexagon cannot have the lengths as stated

[undone sage]

On what basis you are saying please explain that too

[wraith crypt]

Because all internal angles are 120 degrees, drawing a vertical NQ intersecting MO at a point (call it A) means that triangle MNA is a 30-60-90 triangle

This implies NA is precisely half of MN

But the same argument can be done for the bottom triangle, which means NQ must be twice of any edge length, so twice of MR

[undone sage]

lol you wrote this much

Just came let me read

[undone sage]

I see you joined NQ it intersects MO at A, how is MNA 30-60-90, i get that angle NMA= 30 but how did you conclude the others?

As 60,90

Is NA perpendicular to MO

If yes then prove it beforehand

[wraith crypt]

it has to bisect MNO, standard property for regular hexagons

[cedar kiln]

@hollow sleet Has your question been resolved?

[undone sage]

Yes you are correct i didn't check that I calculated it earlier the area and it matched with the answer ,by basics of congruency and Pythagoras. When i see now yes it's incorrect sin theta =5/12 (theta=MNA in your case), it should be 1/2

[cedar kiln]

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[meager glade]

If i sqrt 4p^4 it would be 2p^2 right?

[ebon burrow]

yes

[meager glade]

thanks!

.close

[cedar kiln]

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[hollow sleet]

no

[cedar kiln]

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[crimson sedge]

good morning, i've a question
How can i proof that the graphs 0!/(x! * (-x)!) and sin(pi * x)/(pi * x) have the same graphics?

[tropic oxide]

rewrite 1/(x! (-x)!) in terms of the Gamma function and apply the gamma reflection formula

[earnest socket]

what is (-x)!

need gamma function

[crimson sedge]

i was thinking in something about prod

because in some place i've seen a sin definition using this

[ebon burrow]

Yk what. a sin graph looks like

[crimson sedge]

i'll try this

ty

.close

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[rose dragon]

the quistion is to intergrate using cylindrical coardinates i understand how this is done but i dont know how to get the lower and upper bounds for dr d_theta

[cedar kiln]

@rose dragon Has your question been resolved?

[rose dragon]

<@&286206848099549185>

[rose dragon]

.close

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[tender cobalt]

claimed

[tender cobalt]

How do i take the inverse laplace of this?

I know the answer but just not how to get there

[crystal raptor]

Use a table of transforms

[tender cobalt]

Highlighted prt is what i dont understand

[crystal raptor]

They've times by 1=3/3 to make it look like a familiar transform

[tender cobalt]

how do you know to do this?

[crystal raptor]

You look at your table and see which it's most similar to and then get it in the right form

[tender cobalt]

Yeah i see that is sin(at), What i'm trying to say is how do i step by step change 1/s^2+9 into 1/3*3/s^2+3^2

[crystal raptor]

Times by 3/3

[tender cobalt]

All of it? some of it?

[crystal raptor]

The whole thing

$x = 1\cdot x = \frac33 \cdot x = \frac13 \cdot 3x$

[wraith dagger]

ΣAC

[crystal raptor]

Replace x with whatever you want

[tender cobalt]

that helps abit thanks

Like this then?

[cedar kiln]

@tender cobalt Has your question been resolved?

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[dreamy fern]

how can i solve this

[inner glacier]

Have you done any working?

[dreamy fern]

i did

just a second

[inner glacier]

Can you please send it if possible

Right

[ebon burrow]

I can show you step by step with drawing

but i wont do it for you

[obsidian coral]

Step by step is still doing it

[ebon burrow]

no

[undone sage]

sec(x-y)=1/cos(x-y)

[ebon burrow]

no not show anything

[undone sage]

Now solve further by yourself

[ebon burrow]

just instruction one at a time

[dreamy fern]

idk what else to do

[ebon burrow]

ill give you 1 step but you do it ]

[dreamy fern]

ok

[ebon burrow]

show me it and if its correct we go next step if it aint ill tell you where you went wrong

[brisk dirge]

[dreamy fern]

show u what ?

[spark widget]

HELLO

[inner glacier]

Hint: can we divide and multiply with something?

[crimson sedge]

ayyyo

[ebon burrow]

ill give you the step

then you do what it says

and see if you do it correctly

[inner glacier]

Both numerator and denominator

[spark widget]

1+1=11?

[dreamy fern]

idk

[obsidian coral]

Don't troll

[dreamy fern]

ok give me the step

[spark widget]

oki xc

[ebon burrow]

so try get the L.H.S and R.H.S to = a number

[inner glacier]

what should you divide sinx siny to make tanx tany?

[ebon burrow]

lets do 2

Make the L.H.S and R.H.S = 2

[dreamy fern]

dude thats what im trying to do

[ebon burrow]

by giving x and y a value

[frosty ocean]

Just divide the numerator and denominator by cos(x).cos(y)

[undone sage]

Think of dividing by some term here

[inner glacier]

.

[undone sage]

Nicely spitted

[ebon burrow]

sec(?) = 2

[dreamy fern]

we can divide it by cos x cos y

[undone sage]

At least give a chance boi

Don't spit out

[inner glacier]

Yes

[undone sage]

Control ur urges

[dreamy fern]

nah we cant do that

[inner glacier]

So multiply the num and den by 1/cos x cos y

And see what is happening

[ebon burrow]

bear you finished the question

bc i wanna show you my solution

[dreamy fern]

i tried that

[inner glacier]

Show it please

Send the working

[ebon burrow]

bear

you can i see the way you done it

and compare it to me

mine

[inner glacier]

I feel the best way is to multiply lhs and rhs by 0

0=0

[ebon burrow]

i gac

[inner glacier]

Hence proved

[undone sage]

Just try what he said here

[ebon burrow]

i made it so x has a vakue

so the LHS and RHS = 2

[undone sage]

No shit sherlock

[ebon burrow]

bc sec(30) = 1

so i gave x the value 30