help-19

[white stirrup]

Ohh

Ok got the 90 what about 180k

[wooden python]

cot is periodic and its period is 180°

[white stirrup]

Ok

What do I do then

[wooden python]

well you know cot(θ+180°) = cot(θ) no matter what theta is right

[white stirrup]

Yes

[wooden python]

so any solution of cot(theta)=c gives rise to an infinite family of solutions spaced 180° apart

[white stirrup]

And how do I get 135

Considering tan is positive

[wooden python]

since when is tan positive?

[white stirrup]

I only get 135 by using (180-theta) but we use this when only sin is positive

[white stirrup]

According to equation?

[wooden python]

how does the equation imply tan(1x)>0?

[white stirrup]

Idk I assumed

[wooden python]

ok so you pulled it out of nowhere

put it back where it belongs (throw it out)

[white stirrup]

But how is tan negative then

[wooden python]

tan(1x) can do whatever it wants

it is not involved in the equation

[white stirrup]

How come 135 is a solution

Please explain

[wanton bison]

cos(2(135°)) = cos(270°) = -cos(270°-180°) = -cos(90°) = 0

[odd edge]

@white stirrup Has your question been resolved?

[white stirrup]

Why tan is negative then

[wanton bison]

i dont get the tan positive/negative thing you are asking

when you want to see when a quotient gets 0 then you look when the numerator becomes 0 (and exclude solutions that would cause the denominator go 0); in math: a/b = 0 where b != 0 implies a = 0

cos(2x) = 0 can be solved simply, in case of doubt you can do a substitution u = 2x which brings u back to cos(u) = 0

[odd edge]

@white stirrup Has your question been resolved?

[odd edge]

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[cold phoenix]

hi can anyone help me with this please

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[magic palm]

2236

[magic palm]

Give an example of a quadratic function of the formula y=ax^2+bx+c that never intersects the graph of y=f(x)

[hollow widget]

never intersects what?

x axis? y axis? both?

it will intersect y axis

[magic palm]

uh

[hollow widget]

so i presume u mean the x axis

[magic palm]

at the top it says

The figure shows the graph to the function
y=f(x) where f(x)=x^2-4

I don't understand anything in this question tbh

[hollow widget]

this is the question?

[magic palm]

yea

[hollow widget]

ohh

[magic palm]

Might've missed something

[hollow widget]

okay so you have f(x)

you want it such that the quadratic function y never has a solution to f(x)

[magic palm]

yeah

[hollow widget]

so you do ax^2+bx+c = x^2-4 but you dont want solutions to these so you do discriminant<0

[magic palm]

uh

[hollow widget]

you get (a-1)x^2+bx+c+4 = 0

right?

if you take the RHS to the LHS

[magic palm]

ok wait

why do we want it smaller than 0

[hollow widget]

have you learnt the discriminant?

[lethal spoke]

I don't think a graph obtained by shifting f(x) upwards or downwards will intersect it

[magic palm]

I don't know

Can you give an example

[hollow widget]

do you know the quadratic formula

the -b+-...

[magic palm]

yes

I'm aware of it

[hollow widget]

now there is a square root term yeah

√b^2-4ac

[magic palm]

yes

[hollow widget]

if the b^2-4ac is negative, no real solution exists

because √x for x<0 is not real

[hollow widget]

so here, you take the b^2-4ac (coefficients) and set it less than 0

you get all possible y that never intersect with f(x)

[magic palm]

yea

ok so

we set the coefficient to negative?

as far as i've came there are no real solutions to sqrt -x

[hollow widget]

in this equation, what is a,b,c coefficients?

[magic palm]

huh wdym

idk the value of any of them

[hollow widget]

lets take for example
3x^2+4x+4
what are the coefficients?

[magic palm]

3

and 4

ohh

so it's those with x's in them?

[scenic plover]

Hii, i just joined maybe I can try give a help

[magic palm]

Go for it

[hollow widget]

so a,b,c are 3, 4, and 4

the coefficients of the quadratic

[scenic plover]

Ok so, generally those type of formulas are "generalized" formula which describes a BIG range of different functions.
Depending on the coefficients you put you get different functions

[magic palm]

I see

[scenic plover]

So it wouldn't make sense to write ax^2 + bx + c +d = 0 because the coefficient "c" and the coefficient "d" already describe the same things, which is a number (Real in this case I guess) without any variable attached

[magic palm]

yea I understand that

[scenic plover]

So each coefficient has its role in this type of function, this set of functions are called "quadratic" because you have the x^2

I think the best way to "see that" is opening up something like geogebra and play with it

[hollow widget]

try calculating the discriminant of the quadratic
(b^2-4ac)

[scenic plover]

Literally write the function with the coefficients, geogebra will let you play changing those coefficients and you will see what happen to the function

[magic palm]

is this for solving?

[scenic plover]

You will also intuitively understand when a function won't intersect with the graph of y= f(x) if f(x) is easy

[scenic plover]

I mean, it's for understanding this concept of math, so yeah it is in part for solving

[magic palm]

I've always had troubles with graphs

[scenic plover]

https://www.geogebra.org/graphing?lang=it

Go here

change the language sorry to yours, it was mine italian now

Then literally write this: ax^2 + bx + c = 0

[magic palm]

Do yk how to do this on a graphic calculator

[scenic plover]

You have a phone no?

You can install geogebra is the same

[magic palm]

yeah

[scenic plover]

Trust me, when you will play a bit with the coefficients everything will become easier

[magic palm]

Ok I've used geogebra like twice

[scenic plover]

Imagining the functions on the graph is always what helped me the most and also where i got the better intuitions

[magic palm]

What do I do

[scenic plover]

It's easy, there is just a cursor and you can change the values

You should have something like this no?

Choose a value for each coefficient and then try change them

[magic palm]

there's a box on mine

Where I can write

[scenic plover]

A box ?💀

[scenic plover]

that is right

Can't you see the graph?

You should be able to see this:

Btw you should do the same also with the first question

I mean this one

Try draw your f(x) = x^2 - 4 and then start creating functions

[magic palm]

I do

[scenic plover]

Try get help from chatGpt or any good AI, it's like having a professor next to you.
Don't ask him for the direct solution, ask him questions like "tell me an intuitive way to understand graphs / how do i intuitively answer this question?

[magic palm]

nothing seems to change when i remove bx and c

[scenic plover]

Can you play with it?
You will see that adding a higher value in coefficient "c" will just move the function up

[magic palm]

why's that

[scenic plover]

If you have b and c equal to 0 then it's normal

try put something different than b=0 and c=0

[scenic plover]

If you can't undestand why it moves it up then ask it literally to chagGpt "Why adding a higher value in coefficient "c" will just move the function up for the function ax^2 + bx + c?"

[magic palm]

how do I do that

[scenic plover]

Here you can move the value "a" you should have the same thing also for b and c

[scenic plover]

like in my photo here

[magic palm]

I only see a

[scenic plover]

You don't have nothing else?

that's strange

Did you install the app or are you on the website

the app is faster generally, maybe that is the problem

Though from the phone I still have the chance to change them all, It shouldn't me a problem of Geogebra

[magic palm]

on the website

on my chromebook

[scenic plover]

this is chatGpt answer btw about the "c" coefficient

@magic palm

https://www.geogebra.org/graphing/chv56mmv

Try click this link

I have to go now, but my advice is:

• Play with graphs
• You will probably come up with some questions on why the graph behaves like that when you change the values (if you don't then force yourself to make questions)
• Ask chatGpt the questions
• Ask again what you didn't understand
• ASK ASK ASK and understand and then ask again

Then you will feel like a pro and you will feel rewarded

that's math for me

Good luck 👍🏼

[magic palm]

thanks

i really appreciate it

[scenic plover]

👋🏼 💜

you play valorant btw

Hope on if you want sometimes xD

lillo24#lillo

I am here as well trying to understand deepfully complex numbers, we are not very far from each other

[magic palm]

Barely hop on nowadays but if I do forsure

thanks

@golden rock

[odd edge]

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[merry dagger]

Is this how we know k exists?

More: does anyone know why we use k as the convention?

[quasi sparrow]

that's the meaning of "varies directly"

it's just a matter of interpreting the words to math

k is not universal. sometimes c is also used

your teacher just chose k for you

[merry dagger]

.close

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[proper maple]

calculate the limit for {a_n} in each case

theoretically these should be easy since i've done calc 1

and while these are successions

they are similar to limits

i'm just having a hard time honestly

i was never good with limits, at any rate

[amber schooner]

which one

[proper maple]

just starting

so

1 i guess

multiply both by n + 1/n+1?

maybe

[amber schooner]

no

please don’t

split it

$\frac{n}{n+1} - \frac{n+1}{n} = \frac{n+1 - 1}{n+1} - \frac{n+ 1}{n}$

[clever fjord]

knief

[amber schooner]

split both of them

@proper maple

[proper maple]

yup sorry

[amber schooner]

do you understand

[proper maple]

i'm on it

kind of. i'm trying to work it out

[amber schooner]

do you get what i mean by split the fraction

[proper maple]

but i do understand how you "break it down" until you reach either lim = 0 or something you can work with

[proper maple]

yes

for instance n+1/n is n/n + 1/n

so 1 + 1/n

ohhh

okay

[amber schooner]

mhm

👍🏻

[proper maple]

hm

i don't think i quite followed what you were doing

hh

ohh

i see my error

okay

[amber schooner]

$1 - \frac{1}{n+1} - 1 - \frac{1}{n}$

[clever fjord]

knief

[proper maple]

yup

there

thanks!

okay i think i can work the rest out on my own

[proven cape]

Hi

[proper maple]

weird as it might sound this brough me back to a few strategies

cheers mate, thanks

@proven cape hey if you're looking to get help please check #❓how-to-get-help

[proven cape]

🍿

[amber schooner]

you are welcome

[proper maple]

.close

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[proven cape]

🍿🍿🍿🍿🍿

🍿🍿🍿🍿

[amber schooner]

🤔

[proven cape]

🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿

🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿🍿

.open

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[flint cargo]

I need to prove the following identity

[quasi sparrow]

Did you try factoring (1-y^4)

[flint cargo]

im a little lost where to start

[quasi sparrow]

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

[quasi sparrow]

Then y^2 = t to factor this

[quasi sparrow]

Have you learned this before

[flint cargo]

im not sure

[tranquil basin]

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

[flint cargo]

.close

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[royal laurel]

Its 1170 right?

[tepid pelican]

https://www.wolframalpha.com

try this out

use the math input and type in that integral

seems like it's not right btw

[royal laurel]

I will try it

Im confused

I didnt know how to use this app

[royal laurel]

I think its but i want to check if its really correct

[tepid pelican]

https://www.wolframalpha.com/input?i2d=true&i=Integrate[Integrate[\(40)3Power[x%2C2]%2B4Power[y%2C3]-2x%2B5\(41)%2C{x%2C0%2C1}]%2C{y%2C1%2C2}]

seems like it isnt, wolfram says it's 20

maybe show your work

[royal laurel]

Oh im so sorry

The first integration is from 4 to 5 and the second is from 1 to 4

I just swiped between the og question that i solved

[odd edge]

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[olive sleet]

Hi, guys, can somebody explain to me how this is wrong? It’s for an undergraduate Trigonometry class, writing out the steps in proofing an identity and stating which rules are used to get to the next step.

[warped urchin]

???????????

it looks right

[forest sky]

maybe it wants you to rewrite tan in the same step?

[olive sleet]

That’s what I’m saying, I wonder if there’s a glitch in the system because I’ve checked this over a million times and everything points me to this ^

Also, I looked at the example it wants me to rewrite tan in the next step. Idk why it’s having me do that, i think it’s easier to just do it all at once

[amber schooner]

it’s not a glitch you just have to do it in one step

[olive sleet]

I tried, and it still tells me it’s wrong 😞

[amber schooner]

just write 1 + sin theta

if cosx(1/cosx) + cosx(sinx/cosx) doesn’t work

[olive sleet]

So here’s an example that it wants me to work off of, just a different problem using the same process.

I did try 1 + sin theta and still telling me the same thing, sigh

[amber schooner]

so cosx(1/cosx) + cosx(sinx/cosx) didn’t work?

[olive sleet]

Unfortunately not, but it looks right? That’s what I got when I wrote it down myself. I’ve checked my notes a million times and I can’t seem to understand, I even tried switching the +/- signs

Maybe I should try refreshing to a different problem and see if I run into the same issue?

OMG it’s because I typed in the wrong identity rule 🤦‍♀️ it was supposed to be “reciprocal” and not “quotient”

Thank you for the help, guys! I appreciated it!!

[odd edge]

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[mystic saffron]

to find the arg of the one on the left

do we do

tan inverse (im/re)

[forest sky]

the argument of the left root (let's say it's z) would satisfy tan(arg(z)) = im(z)/re(z), but you can't solve for the argument using only inverse tangent for angles in the second and third quadrants (i.e. negative real part)

[mystic saffron]

we add pi right?

[forest sky]

yes

[mystic saffron]

wait

so if it was on the 3rd q

we also add pi?

like this

[forest sky]

yes, you would get an angle in the fourth quadrant (negative, between -pi/2 and 0) and adding pi would give you an angle between pi/2 and pi

in the third quadrant you would add pi if you want a positive angle, or subtract pi if you want a negative angle

[mystic saffron]

but here they didnt add pi

[forest sky]

in your example it was in the fourth quadrant so there was no need

[mystic saffron]

ohhh

so

when its on the 2nd

we add pi

and if it was on the 3rd

we also add pi?

[forest sky]

well it depends on whether you want 0 < arg(z) < 2pi, or if you want -pi < arg(z) < pi

if you want the first option then you would add pi, and if you want the second option you would subtract pi

[mystic saffron]

i have no idea what u just said 😭

i want the closest arg from the line of origin

[noble ether]

@forest sky I would like 1 mole of glucose with 20 moles of water please

[mystic saffron]

😭

i dropped chem since 10th grade

[noble ether]

Bro

Chem is good

[forest sky]

they are coterminal (equivalent) angles (just add 2pi to one to get the other), so it's based on convention

[mystic saffron]

so in q3 it would be correct if i did both?

[mystic saffron]

yea that avocado wtv shit

[noble ether]

Do you guys know about the jee advanced examination?

[forest sky]

it's correct to add or subtract pi in either situation. it's always just a matter of what range of angles you want the argument to fall in

[tacit wasp]

!occupied

[odd edge]

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).

[noble ether]

Damn

Ok chief

[mystic saffron]

yea understood thanks

[mystic saffron]

lmao

.close

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[wild trout]

don't know where to start

[wooden python]

a substitution seems promising

[wild trout]

u-substitution?

what would I make u then?

[wooden python]

try u := 3 - 2/v

[wild trout]

plugged it into openAI and this is the response I got

[warped urchin]

!nogpt

[odd edge]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[manic sleet]

that just made ur life harder, indeed (u=3-\frac{2}{v}) appears to be the better substitution to make

[clever fjord]

PajamaMamaLlama

[zinc glacier]

please dont ask us if youre just going to do this

[warped grove]

(modping addressed)

[warped grove]

have you tried the substitution u = 3 - 2/v as ann suggested?

[wooden python]

@wild trout ^

[wild trout]

soo sorry for the late reply had to go afk

[wild trout]

not yet

[warped grove]

Go ahead and try it, let us know if you need help with the process

[wooden python]

also ngl like

[wild trout]

mhm?

[wooden python]

if you don't understand a suggestion someone makes, it's better to ask them (or me in this case) about it instead of running to GPT

it feels a bit disrespectful

[mystic saffron]

he was just too lazy to write i think

then click the picture to show u guys

[wooden python]

keep going. figure out what du/dv is, as you normally would with a sub

[mystic saffron]

when he did the substitution

[wild trout]

I used openAI before I even came here but the solution wasn't making sense to me that's why I came to ask here

[wooden python]

@wild trout are you still here

[wild trout]

ye

[wooden python]

have you done what i said to do

[wild trout]

struggling to get du

how have I been in this class for a whole year and I'm struggling to do this idek anymore

[wooden python]

a YEAR?

might i hazard a guess that you also struggle with derivatives?

[wild trout]

everything Ann

everything

[wooden python]

"everything" all the way down to basic counting and addition...?

like ngl if your struggles run THAT deep then we can't do much except like, direct you to khanacademy

[wooden python]

do you know how to take derivatives in general?

[wild trout]

not that bad

[wild trout]

yeah

but some of them are a bit too confusing for me

[wooden python]

ok

do you know the power rule

[wild trout]

eya

yea*

[wooden python]

$u = 3 - 2v^{-1}$

can you take the derivative of this?

[clever fjord]

Ann

[wild trout]

$u' = 2v^{-2}$

[clever fjord]

Inq

[wild trout]

that's my first time using TeXit lol

[wooden python]

ok

[wild trout]

is that right?

[wooden python]

... yes, it is.

im surprised that you said you were struggling before

[wild trout]

:)

[wooden python]

but now i told you once again to do it

with zero other guidance

and you did it

somehow

[wild trout]

there's something wrong with me man

[wooden python]

so was it really struggles or were you like... paralyzed and unable to articulate it

ok

so du/dv = 2/v^2

do you now see how to put that into your integral to make it entirely in terms of u

if you don't then i would rather you say "no i don't see it" rather than go silent

[wild trout]

but where would I put du/dv?

also aren't I supposed to get dv? or sumn

[wooden python]

there are many ways to do it, but the one that requires the least thinking would be to solve for dv

and then replace the dv in the integral w the thing you get

[wild trout]

I'm confused

[wooden python]

$\dv{u}{v} = \frac{2}{v^2}$
\ \
solve this for $\dd{v}$

[clever fjord]

Ann

[wooden python]

i should probably be hand holding you one step at a time and not trying to coerce you into foresight

[wild trout]

I'm wrong aren't I...

[wooden python]

yes you are

1/du * du/dv would have left you with 1/dv and not just dv on the left

[wild trout]

oh yeah you're right

[wooden python]

by one means or another, you will get $\dd{v} = \frac{v^2}{2} \dd{u}$

[clever fjord]

Ann

[wooden python]

do you understand or do you need to digest it still

[wild trout]

I know this is algebra atp but what do I do 😭

[wooden python]

reciprocal both sides

[mystic saffron]

u need to do the pre-requisites to calculus

[wild trout]

so multiply left side with dv/1 and right side with vsquared du/2

[wooden python]

no

[wild trout]

I'm in AP Claculus rn...

Calculus*

[wooden python]

when i said "reciprocal both sides", i meant "take the reciprocal of both sides"

[wild trout]

can't spell right for shi today

[wooden python]

if you wish, you can pretend i said "raise both sides ^-1"

or even "flip both sides"

[mystic saffron]

yeah i know the feeling, i did the equivalent of AP Calculus back in school for a year. Couldnt learn shit.

[wooden python]

also for future reference: ^ for exponents! write v^2 and not vsquared

i kinda have to go to sleep though

this is taking quite a while

[wild trout]

yfeah dw about me, sleep's important :)

I'll try my best to figure it out

thanks for helping

i give up

[mystic saffron]

bro u need to do pre-requisites first.

for calculus

i am not talking about pre-calc tho

like in the UK math books, calculus is taught at A-Levels and they have these questions for u before each chapter that u must be able to solve before proceeding to sit down and learn that chapter. they are called "pre-requisite knowledge". maybe check out an A-Level Math book, then see if u can do the pre-requisite knowledge questions in the differentiation and integration chapters. and whatever questions u are unable to do, u learn the corresponding topics from a GCSE math book. GCSE exams are done fore A-Level exams

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[ebon oar]

let me show you my teacher's work

@wooden python

[wooden python]

oh yes this is bullshit

[ebon oar]

i see

[wooden python]

inequalities and complex numbers DON'T mix

[ebon oar]

thanks

.close

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[orchid torrent]

Yes

You can also cross check this on desmos

https://www.desmos.com/calculator/qo69azrao6

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[soft wharf]

heloo

[soft wharf]

wait guys I want yall to check my answers

[toxic rose]

okay so send em

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[toxic rose]

back

[toxic rose]

i had an errand to run

so

assume that our non-empty subset is A which is bounded below

therefore there exists some real number -z such that for every x \in A, x >= -z

Now let z' be some other lower bound of A

to prove z' <= -z

[low locust]

dont skip over the entire middle step with B

-z is not the infimum in your new notation

its just some lower bound

[toxic rose]

no i was going to add it now i was just thinking of how to phrase it

[toxic rose]

🤔 what i have to assume one lower bound to be the infimum

let B a subset of R defined as B = {y : y=-x for every x \in A}

[low locust]

wrong quantifier

[toxic rose]

should be a colon?

[low locust]

y cant be -x for every x in A

[toxic rose]

hold up

[toxic rose]

then what should it be?

[low locust]

y = -x for some x in A

in quantifiers:

what you wrote: ${y: \forall x\in A: y=-x}$

correct: ${y: \exists x \in A: y=-x}$

[clever fjord]

Denascite

[toxic rose]

but doesnt the later only consider some elements of A and not all elements of A

[low locust]

or just shortform: {-x: x in A}

[toxic rose]

though i doubt this affects the proof

[toxic rose]

oh dang that is much simpler

[low locust]

the latter means "all y such that there exists some x in A with y=-x". so it does include every possible y you could obtain that way

[low locust]

it doesnt, no. but still important

[toxic rose]

ohhhh i thought its

some y such that ....

anyhow lets continue

so B = {-x : x \in A}

now we know that x >= -z for all x in A

therefore -x <= z for all x in A or y<=z for all y in B

meaning B is bounded above

so B must have a supremum, say -z'

therefore -z'>=y and z>=-z' for all y in B

from the first inequality, since every element y of B can be written as -x for some element x in A, we can conclude z'<=x for all x in A

therefore z' must be a lower bound for A

from the second inequality -z<=z'

therefore z' is the infimum of A

is this finally right?

[low locust]

-z' is the infimum

but yes

[toxic rose]

what why

we want the greatest lower bound

[low locust]

sry, z' is the infimum

your names are confusing

[toxic rose]

again why would z' be the infimum

its a lower bound <= -z

[low locust]

you said -z' is the supremum of B

[toxic rose]

yes

[low locust]

so -(-z') is the infimum of A

[toxic rose]

but i probed otherwise/!?!?

???

oh found the mistake

lemme edit rq

[low locust]

well it doesnt help that I'm kinda reading what I'm expecting instead of whats actually there 🤦

[toxic rose]

should be good now

hllo?

[low locust]

should be good. I think

[toxic rose]

okay thats good enuf for me since i am self-teaching myself anyways

i assume proving this for someone who hasnt done RA is an exercise for them?

[low locust]

its doable as an exercise, sure

[toxic rose]

and also

isnt this MCT

monotone convergence theorem

[low locust]

yes

[toxic rose]

i hope thats a thing

okay alr my memory hasnt failed me completely

[toxic rose]

no am asking should i do it

[low locust]

you can try. I personally would just try to to the exercises. the theorems and their proofs teach you how to think and then you can apply that during the exercises

learning RA requires a new way of thinking and without that you wont be able to do stuff like it

[toxic rose]

theres no proof lol thats why i am asking

[toxic rose]

am doing CA tho~

[low locust]

huh what

oh we are jumping from RA to CA ?

clearly a good idea

[toxic rose]

yes definitely a great idea

[low locust]

not like RA is important

[toxic rose]

yeah 😅 (I m so sorry but i rlly wanna learn contour integration properly >_<)

[low locust]

you cant

not with skipping RA

[toxic rose]

i cant?

[low locust]

not what I would call properly

[toxic rose]

just enuf to solve integrals, is my definition of proper rn lol

[low locust]

how about doing riemann integrals properly first

do solve integrals you dont need to learn any analysis

[toxic rose]

wdym?

[toxic rose]

contour integration comes under ca does it not

[low locust]

computing random integrals isnt analysis

not what I would call analysis anyway

[toxic rose]

no no thats not what i mean

i am going throw howie to learn contour integration mainly

so that i can solve random integrals (dont ask why i would like to do this)

.?

[low locust]

well you do you

but just like, you dont need to learn any analysis for this. throwing around epsilons and supremums and whatnot

[toxic rose]

i dont?

wont i need it later on so that ik what is holomorphic

and convergence and stuff

(altho i do have a fair bit of idea on how to prove convergence using MCT, DCT and others)

[low locust]

I mean yes but so far you have done those things without learning analysis already

just by doing calc

[toxic rose]

wait actually yeah holomorphicity doesnt need this

why did i include that

[low locust]

holomorphic just means differentiable

[toxic rose]

yeah cauchy-riemann equation should be satisfied right

[low locust]

yes

[toxic rose]

so i should jsut move fwd?

[low locust]

I mean you can always go back to the beginning if you are stuck somewhere

but if you just want to learn how to compute random integrals, then things like proving MCT just dont matter

[toxic rose]

okay dang

ty

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[split summit]

Uhhhhhh

[split summit]

How do you even integrate a^logx

Anyway

[tepid pelican]

do you need that?

[split summit]

Do I?

Wait do I just need to integrate a^x

And not a^logx

[tepid pelican]

it might work to rewrite it as a sum, because in this case the graph is just a bunch of rectangles

[split summit]

Yeah true

Wait so

[3/4ln(3/4)]^x

Idk exactly what that is but I’m guessing it’s slightly negative

-0.5 or something idk

[tepid pelican]

what

how did you get that

[split summit]

Because the integral of a^x

Is (a^x)/lna

Right?

[tepid pelican]

what about the floor though?

And the log

[split summit]

What’s the floor

[tepid pelican]

I'd suggest you to actually try to sketch the graph

[split summit]

Wdym by flaw

Floor

[tepid pelican]

the greatest integer function

[split summit]

Not flaw idk why I said that

[split summit]

Oh

[tepid pelican]

try doing this

at least the area between like 1/4 and 2

until you realize how the graph actually looks like

and how can you rewrite the integral as a sum

[split summit]

Oh wait

Yeah you’re right mb

Wait but uh

Log2(x) is gonna get bigger and bigger as it approaches 0

[tepid pelican]

smaller and smaller actually

[split summit]

Oh yeah

That’s what I mean

-2, -3 etc

[tepid pelican]

is it a problem?

there'll be infinitely many rectangles

so the sum will be infinite

[split summit]

Since its (3/4)^log2(x)

Yeah

So if it’s infinity

How would the integral be possible

[tepid pelican]

it's improper integral

[split summit]

The answer is between 1 and 5 not infinity

[split summit]

I still don’t get it

[tepid pelican]

you can integrate e.g. 1/sqrt(x) from 0 to 1

although its technically infinity at 0

its basically the same thing as integrating 1/x^2 from 1 to inf

it's infinite distance, and yet can be integrated

have you tried sketching the graph

[split summit]

It gets bigger and bigger though

Closer and closer to 0

[tepid pelican]

yeah okay

have you sketched it at least for x closer to 2?

at lest for x between 1/4 to 2

ik it gets bigger after that

[split summit]

Yeah I did

But I’m still unsure because of the 0 part of the integration

[tepid pelican]

it should look kinda like this, is that right?

@split summit is that how your graph looks like?

[tepid pelican]

dw about this too much, it will be clear once you rewrite it as a sum

[split summit]

Yes

[tepid pelican]

okay great

notice that it consists of infinitely many rectangles

[split summit]

Yeah

[tepid pelican]

and the integral is just sum of areas of those rectangles

[split summit]

I’m unsure what to do with the left

Yeah ik

[tepid pelican]

start from right

what's the area of the rightmost rectangle?

[split summit]

But I’m still confused because the left side is infinity

What do I do with the left

Ez

It’s e^2ipi

[tepid pelican]

its infinitely high but infinitely thin as well

[split summit]

Aka 1

[tepid pelican]

okay, great

what about the second one from right?

you dont need to calculate it, just tell me the expression

[split summit]

Wait is the y axis root 2 or something

[tepid pelican]

what do you think?

you know the function of which its a graph

you should be able to get the exact number

[split summit]

Wait hold on lemme work that out

Oh

Bruh

It’s 4/3

So 4/6

Is the area

[tepid pelican]

yep, or just 4/3 * 1/2

[split summit]

Right

2/3

So yeah

[tepid pelican]

okay, what about the third one?

Or if you can already generalize, what about the nth one?

[split summit]

16/9

Wait no

Not the area

Hold on

4/9

Wait

[tepid pelican]

yes

[split summit]

Ohhh

[tepid pelican]

can you do this now?

1, 2/3, 4/9

[split summit]

So it’s (2/3)^(n-1) basically

[tepid pelican]

exactly

[split summit]

It’s a geometric series

[tepid pelican]

yep

and even infinite geometric series can have a finite sum

[split summit]

So 1/(1-(2/3))?

Is that the infinite sum for a geometric sequence again

I forgot

Oh okay

[tepid pelican]

yep

a/(1-r) iirc

[split summit]

Yeah

3

The answer is c

Aight tysm

[tepid pelican]

yes

np

[split summit]

I’m done with this paper

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[hollow bluff]

i need help on why does it start and finish at the same height

[quasi sparrow]

plug in t=0 and t=30 into h(t)

[hollow bluff]

i did that already

[quasi sparrow]

and ?

[hollow bluff]

but it finishes at 10

idk why

is it bc it's a loop?

like it starts and ends at the same spot?

[wispy river]

Correct

[quasi sparrow]

what do you mean "but"

yes h(0) = h(30) = 10

[wispy river]

Have you graphed it

[wispy river]

This answers your questions right

[hollow bluff]

i thought there was some technical explanation with physics

[wispy river]

Look at the equation without the + 10 part

0 and 30 are its roots

And since your domain is between them

[quasi sparrow]

yes. roller coasters usually begin and end at the same spot to let the next group of people in

[wispy river]

When you apply vertical transformation of +10 they end at same spot

[quasi sparrow]

so the height wouldn't change from start

[hollow bluff]

i thought there was smth to do with the energy being used for some reason

[quasi sparrow]

sure you can include whatever physics you want

[hollow bluff]

also what would be the best way to describe a dilation

or do i have to make a new thing for a new qs

[wispy river]

Whats your question

[hollow bluff]

how to describe a dilation

the -0.00183

and -0.00122

[wispy river]

The graph is scaled vertically by a factor of _

[hollow bluff]

and like in general

[wispy river]

when sign is negative you can usually say it is reflected about x axis and then scaled by teh magnitude

[hollow bluff]

sign as in the coefficient ?

[wispy river]

yes

[hollow bluff]

how would i say as a gets bigger it gets narrower

in like more mathematical terms

[wispy river]

I think the generally used terms are stretching/ scaling (or compression)

[hollow bluff]

and like with decimals

like as it approaches infinity it becomes narrower?

and how would i say as it gets smaller it becomes wider

because it'll go to negative numbers and just flip

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[edgy ocean]

I don't understand how these cannot be congruent triangles:

[wooden python]

it's not that they can't

it's that they need not be

[orchid torrent]

[https://math.stackexchange.com/questions/1483278/disproving-a-s-sangle-side-side-congruence-condition]

[edgy ocean]

If you expand or shrink the base line it will change the congruent angle.

[turbid comet]

Ssa congruency is unique to right triangles

[wooden python]

no, that's the whole point. it doesn't.

[turbid comet]

not others

[wooden python]

in the diagram @orchid torrent just shared, line AB and angle A are held fixed and line AC/AD is not rotated but just stretched and shrunk

i could probably come up with some concrete numbers to show you SSA congruence like this really can fail

if you want @edgy ocean

[edgy ocean]

I will take your word for it since you are the experts here. I'll just keep studying it. Thank You.

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[torn cobalt]

Greetings,

I am currently preparing for a math exam to get scholarship. I am revising the old exam of 2019.

I struggle to understand how to draw the graphic (I looked on internet how it drawn and copied, but I don’t get how the person drew the graphic) and how to flip the parabola from negative to positive.

[torn cobalt]

I already found the roots for the parabola. However, that’s it…

[quasi sparrow]

yes |x^2 - 3x+2| is always on or above the x axis

true for anything in absolute value bars

|anything| >= 0

[torn cobalt]

Okay. That means the parabola is already positive?

Hmm, I am looking through the video explaining how to solve this problem. The person from the video is searching for ? in ? < k < ?.

[warm roost]

why did you use the quadratic formula? you found roots by factoring

[torn cobalt]

😀 … I am simple-minded. I forgot how to factor. That’s why I used the quadratic formula to find the roots.

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[stoic viper]

how do you go about proving 1

[stoic viper]

i know for 2 its yes but i need help with 1

[sharp oak]

Might help to translate that mess of symbols into your own words

I will use the word "partition". C and D partition B.

[stoic viper]

sure

c and b do not have any elements in common but togehter make B if and only if the inverse of c and d make a and the inverse of c and d is an epty se

theres a partion for the subset of a too ig

@sharp oak

[leaden karma]

Yes

C and D form a partition of B if and only if their preimages form a partition of A

[stoic viper]

so i mean how do i go about proving this mess tho

lets start with the first direction

wait

you just spam the defintion of image and pre image

its easy

[sharp oak]

f is bijective.

That means f is surjective and injective.

Let's start with surjectivity:

[stoic viper]

bro i forgot about that 😭

f is bijective <=> right plus left inverse

can we use that to just spam it

@sharp oak

would that work

Would the fastest way to prove 1 be to say that f is bijective => f has a left and right inverse and then prove the directions by starting with the hypothesis then just apply the definition of left and right inverse.

[sharp oak]

Basically what I'm suggesting yeah, haha

[stoic viper]

shiii W

ok this question is easy

[sharp oak]

Ideally you'll use surjective to get half of *, and injective for the other half

[stoic viper]

ok ok

i mean surjectivity => right inverse

so for 2 its yes correct

[sharp oak]

You might need to define the inverse images and allow them to partition A, then see what f does to them

[stoic viper]

what does htat mean

[sharp oak]

Inverse images are the f-1(C) and f-1(D).

A partition of S is a perfect split of S. Subsets whose union is S, and whose intersection is empty.

[stoic viper]

yes that makes sense

also

how would you even start the proof

you wuoldnt start it like this right, ket x e D and not in C

then blahb lah

[sharp oak]

Assume f is bijective. Show property * holds.
Note property * is an iff, so there's two things to prove there. The forward statement and the backward statement

So, these are the two proofs:
Assume f is bijective. Show the forward direction of * holds.
Assume f is bijective. Show the backward direction of * holds.

[stoic viper]

ye

its more like how do i start the direction

gimme one sec

$\implies$ Assume that $(C \cap D = \emptyset) \land (C \cup D = B)$ holds.

then what I am confused about is how do we begin to apply the defintions of an inverse

[clever fjord]

SushiMan

[stoic viper]

@sharp oak

[odd edge]

@stoic viper Has your question been resolved?

[stoic viper]

<@&286206848099549185>

[neat galleon]

I would begin with what it means for f to be bijective.

And then consider what that means for the inverse elements

[neat galleon]

Basically apply f^-1 to this picture and put that into a proof if that makes sense

Perhaps a proof by contradiction might also help, if that makes more sense to you

Ie assume the left hand side is true. What would it mean, for example, for the union to not equal A and the intersection to be non-empty

I don’t know if you can use this fact @stoic viper but the inverse of a bijection is also bijective

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[shrewd trellis]

hey this is kinda unrelated but how do I improve my hand writing and be more neater in maths

[shrewd trellis]

just want to make it ease for my maths teacher!

[summer grove]

Practice

[shrewd trellis]

I been practicing

[summer grove]

More

[shrewd trellis]

im talking about tips

and tricks

like formatting

[wooden python]

can you show what your handwriting is like right now

[shrewd trellis]

ofcourse ill show some of my previous work

[wooden python]

i could maybe give you a sample equation to write out to look at your handwriting from a mathematical standpoint

[shrewd trellis]

actually sure

i mean my hand writing on paper is probably neater than in ipad

i woudnt say my hand writing is neat but i mean alright

[wooden python]

ok here's a few i'd like you to write on paper:

\begin{itemize}
\item $4{,}602 \cdot 19{,}357 \approx 8.908 \times 10^6$
\item $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
\item $\sin^2(\theta) + \cos^2(\theta) = 1$
\item $\int_0^{2\pi} e^{i\omega t} \dd{t} = 0, \quad \omega \in \bZ \setminus {0}$
\item $\frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)} = 2R$
\end{itemize}

[clever fjord]

Ann

[wooden python]

dont worry about the meaning of any of these if you don't understand them

since we're focusing specifically on handwriting, i want you to just handwrite these out

on paper

and we'll go from there

[shrewd trellis]

ight 1 sec

[wooden python]

good job on setting this goal for yourself in the first place btw

[shrewd trellis]

im prob gonna write neater because that now im aware and cautious

but if i was unaware like in a test

maybe not

[wooden python]

you could send me 2 versions: normal-speed and neater

here are my own renditions of these btw

[shrewd trellis]

thats pretty neat

why is it sending in a file

[wooden python]

maybe it's too big? check the filesize

[shrewd trellis]

ill just a ss of the file

,rotate

[shrewd trellis]

,rotate

[shrewd trellis]

,rotate

[shrewd trellis]

not much difference

[wooden python]

alright

let me take a look now

[tacit wasp]

Both are pretty readable honestly

Probably work a little on writing the number 4, I'd say

[wooden python]

i can see what i think are issues with your $\pi$, $\gamma$, 4 and 7

[clever fjord]

Ann

[wooden python]

vertical spacing is a bit wonky on this fraction here

the -b ± looks like it's floating a bit

this is... not how gamma is supposed to look, lmao.

it's not a y.

it's a loopy kinda thing with the loop pointing downwards

(see my pic)

[shrewd trellis]

so how do i improve these

mistakes

especially the wonkly straight lines

[wooden python]

• start putting a stroke through your sevens
• make your four lean to the right less -- maybe consider writing it with an open top
• fix your shapes for gamma and pi
  these are the immediate fixes i can see

[shrewd trellis]

cuz in a test i prob dont need a ruler as it will just take time

[wooden python]

besides that i wanna say your handwriting is decent as-is

like one GOOD point that i can see is that your equals signs are aligned vertically with fraction bars instead of with numerators

actually heres one more formula i want you to write out:

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{1}{2}x^2 + \frac{1}{6}x^3 + \dots$

[clever fjord]

Ann

[wooden python]

i dont think any of your straight lines are particularly wonky from what ive seen

[shrewd trellis]

start putting a stroke through your sevens
make your four lean to the right less -- maybe consider writing it with an open top

i dont understand these 2

u mean the 7 almost like a T?

except thhe I is more diagnoal from the right side

[shrewd trellis]

also with the infinite symbol, i always just change my page horizontally and write an 8 cuz 99% of time it is just really wonky

@wooden python

,rotate

[strange aspen]

my guy ,rccw to counter-clockwise rotation

[wooden python]

ehh kinda?

look at how i write 4s and 7s

thats what i meant

[wooden python]

ok yeah thats actually very good

your vertical spacing is on point

[strange aspen]

you could try writing the infinity sign from the left instead of right (eaiser for me this way) and try closing that 0
but this is readable

[wooden python]

as for infinity... probably worth just practicing that one over and over

i personally do it by starting at the intersection and going northwest

[shrewd trellis]

so is my 7 incorrect? why is a stroke needed

[wooden python]

i wouldn't say it's incorrect, it just looks nicer with a stroke

[shrewd trellis]

ohhh

[brittle plinth]

7 without a stroke is a sin

[wooden python]

and impossible to mistake for a 1 that way

[shrewd trellis]

true

[ocean bramble]

The problems i see are:
"4" (make sure the top is open so it's more clear)
"1", "2" and "7" (Make sure on 7 you cross the middle so it's extremely clear it's a 7, make sure the 2 is clear and rounded unlike a z)
"z": as with 7, make sure it has the middle crossed
"integers" and "reals": they require the double line.
"gamma": it's not a "y"
"x": i'd recommed 2 straight lines crossed instead of two curved lines, which is easier to fuck up
"multiplication x" use the dot, not the x for multipliciation

[wooden python]

i had him do both so that he's not blindsided if he has to write cartesian product at some point

so that was purposeful

regarding the · vs. ×

[ocean bramble]

fair enough, but that doesnt happen on the "times 10 to the power of"

[shrewd trellis]

my z and 2 are so identical

needa fix that

[ocean bramble]

and that's why you cross the z

[wooden python]

oh yeah speaking of 2 and z

[ocean bramble]

same as you cross the 7 so it cannot be mistaken with a 1

[wooden python]

i'm gonna show my repair strat for that

since i don't usually cross my z's

[brittle plinth]

personally I never cross z

[shrewd trellis]

never heard of crozzing a z before

[brittle plinth]

I just do a little twist at the left of the 2

[ocean bramble]

my z's, and a 2 for comparison

[twilit smelt]

what is that thing on the up right

[ocean bramble]

a z

[brittle plinth]

capital Z

[ocean bramble]

no, that's small

[brittle plinth]

wait what

[brittle plinth]

lmao

[twilit smelt]

Im in shock

[brittle plinth]

same here

[wooden python]

oh actually one more thing overall

[ocean bramble]

i typically only use the top left for "z as a variable" and the top right for "z as text", since the flourish is faster than lifting the pen and crossing it

[wooden python]

make your digits taller than your letters

[ocean bramble]

^THIS. So much this. This makes it so much clearer

[brittle plinth]

seems like we use comma and decimal point differently

[wooden python]

oh i just had an idea

[brittle plinth]

we use comma for the decimal point and the dot to seperate 3 digits

[wooden python]

try this

bit of a handwriting tonguetwister

[shrewd trellis]

,rotate

[wooden python]

,rotate 180

[wooden python]

you forgor the brackets 💔

[brittle plinth]

the 5s

[wooden python]

aside from that though you're looking very good on spacing and sizing

[shrewd trellis]

oh damn the brackets

[brittle plinth]

that g is giving me nightmares ngl