precalculus

[brazen scaffold]

here are some fun questions (not asking for help on these) just putting them out here for fun especially 10

[tired garden]

so obviously, by distribution we get

$$(1-e^{in\theta})(1-e^{-i\theta}) = 1 - e^{in\theta} - e^{-i\theta} + e^{n\theta}$$

[obsidian monolith]

Cozmogrgdfschkipkhrshtensi

[tired garden]

each of these 4 terms correspond to a particular term in the numerator

which terms are you having trouble converting?

[willow skiff]

Read the just putting them out for fun part

Oh wait the prev q

[viscid thistle]

Heya guys, is this the channel for asking questions? Or is there a dedicated channel for that. I havent been on the server for a while 😅

[willow skiff]

If your question is about precaclulus, sure

#❓how-to-get-help otherwise

[viscid thistle]

Yes it is lol

Is it fine to shoot the question?

[willow skiff]

Sure

[viscid thistle]

Alr

So im currently on filling missing info for a sinusoidal function

I have so far y= 7__(2x + π/6)-4 , but i dont know how to determine based off the given equation whether its cos or sin

[willow skiff]

Assume it's cos, then you can just sub in x = 0 and see if the y matches with the graph

[viscid thistle]

So basically
y= 7sin(2x + π/6)-4
Or
y= 7cos(2x + π/6)-4

What if you cant graph?

Im on #10 here. This is the assignment itself

So i mean yeah i can kinda js wing it and put Cos into the function, but I dont know if there's any real way to calculate if its sin/cos without anything but that given equation, yk?

[willow skiff]

Ah you can choose either one I think

Are there any other instructions for that part?

[viscid thistle]

There arent

But my teacher specifically chose Cos

She didnt put cos + sin , so I'm assuming she put 1 answer in, and thats the ONLY acceptable answer

[willow skiff]

Ah it assumes that cos is the base function

[viscid thistle]

I dont remember being told anything about that during notes / discussions tho 😭

[willow skiff]

But there's nothing wrong with sin either, it satisfies all the other boxes

[viscid thistle]

Hm, i see

How come it could be both?

Cz i mean you have the amplitude, omega, phi, B, and the period. Isnt that everything you need to determine if its cos or not?

This is so scuffed 😭

[willow skiff]

Well, the phase shift relative to what?

Relative to a pure sin or cos graph, of course

That's how

[viscid thistle]

Hmm

[willow skiff]

Oh they're using a different form to what I'm using ah

[viscid thistle]

Form?

[willow skiff]

I think that's the less useful form but I see

Yeah like, ax + b vs a(x + b)

[viscid thistle]

Oh i see

Do you wanna see the base equation we use??

If that'd help any

[willow skiff]

Uep

It probably has a cos

[viscid thistle]

Kk

Hmm, in all the other notes, she specified beforehand if it was cos or sin graphs.

This review worksheet, she doesnt say if its sin OR cos. Wth

[willow skiff]

Yeah so I see why now

Like both are fine exactly

That's just one of the possible functions

[viscid thistle]

You're sure i wont get marked if I say sin instead of cos?

We never discussed anything of the sorts where it's fine to use either or 😭

[willow skiff]

Well your job is to understand the concepts

Not to avoid punishment

[viscid thistle]

Thats true

[willow skiff]

Who cares tbh

[viscid thistle]

Ig? Im not tryna do bad on my test tho 😭

And i dont understand the concept which is why i ask. I dont want my lack of understanding to bite me in the ass

[winter comet]

you'd think until you fear your professor's grading methods. . .

☠️

[viscid thistle]

Exactly why i ask 💀

Everyone's telling me both work right..

But my teacher only listed cos

And she never talked about this 😭

American EDU, rahhhh..

I mean based off this convo tho..
(if)Cos/sin = N.A , Ans = Cos

[woeful star]

someone help me on analysing nature

cuz like it's confusing

[limpid hazel]

thats def not precalc

😭

[willow bear]

do you have an actual question to ask

[woeful star]

like the nature of a function

extrema

stationary point

and stuff

what were you thinking

like analysing trees

[willow bear]

ok so you are working with a function and you're having trouble finding its extremum points and where it increases/decreases and whatnot.

[woeful star]

bro this is mah channel

[woeful star]

yeszir

[willow bear]

please don't call me "bro" or "sir".

[woeful star]

ik it's like f'(x)=0 stuff

but like i can't understand the other stuff

like concave

[willow bear]

could you edit those "bro" and "sir" out, please?

also, show the function you're working with at the moment.

[woeful star]

ok

just any function

best is like eulers numbers functions

[ornate vessel]

hello i have a calculus problem...
not differination or intergration but looking what where the period repeats itself...

[woeful star]

like e^x)(x²)

[ornate vessel]

i cannot find it

"Over the next nine months when is Tamara able to go bike riding? ie when is her physical rating at 7 or above (out of 10), AND her emotional at 6 or above (out of 8) for a period of four days?" -> y axis is the monitor (emotional and physical)

[woeful ermine]

Consider the function f(x) = ln(x+sqrt(x^2+1)). The derivative is 1/(sqrt(x²+1)) and the function is continuous. Can I conclude that f is strictly increasing?

I know it is for any finite x, but how about x-->infinity? I'm not sure bcs the derivative is zero

[willow skiff]

that means the function has a horizontal asymptote

regardless, f is still strictly increasing cause f'(x) = 0 has no solutions

[willow skiff]

also you can use the fact that the composition of two increasing functions is increasing

[woeful ermine]

Okay thanks

[willow skiff]

no worries

[warped shuttle]

anyone can help ?

[twin geode]

3

[warped shuttle]

the key says it's 12 but idk how

[twin geode]

what do you got so far

[willow skiff]

that is cursed notation

I know it's $\log_{\sqrt[3] x} 8$ but jeez

[obsidian monolith]

south

[willow skiff]

pay attention to your spacing please with exponents and logs

[twin geode]

yea i was a bit confused

[warped shuttle]

wdym

[willow skiff]

how you've written it

makes it really hard to tell which is the base and which is in the log

[warped shuttle]

ah ok,

how can i find it's min value ?

[willow skiff]

$\frac{3 \log 2}{1/3 \cdot \log x} + \frac{2 \log x}{1/2 \cdot \log 2}$, okay correct so far

[obsidian monolith]

south

[willow skiff]

yeah then you can just let $u = \frac{\log 2}{\log x}$

[obsidian monolith]

south

[willow skiff]

use AM-GM to minimise $9u + \frac{4}{u}$, easy if you know AM-GM already

[obsidian monolith]

south

[willow skiff]

if not learn how it works

oh yeah you need to check that the equality case, 9u = 4/u or ||2/3 = log 2 / log x|| results in x > 1 too, don't forget

[warped shuttle]

like this ?

[willow skiff]

yes

please write your log better

$\log_x 2$

[obsidian monolith]

south

[willow skiff]

do you see the big difference

[warped shuttle]

yes, ok

in our math textbooks is the same way i write it so i am used to that

[willow skiff]

I've never seen that so that's weird

I've seen $C^n_r$ for n choose r before, so I know it does depend on region

[obsidian monolith]

south

[willow skiff]

(usually it's $^nC_r$)

[obsidian monolith]

south

[willow skiff]

but like.... for logs you've got to be kidding me

[warped shuttle]

yea we have this too

[willow skiff]

if that's how 90% of the world writes it

[warped shuttle]

or just

[willow skiff]

which country are you btw?

[warped shuttle]

iran

[willow skiff]

oh no wonder

[willow skiff]

ah that makes sense

[warped shuttle]

lol why

[willow skiff]

something about the writing direction being right-to-left

I've seen really weird maths terminology from Israeli maths students too

the whole Middle East does maths weird, no offense

[willow skiff]

to the point where I can't understand anything

okay maybe their English is not good but like maths was supposed to be universal

[warped shuttle]

i think it's due to the history behind it idk,

[willow skiff]

yeah different developments

I mean if you have old French textbooks then they probably write the same way as everyone else

[warped shuttle]

also the numbers we use are smaller and it's easier to differentiate between each other than english so maybe that's the reason the log is written that way

the original notation

[willow skiff]

omg I have a headache

after reading that

[warped shuttle]

lol it's not that bad

[willow skiff]

I'm so not used to that

that just looks wrong hahahahaha

[warped shuttle]

is this how you would write it ?

[willow skiff]

yep!!

nice job btw

maybe we just needed a little more patience between different cultures

[warped shuttle]

How did you conclude that we need AM-GM to find the range and thus the min value ? It seems quite random

[tired garden]

as with most all techniques, identifying them requires some level of intuition and experience, but a general tip is to try and reverse engineer the idea, which happens to work really well in this particular case

why did am-gm work so well here? because the product when calculating gm eliminated all the variables and became a constant

so basically, whenever you want to optimize an expression where you are adding instead of ideally multiplying

[willow skiff]

if you start with AM-GM that's the first example you'll see

[tired garden]

am-gm does exactly that

[willow skiff]

there's more contrived uses like splitting 2w into 2w/3 + 2w/3 + 2w/3

also the equality case (all terms equal in the AM-GM) gets undermentioned

[warped shuttle]

This was my first interaction to AM-GM

We don’t have AM-GM so i was thinking of maybe using the derivative of the function after we substitute it with u

Yep

[pine geyser]

lol

that type of problem is solved using the inequality a+b/2 >= sqrt(ab)

[warped shuttle]

What’s the matter

[pine geyser]

thats why i asked

[warped shuttle]

We don’t have AM-GM in our math textbooks right ?

That inequality was the first time i was seeing it

[pine geyser]

yes that has been removed

also these questions were usually asked from tajrobies, depending on what u r studying, it might be different

[shadow summit]

whatever this is, i hate it.

[warped shuttle]

Nah i’m in the math-physics group, why would it be asked for that group

[warped shuttle]

Lol

[willow skiff]

it's weird that you don't have AM-GM

pretty common worldwide to varying degrees

[pine geyser]

idk they just do that, i havent seen such a problem in math college exam, but remember that in 12th you will be asked to prove the AM-GM inequality

[pine geyser]

ye exactly

[willow skiff]

wait guys is this for konkour

or is this different

[pine geyser]

yes

[willow skiff]

really?

IDK, well I read the graphic novel Persepolis

[pine geyser]

yes it was asked around 4-5 years ago

[willow skiff]

there it got a brief mention

lmao that's interesting

that's not an insane question for that level

[tired garden]

actually i find AM-GM-HM to be much more important, since HM is used more commonly in day to day imo

[willow skiff]

I've seen all sorts of fucked up shit that gets asked to high schoolers

just for an exam

[pine geyser]

well maybe cuz its not for math students xD

[willow skiff]

JEE is only the tip of the iceberg

[willow skiff]

oh right I see

[tired garden]

wtf south, do you just have random knowledge of every country on the planet

[willow skiff]

I can play 30 anthems on the piano, don't ask me how

[pine geyser]

JEE is way harder than konkur as far as im aware

[tired garden]

peak autism of the best kind

[willow skiff]

but I heard people study like crazy and go to tutoring in Iran

just for konkour, so

[pine geyser]

yes

alot of money are spent

here just to study for the stupid exam

[willow skiff]

this is nice though

[shadow summit]

post the iceberg

[pine geyser]

its basiaclly used to earn money

[willow skiff]

Turkey is the exact same sadly

[willow skiff]

I don't have it

someone needs to make it

[pine geyser]

oh u studying in turkey?

[willow skiff]

and no I'm not Turkish

[shadow summit]

you make it now

[pine geyser]

oh lol

[willow skiff]

have fun figuring out who I am

[pine geyser]

nationless?

lol

[willow skiff]

this is so relatable though

like burning / throwing away textbooks after the exam

[pine geyser]

yeah now i see

beautifull

[willow skiff]

omg literally this is another JEE

[pine geyser]

bruh what are u sending u r not supposed to send stuff like that here

[warped shuttle]

Yea but konkour is basic the materials coverd in the high school which konkour is based is easy,

[pine geyser]

in chill channel

[willow skiff]

I don't know what it says

oh it's not chill

[warped shuttle]

That not jee

[willow skiff]

we're in #precalculus

[pine geyser]

those are the top 10 students

[willow skiff]

knew it

knew it knew it hence I said

[rose mural]

Precalculus is not that hard

[warped shuttle]

Top 10 people in konkour 1392 Science major/group

[willow skiff]

literally means figuratively

lmaooooo

[warped shuttle]

Didn’t see the another word

[rose mural]

I think the only part that is hard is the prove and law of sine, cosine

[willow skiff]

oh there's so much worse in theory

[rose mural]

: O

[warped shuttle]

Where are you getting these lol

[willow skiff]

Google

it's from 2013 idk

http://photo-uploader.blogspot.com/2013/07/konkoor-sarasari-iran-1392-results.html

[pine geyser]

btw you are supposed to solve each math problem in under 1-2 mins

[rose mural]

This is soso, I think

[warped shuttle]

Same as jee i think

[pine geyser]

hmm idk

[willow skiff]

interesting

you think law of sines and cosines is harder

[rose mural]

yES

[willow skiff]

wait you need a VPN to use Discord right

[rose mural]

No, I mean the prove question

[exotic barn]

how are you still not green

[pine geyser]

bruh stop getting information about us lmao

[willow skiff]

ah cause of US sanctions

that's kinda messed up

[pine geyser]

well cuz im alien? im already green i dont need a green name

[willow skiff]

Discord is required under US law not to service Iran

[warped shuttle]

No it’s internal

[willow skiff]

oh hmmm

it's like both, worst of both worlds

[rose mural]

Like this kind of questions, my brain need to run so fast last year

A lot of equations to memorize

[willow skiff]

omg I'm reading so much lore

I did watch that YT documentary about Iran as a country and how the Islamic Republic came to be

came out recently I think

it's fascinating, it's like another China but no one knows about it well

the average Joe at least

[rose mural]

I am from Taiwan

[willow skiff]

ah

[rose mural]

[pine geyser]

thats pretty cool you have alot of info on these things

i was almost crying studying our history last year

[rose mural]

US History is fun

[pine geyser]

thx god its over

[rose mural]

[willow skiff]

ua hok-kien ua thian bo

聼無

[pine geyser]

dayum

[rose mural]

I don't know that language

[willow skiff]

Hokkien? really?

[rose mural]

你好

[willow skiff]

oh you only know guoyu

like most of the younger generation, sadge

[rose mural]

yes

[willow skiff]

Hokkien is like fairly uniquely Taiwanese though

Fujian and malaysia ofc

[rose mural]

I hope China don't attack us

[willow skiff]

but like Taiwan's identity doesn't come from Mandarin

anyways

[rose mural]

[willow skiff]

it was imposed on you guys by the KMT who were just as brutal as the CCP before the 90s

white terror, 228 and shit

I think I've been to the 228 park, xianzai wang ji le

[rose mural]

How do you know all about this

[willow skiff]

well Taiwan and HK are pretty much neighbours

[rose mural]

You are from HK?

[willow skiff]

I think I've exposed my identity

[willow skiff]

correct

[rose mural]

.

[willow skiff]

don't live there now

[willow skiff]

milk tea alliance and whatnot

I mean like culturally and stuff as well

[rose mural]

I know you protested before.

[willow skiff]

lmao. yeah

kinda sucks to look back on it now

we did so twice actually, 2014 and 2019

thanks for the support ig

[rose mural]

At that time, Taiwan media were reporting on it every day.

Do you live in Singapore now?

[willow skiff]

good guess, nah

[rose mural]

Intersting

I remember many HK people immigrated to Singapore

[tired garden]

i recently learned that canto is actually closer to ancient chinese than guoyu, by far

i feel cheated and lied to

[willow skiff]

On average Canto is more conservative

But for instance, Canto has a massive simplification in the initials (loss of palatial vs retroflez distinction as late as the 1930s)

So Canto preserves finals better, such as the plosive stops p/t/k ofc

A lot of people don't really know what they're talking about

It gets mixed in with other myths such as Cantonese lost the vote to be the national language of KMT China by one vote

If you look at the Middle Chinese reconstructions, both differ by quite a bit, increasing with time

[steel kernel]

Why if we take a derivative of a quadratic function, we get its maximum or minimum point?

[river drift]

the maximum and minimum points of any function will occur where the derivative is 0

[arctic dagger]

derivative is slope

[steel kernel]

OHHHH

Yeah

Make sense

[willow skiff]

lol

[loud knot]

people

How do u deal with functions specifically domain/range stuff

[tired garden]

too broad, can you be more specific

[loud knot]

ok like

ur asked to find the range of a composite function

lets say ln(x^2+1)

or like

x + 1 / x - 1

[tired garden]

there is no general method

[loud knot]

fuck

[tired garden]

you have to apply what you know and intuition and then test and verify

but a quite general tip that helps a lot

whenever you have functions composed into each other like your first example

determine the range of the inner function

and thats the domain of the outer function, which will inform the range of the outer function and therefore the function as a whole

go through the layers of the onion

[loud knot]

Oh thats acc quite helpful

[tired garden]

for rational functions like your second example

you are going to need to find asymptotes and minima/maxima

which, in the cases of school problems, probably going to be fairly nice

but they are not necessarily nice in general

[near dove]

Sorry for bad handwriting

[willow skiff]

it's always good to explore what happens yourself

[near dove]

I did, I wanna see what everyone else gets from it

[willow skiff]

however, note that if $\frac{0}{0} = n$, then multiply both sides by $0$ and you get $0 = n \cdot 0$, so any value of $n$ will work

this shows that $\frac{0}{0}$ is not defined (indeterminate)

$\frac{1}{0}$ is also undefined for a completely different reason

[obsidian monolith]

south

[willow skiff]

what you wrote only makes sense to you

I don't know what you mean at all

how are you even adding 2:0 + 1:1

[near dove]

What if that's not an issue, what if it's a feature? 0/0 or 0:0 Is a variable

[willow skiff]

the issue is, a variable doesn't make sense on its own

you need an equation with that variable, say x^2 + 5x + 6 = 0, so that you can eventually know what x is

0/0 isn't even a number

so you can't do any operations on it

the point of a variable is that it represents some unknown number

[near dove]

Exactly, 0/0 is just x and it doesn't have a value until you put it in a formula, I can't accept that you have a number and an operation but you can't perform that operation on that number

"not a number" has never come from an operation on two numbers

[willow skiff]

there's no rule of maths that says that

[willow skiff]

well how about 1/0 then
if 1/0 = n, 1 = 0 * n, which is impossible for every n

[near dove]

But this is the only case where it happens and it just so happens to be something we just can't define, aliens would laugh at us for calling anything "Indeterminate" and then saying it's also not a number

[willow skiff]

so 1/0 cannot equal a number

[near dove]

Unless you define an n such that n*0≠0

[willow skiff]

that's one of the axioms of maths

any number multiplied by zero is zero

[near dove]

And we run the risk of what without that Axiom? It still works with other numbers, you only have to define a single one where it doesn't work like that and the rest of the system barely realizes

[willow skiff]

I am talking about these ones

[willow skiff]

okay but to define it properly, you need to have 0/0 = some number

it can't be all numbers at once

that's not what the equality sign means

[near dove]

Yea and nothing changes, the rules are still there just not for whatever n/0 is

[near dove]

Where does it say that in the rules? x is a number you just don't know what it is yet, when you solve 0/0 and set it equal to x it has a value but you can't know what it is until it's in some formula

[willow skiff]

oh that's a very quantum-mechanics interpretation of mathematics

as in 0/0 is in a superposition of all numbers, well.....

I can't disagree with you then

but then everything in mathematics will change because of what you said

and I think I'll leave it to you to see what happens

[near dove]

now you're getting it, I was hoping I'm not going mad

[willow skiff]

so you'd need some notion of a probability that x is some number

if we just take the real numbers, the sum of all these probabilities has to be 1

[near dove]

I was thinking sort of the same thing, maybe some function that takes the formula and tears the value out, I just don't know alot of probability

[willow skiff]

also yeah we get into infinitesimals again

the probability that 0/0 is some number exactly is 0, cause it's infinitesimally small
but the sum of infinitely many infinitesimals doesn't always need to be 0

yeah okay I just needed to know you were thinking about this probabilistically

then you can use conditional probability (Bayes' rule) to update the probabilities after each event

[near dove]

I'm gonna be taking probability soon and I do intend to continue working on this subject, solving n/0 and 0/0 also solve quite a few undefined values, what I've found is that in many cases just basic Algebra can pull out the value of x in a formula as most of the time performing operations in x follows normal rules like 0x=0 and x/x=1 (idk if that one is always true) I'm honestly really exited to learn more math so I can keep working with this

I've come down to two different answers for n/0 (n≠0) but neither of them are very good and the worst one seems to be the most plausible

[tired garden]

i have a feeling that once you explore these ideas more deeply youre basically just going to reinvent ||limits||

i doubt there are many nonstandard interpretations of this that would be internally consistent

but maybe im wrong

[near dove]

From all I've tested so far (which is arguably not even undergraduate level) it seems consistent enough, but the problem only really stands with the weirdness of having a natural variable and the gender crisis of n/0

[tired garden]

show some of your testing?

to be rigorous, you should figure out exactly what rules of math you are picking and choosing and then explore all of the consequences following those rules rigorously and exactly

[near dove]

It's mostly been informal "evidence" rather than proof, I'd like to learn more complex mathematics before actually pursuing this idea cuz I could be totally and embarrassingly wrong but I can show you some of what I have done so far

[willow skiff]

I think that's a good thing then

like try to convince yourself and justify things through testing things yourself

[orchid snow]

guys who wants to solve hard math

say me

[willow skiff]

then you'll come away with a much deeper impression and appreciation of what centuries of mathematicians have tried to do

of course you have to set some ground rules, like the axioms I suggested

[orchid snow]

?

[willow skiff]

but the truth is no one likes to be told things and be forced to accept them without justification

that's not what being rational or educated would be

[near dove]

I agree, but I also believe that "undefined" isn't a thing and the universe will laugh at us forever because we think math is just a thing we made, I intend to do something called "the big proof" where I just go from the basic axioms and rules of set theory and maybe even lower than that and construct proofs for basically everything from there, ik this has already been done a few times but we still don't have a definitive definition for what a "number" is in our system which I have an issue with but this proof will include Division by zero and a few undefined logs

Like I said in the Initial post It's not really a proof so much as an evidence

[orchid snow]

bruh

anyone gonna solve my question

[near dove]

Uhhh cos(14+1/2)

😁

[willow skiff]

well check the other channel

[orchid snow]

bruh

[willow skiff]

your fault for posting in 3 places at once

[orchid snow]

not 3 places

[willow skiff]

more than that? wow

[tired garden]

well if you want feedback on it, just post it and we'll probably give feedback
"complex mathematics" isn't necessarily entirely needed, depending on what you're trying to do

[near dove]

Well what I'm trying to do has been called impossible and indeterminate so 😭

[tired garden]

spoiler alert, you can't actually construct proofs for everything
when you do go into "complex mathematics", aka proof theory and model theory and such, you'll find out that there exist mathematical statements that are true for which there is no proof of, in some technical sense
as for the undefined thing, it's cool that you're excited about these grand notions regarding math, just don't forget that when you're actually trying to learn and explore you pull it back and work rigorously from the bottom up, stay grounded in concrete notions and rigorous logic, because it's VERY easy to find or make incorrect mathematical proofs that look fine, and a single false step poisons an entire proof in a way that anything false can be proven true

[tired garden]

in the classical sense, but like i said, just decide what your formal rules are and show your steps and work from there

you're trying to create nonstandard mathematics so just pick your rules and just do it

[astral canopy]

Was it a bad idea to take college pre cal as a highschool junior ?

[tired garden]

no?

pre calc is a fairly accelerated route for high school juniors but not so accelerated that it's rare, that's what i did in high school

all of my classmates were pretty much same grade level

if you're feeling that you're struggling on a personal level, then i will say this

[near dove]

Yea yea I've heard godels preachings and I don't follow them, there was something clearly wrong, there must be some set of axioms that are the only ones and that construct the basics of set theory and logic where any true statement could be proven from them unless it itself is an Axiom, that's what axioms are for, I believe this only because if it is false then the universe cannot possible decide what is true or false and there must be a system outside of it which enforces these specific rules and can handle the inconsistencies, but then that system must have one outside of it as well and it keeps going forever

[tired garden]

precalc is a significant jump in difficulty from all of your previous classes because there's a broader mentality shift that isn't usually explained

prior to precalc you've mostly just been dabbling in algebraic manipulations

and while that won't ever go away, that's core to math, you are expected now to think about functions functionally

a lot of the topics in precalc are built upon understanding and working with the properties of functions

start thinking about functions as a "whole", and what happens when you put them together in various ways and what to expect from them

[tired garden]

yeah maybe the details are a bit difficult but that's actually the gist

[astral canopy]

Do you think me doing college calculus 1,2,and 3 all in my senior year (1 in fall, 2 in spring, 3 over summer) would be too much while also interning at Lockie Martin for aerospace engineering?

[tired garden]

this is outside of the scope of this channel but we can actually list an infinitely ever increasingly stronger hierarchy of axioms such that stating the axioms themselves is so difficult as to be near impossible but we know they are there

and they do pronounce objective truth in some sense

[winter comet]

it's possible, do you think you can?

[astral canopy]

I mean it prob won’t be too bad

[tired garden]

no clue about the internship, but i brainfarted earlier, i did precalc in sophomore

this would mean you would need to squeeze calc 1-3 in one year, which is kinda intense

i did calc 1 junior and calc 2 senior

calc 3 there are like a few more prerequisites like linear algebra

i would say to do all of that is significantly harder than doing precalc junior year

i would never tell you don't do it, just be aware that it's a lot

[winter comet]

you need to learn some topics considered linear algebra but its not generally prereq...

[tired garden]

i can tell you this much

[near dove]

What if there was just one that is so powerful that all of the other laws and definitions just pop out, maybe not exactly like that but something similar with no possible contradictions or inconsistencies

[tired garden]

calc 1 is not awful, there's a chunk of theory and foundational building blocks to set up, but otherwise it's mostly about getting the idea of what calculus is about and getting some muscle memory of the basic ideas

[astral canopy]

I mean I’ve already done a couple college level maths like college algebra, contemporary math, and right not college precal so I’m guessing the first 2 prob won’t be too bad

[winter comet]

one what? axiom?

[tired garden]

calc 2 you start introducing some theory but otherwise it's mostly heavy algebraic intuition and manipulation

calc 3 is back to a lot of theory and the computations here start to get real annoying

but there is an overarching theme to calc 3 that once you get, all sort of clicks together nicely

[winter comet]

i mean don't understimate it, but for me saying that also don't overestimate it lol

[winter comet]

you mean generalized stokes ig?

[tired garden]

again, good that you have this curiosity, but start from the ground up, don't go flying into hyperspace with no rigorous foundations

[near dove]

Yea, maybe not just one but not half a gazillion for each branch, you should be able to build the axioms of each from just those of the first

[near dove]

Of course, that's half the reason I came here to get critiques cuz I really don't know much, but I also know that math isn't just a thing that exists, and the universe is definitely clever enough to build itself from a single Axiom, or even none at all

[winter comet]

axioms are supposed to be independent though, thats the point. . .

[near dove]

And they can be, but not independent in the way that Probability is a completely different language from Geometry

[tired garden]

im going to say this again, it's good you're enthusiastic about this, but start from foundations before you make sweeping unfounded/incoherent claims

and this is the wrong channel for this

if you really want to pick the brains of people who know this stuff go to #foundations but keep in mind this is usually postgraduate level subject material

[near dove]

What exactly do you have an issue with? Is it not a natural claim that the universe we exist in could construct itself entirely from just a few simple rules? It's really not that big of a stretch to me, do you think our jumbled bunch of monkey people axioms are the most basic of all? Doesn't seem right

[tired garden]

wrong

channel

just don't forget that when you're actually trying to learn and explore you pull it back and work rigorously from the bottom up, stay grounded in concrete notions and rigorous logic, because it's VERY easy to find or make incorrect mathematical proofs that look fine, and a single false step poisons an entire proof in a way that anything false can be proven true

im not repeating myself anymore

[winter comet]

math may be used to represent the universe in some sorts of ways, but it isn't the universe...
I can't talk about the universe, but for math
those "few simple rules" are the axioms. and there is more than a few. it doesn't seem possible to condense them or else there would be less axioms in the first place...

[near dove]

That is literally the whole point of what I'm trying to do, you physically can't build everything's from the bottom up and it's an issue

[winter comet]

you have to define the bottom

and those are your axioms

the axioms are the bottom

and then you can build everything else in that field from those axioms

and there are a lot of axioms depending on what you want to be possible in your field

field as in area of math

[near dove]

And that's the misconception, math was developed from the laws of the universe and must be consitent with them, therefore they describe the laws of the universe, so long as 1+1=2 math is real

[winter comet]

it wasn't developed from the laws of the universe as much as it was developed in an attempt to describe the laws of the universe

[near dove]

And maybe we just haven't found a way to condense the axioms yet, why would you think we know all of them?

[winter comet]

math isn't an inherent truth to the universe, it is a (mental) world that we humans built up in order to try to make sense of the universe
so we've made a finite amount of axioms to do this

[near dove]

Literally the same thing, an attempt that works is called success, we are attempting to describe the laws of Reality y writing down the laws of reality

[tired garden]

your comments are becoming more and more unhinged to the point where they are barely even math anymore

please just go pick up a book or something

[winter comet]

we just havin a conversation lol ☠️

[tired garden]

yeah about like abstract philosophy and things that aren't even true

no one thinks we know all the axioms

we almost certainly don't

[near dove]

1+1 is always 2 everywhere in the Universe, if this is true and all the rest of math is consistent with 1+1=2 then it follows that they also must be true or at least linked to the truth in some Mathematical way

[winter comet]

we defined them wdym ._.

[tired garden]

ok w/e idc anymore

keep going then

jfc

[near dove]

How can anyone possibly believe humans could invent a system like this, it's genuinely selfish behavior and the biggest reason things are still left undefined

[winter comet]

"1+1 is always 2 everywhere in the universe"
wdym ._.

[near dove]

It took you that long just for that

[winter comet]

i don't know how to explain LOL

[near dove]

Yea, it seems logical to me that 1+1 always equals 2 everywhere

[winter comet]

1+1=2 doesn't have meaning irl until you give it contextual meaning

[tired garden]

it's literally not even true in GF(2)

or boolean algebra

so you just have no idea what you're even talking about

zero clue

[winter comet]

you mean you don't believe humans invented math?

i don't understand what you were trying to say

[near dove]

You can't genuinely be serious, you don't have to understand the concept of one for one to exist, the universe performs these operations without needing context of what one is because it literally built the idea of one, and i said everywhere in the Universe 1+1=2 I haven't heard of the universe using a system where when you have one thing and one other thing you have anything other than two things

[tired garden]

then you haven't studied the math

go read a book

[winter comet]

the universe doesn't "use a system", you use a system to see the universe

i think you have an idea that math is ingrained into the universe but its not like that :l

[tired garden]

you can't start talking about axioms and foundational theory and then claim that 1+1 always equals 2

if you do this then you don't understand what formalization is or at least what the process of rigor looks like

go read a book

[near dove]

Show me a physical actual point where in the actual universe one thing and another thing isn't two things, I don't think you understand what I'm trying to get at here, there is an underlying Mathematical truth to everything, which can be built from only a few axioms

[tired garden]

i literally just told you

GF(2) and boolean algebra

boolean algebra ffs

[near dove]

There's no proof that it is, or that it is not, it only makes sense that if you can always describe the thing using these rules then the thing follows those rules, when you kick a soccer ball it's gonna go flying, it does that for a reason, are you gonna tell me quarks don't exist? Those are Mathematical Objects but are entirely real

[near dove]

I'm asking where does the universe care about these systems

[tired garden]

are you asking where the universe cares about classic logic

[near dove]

What physical Phenomena can be described such that 1+1≠2

[tired garden]

if that's seriously what you're asking me then idk why you're even talking about axioms and logic in the first place

you clearly don't understand formalization

you are going off into unhinged incoherent rambling about nothing that makes any sense

im trying to help you by telling you to slow down

[winter comet]

(i don't agree with your way of thinking in the first place, but just for the funnies)
1 apple + 1 orange != 2 apples

💀

1 + 1 != 2

[tired garden]

but you just go further and further off into hyperspace to the point where nothing you say is even true let alone makes sense

[near dove]

Things don't just happen because magic, they have rules and systems that enforce them, it makes sense that math would be that system and that it would be consistent with itself, when you push a thing it moves because of Electromagnetism, you fall when you jump because of Gravity, the universe has laws because there is a system that enforces it

[tired garden]

you are not even listening

[astral apex]

this is widely debated, can't really say it is or it isn't like it's a settled fact

[tired garden]

why do you bother typing to have a conversation if you're not going to read anything anyone says

[near dove]

Everything you say is either nuh uh or blah blah monkey people language axioms ooga booga you don't understand

You cannot show me where the universe physically does not follow Mathematical laws, it only makes sense that math is true and very real

[astral apex]

it's not so cut and dry that way either

[near dove]

The whole point of math is that it does follow Mathematical laws

[astral apex]

we make models to try to explain the universe. Our models have improved over time. But we shouldn't literally identify what the universe is doing with our models

[tired garden]

you are trying to talk about formalization when you don't know what formalization means

this is the key thing

[near dove]

Right, but that's only because we cannot possibly know everything, we will always have to update out model to reach Mathematical truth

[tired garden]

in the context of talking to elementary students, i would say "1+1 always equals 2" because im not about to explain to them formalization and axioms and nonstandard math

[near dove]

The only thing I am trying to convey is the fact that the universe can be expressed using Mathematical laws

[tired garden]

we are referring to the commonly accepted notion of these ideas

[winter comet]

oh, interesting

[tired garden]

but you are trying to talk about axioms and formalization

but you don't know what formalization is

you started with trying to define 0/0

if you care about expressing the truth of the physical universe, then im sorry, there is no physical representation of 0/0

do you or do you not care about axioms and formalization

[astral apex]

various forms of mathematical intuitionism seem to have increased in popularity, but there are still mathematical realists and they're not easily dismissed

[near dove]

I only want to talk about the universe following Mathematical laws, fromalization comes later when I actually know something, you made it about formalization when I was only throwing ideas around

[tired garden]

if you do, stop, you have no idea what you're doing, go home, study

if you don't, you're in the wrong channel and why are you studying 0/0 or n/0

[near dove]

If that is what you think

[tired garden]

if you want to keep yelling "show me where 1+1 is not 2"

then im gonna yell "show me where 0/0 means anything physically"

this goes around forever in circles

this is stupid

do you or do you not care about formalization

[near dove]

I think you're completely missing the entire point

[tired garden]

says the one who says he hasn't studied probability or anything beyond precalc

[astral apex]

to the extent we can agree there really are "objects" in the universe, whatever object means, I think we can agree that when there's 1 object and another object, then there are 2 objects

[tired garden]

i tried to be charitable by commending your curiosity but giving you practical feedback

but instead you're talking over me and having a debate with me

so im not being charitable anymore

[winter comet]

well i mean in our mathematical way of thinking lol

[astral apex]

I'm speaking of a pre-formal notion of objects and of counting/adding; we could say that any attempt at axiomatizing this notion has to "get it right" and agree with our pre-formal idea

[near dove]

What does it matter how much you know if you have no idea what you are actually dealing with? You can't even accept the Mathematical truth of the universe but you still study it for whatever reason, I was not reaching for a debate, I was expressing my ideas and you have done nothing to genuinely show my I am wrong which is something I was looking for, it turns into a debate when I'm looking for the answer to a question and it isn't given to me, when I am looking for guidence by people who know more and not even they actually know

[astral apex]

what was the question?

[willow skiff]

oh man

[winter comet]

would there be ambiguity towards math and how ingrained it is in the universe because they are not well defined?

(my question, not the og question)

[near dove]

It wasn't really, I was just thinking about Division by Zero alot and so I took a Crack at it knowing it probably wouldn't be correct but I wanted to know why, later I was just talking about how I believe there is a Mathematical truth to the universe and that anything within that system should be provable or the universe can't possible decide what is true or false

[willow skiff]

#precalculus message

[tired garden]

the guy who asked "how can we define everything" is now telling me nothing i say means anything because "why does math math"

im about to ping a mod

[near dove]

No no, "why does the universe universe"

[tired garden]

are you fucking serious m8

[winter comet]

there's no reason to get mad 😔

i mean there could be a reason but like

yall shouldn't imo

XD

[astral apex]

Ok. Well even if the universe is literally a mathematical structure evolving according to some mathematical rules (which I actually believe), that doesn't imply you can observe the universe to come up with some appropriate definition for 0/0

some things in math simply don't make sense

[near dove]

No of course not, but you should be able to builde the basic rules and prove the rest from there, even if 0/0 doesn't show up physically doesn't mean it isn't real

[willow skiff]

maths is like a logical game: you start with some building blocks and all other building blocks have to come from the foundations

[winter comet]

does math have a definition?

[willow skiff]

I mean you can come up with rules where 0/0 exists as a number, sure

you can't guarantee that loads of other things won't also break

[near dove]

It could with a strong enough system

[astral apex]

exactly. In fact you can demonstrate that lots of things will break

[near dove]

True, but then wouldn't they then be fixed, not broken?

[willow skiff]

you don't know that unless you try it out

[winter comet]

a system for what?

[near dove]

Ya momma tiddy milk

[winter comet]

if 0/0 could be defined or could be left undefined, doesn't that ambiguity mean its not true to the universe and is instead a way we use to interpret the universe?

[winter comet]

i take back what i said about getting mad

[tired garden]

you cannot say this and then accuse me of not finding a physical example of 1+1 not being 2

even though i found you one

you don't listen

[near dove]

The universe would be and is currently able to perform the operation whether or not we know it

[turbid sequoia]

1 illogical man + 1 illogical man = 2 illogical men

1+1 = 🪟

[astral apex]

"Pure mathematics is the area of study in which we don't know what we're talking about nor whether what we say is true." - Bertrand Russell

[near dove]

Because that is clearly not what I am talking about and you continue to miss the entire point

[tired garden]

<@&268886789983436800> can we force this to a more appropriate channel

[near dove]

Blasphemy

All of it is barnacles officer

I'm just a humble wizard

[winter comet]

honestly tho fr

[winter comet]

you must be buddies with that other wizard from the psych ward

[near dove]

Some secrets are meant to be kept

[astral apex]

0/0 is used in algebraic structures called wheels. Is that real enough for you?

I'm not aware of any physical process being modeled by that structure though

[tired garden]

he literally doesn't even accept boolean algebra

[astral apex]

and even though 0/0 is a thing in wheels, it's still not a thing in more common structures like the real numbers

[near dove]

I think ive heard of that, it's an interesting concept and the one I've come up with is quite similar

It's entirely on accident tho, really the only way it actually works

[north forge]

this is completely unrelated but i was JUST on that guy's wikipedia page after clicking the second link of every wikipedia article i was on wow what a crazy coincidence

[willow skiff]

I think the point of mathematics is exactly such that it isn't real

you can make a million different mathematical universes with a stroke of your pen, and they exist on paper

real life is pretty boring, arbitary, and messy

mathematics is hence a lot more imaginative

all play starts with a few rules that can create massive things

[willow skiff]

wait that's insane

thanks for that; I had no idea

the formula makes 100% sense

[astral apex]

glad I could share something new and interesting to you! you seem like you know lots of math already so that doesn't happen often

[astral apex]

here's my perhaps unhinged take - in some abstract sense, those mathematical universes are just as "real" as our universe - its just that we happen to be inhabiting ours so ours feels more real to us

[willow skiff]

no like I switched degrees such that mathematics is no longer my undergrad

my highest course attempted and passed was topology

[near dove]

It can build our reality as well though, it can be real and have that ability, maybe those other realities are also real, but ours has very specific constraints that can also be build using mathematics

[willow skiff]

gradually a lot of uni maths of mine will decay and I'll have to restudy it to fully understand the concept again

[astral apex]

I get it, I try to keep mine from decaying too much

[willow skiff]

it's okay it's like Britain's fading colonial empire or some shit

[astral apex]

it's probably been over 5 years since I've solved an actual differential equation, which slightly worries me

I think I could still do really easy ones

[willow skiff]

I chose to do this cause maths doesn't interest me at all as a career

[tired garden]

doesn't really matter if you can still solve differential equations imo

everyone has their own path

i focus almost entirely on teaching like elementary-high school material and there is more than enough to last me a lifetime

i still study higher level topics, but they're more to inform my teaching lower down than anything else

and even if you forget it'll be easy for you to pick it up again

don't think you should be worried at all

[plush sentinel]

anyone, i have like small problem, whenever I prepare for test I never make mistakes, but when the test came in, I always make some mistake of type like multiplication of brackets, and even now I completely missed and misstyped a whole equation

any tips how to get rid of that?

[willow bear]

do you use up all your time on test day?

[plush sentinel]

well usually yes, but that day with the equation I was very confident that it was without a mistake, I used like 25 mins from 45 mins

[willow bear]

next time, use those remaining twenty minutes to double and triple check for stupid arithmetic errors

and otherwise, before test day, time yourself while attempting the tests

[plush sentinel]

okay

[calm yarrow]

Hey Guys, can anyone tell me how to approach calculus like what are the prerequisites that i always need to remember ?

[uncut mulch]

algebra, geo, trig, functions, exponents, logs

[calm yarrow]

thanks, I'm Starting now

[spare ore]

Hello! I know my answer is probably way off, ive been experimenting and I am just so totally stumped. could anyone help me out? I just cannot figure out what I am missing from this equation.

I know there are two verticals and a y intercept (0,1) and it seems there is an x intercept at (2,0)

I know this is probably stupid easy but I think I've got a serious case of the fridays haha

[winter comet]

plug in x=5

[tired garden]

remember that the graph of 1/x

one side is positive and one side is negative

notice that x=2 is not a double root, or else it would lie tangent to the y axis and stay positive

hence there is only a single (x-2) factor

notice the x=4 asymptote is negative on BOTH sides

so similarly, it can't have a single (x-4) factor in the denominator

this is a "double" asymptote

hopefully that should be all you need to fix your answer!

[spare ore]

it was!! thank you so much :) my professor spends the whole lecture giving definitions of the baby steps versions so we never officially went over double asymptote but that really helped <3

[viscid thistle]

can someone send me a list for all the rules for log

there is this question log32 + log8

I just wrote it as log256

but answer says 8log2

isn't one of the rules log a + lob b = log ab

was I supposed to simplify the log32 to 2^5 and log8 to 2^3

[river drift]

either that or you could take 256 = 2^8

[viscid thistle]

so log256 and 8log2 is both correct?

[river drift]

yes, but the second is more simplified

[viscid thistle]

the question says to simplify it

so do I use the second one

[river drift]

the second one is the correct answer, then

[viscid thistle]

what about if the question said to solve it

[river drift]

well "solving" would mean you were isolating a variable of some sort

although you may still be expected to simplify your solution

[viscid thistle]

can you give me an example

so the equation I gave, you can't solve it? only simplify?

[river drift]

e.g. "solve log(x) = 3" or "solve 4^x = 12", etc, which would involve rearranging it as "x = ..."

[viscid thistle]

oh

wait can you explain how to simplify log 32 + log 8 again

i still don't get how the answer is 8log2

ohh wait i get it

[viscid thistle]

can log(1/8) be flipped into something simpler

[winter comet]

log(a/b) = log( (b/a)^(-1) ) = -log(b/a)

[viscid thistle]

does anyone have a video I can watch for the basics of log

[willow bear]

organic chemistry tutor

[inner topaz]

can be rewritten as $\log{8^{-1}}$

[obsidian monolith]

Ryse

[viscid thistle]

he teaches calculus/algebra too?

i thought he only teaches chemistry and physics

[willow bear]

yes

[elder lintel]

I have took note since I studied ,u can refer to

[viscid thistle]

Does anyone know why the tabular method is wrong for this one? I dont know when i should use it exactly and sometimes i put the expression under the wrong one ( between U & du in the table) how do i know which one is suitable??

[inner topaz]

i mean first of all it should be

$(x-1)^\frac{1}{2}$

[obsidian monolith]

Ryse

[inner topaz]

try putting both those functions on a graph on desmos or smth

ignore the +c part

[viscid thistle]

Woops, i didnt see the minus

Im guessing both r correct answers?

If the question was a MCQ one and the correct option is different from the answer i got can i just input a large number in the option to see if it aligns with mine? Or does that not work

[inner topaz]

there are often different ways to solve integrals

[viscid thistle]

Bc i heard inputting large values can help with that

[inner topaz]

you can probably rearrange the solution in some way to look like the other one

or it can also depend by the +c constant

like for integrating csc

you could use weiestrass substitution

[viscid thistle]

So both answers r correct or no? Im new to integration so idk much abt it

[inner topaz]

or you can also multiply and divide by cscx + cotx and let u be that, doing u sub

you will end up with different answers but they're the same because maybe the constant of integration can be different from the other one

[inner topaz]

yes

both correct

[viscid thistle]

Idk what those r bc for some reason we never ever use those terms in our maths

[viscid thistle]

Thank u

[inner topaz]

u sub you probably know, since you know the DI method

[fathom sphinx]

Hi is my simplified expression for part 10a correct? ( my book doesn't have the markscheme)

[willow bear]

seems so

[fathom sphinx]

Ah alright thx!!!

[fathom sphinx]

What the hell is modular arithmatic ; - ;

[gloomy turtle]

Basically Division but for remeinders

Gosh I cant spell

[gloomy turtle]

For example, 5 / 2 = 2 R1

we can rewrite this as: 5 = 1 (Mod 2)

[fathom sphinx]

ohh i see thx Loitering! i was tryin to prove smth by induction since i didnt have the ms i used ai and it said i can prove smth by induction using modular arithmatic

[gloomy turtle]

Ah I see

[fathom sphinx]

It was question 11

Gosh sorry for the quality

[gloomy turtle]

Oh yeah, classic modular arith question

[fathom sphinx]

☠️ i need to learnnn that!

[gloomy turtle]

Hehehe its quite easy once you get the hang of it

the worse part is all the manipulation

[fathom sphinx]

wait so can i jst leave my working as it is and just move on ig its correct?

Gosh i miss when math was simple

addition, subtraction, simple division not this induction, integral and other shit

[fathom sphinx]

🔥

[gloomy turtle]

yeah

if its induction then once you got the base case and the inductive whatever you call it

[fathom sphinx]

oh thanks again Loitering!

[viscid thistle]

been having a lot of fun with these 2 equations recently

[daring tapir]

isnt that basically just the integral of 0 dx from 0 to 1

[viscid thistle]

maybe :3

[hasty fog]

Hmm that looks like a Harmonic progression in the power

Maybe I am tripping here

[viscid thistle]

Idk but it was fun learning how to solve it

[hasty fog]

I'll try it out later, thank you :D

[viscid thistle]

Your welcome :3

[rustic niche]

This is NOT pre calc

[winter comet]

those 2 are also not equations

[viscid thistle]

can confirm this is infact postcalculus not precalculus

[winter comet]

what about just...calculus :>

[viscid thistle]

yeah but that doesn’t sound as cool

[floral path]

why does this work???

[viscid thistle]

log(a/b)=loga-logb

and logx^y=ylogx

[floral path]

then what's loga+logb?

[viscid thistle]

loga+logb=logab

[floral path]

That makes sense.

what about this though?

[viscid thistle]

simplify log(sqrtx) into log(x)/2 bc sqrt is just to the power of 1/2

then logx⁴ turns into 4logx

then bc there's minus divide them

wait

I did something wrong lme get paper out 😭

[tulip nacelle]

LMFAOOOOOO

[floral path]

???

[floral path]

This is confusing me:

[tawny hedge]

The first two natural logs cancel each other and make ln(1), then you use the properties of log to subtract the two remaining natural logs. Then just factor x^2-64 using difference of perfect squares.

[formal wren]

HELP ME

[winter comet]

if g(x) = 1, that means 1 = sec^2(x) + tan(x) right?

💀

[formal wren]

Lol

Every time u clutch up

Wait so like

[formal wren]

Yes

That’s right

[winter comet]

do you know any trig identities involving sec^2(x)

[formal wren]

YES

TAN^2x+1=SEC^2x

[winter comet]

yee

[formal wren]

The x isn’t in the power

[winter comet]

ofc

so then you would agree that sec^2(x) - 1 = tan^2(x) right?

i mean doesn't really matter LOL

[formal wren]

Yes

[winter comet]

can you use this in ur equation

[formal wren]

I think

Tan%2x+1+tanx=1

[winter comet]

mhm, can you simplify n stuff?

[winter comet]

do you see how to do it from there or...

[formal wren]

No

Because I tried

Abd got stuck

[winter comet]

well i mean you can subtract 1 from both sides right?

[formal wren]

Yessss

Wait

U can?

I thought it’s tied to tan^2x

[winter comet]

no
tan^2(x) + 1 + tan(x) = 1
commutative property of addition says that it's the same as
tan^2(x) + tan(x) + 1 = 1
and you can subtract 1 from both sides to get
tan^2(x) + tan(x) = 0
right?

[formal wren]

Ohhh

I see

I got

[formal wren]

Tan x=0 and tanx =—

-1*

[winter comet]

yeah

so now you need the solutions of those for x in [0,2pi] ri

[formal wren]

Doesn’t seem like an answer choice though when I do inverse

[winter comet]

doing the inverse only gives you one solution

[formal wren]

How

U have 2 solutions

=0 and =-1

[winter comet]

if you think about the unit circle

tan(x) = sin(x)/cos(x) = 0 only happens when sin(x) = 0 right?

[formal wren]

Idk

Wait

How

Doesn’t that mean 1/cosx=0

Too

[winter comet]

for what values is 1/cos(x) equal to 0

what number that, when you divide with it, gives you 0

[formal wren]

0?

[winter comet]

it can't be 0 right cuz you can't divide with 0

[formal wren]

WAIT IM SO Confuesd

I’m sorry

Can we rewind

[winter comet]

sure

[formal wren]

Tanx=0

Tanx=-1

Inverse u get

0

3pi/4

And 7pi/4

[winter comet]

what about 2pi?

[winter comet]

you agree that there are multiple x values that satisfy tan(x) = 0 right?

[formal wren]

0 or 2 pi wait and also pi

[winter comet]

mhm

[formal wren]

Yess

So what do I do

[winter comet]

well you've got some values that you know satisfy it either equation, but are those all the values in the interval [0,2pi] that satisfy the equations?

[formal wren]

I. Don’t think

So

[formal wren]

The answers don’t have all of them

@winter comet I NEED U

Wait nvm

I think I figured it out

Thank you

[formal wren]

I need help

And also this one pls

[jade sand]

Can anyone help me on how to simplify this?

[tame pike]

I need some support with this problem.

[lean cove]

Which parts?

[tame pike]

Positive & negative

[edgy tree]

Your working is correct just multiply both sides by 2 and youll get A

[lean cove]

For what x values is the function negative (below y axis).

And for positive for what x values is the graph positive

[tame pike]

Ok

[dusky tusk]

just subtract the exponent of the numerator variables, 3x^(3/2 - 2)* y^(3-(-1/2), you get (3x^-1/2)(y^7/2)

then multiply both exponents by -2

u get 3xy^-7

which is 3x/y^7

[jade sand]

My answer was x/9y^7

[near surge]

dose anyoe know of a calculus study guide. im falling behind in my class and im freaking out

im taking calc 1, and the past 2 weeks iv been in and out of school. just need a quick way to get cought back up before my unite test... subjects are optimization with, lo hospitals rule, newtons method, mean value theorem and curve sketching

[river badger]

do u guys understand this

[willow bear]

wtf is an existentialist advocate??

[willow skiff]

why is there random pseudo-philosophy, exactly...

[dusky tusk]

ah i forgot to raise 3 to the power of -2

[jade sand]

Its fine, thanks for telling me the approach to take in order to solve it (:

[jade sand]

I discovered my passion, all this time i thought maths/phy wasnt my cup of tea cuz school teaching just didntvmake it fun, now i graduated school, so i have no restraints, stuff is more fun, and i realized just how much fun this stuff is, i wanna dig deeep in this stuff, so im starting by clearing out the basics, so thank for the help to discord

[willow skiff]

no problemo!

if you have any maths question just ask

or in the physics server for the physics questions you have

[jade sand]

👍 thanks!

[hoary willow]

Hello, I have a question. Why does the tangent line estimation (f(x)~f(a)+f'(a)(x-a)) work? I mean, I don't understand why multiply the derivative with (x-a)

[uncut mulch]

its point slope formula
with slope at the specified point
and the point of tangency

[hoary willow]

Oh

Thanks

How did I not think of that?

[white ore]

CAN SOMEONE HELP ME WITH MY HOMEWORK

[viscid thistle]

Send your question here (or in #1021175428326633542)

if someone knows how to answer it, they'll respond

[viscid thistle]

the domain of a function is all the values of x that the function accepts. Looking at the x axis, can you tell what values the function accepts?
Similarly, the range of a function is all the values of y the function can output. Looking at the y axis, try finding the function's range.
Be sure to make a note of hollow and filled circles

[viscid thistle]

f(x) is defined as whats known as a piecewise function. It has been defined in pieces, for x<1, then x = 1, then x>1. For these separate intervals, try plotting 3 different graphs. Remember that for x<1, the value -3 does NOT extend to x=1 (and thus use a hollow circle)

[whole void]

yeah. It’s a pretty interesting discussion for what counts as a “piecewise” function. But maybe it’s too pedantic

Maybe people would say they |x| is piecewise

but would feel less comfortable saying sqrt(x^2) is

[viscid thistle]

I was just trying to make sense of the name "piecewise".

[whole void]

yeah

but still

[viscid thistle]

A piecewise function is just a function that is defined in intervals.

at least thats as far as I see it

[wheat oar]

Do you have a Calculus textbook? Those topics in that unit can be found in or around Chapter 4 of most modern Calculus textbooks. Just read through the sections that you are struggling with and work through as many exercises as you can at the end of each of those section, and you should be caught up easily.

[river drift]

"piecewise" is not really a property of a function but of the formula used to express that function

e.g. you can express just about any "piecewise function" as a sum of the terms multiplied by the unit step function, etc.

[merry tide]

Whats up my Pre Calculus kids

[edgy adder]

whats a pre calculus kid

[bleak rock]

Open Course Ware & Pual’s online notes

[knotty goblet]

Ye what is pre calculus

I have a question

[dusky tusk]

before calculus

[knotty goblet]

Oh so like no calculus stuff

[wheat oar]

Pre calc is algebra and trig which technically is calculus stuff

[round magnet]

hey guys sorry for asking this kind of question but uh is there any good source for precalculus or calculus?(and perhaps stats with prob)

[jade sand]

I just solved 3 problems from stewart 9e 🎉😎

And btw, I noticed that, unlike most other academic books, stewarts book is quiet readable without getting confused for 2 hours straight

[jade sand]

YouTube is one of the best sources, search up precalc cource contents and learn them by searching then up, if you have doubts you can always ask here at discord or consult a teacher

[wheat oar]

Nice! I'm almost ready to get myself a Stewart Calculus book

Stewart is very readable. I've been working through a Stewart Pre calc book for the past few months and I've only had to look up extra explanations a handful of times

I'm thinking about getting the 7th edition of Calculus because that was the last one that he published before he died

[bleak rock]

khan academy

[obsidian monolith]

no one親切です

no one親切です

no one親切です

[jade sand]

There is a pdf version of early transcendantals(dont mind the spelling pls), on the internet if youre comfy with using your device as the book, edition 9

[viral warren]

i learned my calculus through paul's online notes

[spare ore]

Hi yall! Im studying for upcoming exam and I swear this problem feels easy (I've gotten the other examples right) but however this one has stumped me.

The key says the answer is (-∞,4)u(4,∞) (option a) however I seem to be getting stuck.

The way I do is it that I right out each step and then combine what I can so here I got

(-∞,0)
[0,4)
(4,∞)

So when I combine them (before solving) i get (-∞,0)u[0,4]u(4,∞) but I get confused how the included 0 gets left behind, I was under the impression that if its in a bracket it has to be apart of the problem? or it could just be me slowly losing my sanity. thank you so much in advance <3

[viral warren]

ok

so

sorry if my language is poor, i am quite a young student, especially for this math

but

(-inf,0) U [0,4) is essentially (-inf, 4)

it would be best depicted on a number line

we will represent this with a diagram such as this

let's try this again, (i'm trying to phrase it as specific as I can)

We have the two intervals plotted on the number line, with the color corresponding to their respective intervals.

Now, you did mention a union, which means we are including all values included in the interval

0 may not be included in the "blue" interval, but it is included in the "red" interval

Therefore, 0 is a value included in the union of these intervals

Your answer is not necessarily incorrect

However, you can "simplify" your interval

By understanding that you can "merge" the intervals

If you look back at the drawing and tried to formulate an single interval that can describe both intervals, x<4 would be a valid interval

[tawdry pilot]

this is NOT precalc

[jade sand]

This is not the channel you wanna be asking that, try in #math-discussion ?

Tbh, they should make one channel for calc discussion/help

[woeful star]

this is pre calc bro

not professor degree level calculus

[woeful star]

#calculus and #multivariable-calculus

[jade sand]

Ohh, its not visibke in side list, i guess, oh right maybe cuz i chose myself as ug

[woeful star]

i also realised there are 50 more channels like yesterday lol

i've been here for a month

[jade sand]

0-0

Can ya help me out with a silly q?

[woeful star]

ok

my limit is level 2 calculus NZ

some integration

[jade sand]

Its just algebra

1-(-x) ^(4)

[woeful star]

ok

[jade sand]

This

[woeful star]

so 1+x^4

is it like a nequation

[jade sand]

Is it gonna be 1+x^4 or 1-

Plus, right?

[woeful star]

ye

[jade sand]

I got confused due tk the brackets lol, thy

[woeful star]

lol

PEMDAS

parentheses eponent multiplication division addition sub

exponent comes before the addition and stuff

#prealg-and-algebra

[jade sand]

Nah nah, k was like alr so we have -(-x) , that a +, but the -x is squared so maybe the signs change differently

Ok

[woeful star]

-(-x)=+x

[jade sand]

Ya, i know that much, its just some silly ape problems lol, sry

[woeful star]

💀

[jade sand]

Lol

Wait, uh multiplication is before division right? BODMAS?

Im south asian, this is what we use here

[woeful star]

idk

multiplication and division have same priority just depends which one comes first