precalculus

[inner topaz]

so if we had 2 2s and 5 2s

we get 7 2s in the end adding them all up

similar thought process with quotient

[frail ember]

so 2 * 2 / 2 * 2 * 2 * 2 * 2?

[inner topaz]

yeah there we are removing 2s instead

we are simplifying the twos we have on top and the bottom but the bottom will still have 3 left

[frail ember]

1sec

[inner topaz]

what's your main language?

[frail ember]

like i see how the result is the same, but havent we subtracted 4?

[frail ember]

swedish

[inner topaz]

we did not subtract 4

[frail ember]

ah 5 - 2

nvm

[inner topaz]

you can say that we divided by 4 both on top and on the bottom

[frail ember]

okay, i see

i guess ill have to simplify stuff to understand it

[inner topaz]

well that doesnt rly explain the problem because then it would also involve applying it again so nvm

but yeah for example 2/7

lets take ugly numbers

if you multiply both the numerator and denominator by the same number

you still get the same ratio

4/14

[frail ember]

yeah, since u scale them relative

[inner topaz]

or 14/49

ye

[frail ember]

yeah, that brings me back lol

[inner topaz]

if i said that 1000 meters is 1 km

4000 meters is 4 kilometers

doesnt change the fact that 1000 meters is still 1 km

[frail ember]

yeah, i guess i just have to think about division as fractions (bråk in swedish) and not as a value if that makes sense

[inner topaz]

yes its best to start looking at divisions as fractions

[frail ember]

and then simplify

[inner topaz]

(they are the same thing)

[frail ember]

yeah, and with fractions you can simplify too

which makes it a lot easier

[inner topaz]

it is definitely way easier

[frail ember]

okay, ill have to look over this tomorrow, but it makes more sense now

[inner topaz]

but you can do it with division too technically

[frail ember]

this really helped. i also have a question

[inner topaz]

we just use fractions after instead of the : sign

[frail ember]

what do you mean?

idk if you know about khans academy or if its good etc, but i have these bookmarked in order. does this make sense? (thought, pre calc should be before calc bc)

[inner topaz]

think at the beginning division is taught using the : sign or at least where i live

like 10 : 5 = 2

but after we just use fractions

it has the same meaning

10/5 = 2

[frail ember]

ah, yeah, same here, but forgot about that since its very early on

havent used that for like 15 years xd

[inner topaz]

trig def after algebra stuff

precalc yes before calc bc

[frail ember]

okay, ive had a linear algebra course and passed, but mostly just because i memorized patterns

[inner topaz]

think differential equations you can do it aftermultivariable but i myself havent learnt that stuff yet

[inner topaz]

matrices and linear transformationsv

?

[frail ember]

yup

[inner topaz]

i'd recommend watching 3blue1brown videos for that

explains it very nicely

i rewatched it like 5 times to fully understand it

[frail ember]

however, i mainly know how to apply the mathematics, but theres a lot i dont understand on a deeper level

[frail ember]

yeah, he's great

[inner topaz]

https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&si=jJ2s53bjC4d6kUe2

[inner topaz]

usually this stuff is taught in uni

[frail ember]

i understand how the cosine funcs etc (SOH CAH TOA) returns what they do, but a lot of other stuff i dont get on a deeper level

[frail ember]

yeah, im outa uni xd

im 25 man

[inner topaz]

ay never too late for math

[frail ember]

yeah i know. im a software engineer, mostly focused on 3d rendering where you mostly just use applied linear alg (matrix transforms, vector maths like dot or cross product). but ive come to a point where i need to learn calculus and more advanced math to read papers etc since a lot uses derivatives and integrals

[inner topaz]

concept of derivative is not too hard to understand

integral kinda harder to explain why formula works

[frail ember]

yeah, i understand the concept, but most papers use math heavy notation

[feral ferry]

Khan Academy is how I learnt calculus :)

[inner topaz]

https://youtube.com/shorts/PGK-RXA8Ye8?si=UnZqBu_WxF9yBRas quick brainrot video explaining it

[feral ferry]

actually needed to re-learn algebra tbh

[frail ember]

@inner topaz like this: https://google.github.io/filament/Filament.html#materialsystem/diffusebrdf:~:text=is a Lambertian function and the diffuse term of the BRDF becomes%3A

[feral ferry]

stuff they taught in school wasn't really thorough enough or maybe I didn't pay attention

[frail ember]

@inner topaz regardless, thanks for taking the time to explain. ive got a lot to learn and ill hopefully stay dedicated

[inner topaz]

no problem!

[inner topaz]

too much brain

[frail ember]

yeah, now you see why ive hit a dead end lol. if i wanna evolve my skills and learn more advanced rendering techniques, ill need to understand this at some point

[feral ferry]

makes sense

[frail ember]

cause its really frustrating visualizing ideas, having the coding knowledge of implementing it, but not being able to simply because you suck at non-lin alg math

[inner topaz]

yea

usually people dont even solve it they just let some software and stuff do it no?

power of wolframalpha or graphic calculators

[frail ember]

a lot of people just steal a formula and adapt it to programming. ive done that before too. but the problem is when you need to actually understand the maths behind the formula, or even the formula itself. in comp sci and render-related research/techniques it can be very heavy math notations as you can see.

you might need to understand the formula if you wanna extend it or change it. you also need to understand the math if you wanna be able to create new formulas

ex. you wanna scale something between 1 and 0 based on a max distance of 5 in a certain way. then you can use this and just replace the variable x with the distance:

this is simple, but you might want a more complex response which requires you to be good at math

[mellow cypress]

His differential equations series is buns

[severe pond]

how can i simplify this expression?

ignore the lim, thats part b. i just need to simplify the sin(x+1) / sin^2(x-1). the denominator expands to sin(x-1)sin(x-1) which doesnt cancel with sin(x+1)

[exotic lion]

Help me with No.3 and No.4

[viscid thistle]

For question 36 isnt there no point of inflection? The answer key says its B tho

[sturdy hound]

someone pls help it is very late i need to solve this (second pic is my work)

nvm i have the anwer

[inner topaz]

think it's sin(x) + 1

[severe pond]

any context behind it? id like to understand too haha

[willow skiff]

$\sin^2 x - 1 = (\sin x - 1)(\sin x + 1)$, difference of two squares

[obsidian monolith]

south

[severe pond]

ohhh so its not actually sin(x-1) * sin(x-1) then

the notation confuses me

[inner topaz]

also if it really was sin(x+1)/sin^2 (x-1) the function would be continuous at 3pi/2 so just plug in the values

[willow skiff]

yeah like that's a completely different thing that can't be simplified

sin x + 1 always means just (sin x) + 1

[severe pond]

got damn im more confused than ive ever been before

[willow bear]

$\sin x + 1$ means $\sin(x) + 1$ by the way, not $\sin(x+1)$.

[obsidian monolith]

ann.in.a.teacup

[willow bear]

this is why you should always put parentheses around the inputs of trig functions

[severe pond]

so its actually... uhhh... hang on lol . "sin^2(x) + 1" ?

my brain is melting and dripping out of my nose

[willow skiff]

yes

[willow bear]

yes

[willow skiff]

in the picture they mean sin^2 (x) - 1 though

[willow bear]

if this is happening for realzies you need to be calling 911 ON THE DOUBLE.

or 112 depending

emergency services

[willow skiff]

it's figurative lol

[willow bear]

ambulance

whatever

[severe pond]

so its Sin(x)Sin(x) - 1?

[willow bear]

sure yes

[willow skiff]

yes

[willow bear]

(sin(x))^2 - 1

[severe pond]

why is this notation so confusing

[willow skiff]

it's like if I write cant

I mean can't = cannot and not the noun cant (a secret language)

it's similar with mathematics; some brackets don't need to be written cause they are implied

[winter comet]

don't you know the order of operations? pemdfas

[willow skiff]

in particularly the brackets around x for trig functions, so tan x, csc^2 x, and so on

[winter comet]

i know thats where f shouldn't go but it sounds funny 💀

[willow bear]

except that in my opinion writing sin x is just bad and looks bad

[willow skiff]

that's just your opinion though

[winter comet]

i agree though

[willow bear]

yeah but it's a correct opinion, because that's all the opinions i hold.

[willow skiff]

if you apply a descriptive rather than a prescriptive approach to the way people communicate

people absolutely write sin x all the time

[willow bear]

i hope it is clear that i meant the last message in a sarcastic if somewhat self-aggrandizing way

[severe pond]

ok so the denominator is actually a difference of squares BECAUSE similar to x²-4, its like Sin(x)² - 1.
thus, it factors to Sin(x) - 1 and Sin(x) + 1

[willow bear]

whence the emoji

[willow skiff]

that's why mathematics is a lot of the time about communication

[winter comet]

people can also write 5/4/3 . . .

[willow skiff]

you don't want to write something that is ambiguous, that's true

[willow bear]

it factors into (sin(x)+1)(sin(x)-1) yes

[winter comet]

but they shouldnt...

[willow skiff]

yeah that's when it's ambiguous imo

[severe pond]

damn i start to have a stroke when i try to insert trig into algebra hahah my brain is very smooth and reflective

[willow skiff]

be lazy with brackets, in the right way

[willow skiff]

if not (5/4)/3, then at least write 5/4 / 3

the space helps a ton

[winter comet]

technically its not, from what i know the order of operations goes left to right when you do operations at the same priority

but yea

[willow skiff]

I know but then that's just bad communication imo

a lot of this is based on how others communicate

it's very subjective as you can tell

[winter comet]

i would just try to leave it as unambiguous as possible

without doing too much extra work ofc

💀

[safe basin]

Js get rid of fractions atp 🙏

[severe pond]

this doesnt look right to me still

[willow skiff]

cause it's sin(x) + 1

not sin(x + 1)

[severe pond]

ffs i want death

[willow skiff]

yes, finally that's correct

[severe pond]

thank u

i decided to drop out

[willow skiff]

,w 1 divided by sin 3pi/2 - 1

[obsidian monolith]

Results provided by WolframAlpha

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Requested by sooouth.

[astral apex]

made a little cycloid animation in desmos. I realized there’s no calculus involved, so I guess I’ll share it to this channel https://www.desmos.com/calculator/5yxenbv39u

[solar olive]

no but actually i agree, sin x is horrible

we ought to be concise as possible and NOT omit any parentheses for function calls

[willow skiff]

Haskell's philosophy disagrees with you

[solar olive]

im sorry but haskell is for NERDS..

[fathom sphinx]

Is my Inductive step correct? For question 10

[willow skiff]

correct so far!

[fathom sphinx]

Oh I was worried about the (2k+1)²+(2k+2)² the most lol

Thx south!

[turbid bloom]

wtf is this

i didnt get a single clue of what was being said

why is e involved

thats my main confusion

why tf is e involved 😭

look at what yall are doing above makes me feel so dumb 😭

[summer ruin]

euler's formula

[viscid thistle]

Well you're looking at imaginary numbers; numbers of the form a+bi, where i = root(-1).
We can plot this numbers on a plane known as the "argand" or "complex" plane. Basically, you plot a point with 'a' as the x axis, 'b' as the y axis.
Join this point to the origin (0,0). The angle made by this line with the x axis is known as the "argument" of the complex number, usually denoted by θ or φ. You can use trigonometry to evaluate this argument (tan(arg) = b/a).
Euler gave us a formula telling us that any complex number (a+bi) can also be written in an "exponential" form: re^(iθ), where θ is the argument and r = root(a²+b²).
This exponential form is equal to a+bi, i.e. a+bi = re^(iθ)

[willow skiff]

look what happens when we multiply two complex numbers together in polar/exponential form:

$$r_1 e^{i \theta_1} \cdot r_2 e^{i \theta_2} = (r_1 r_2) e^{i (\theta_1 + \theta_2)}$$

so, the angles add and the magnitudes multiply
that's exactly what we want from a complex number!

[obsidian monolith]

south

[willow skiff]

(there's a formal derivation using Taylor series; if you want that just search up e^(ix) = cos x + i sin x derivation online)

[flint kestrel]

Is $\int \frac{\Delta y}{\Delta x}=\frac{dy}{dx}$ or $\int \frac{\Delta y}{\Delta x} \neq \frac{dy}{dx}$

[obsidian monolith]

Sapphire (Stacie)

[flint kestrel]

Oh I forgot that $\Delta x$ has $\lim_{\Delta x \to 0}$

[obsidian monolith]

Sapphire (Stacie)

[fading monolith]

Neither

Integral of a derivative will give you the initial function due FTC

The lim as Δx goes 0 of Δy/Δx is y' or dy/dx but do not consider dy/dx as a fraction

[raven laurel]

can anyone explain how to do gauss jordan elimnation using matrices?

[willow skiff]

https://www.youtube.com/watch?v=9PNCjHemIhI

https://www.youtube.com/watch?v=Nxs_OARoUgE

I don't know what you mean
does the 2nd video help?

[elfin niche]

Hey I’m doing this problem and I am asking if the 3 of 4x/3 is apart of the hori stretch or is it a left right transition

[willow skiff]

it's not a translation! a horizontal translation would be f(x - a) or f(x + a)

it's a compression, so a horizontal compression with factor 4/3

that's also a horizontal stretch of 1/(4/3) = 3/4

[elfin niche]

Ohhh

[willow skiff]

yeah

[rain flower]

hey guys how i solve this

(1-i)^96

is a complex numbers problem

[scarlet wyvern]

how do you solve this: 3sin(2x) + 2sin(x) -3cos(x) = 1

with like only the pythag, sum and difference, double angle, and half angle identities

for domain of all reals

[hollow apex]

(1-i)^2=1-2i+i^2=1-2i-1=-2i, then sub that in I think

[hollow apex]

3(2sin(x)cos(x)) + 2sin(x) = 3cos(x) + 1

2sin(x)(3cos(x) + 1) = 3xos(x) + 1

2sin(x) = 1

but that does mean cos(x) can't equal -1/3

[fathom sphinx]

What does undefined mean in math? does it mean that something tends to infinity? or smth

[summer ruin]

it means that it has no meaning

[fathom sphinx]

oh-

thx transparent!

[rain flower]

yeah maybe you're a right

[inner topaz]

turn it into re^itheta

[hollow apex]

isn't that overkill, because (1-i)^96=(-2i)^48=(-4)^24=whatever that is

[fathom sphinx]

when i put ts(x) isnt the result supposed to be 3-3/x+1/(3/x+1)? markscheme says 3-3/x-1/(3/x+1). Markscheme is on the right

[inner topaz]

nah

i mean turning it into re^itheta works for pretty much anything

and it doesnt come out ugly too

$\sqrt{2} e^\frac{i\theta}{4}$

$\sqrt{2} e^\frac{i\pi}{4}$

[obsidian monolith]

Ryse

[inner topaz]

idk why i used theta

sqrt2 to the 96 is nice

e to the whatever is nice

imaginary part cancels

real part becomes 1

it's generally the normal way to do it

[vivid spade]

can anyone help me with a maple lab project ?

this is what i have currently

[scarlet wyvern]

wait but if you divide the cos instead of the sin then you would end up with cosx = -1/3

and then the sinx answers cant exist

[hollow apex]

I think what's going on here is that it represents two mutually exclusive sets of answers

x=sin-1(1/2) or cos-1(-1/3)

but not at the same time

both work when subbed in

[scarlet wyvern]

yea i looked on desmos it says all answers exist but im confused as to why

cause the sin solutions only work when cos is not -1/3 but my cos answers only work when they're -1/3

[hollow apex]

I think its just that there are two answers, when you divide by cos, you are stating the cos is not -1/3 and vice versa

[scarlet wyvern]

oh wait ok i see i see

bruh thats so dumb

[full nest]

Damn.. y’all really mathematicians

[winter comet]

BRO WHAT R U DOING IN EVERY CHANNEL

[full nest]

Idk 😭

[willow skiff]

just like your username

[arctic dagger]

,w incessant

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lkjsfkjsiu

[arctic dagger]

ah ok

cess as in cessation and cease

[bitter sand]

Is the blue line still a asymptote ?
By definition it should be, right ?

[winter comet]

yes

[bitter sand]

aight

its just weird to think about it I guess

[winter comet]

the asymptote occurs when your graph is unbounded, but it doesn't care about the other parts of the graph

like for horizontal asymptotes, the asymptotes can intersect the graph at places lol

[bitter sand]

ye right

thanks

[elfin niche]

I don’t understand how sec is on the 2nd and 3rd quadrant

[arctic dagger]

maybe it's not sec but the angle x

[sturdy hound]

can someone help me find practice problems like these, id really appreciate it

[cedar saddle]

I could give you some later.
Give me some moment.

[sturdy hound]

ok thank you so much

[cedar saddle]

Yeah

I believe I could only give the trigonometry one.

Because that's what I have here.

[sturdy hound]

im fine with that

[sturdy hound]

hello do u still have the problem?

@cedar saddle

[cedar saddle]

You need it like right now?

Is it urgent?

[sturdy hound]

yea my test is tomorrow

[cedar saddle]

Where are you from?

[sturdy hound]

dawg just give me the question

[cedar saddle]

Then sadly I can't help you if it's that urgent.

[sturdy hound]

how does where im from have to do with a math question

isnt math universal

[cedar saddle]

I need to know how much time I have left.

The book is at home.

[sturdy hound]

ohh

[cedar saddle]

While I'm outside.

[sturdy hound]

ok understandable

[cedar saddle]

Yeah sorry.

[sturdy hound]

no its fine i thought u were just avoiding giving me the problem

[cedar saddle]

In the meantime, you can have a look at this first.

[sturdy hound]

ok tysm

[cedar saddle]

Welcome.

[sturdy hound]

btw i would probably have like 2 hours left max

[cedar saddle]

Whoa.

What's your test about?
Algebra and Trigonometry?

[sturdy hound]

discrete maths

i just mean like 2 hours before i go to bed btw

prob like 30 min now

and within that we neeed to know abt sequences and series, matrices, vectors, and proof by induction

[cedar saddle]

Wow.

[sturdy hound]

y wow

[cedar saddle]

Nothing.

[latent musk]

quick question: if i had a circle radius 4, would the horizontal displacement of the angle measure pi/6 be 2sqrt(3)?

[sturdy hound]

yes

[latent musk]

thanks

[marble tapir]

will 2 days to study for my precalc test be enough

[winter comet]

depends

[arctic dagger]

2 days of weekend lel

[marble tapir]

nah tuesday nd wednesday im clueless ab it rn its like vectors tho is that hard

[arctic dagger]

idek

[winter comet]

most likely not too hard but

hard is subjective :l

[marble tapir]

so what u think

[winter comet]

its possible if u lock in fr

[marble tapir]

its cooked huh

but its a half test i dint expect him to give us one bro

[winter comet]

really just depends on what you can do and what they give you lol

[marble tapir]

but atleast it's only worth half the points

[winter comet]

and i know neither so...

[marble tapir]

and tips on studying?

[winter comet]

bro 💀

[marble tapir]

do I js drink coffee nd crank it out

ion even be drinking coffee but might as well

[winter comet]

yeah bro jus try n get it done

[marble tapir]

thursday my birthday too he knows what he doing

[marble tapir]

imma try to ask some sweats if thats the method

[winter comet]

ayy 😭 well happy birthday man

[marble tapir]

thx

[winter comet]

i mean
the main thing is you wanna get it done and not be doin other stuff (like thinking about whether you should be getting it done?) 💀

jus gotta lock in on it frfr

[marble tapir]

i mean i got other work to do still

[winter comet]

yeah

[marble tapir]

js gotta thug it out bru

[winter comet]

mhm

[cedar saddle]

It would be a Yes for me.

[marble tapir]

alr that means its free for me if yes for u

nah im js playing thx

should be possible at least

[granite ibex]

is it just me or is this a terrible way to describe this equation... https://i.imgur.com/ii3qRjm.png

how can they not say what to add 9 by

[viscid thistle]

Wouldnt "square, add 9" mean x²+9?

[granite ibex]

nah because that's not what it says, it says take the square root

[viscid thistle]

Yea but the literal first word is "square"

Root(x²+9)/7

[granite ibex]

no it's not, the first word is add

[arctic dagger]

maybe it's a cropped image

[granite ibex]

I see the confusion tho

yeah

[granite ibex]

dude

https://i.imgur.com/I6wzC3d.png

it's just an example

[viscid thistle]

Ohhhh

Tbf that comma looks like it exactly fits next to add 9

[granite ibex]

😆

[viscid thistle]

Mbmb

[arctic dagger]

I don't think it's terrible. it's like implied you're performing the operation step by step to a given variable (x)

[granite ibex]

I guess. Never seen it before though.

[astral apex]

it's fine, they're just leaving out mentioning your input number. Like we could describe the function f(x) = x + 9 as simply "Add 9 [to whatever you input is]"

[elfin niche]

I’m doing matrices for precalc and I was wonder does the x in 2x=3(e+f) needs to have the two removed are does it stay like that?

[winter comet]

if you're trying to solve for x then you'd divide by 2 yes...is there more context to this tho...

[winter comet]

oh yea you'd want to divide by 2 to get X alone

[elfin niche]

ok

[elfin niche]

Did I get x by itself right?

[sour phoenix]

Hello everyone

Please does someone know a good youtube video where I can learn Curve Sketching?

[fathom sphinx]

To sketch functions with range and domain can i use a table of values? like say from x=-3 to 3?

[uncut mulch]

yes

[fathom sphinx]

For the part b i wrote the range as y>1/9 but markscheme says y<1/9 and for part c i wrote the domain as x>1/9 but markscheme says x<1/9 .My question is why does the sign change?

[willow skiff]

the sign flips when you take the reciprocal

given that x > 4, x + 5 > 9
and now 1/(x + 5) < 1/9

it's like how 2 < 3 implies 1/2 > 1/3

this comes from $a > b \implies \frac{a}{ab} > \frac{b}{ab}, \frac{1}{b} > \frac{1}{a}$

[obsidian monolith]

south

[fathom sphinx]

Oh I see. Does it only apply to the reciprocal?

[willow skiff]

there's a lot of other functions too

it applies to any decreasing function

[fathom sphinx]

If only life was that simple..

[willow skiff]

1/x is always decreasing for example

[fathom sphinx]

Fr

Ah I see

Thx south!

[willow skiff]

a logarithm with 0 < base < 1 is always decreasing

e^(-x), so many others

[willow skiff]

no worries!

[fathom sphinx]

So south when do I graduate from sociology

!!

[willow skiff]

never.

[fathom sphinx]

WHAT!!

[cosmic crow]

if you wanted to reflect y=x^3 across the line y=x would it become y = -((-x)^3)?

[whole void]

nah

what u have is just x^3

[inner topaz]

if y = x you literally swap y and x

[echo sinew]

This is equivalent to the inverse, which is ||³√x||

[arctic cloak]

I havent taken precalc just trig and algebra am i cooked

[willow bear]

what is coming up in your immediate future that's making you think you might be cooked?

[arctic cloak]

Differential equations calc 1 2 and 3 and statics and thermodynamics and matlab

oh immediate
calc 1 this summer

[willow bear]

in that case calculus 1 will probably be painful but calculus classes tend to have a precalc review at the beginning

so maybe you will survive

[sweet path]

Trig equation, solved in 2 different ways. First way I divided both sides by sin(x) and therefore lost a solution when sen(x) = 0. I should always avoid dividing by either sin, cos or tan, right?

[willow bear]

you should not AVOID it as such, but you should know the consequences of doing it and adapt accordingly

if you first take the time to account for what happens when sin(x) DOES equal zero, and then divide by it to look at what happens when it doesn't,

then that will also be valid

[leaden cave]

Hey I just had a quick question, I am currently self studying calculus and am having trouble with what is the best way to compute 5^23/5^21 without a calculator and without me having to write out 5*5 23 times and then again but 21 times

[willow bear]

exponent laws.

$\frac{a^m}{a^n} = a^{m-n}$ specifically for this case

[obsidian monolith]

ann.in.a.teacup

[leaden cave]

so then it would just turn out to be 25

[willow bear]

indeed

[leaden cave]

You are an amazing human being have a wonderful day or night!

[blazing kite]

How would you outline the skeleton of set theory

Is it just a finite list of axioms and theorems based on them or something more

[rapid spade]

Shouldn't it equal to sin(2x) & not sin (x) ?

[wanton isle]

yo guys are polar equations and polar graphing in precalculus or in calculus 2

[slim steppe]

From my semester at college experience, calculus 2

[livid mica]

Hi

Im going to have an aneurysm

trying to understand the unit circle and i have to memorize tan sin cos cot csc sec and all that jazz in a few days

and im just a wince pissed off

it makes no sense and sure youre supposed to find the pattern but it logically just doesnt make sense to me

how do I go from 5p/6 to 7p/6 then right back to 5p/4

how does this make sense

the only pattern I understand so far is the 6 4 3

[winter comet]

both. . .

[livid mica]

I forgot to say please, just really frustrated

[willow bear]

i think you're focusing too much on which values happen to be adjacent to each other

when really what this picture shows is three (maybe two) more straightforward patterns overlaid on top of one another:

• going in steps of pi/2 (quarter circles)
• going in steps of pi/4 (2 steps to a quadrant)
• going in steps of pi/6 (3 steps to a quadrant)

[livid mica]

understood

tell me please

is there any logic besides patternfinding and memorization

im not used to applying this to math except for loosely

for memorizing specific formulas then working out a problem

I dont enjoy this

[willow bear]

not sure what you mean here

the values of trig functions at all of these angles can be derived from two basic shapes: a square and an equilateral triangle

plus symmetries of the unit circle

[royal silo]

is anyone else really clueless on parametric circular and elliptical vectors?

[queen grail]

a unit circle is called a unit circle because it has a radius of... 1
which means the diameter is... 2

the equation for circumstances of a circle is diameter multiplied by pi
and since the diameter is 2 the circumference of the unit circle is 2pi

what is another way to measure circumference? degrees.
circumstances of a unit circle = 360°

which means 2pi = 360°
if u divide both sides by 2, it's pi = 180°
divide by 4, it's pi/2 = 90°
divide by 6, it's pi/3 = 60°
divide by 8, it's pi/4 = 45°
divide by 12, it's pi/6 = 30°

[rapid spade]

π = 180°
So put 180 in place of π & divide. It should make sense

[warped shuttle]

is the inverse of every increasing function, increasing and every decreasing function, decreasing ?

[willow skiff]

correct

there's a theorem relating the gradients of inverse functions

say you have (change in y)/(change in x) for f(x)

for f^(-1) (x), the gradient of the corresponding point across y = x is (change in x)/(change in y)

(change in y)/(change in x) * (change in x)/(change in y) = 1

so that means that the slopes must have the same sign

now recalling positive slope = increasing, negative slope = decreasing
the result follows

[warped shuttle]

Thanks !

[cerulean orchid]

Hi guys

[scarlet wyvern]

anyone got law of sin and cos practice?

[livid mica]

im reading this in vanellopes voice

[shy falcon]

😄

[river drift]

<@&268886789983436800> steam scam

they just keep coming

[brazen scaffold]

reallly good video on deriving and explaining the hyperbolic functions and where they come from
https://www.youtube.com/watch?v=NVC1w4_ulzI

[arctic dagger]

how long is the video

sinh ka noko noko noko cosh tanh tanh

[brazen scaffold]

its a 30 mins but its very enjoyable and thorough and it doesnt hand stuff down from up high

[acoustic tartan]

How do I solve these types of problems? I looked at the given examples, but it didn't make much sense to me.

[brazen scaffold]

plot z1 and z2 on an argand diagram

[willow skiff]

magnitudes multiply and angles add

the arctan(y/x) formula is incomplete, because it only gives a 1st or 4th quadrant angle

so after plotting you will know whether to subtract 180 degrees or to add 180 or 360 degrees

[woeful star]

help with trig sub pls

[arctic dagger]

what is trig sub

[river drift]

https://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx

[arctic dagger]

i thought precalc has it's own use for trig sub

[low latch]

hey guys, what r the main components for pre calc that i should know (im taking honors pre calc as a sophmore next year)

[uncut mulch]

polynomials/ functions
rational functions
trig
exponent/logs
intro to limits

[winter comet]

also possibly seres, polar/parametric

[stoic crest]

can someone help with this problem?

[winter comet]

what's the problem

all i see is an undefined expression that is equal to a box

💀

unless dx isn't supposed to be a differential

and literally the product of d and x

but theres still no instructions what r we supposed to do with it

so yea whats the problem

[inner topaz]

is this some kind of 0^0 problem

[acoustic hound]

Same conclusion here, even taking log doesn't help

[sturdy hound]

question: find the angles (radians) at which the radius will equal 1
can someone explain how my teacher found the other two values 7pi/6 and 11pi/6? i get the first two values but i dont understand how my teacher got the other two values.

[willow skiff]

the period of cos x is 2pi

so you could also have 2theta = pi/3 + 2pi and 2theta = 5pi/3 + 2pi

that gives you theta = pi/6 + pi, 5pi/6 + pi

[inner topaz]

you let r = 1

so $1 = 2\cos{2\theta}$
$\cos{2\theta} = \frac{1}{2}$

the angles for which the cosine of $2\theta$ is equal to $\frac{1}{2}$ is just 60 degrees and 360-60 = 300 degrees

change them into radians it's $\pi/3$ and $5\pi/3$

so
$2\theta = \frac{\pi}{3}$
$2\theta = \frac{5\pi}{3}$
$2\theta = \frac{7\pi}{3}$
... and so on adding 2pi everytime if you want some "bigger" angles

values for theta should be quite clear just isolate theta (divide by 2 both sides)

[obsidian monolith]

Ryse

[inner topaz]

generally 2 solutions is enough since yeah they kinda repeat

[fiery crest]

I really don't understand polynomial and exponential functions at all

[tired garden]

like, you dont understand their definitions? or you dont understand their properties?

can you be more specific

[fiery crest]

like idk we were doing something completely different last week and now it wants us to find a exponential equation from 2 points and stuff

[tired garden]

ok so what questions do you have

do you know what an exponential function is? are you having difficulty solving that problem?

[bright abyss]

bro precalc

;(((

too light

[sturdy hound]

i think my teacher wants us to find all possible solutions from 0 and 2 pi

[surreal storm]

Send a specific problem you need help with

[safe basin]

or if u don’t have an example on hand at least narrow down what you’re asking

[surreal storm]

Right

@fiery crest

[sterile halo]

hey recently i came across to learn differentiation from 3blue1brown youtube channel. There he explained about how to visualize the function x^3. He started saying that "differentiation is nothing but a tiny rate of change" and showed an animation where a cube's dimension got slightly increased. I don't know why he increased the dimension that way. I need help in understanding why he did that. The title of the video is "Derivative formulas through geometry | Chapter 3, Essence of calculus" and time stamp is 4:47

[willow skiff]

ah, the point isn't that you increase the cube's volume by say 1 unit directly

you increase the side of the cube by 1 unit

or by 0.01 units and so on

[versed acorn]

He was trying to show why the rate of change/ differenciation of x^3 is 3x^2, he couldve increased or decreased slightly but yeah he went with increasing it by a little amount, now the extra increased part could be divided into 3 squares (it has a little bit of width but we ignore it as dx is very very small) and a few other corner parts, now if you add the areas of the 3 sides, x^2 + x^2 + x^2 you get 3x^2, which is the differencation or rate of change of a cube.

[willow skiff]

if you think of x^3 as a function, the input is the side length of the cube, and the output is the cube's volume

you want to make a tiny change in the input

and see what the change in the output would resultingly be

that's the principle behind differentiation

x is the side length, and dx is a tiny, tiny change in the side length

then Grant (the 3b1b) guy proceeds to find the change in the volume in terms of x and dx

then let (dx)^2 and (dx)^3 become 0

[sterile halo]

Thanks @willow skiff and @versed acorn . I still have doubt shouldn't there be 6 squares instead of three?. I don't know why but when i think about "increase" , I imagine the whole cube to be bumped up

[willow skiff]

I think you've confused the volume with the surface area of the cube

oh wait no

like you're increasing the volume by making the base longer, the height longer, and the length longer

you make the base longer in 1 direction

[versed acorn]

exactly

[willow skiff]

and the height and length longer also in 1 direction

so 3 squares in total

[sterile halo]

Nice @versed acorn and @willow skiff . Now i can imagine why he did that

[willow skiff]

no worries!

yeah I mean for me it's easy to say just expand (x + dx)^3, goddamnit

but I now see the visual explanation is also fairly satisfying

[sterile halo]

yeah it does

[willow skiff]

beauty of maths

[viscid thistle]

hey would anybody be down to tutor me for pre calculus? this is my senior year and im currently failing that class and need a lot of help haha
we are currently working on trigonometric identities and equations

[willow skiff]

sorry, we don't do tutoring on this server

[viscid thistle]

aw

[uncut mulch]

you are however free to claim channels and post hw you're struggling with
and many will be happy to assist in clarifying issues

[tired garden]

which is honestly almost as good as tutoring

you should take advantage of it

[willow skiff]

I mean also look at the above advice

there's genuinely no limit to how many questions you can ask in the help channels, as long as you ask one at a time

[tired garden]

and its free!

[viscid thistle]

hello guys

[surreal storm]

Hello

[viscid thistle]

wazup everybody

[viscid thistle]

does anyone have a pdf file for this book??

[arctic dagger]

try in #book-recommendations

[crude quest]

i want ot get the derivitave of this functiion but how do i deal with " c " ?

i assumed "c" was a constant but when i checked the asnwer it told me i needed partial derivitave

[willow skiff]

looks like the chain rule then

so when you differentiate cu, you get dc/du * u + c

[chrome inlet]

heres ur average indian math problem

[willow skiff]

what the hell is the pattern

how does the last term work

[chrome inlet]

Jee adv 2022

I didn't get it

You somehow have to find the general term and then integrate it

[willow skiff]

finding the general term is a nightmare

they should just give it

[chrome inlet]

Yea if that was the case everyone in india would get into iits

[willow bear]

this is so fucked

[willow skiff]

agreed

[chrome inlet]

guys you do realize that my classmates actually solved this bull shit

in like 10 mins

[willow bear]

i heard that jee adv requires knowledge of trickery more than it does math

[chrome inlet]

I have been preparing for that since the 6th grade

and im in 10th now

and I can confirm

yes its true

@timber forge

[willow skiff]

is that adv btw?

the problem

[chrome inlet]

yes

[chrome inlet]

One of the geniuses who solved that

[willow skiff]

Sir I am 16 weeks old in my mom's womb. I am unsure of whether my mother is planning to get me aborted or keep me.

[chrome inlet]

wtf

[willow skiff]

oh you don't recognise the copypasta?

https://www.reddit.com/r/DesiCopypasta/comments/op7acg/im_in_my_mothers_womb_right_now_is_it_too_late_to/

[chrome inlet]

oh shit

I dont read reddit

im prepping for jee

dont got time for that

@empty vine

One more genius

[timber forge]

@willow skiff

finding the general term is actually easy

so

[chrome inlet]

yea

the integration is hard

asf

[timber forge]

first write the general term for the first 3 terms given

Tr

then substitute n in that

then you get the last term

so all of it has a general term

[chrome inlet]

In the last term r = n

I just figured it out

[icy jetty]

The n has to be distributed to the remaining n terms

[chrome inlet]

n tends to inf

[timber forge]

hmm

[chrome inlet]

and r is the no of term

like rth term

like for the first term r = 1 and the 2nd term r = 2 and so on till r = n

[icy jetty]

So try to find the rth term

As a formula

Ignore the first n for now

[empty vine]

if u need help

[solid spire]

Ez

[chrome inlet]

the rth term is (16r + 9n/4rn + 3n^2)-1

[willow skiff]

thanks kheerii was explaining the whole time

I got it now

[icy jetty]

Yes

[empty vine]

in the middle i got deviated and was trying random bs

[chrome inlet]

lol

[icy jetty]

The n in the beginning can be distributed to all the terms to get rid of that 1

[solid spire]

Lemme send my sol

[empty vine]

then like didi the converging series bs

*did

small flex but i went to the 2nd state of MO in my country

small compared to u guys accomplishment ig

[chrome inlet]

bro send that in #competition-math

[empty vine]

but then we had summation bs

[empty vine]

mb

[chrome inlet]

wait how did u take n= 0?

[solid spire]

When tf did I take that

It's infinity

[empty vine]

how tf did he get the ans in a pg

[solid spire]

Idk

[empty vine]

it took me like 2 to generalise and 4 to integrate

ig im dumb

[solid spire]

Nah tf

[empty vine]

i dii int by substitution

[solid spire]

U ain't bruh

Nice

@chrome inlet

[chrome inlet]

beside the place u wrote r= 1

[solid spire]

U got it?

[chrome inlet]

yea i got it

[solid spire]

Wait lemme check

[chrome inlet]

but

[solid spire]

Nah that's infinty

It looks like 0

Lol

[chrome inlet]

k

[solid spire]

Yeah

[solid spire]

Hm?

[chrome inlet]

you took limits from 0 to 1?

[solid spire]

Yeah

I wrote the explanation for thaylt

That*

[chrome inlet]

wher

oh nvm

[solid spire]

Yeah lol

[chrome inlet]

yea ok i see it

[solid spire]

Yeah

[fiery crest]

im doing precalc 1 all online and my teacher gives way too much stuff to watch/read what should i do to learn each part instead?

[torn robin]

Just put some priority over that. work on stuff where you will have soon a test about it

[turbid sequoia]

Say you were to have

$f_1 + f_2 + f_3$

[obsidian monolith]

whyhello

[turbid sequoia]

Can we write this as

$\sum f_t = f_1 + f_2 + f_3$

[obsidian monolith]

whyhello

[turbid sequoia]

Let f be force

and f_t be total force

Or is it inappropriate to use the summation symbol in this way

[willow bear]

it is inappropriate

just $f_t = f_1 + f_2 + f_3$

[obsidian monolith]

ann.in.a.teacup

[turbid sequoia]

I mean

Ive seen physics textbooks use the symbol is this way

For example

$\sum P_{before} = \sum P_{after}$

[obsidian monolith]

whyhello

[turbid sequoia]

and

[astral apex]

if f_t is defined as the total force, then you shouldn’t use the same t as an index in the sigma notation

[turbid sequoia]

$\Delta_rH = \sum n \Delta_fH^{\circ} products - \sum n \Delta_fH^{\circ} reactants$

[astral apex]

you could use something like i or j and it’d be fine

[turbid sequoia]

weird

how 2 get ∆ symbol

anyways you get the point

[turbid sequoia]

I see

[astral apex]

$\Delta$

[obsidian monolith]

ManifoldCuriosity

[turbid sequoia]

there we go

[obsidian monolith]

whyhello

[turbid sequoia]

But yeah

Im just confused with its use

or is this just a physics thing

[astral apex]

what’s use?

[turbid sequoia]

The summation symbol when it comes to this context

[turbid sequoia]

or this

Because its inappropriate

[astral apex]

I think they were just saying if f_t is defined as the total force, then it’s inappropriate to put a sigma in front of f_t like that

[winter comet]

would it be inappropriate because f_t would mean the total force rather than the force at index t?

a

you can still use the summation/sigma notation tho

just the f_t could be a bit confusing

[astral apex]

honestly though f_t isn’t a common notation for a total force, and it looks kind of weird. Suggestive of some kind of time parametrized function

[willow bear]

if you wanted to be really silly you could say $f_t = \sum_{i=1}^3 f_i$

[obsidian monolith]

ann.in.a.teacup

[astral apex]

it’d be more typical to write something like $F_{\mbox{net}}=\sum_{i=1}^3 F_i$

blargh!

[obsidian monolith]

ManifoldCuriosity

[astral apex]

or F_tot

for total

[winter comet]

tater tot

[turbid sequoia]

ahhhhokay

I see

thanks guys

[turbid sequoia]

but what about in this situation?

another example would be

uhh

$H = -\sum p(x)\log(p(x))$

which is the formula for information entropy

[willow bear]

there is a dedicated \log command

you should use that

$-\sum p(x) \log(p(x))$

[obsidian monolith]

ann.in.a.teacup

[turbid sequoia]

ohhh okay

🌚

[obsidian monolith]

whyhello

[plucky dove]

Zurp

[finite hill]

anyone got the ap precalc mathmedic?

[zenith hatch]

guyss i need helppp

[safe basin]

[tough lake]

I’m in pre calculus 11 and I don’t like graphs all that much although I don’t mind doing them

I’m taking pre clsuxlus 12 and my friend who took pre calculusis 12 saying that it is all graph pre calculus 12 is all graphs

Here is the cirriclulum can someone tell me who knows this cirriclulum if this is all graph:
Arithmetic and Geometric Sequence and Series

Unit 2

Transformations

Unit 3

Polynomials

Unit 4

Exponential and Logarithmic Functions and Equations

Unit 5

Rational Functions and Conics (just very basic Conics)

Unit 6

Trigonometric Functions

Unit 7

Trigonometric Equations and Identities

[winter comet]

besides the first one those should all have a fair amount of graphing

like "transformations" sounds entirely like graphing lol

the last one maybe less as well

[winter comet]

i mean, it generally is lol

[inner topaz]

yeah you will be seeing a bunch of functions

they're not bad though

[runic dew]

i wanna learn calculus where should I start and what should i have already learnt

[warped shuttle]

is this proof valid for the power rule ?

[daring ridge]

bro which grade do they teach this stuff in, i can see differentiation and limits but wtf

[warped shuttle]

there is basically nothing more than limits and differentiation tho ?
the first statement is the Binomial theorem(https://en.wikipedia.org/wiki/Binomial_theorem)

[daring ridge]

really impressed

but where are you reaching with it

you know this so what,

[warped shuttle]

grade 11

[daring ridge]

in which fucking country

[warped shuttle]

iran, although differentiation is for grade 12 i just studied it earlier

[daring ridge]

bro, you guys must be solving the time travel eq in uni

[warped shuttle]

we had integrals at grade 12 before but they removed it

[daring ridge]

im writing JEE Adv in like 80 days, but im dead ass sure even they dont go this much

[daring ridge]

i have integral calc too, love it man, its soo like fun and challenging and there's no limit, and the bad part is there is no limit

[warped shuttle]

yea limits are easy

[warped shuttle]

nah JEE Adv is more complicated

[daring ridge]

yeah sure not in calc, ive solved most previous year q's and nothing even reaches what youve written

[viscid thistle]

This?

[daring ridge]

im talking the third line,

[daring ridge]

your pronouns are crazy, you should bet get a lot of girls, or boys

[viscid thistle]

I mean he's used binomial and definition of limits

[warped shuttle]

is it correct ?

[viscid thistle]

I just took everything lmao

[viscid thistle]

Yeah seems to be good

[daring ridge]

tell me one thing, where is all the population going

learning complex math and phy,

and then end up doing MBA and work smth totally different

[warped shuttle]

that's where the money is

[warped shuttle]

thanks

[viscid thistle]

Arts 🤣

[viscid thistle]

Best of luck man!!!!

[warped shuttle]

what are the ways to find a function's Range if we have only the equation ? do we need to differentiate it ?

[daring ridge]

analyze its behavior (e.g., vertex for quadratics, limits for rationals) based on its domain, and differentiation isn’t always required unless finding critical points helps determine extrema

[viscid thistle]

Well there can be different methods.
A linear/linear fraction $\frac{ax+b}{cx+d}$ range can be found by taking it equal to y and ensuring denominator not 0.
Some functions may require more in depth thinking. Differentiation isn't always required for range tho.

[obsidian monolith]

UnexpectedTaco

[fallow egret]

Alr I have a stupid question, how do you approach this? I tried l’hopital etc

$\lim_{x \to \infty} \frac{e^{2x} - 3e^{-x/2}}{e^{x/2} + e^{-x/2}}$

[obsidian monolith]

_Sander_

[daring ridge]

l'hsopital untill you pass out

[fallow egret]

No it doesn’t work

[winter comet]

what about dividing by e^(2x)

[fallow egret]

I keep getting inf/inf

[warped shuttle]

because derivative of e^x is e^x

[viscid thistle]

Lhopital wont really get to you anywhere cause dy/dx(e^x)is just e^x anyway

[fallow egret]

Wait I wrote it wrong

[daring ridge]

whos from india or gave jee here??

[fallow egret]

Its the limit of -inf

[winter comet]

lotsa people frfr

[fallow egret]

Wait i got it

Nvm

You multiply by e^x/2

Top and bottom

Thx anyways

Yeah i have -3 now

[daring ridge]

how do you people do math guys, i feel i have soo less days, and my phy and chem is on par with advanced, i feel i should let go of it

but i also think somehow getting good can give me a really good edge

[warped shuttle]

Imo sharpening your math skills will make you better at phy and chem

It helps strengthen your problem solving skills

[brazen scaffold]

im not sure how to do ii)

[inner topaz]

is that an n

[brazen scaffold]

yea

i think those guys set me up

theres no i in that 2πn

so i cant convert to mod arg form then combine

[inner topaz]

i dont think it's even true lol

[brazen scaffold]

yea they forgot the i 😭

[inner topaz]

yea

[brazen scaffold]

im suing this book man 😭

im getting my skl a refund

[inner topaz]

can rewrite that as
$e^z * e^{2n\pi}$

[obsidian monolith]

Ryse

[inner topaz]

that's just a constant

you cannot tell me ke^z = e^z

for any k

[river drift]

well it would be true if k = 1

[inner topaz]

i mean yea

[brazen scaffold]

if they had the i in 2πn

[inner topaz]

when n = 0

[brazen scaffold]

then it would be true

[inner topaz]

ye

[brazen scaffold]

but they dont have i 😭

[river drift]

which is why it would be true if it was [ e^{z} = e^{z + i2\pi n} ]

[obsidian monolith]

cloud

[brazen scaffold]

ye

[inner topaz]

objection, trick question!

[terse ridge]

If you know taylor expansions, i would use that

Or you can convert to polar cords such that your expression would become r*e^(i * theta) where r is sqrt(a^2 + b^2) and theta is the arctangent of a / b

[brazen scaffold]

it turns out

that ii) is plain wrong

[brazen scaffold]

theres no i in the 2πn expression to convert it anyway to the nice mod arg form of cos(2πn) + i sin 2πn which for all integers n is gonna be 1

so that question is just wrong 🔥

gonna be sending emails to the authors fr

[terse ridge]

well we are assuing that z is complex no?

wait ur right

[brazen scaffold]

a

[terse ridge]

i would ask chatgpt 😭

[brazen scaffold]

there is no chatgpt its just plain wrong

the question itself is wrong

[terse ridge]

wow

[brazen scaffold]

the statement is wrong

[terse ridge]

thats actually insane

[brazen scaffold]

🔥

[terse ridge]

welp youre gonna be famous

[brazen scaffold]

gg

[brazen scaffold]

this book has some mistakes throughout it which is weird

since its supposed ot be

the 7th edition lmfao

[random flax]

Can someone help me with these problems please? We have to factor completely.

[arctic dagger]

,,(a\pm b)^2=a^2\pm2ab+b^2

[obsidian monolith]

0_א

[random flax]

Can u help further please like steps if possible.

[arctic dagger]

the key is to recognize a and b

and on how to turn something into a²±2ab+b²—can be achieved usually be factoring out a factor(s)

if you can't, personally i think it's pointless to learn that. idk i might be wrong

[past widget]

27

[arctic dagger]

find it's discriminant?

[whole void]

use vietas

[steel kernel]

Why suddenly there is d/dx (5x+3)?

[winter comet]

the chain rule
d/dx [f(g(x))] = f'(g(x)) * d/dx g(x)

[willow bear]

!nogpt

[tender quest]

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).

[willow bear]

do you still need help with this?

[viscid thistle]

starting to learn calc now

😞

I hope it will not be too hard

[willow bear]

this is not yet calculus

also the hardest part of calculus is the algebra

[viscid thistle]

oh no

😭

any tips

[willow bear]

that was my biggest tip

[turbid sequoia]

if good at algebra = greatnees in calc

if bad at algebra = howd u even make it into calc

[vernal lynx]

one rule is missing in this chart

log a to the base b = log a to the base c divided by log b to the base c

theres another one for change of base

log b to the base a = 1 divided by log a to the base b

its known as change of base method

[vernal lynx]

i would recommend to use this one

[viscid thistle]

i am pretty bad at algebra

i forgot how to rearrange

formulas

do u have any videos I can watch

[vernal lynx]

https://youtu.be/gRbortS-ZqA?si=eU2G7ykVFtTEZHI_

try this video

[viscid thistle]

does it go into complex problems

i know how to do the easy ones

also thanks

[vernal lynx]

complex problems as in ?

oh in case its xy or smth

wait ill check for that

[viscid thistle]

u factorise if that happens?

[vernal lynx]

mostly yeah but depends on the question

not all the time

ill give an example

by complex you meant smth like these right ??

by the way this will go further off topic since this is a channel for precalculas

but again these basics should be well versed before starting it

[warped shuttle]

Would start of calculus be limits ?

[willow bear]

yeah

[summer ruin]

the first derivative for C is not positive for x < 1

[terse ridge]

Oops my fault

I use o1 pro and it works pretty good for me, but not everyone has it

[willow bear]

all GPT models are inherently not able to distinguish fact from fiction

[terse ridge]

I mean yea but the reasoning models and higher compute models use better algorithms and can assign closer weights. They essentially do the same thing humans do: Say probable words, they just use an explicit algorithm. And that’s not to say they can’t be useful. Obviously I wouldn’t trust it with postgraduate math, but even free users have access to the o3 deep reasoning model, which I am very confident can handle precalculus and calculus 1. In my experience it has very high accuracy with all math (precalc, calc 1-3, linear algebra, set theory, real/complex analysis), only making minor compute errors due to programming language issues, not only that, it aces standardized tests, scores above average on math Olympiads, and overall has very high PhD level math scores. And they can distinguish with deep reasoning models, they will discern contradicting information and fact check things online using reputable sources. Also, it is trained on human data and patterns, so no matter what, everyone inherently does not know fact from fiction, it is all dependent on our interpretation. ChatGPT uses a mathematical interpretation to give the best answer 🙂. I do agree that this server is not the place for that because there’s no point in asking for an answer just to get one you could have found yourself, however it is wrong to say that ALL ChatGPT models are inherently wrong due to their training process and the way they function. In my case, I referred them to ChatGPT due to an error in the book that would have been fixed by the LLM, I was not giving him a ChatGPT answer. Oh, also, look at the #rules try to back up arguments with objective facts.

[tired garden]

still dangerous to use LLMs as a source

try not to use it if you can help it

none of those metrics really matter because it cant actually reason or discern truth

[terse ridge]

That’s fair, but with new models, they will search the web and cite their information.

Thank you for that perspective.

I got kinda fired up because the other guy was kinda snarky.

And discerning truth is a tough thing because technically when we do math, we operate under rules and axioms. The computer does the same thing, and it can reason out what’s going to work and what’s not going to work. So while it may not have an intuition of right vs wrong, it can certainly figure out mistakes.

I believe that it’s a useful tool to learn concepts, but it should not be doing your math work. However, the metrics do play a role because in higher level math, it does require the model to have everything right or else the problem won’t work out, in which case it will correct itself until a logical flow is achieved and verified with Python code. The computer checks its answer against a Python program that it makes to solve the problem.

[tired garden]

it cant verify the program works correctly

unless it has a finite set of expected outputs and checks every output

LLMs do not operate under formal axioms the same way math does

it is a statistical sampling of "what character is most likely to appear next?", trained on how to deceive humans into thinking its output is human generated

this is why we say it fundamentally is not a good source, ever

this is definitionally how all LLMs work, at their core, no matter how many other auxiliary AIs you slap on top of it

it is always prone to error and is easily tricked into being overconfident, sometimes with no way to verify depending on the topic

im not here to start an argument, im simply telling you how it works

use it at your own risk, and certainly dont promote its usage here

other person was correct and imo not snarky, just terse

[terse ridge]

Idk I think that if someone says “my fault” my default response would definitely not be that, but that’s fine ig

[tired garden]

just saying "my fault" indicates you understood you broke the rules, but you may not understand why you shouldnt use AI for logical reasoning

ann responding was to give you a terse one sentence response as to what they believe you hadnt understood yet

[terse ridge]

I did acknowledge it though

I said I use a very advanced model and that may not be applicable all the time

In any case I think that an actual explanation would have been in order instead of a short snap back

[tired garden]

you reflexively defended the use of AI with a giant wall of text not appropriate for the channel

[terse ridge]

Sure! Here’s a more detailed and persuasive response that explains why LLMs are often correct while addressing the concerns raised:

“I get where you’re coming from, and you’re absolutely right that LLMs don’t follow formal mathematical axioms in the same way a proof system does. They generate responses based on statistical patterns rather than strict logical derivations. However, that doesn’t mean they’re inherently unreliable or incapable of producing correct answers most of the time.

LLMs are trained on vast amounts of high-quality data, including rigorous mathematical texts, proofs, and problem-solving methodologies. Because of this, they often replicate correct reasoning with a high degree of accuracy, especially in well-documented fields like calculus, algebra, and statistics. When they make mistakes, it’s usually due to limitations in context, misinterpretation of ambiguous prompts, or overconfidence in certain probabilistic outputs.

That said, their effectiveness depends on how they’re used. If you treat them as a tool—like a powerful but fallible calculator—rather than an unquestionable authority, they can be incredibly useful. For example, they can:
• Solve structured problems correctly the majority of the time.
• Provide step-by-step solutions similar to human reasoning.
• Offer explanations and alternative approaches to problems.
• Assist in debugging errors in calculations or code.

The key is knowing when to verify outputs, just like you would double-check a human’s work or a calculator’s result. Dismissing LLMs entirely ignores their practical benefits, just as blindly trusting them can lead to errors. The best approach is to use them critically and responsibly, leveraging their strengths while understanding their weaknesses.”

This response acknowledges the concerns while making a strong case for why LLMs are still highly useful and mostly correct.

[tired garden]

.... did you just chatgpt me as i was explaining why you cant use chatgpt for reasoning

are you serious mate

[terse ridge]

Yes

Look at it

And tell me it’s wrong

[tired garden]

im not reading that

[terse ridge]

Tell me it’s not what I said

Welp

[tired garden]

i have studied AI myself

[terse ridge]

Ignorance is bliss

[tired garden]

im not here to start an argument

[terse ridge]

I’m not either

I am just trying to help people

[tired garden]

you are quoting chatgpt at me while im explaining why not to use chatgpt

ok

can you tell me what AI alignment is

[terse ridge]

And if that means they use a 99% effective outside source then so be it

[tired garden]

what is AI alignment

[terse ridge]

That doesn’t matter

That’s not what I’m arguing

[tired garden]

ok you have zero idea what youre talking about

[terse ridge]

And there it is

Lmao

All I’ve been doing is trying to say that AI is an effective tool

And you insult my intelligence and resort to off topic questions

Oof

“AI Alignment” is self explanatory

It’s in the name

[tired garden]

if you dont understand algorithmic bias, under and overfitting, explainability issues, alignment, prompt injection attacks, then you dont have any clue of the basics of what can go wrong with AI, and you are not equipped to be making these comments with authority

[terse ridge]

Womp womp

[tired garden]

stop promoting LLMs and I recommend you stop using them as much as possible

[terse ridge]

Why

What’s so bad?

I’ve never had an issue

[tired garden]

i literally gave you an explainer and bunch of topics to read up on

[terse ridge]

I use it avidly for high level chemistry and math

Never been wrong

[tired garden]

and you decide to start an argument with me instead

[terse ridge]

Nope

I said it’s an effective tool

You said no

I said yes

You insult my intelligence

Boom

Argument

I want people to have the best opportunity to learn

And sometimes the computer just does it better

Not only that, it is more reliable

[tired garden]

not sure if this is an appropriate ping but gonna try, can <@&268886789983436800> clean up this channel a bit? i apologize for my role in the derailing

[terse ridge]

Fair enough

Literally 0 things in the rules saying I can’t refer people to a resource that is highly effective, don’t insult my intellect. There was no reason for Ann to respond like that, there was no reason for you to respond like that

[tired garden]

!nogpt

[tender quest]

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).

[tired garden]

thats a rule

[terse ridge]

Look at the last sentence

I told him it look it up

[half star]

that refers to passing LLM answers as your own

but I agree this convo has gone way past the scope of this channel, move to e.g. #serious-discussion if you want to continue it

[terse ridge]

Fair

[terse ridge]

One question though, is it reasonable that say ChatGPT is an effective tool given its benchmarks (referring to it explaining a subject). For future reference, I don’t want to do this again.

[half star]

there's a lot of debate surrounding what said benchmarks actually measure so a big number on those doesn't automatically mean it's accurate, you should still view it as a tool and make sure to check the output thoroughly. The issue is that a beginner is usually less equipped than an expert to fact check, so in no way an LLM should replace e.g. a teacher or a community like this. At most it might complement it

[terse ridge]

Alright then, thank you for the clarification, I’ll make sure to be more specific

[half star]

(Last on-topic msg around here, for reference)

[brazen scaffold]

just going to put this here in case someone offers help for it
ive gotten the denominator in part 3) but i just cant get the numerator at all