precalculus

[smoky schooner]

UAE

[random swallow]

Are you sure that's a good idea?

[tame linden]

Wdym 👀

[random swallow]

Like, that book is college level

For computer courses

[tame linden]

Yes I am aware
I'm in my first year

[tame linden]

.

[random swallow]

Oh that's good then, considering that you mentioned precalc I thought you were a kid

Like me

Lol

[tame linden]

Im doing that too, im kinda weak in maths

[random swallow]

No more, keep grinding

[tame linden]

I studied a lot but i still got a very low score in my quiz 1

[random swallow]

Issokay

[tame linden]

So I'm gonna study harder 🥲

[tame linden]

😭🫂

[random swallow]

Make sure to not overwork yourself

You got this

[tame linden]

Thankyou 😭😭🫂🫂

[random swallow]

Bye

It's nighttime in my timezone

[tame linden]

Mine too, it's 1:30am

[random swallow]

Fellow indian😭

[tame linden]

Omg 😭🫂

Unexpected

[random swallow]

Hell ya

Yayyy

[tame linden]

Wanna be friends

?

[bronze geyser]

where

olympiads?

or meritus academy now ig

[random swallow]

Sent u req

[keen bone]

none

[bronze geyser]

oh

just self teach?

[keen bone]

no, i dont wanna tell u. u alr know too much 😭😭😭

[bronze geyser]

https://klipy.com/gifs/evil-grin-evil-smile-2

Bro i cant even do nun if i know

[keen bone]

eh true but still

[bronze geyser]

patrick has elite ball knowedge

[keen bone]

HEYYY RICKLI UR AN INFANT

[bronze geyser]

id rather be an infant than an unc

https://klipy.com/gifs/balls-warp

[keen bone]

ur the oldest here...

[bronze geyser]

And the most knowledgeable

https://klipy.com/gifs/parker-dirt-off-shoulder-dust-off-shoulder

[keen bone]

hmmmm sure

ricklis here

[bronze geyser]

ricklis here

[valid topaz]

wut

[keen bone]

@valid topaz

ur the smartest

[valid topaz]

no

[bronze geyser]

Elite ball knowledge users all understand one thing

stay humble

https://klipy.com/gifs/lebron-elite

[valid topaz]

mhm

[simple tundra]

any of you guys know anything about probability

[smoky schooner]

Read mentality to ace math books or summaries

[smoky schooner]

What type of probability

Like geometric for exp?

[bronze geyser]

probability is difficult for me

just use tree diagrams for begginers

[simple tundra]

combinatorics

[grim rock]

HII WEN

i’ve spotted you in the wild

[undone pumice]

theres a probability channel #probability-statistics igs. all ive done is the basics taught in like an "integrated" algebra-stats-geo type course so idrk if im that good

[keen bone]

hiiii

[keen bone]

hihi

[spice crown]

can you prove that at least one of $\pi\pm e$ is irrational

[obsidian monolith]

Tangent

[hoary thorn]

Yea it is very simple

Let a = π + e

b = π - e

a + b = (π + e) + (π - e) = 2π

Now, if a and b are both rational, a + b, i.e. 2π should also be rational

But, 2π is not rational (kI = irrational, where k = rational number (other than 0), I = irrational number)

Hence, at least one of a and b is irrational

But we cannot prove that both a and b are irrational

[crimson lintel]

,w is pi +e irrational

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by hereisa_ghost

[smoky furnace]

can anyone suggest a good youtube channel/playlist/course/series to learn calculus

im familiar with the basics, integrating formula, differentian, UV rule U/V rule etc.

[valid topaz]

professor leonard and 3b1b

[smoky furnace]

substitution method

[smoky furnace]

oke i'll check them out

thank you

im having trouble with understanding/learning the use of trigonometric formulae in integration, so must i revisit basic trigonometry?

the only problems im having is with the difficult ones

like

int (1/quadratic)

those ones

x^2 - a^2

[valid topaz]

ohh

[smoky furnace]

otherwise im ok with trigonometry

[valid topaz]

there's a formula for that

[smoky furnace]

yea

i have written the formulae

hold up

the difficulty im having is with remembering these and implementing during exams

and partial fractions method

like it doesnt seem to occur to me

during examinations

[valid topaz]

well partial fractions rly doesn't have many formulas

js need to remember the basic cases

[smoky furnace]

i cant seem to remember

like

when i solve questions

i usually kind of have to look at hints

[valid topaz]

well the only advice i have is to do a ton of problems - important stuff is something you start to retain at that point

[smoky furnace]

oke

is mtg ok to solve questions from?

[valid topaz]

what's mtg?

[smoky furnace]

https://amzn.in/d/0fGZeEWf

i bought this book second hand as i cannot afford a new one

[valid topaz]

i mean jee does have pretty good problems (not speaking from experience tho)

so ye

[smoky furnace]

oke mate

thanks for the help

[tacit wren]

what counts as precalclus?

[raw hill]

As per the channel description,

[tacit wren]

Ohh

[raw hill]

Note that us precalculus is a bastardised compilation of stuff under a trenchcoat, at least half of which should have been covered in prerequisite courses

[tacit wren]

What if I already do calculus but im still precollege?

[raw hill]

then go to the #calculus channel.

[tacit wren]

mhmm

[raw hill]

As per whereever you select your roles, the education role is based on the math you do, not the formal education level you're in

[tacit wren]

Ohh okayy it didnt show up for me before

cuz i pciked i was pre college

[tacit wren]

I see

ama do so

[raw hill]

I think they based it on the "average" American trajectory, where they first do calculus in university

But I digress

[tacit wren]

Yeah i get wymm

i did calculus when i was 17 so kinda weird

[undone pumice]

mm i agree, i just went into browse channels and handpicked a few early uni like stats, calc that id also want (well im 14 but learning calc outside of school, will take calc when im 15 so i js go there when i need help)

[viscid thistle]

Should I use Desmos for polar or is there another software that’s better

[tacit wren]

Yeahh i feel u

[exotic barn]

Desmos is ok

[fossil kindle]

desmos

[valid topaz]

desmos is good for polar

[jaunty lake]

anyone know how to do this cool stuff

[hasty mica]

ln is just log base e

[unreal zenith]

what sultan pigeon said. ln and e always cancel each other when written like this: ln(e^x) or e^ln(x) to give x, where can be a function or any other variable

so answers are:
-11
6
sqrt(2)
-3

[undone pumice]

yeah what the other two said, basically they undo each other sooo its just simplifying basically

[bronze geyser]

Yeah what the other three said, just unwind it like its a tangled noose yk

[eager meteor]

a) -11
b) 6
c) root(2)
d) -3

[grim rock]

is it just to what the power e is to

[pseudo crown]

it is more like a property of log, suppose you had log 10^8, we will assume the base to be 10 for now, you can take the 8 in the front and then you would be left with 8*log10 which is just equal to 8 because log10 with base 10 is 1

[round geyser]

Remember ln ^ e or e^ln is always 1

[jaunty lake]

what about just lne?

same as ln^e i suppose?

[signal cipher]

guyss well give me tips this year calculus will start

[undone pumice]

Yeah, natural log is sort of like a function. Plug in e, get 1

ln(e^a)=aln(e)=1a=a as another example of how this could be useful

[uncut mulch]

make sure you understand algebra, functions,geo, trig, exponentials, logs before starting calc

[undone pumice]

im also starting calculus this year (well, at the start of the next school year) and, hmm, id say the big thing is to just have strong fundamentals. understand what a trig function looks like before you learn how to differentiate it, and such

also need strong algebra fundamentals for algebraic manipulation purposes

[round geyser]

How can we derive log_a^b = b*log_a

[undone pumice]

its a property

Power Property of Logarithms

[round geyser]

Is there a similar one on laws of exponents

[valid topaz]

define what a log is and raise it to the power

[round geyser]

Yes

[round geyser]

Is that similar

[undone pumice]

yeah

[round geyser]

Now we know laws of logs are inverses of laws of exponents

[undone pumice]

Basically imagine you have log((a^m)^n)

And lets say the base of that log is a

we know the result should be m^n

[round geyser]

log(ab)=log a + log b (-) a^m* a^n = a*m+n

Like that

[undone pumice]

uh

[round geyser]

I was trying to relate what’s the addition rules on logs to exponents

[marsh bloom]

uhm no

the result shld be m*n

[undone pumice]

oops wait thats what i meant

[marsh bloom]

Then correct

[nimble sorrel]

hello
I am working through precalculus by stewart, I was wondering if anybody has advice concerning the amount of exercises I should be doing (there are like 100 per subchapter)

[gaunt surge]

Hey man, if you want to try question related to jee you can try an app marks it have questions you just have to go that app and choose engineering it have specific section mains and advanced

You can do those questions without having to buy MTG books or any book for jee : )

[somber ingot]

What does MTG stand for?

[gaunt surge]

Modern times group it's just a company which sells book for competitive exam like jee neet bitsat in India( previously i was wrong about the fullform now i have corrected it )

[somber ingot]

Are you good at Precalculus?

[gaunt surge]

Depends on the level of question

But surely will try my best to solve it

[somber ingot]

What is Precalculus abt? i've never taken the class b4

[undone pumice]

uhh

a lot of it is like

algebra review

and then theres like some trig work

log work

[gaunt surge]

Yeah

[undone pumice]

umm matrices work

learn about some stuff u need for calc like, difference quotient, concavity

just ... what it sounds like. foundations to take calculus and stuff i guess

im in the class rn so there might be stuff im missing in my overview cus like we haven't learned it yet butttt yeah

[somber ingot]

Oh I did some Precalculus in my Adv Algebra class then

[gaunt surge]

Some previews what we are going to study in calculus and it does act like basic foundation of calc( differentiation and integration)

[undone pumice]

yeah its like

covering past classes

[somber ingot]

Doesn't pre mean before?

[undone pumice]

well like

its like

uh

it just like

goes over some of the stuff u learned in past classes

and builds on it

igs

also something else is like, at my school. you can take precalc in 10th grade if u take integrated 2 in 9th grade

[somber ingot]

do you learn new ideas?

[undone pumice]

and pass with an A

[undone pumice]

some

eg: concavity

[somber ingot]

What is integrated 2 abt?

[undone pumice]

inverse of rationals

[undone pumice]

ummm

[somber ingot]

WHat is concavity?

[undone pumice]

its like

[somber ingot]

Oh nvm

Inverse of rationals?

[undone pumice]

the rate of change in the rate of change of a function

[undone pumice]

like

how to take their inverse

like dyk the inverse of a function rn? like, inverse of x^2 would be sqrt(x). so imagine that with rationals (its just algebraic manipulation that i haven't done before this class(

[undone pumice]

or if kids in integrated 2 dont pass with an a, they take integrated 3 then precalc in 11th. soooo some kids in my class are learing new stuff from skipping from integrated 2 that was covered in integrated 3

[gaunt surge]

Concavity is like you get to know the curvature of the graph on the basis of Double differentiation ( what sign it's show will tell you how the graph curves is going to be )

[undone pumice]

yeah, concave down means the graph is changing at a decreasing rate, and concave up means the graph is changing at a increasing rate

[gaunt surge]

If (f(x)) < 0 ( negative ) it's going to downward parabola

If (f(x))>0 ( positive) it's going to be upward parabola

[undone pumice]

im assuming you mean f''(x) for like second derivative

[gaunt surge]

Yeahh

Bruhh

Nvm

[gaunt surge]

So you are doing Integrated math 2 ? what things are taught in that course

And it is from which country ? ( Meant to say who can take this course )

[undone pumice]

Im in the us, maybe its a california thing dk abiut other states, here 9th, 10th grade (accelerated versus regular track)

[undone pumice]

no thats what accelerated 9th graders on the advanced track take

im in ap precalc. , um lemme google the contents (dont go after me for ai overview)

[gaunt surge]

Sure

Thanks for information

[valid topaz]

hmmm

[somber ingot]

Can you give me an example please?

[somber ingot]

What does curvature mean?

[gaunt surge]

In basic sense it means curve ---> ( <--- like this

[undone pumice]

@somber ingot bump

[somber ingot]

?

[somber ingot]

Ohh okay. Thanks

[gaunt surge]

She meant to say curve but more in a professional way

[undone pumice]

like

concave up means its increasing mire and more

if increasing you can think of this like, an exponential

if decreasing but concave up, that means its decreasing but getting less decreasing, closer to 0

and if its decreasing concave down, it keeps deceeasing by more and more

if its increasign concave diwn, its approaching 0, increasing by less and less

[gaunt surge]

I think you should tell her the meaning of concave then go with the definition

[somber ingot]

What other Precalculus terms are there?

[somber ingot]

To infinity?

[undone pumice]

well, functions can switch concavity

[round geyser]

Made me thought of sin and cos graph

[undone pumice]

yeah sin and cos is an example of like

switching concavity

which can be represented

with interval form

[round geyser]

anyway I’m now doing Q1: theta, Q2: pi-theta, Q3: pi+theta, Q4: 2pi-theta

U know what I mean

[undone pumice]

like this

[undone pumice]

yeah

the like co identity whatever

[round geyser]

Do u what is that

[round geyser]

Co-terminal angle

But in radians

[undone pumice]

yeah

ik wut u mean

[round geyser]

Good

[undone pumice]

thnakfully my class is done with unit circle work

we're on like

csc, cot, sec

[round geyser]

I think doing radians is way easier then degrees

[round geyser]

I just go over that

Went*

Btw I get 91 on the test

[undone pumice]

my teacher said on the ap exam we're expected to work in radians so uh

yeah

[round geyser]

My teacher even taught us the shortcut

[undone pumice]

nicee

[round geyser]

Like 7pi/6

pi/6 is 30

Take 7 and multiply by 30

For me that is easier then multiply by 180/pi

[undone pumice]

yeah thats what i do

in my head

its kinda just what i figured out after a while

but, i have the unit circle memorized in radians anyway, so not like it matters too much

[foggy forum]

2 pi radians = 360 degrees is all you need tbh

[round geyser]

Also pi radians =180 degrees

Ryze

[foggy forum]

yeah

[round geyser]

Do u know what’s this

[foggy forum]

no i dont think so

can you explain it?

[undone pumice]

basically like

if you have like, 5pi/6

and you want the reference angle

5pi/6 is in quadrant 2

pi-5pi/6=pi/6

use pi/6 and change coords signs

to find values

type stuff

make sense?

[foggy forum]

wdym by reference angle

isnt 5pi/6 just 150 degrees?

[undone pumice]

yeah

uh reference angle is like

that angle in quadrant 1

like the equivalent of it

some people memorize quadrant 1 and just use reference angle to figure out everything sign

[foggy forum]

okay

i suppose

[round geyser]

Reference angle to memorize
pi/6 radians= 30 degrees
pi/3 radians =60 degrees
pi / 4 radians= 45 degrees

You notice 3 goes to 6 and 6 goes to 3

And 45 take it’s 4 and place it over pi?

[somber ingot]

Yeah I notice that

[gritty shale]

frq 3

[undone pumice]

? do you need help with..?

[gritty shale]

oh i alr took ap precalc

idk why i didn’t finish what i was gonna say

i loved frq 3

[undone pumice]

i lwk hate it

i dont mind the calc ones

1 and 2

but 3 and 4 lwk kindda hell for me

got marked off like 3 points on the last test cus i erm might have misread frq3 and misjudged the period..(in my defense it was sumn in fractions) and that test lwk dropped my grade 8% (before curve)

[rocky silo]

What’s frq3

[undone pumice]

uh

we're talking bout

frq3 for ap precalc

specific style of question (aka trig modeling)

[rocky silo]

I’m in ap precal

[undone pumice]

are you guys also on trig

[rocky silo]

Idk what that is

[undone pumice]

um

[rocky silo]

Yup

[undone pumice]

the ap exam will give you frq's (long word problems)

[gritty shale]

i dont like calc frq

[undone pumice]

i mean frq2 is usually just algebraic manip or regression work

[gritty shale]

oh for precalc

[undone pumice]

xd

[rocky silo]

Oh free response q3??

[undone pumice]

uh...

yeah

[rocky silo]

I have not been studying for so test

Ap

[undone pumice]

oh

well u should at least study a bit in april

cus exams in may

[rocky silo]

Wait really

It’s fine I never really study for precal either way

[undone pumice]

fair

i js usually

study how youre supposed to

word the responses

[rocky silo]

my teacher hates me

[undone pumice]

i mean my teacher makes every test close to the ap exam so we're kinda set up for success enough

[undone pumice]

😭 mines too dw

[rocky silo]

My teacher grades so hard

[undone pumice]

oop

[rocky silo]

Genuinely praying on my downfall

[undone pumice]

tests (half unit) are like 60% of our grade

[rocky silo]

Same

[undone pumice]

and we only have like 3 tests this semester

so the last one (our second test of the semester) dropped my grade 8 fricking percent before a curve

went from 106% to 98%

and i lowkgenuinely didn't even do bad i got like a 85 or sumn

[rocky silo]

He took of the entire question cus I put (2x-2)(2x+2) instead of 4(x-1)(x+1)

Kind My fault tho

[undone pumice]

oop

[rocky silo]

Damn

106??? What is ur curves

We don’t get any

He thinks curves are for the weak or smth like that

[undone pumice]

if like

a lot of the class does bad

quizzes get curved

[rocky silo]

half my class fails and he doesn’t care

He just tells them to do better

[undone pumice]

oop

um

wow

[rocky silo]

W teacher

[undone pumice]

so far all our quizzes (out of 18) got curved down cus idk i think my class struggles with trig-

and then this is the tests scores, the last test got curved 2 points and the first one got curved 3 points

[rocky silo]

U mean out of 17?

[undone pumice]

they were out of 18

but the curve was 1pt

[rocky silo]

That’s a lot of curve

[undone pumice]

so they all got bumped down to out of 17

[rocky silo]

Ohhh it reduces the amounts of questions

Tuff tuff

[undone pumice]

so original score like 14/18 becomes 14/17

[undone pumice]

yeah

[rocky silo]

That’s nice

My teacher is the reason I hate partial credit

[undone pumice]

oof

[fossil kindle]

105.8% is insane

i mean it helps the grade alot soo

[viscid thistle]

im gonna be taking ap calc next year is it hard

in ap precal rn

[uncut mulch]

depends how well ur doing atm

if ur good with ur algebra, functions, geo/trig, exponents/logs you should be fine
If not, it's going to be a struggle

[viscid thistle]

For polar coordinates if I can memorize the diff transformations am I chilling for calc bc?

(Ik how they work)

[blissful night]

Wow bro! You are on the top of the line ... Keep it up mate!

Btw @undone pumice
If you don't mind , would you be able to share your tests coz I really want to know how trig and calculus is taught, the standard, the level that it is in your country/ school

[undone pumice]

um I mean maybe, I'm not in calculus this year though. Next year I'll be in calc ab so i can try

[rigid pond]

can somebody help me with this equation? I’m still learning calculus

y = x^2 - 4x + 3

[blissful night]

Yeah what do want help with?

[rigid pond]

i’m trying to understand how to factor this

[blissful night]

Sure but i would be glad even if you could share the trigonometry one

[blissful night]

You know middle term factors?

y = x² - 4x + 3 = x² - 3x - x + 3 = x(x - 3) -1(x-3) = (x - 3)(x - 1)

[undone pumice]

thats not calculus... but...

do you understand methods like, x factoring,, or others?

[rigid pond]

pre calculus

[undone pumice]

yeah i figured

[undone pumice]

so you wanna think of two numbers that multiply to 3 and add to -1

*add to -4

[blissful night]

He has a doubt in quadratics

[undone pumice]

and if they add to a negative number and multiply to a positive number, then they must both be negative

so what two negative numbers add to -4 and multiply to 3?

[rigid pond]

so I’m assuming the answer would be -1 and -3 correct?

if you’re breaking it down like that

[undone pumice]

yup

[quasi meadow]

The roots would be 3 and 1

[blissful night]

@rigid pond
So exactly what evelyn said, but you can actually be quick at this method if you can prime factor out the number which you get on multiplying the coefficient of x² and the constant part. Once you can factor it out, you will get the combinations which will give you the desired pair

[blissful night]

Nope 1, 3

Only if y = 0

[undone pumice]

yeah i was gonna tel them to now put it into the parentheses

[blissful night]

Yeahh x= 1 or (x-1) = 0 same thing right

[undone pumice]

so plugging in you would get (x-1)(x-3)=0

and for it to be 0, one of the parenteheses has to equal 0

so either x-1=0, x-3=0

now solve for x and those are the answers~

[blissful night]

It's not really calculus... More of quadratic equations

[undone pumice]

you got this glgl

i guess more algebra right?

[rigid pond]

More so pre-calculus

[blissful night]

No problem..... Keep learning, calculus isn't tough, trigonometry is

[valid topaz]

hmmm

[rigid pond]

eventually, I want to get to that step to where I learn trigonometry but let me start here

[valid topaz]

active now

[undone pumice]

xd yeah i noticed it changed color halfway thru yapping last night

[valid topaz]

hmmmm

[blissful night]

Sure, get hold of algebra first

[rigid pond]

it was more so of a pre-calculus equation in quadratic function

like u said

[blissful night]

Yep exactly that

[foggy forum]

you dont even need to split the middle term

where a=1 you just need to think of factors of c that sum to b

x^2-4x+3, -3 x -1 = 3 and -3-1 = -4 (b)

[tardy fog]

is this like the level of differentiation / integration?

[raw hill]

#calculus exists.

[tardy fog]

ah i didnt have access to it

ill select undergrad

[foggy forum]

yeah at a basic level

[undone pumice]

yeah, as u advance in hs u may wander into topics covered typically uni, i recommend going to all the channels and just cherry pickign what u need. Eg: i habe calculus and stats selected but not other uni topics

[viscid thistle]

Trig actually sucks I can’t wait for sequences

And sums and vectors😛

[undone pumice]

omg real (well we did sequences last unit is vectors and matrices for us rho rah)

[valid topaz]

i have scars from linear alg

vectors

[simple tundra]

you guys do vectors in precalc right?

[undone pumice]

yeah

at a kinda basic level

[simple tundra]

oh ok

[undone pumice]

its our next unit after trig suposedly

[simple tundra]

like is it ap precalc

[undone pumice]

so idk how much in depth it goes tho ik its on our syllabus

[undone pumice]

yeah unit 4

[simple tundra]

oh

[undone pumice]

not tested on ap exam tho

lemme pull it up

[simple tundra]

is it matrices or unit vectors like ijk

[undone pumice]

whats a unit vector?'

is it like the coordinate plane mapping thing

oh wait no nvm

[simple tundra]

its like the ijk stuff with the " ^ " thingys on top

[undone pumice]

uhhh idrk

lemme think

heres all of unit 4

oh yeah

there is unit vectors

[simple tundra]

yeah thats it

[undone pumice]

... looks like a fun thing im so very much looking foward to learning sigh well... i guess theres your answer then

[simple tundra]

is this from ap classroom

[undone pumice]

yeah

[viscid thistle]

trig identities is over. (for now)

dw Its sorted layer by layer

[undone pumice]

heres like the expanded list of the two lessons covering vectors ^

the rest is like matrix work

[undone pumice]

holy

[sleek wolf]

What the f is that

[viscid thistle]

my work😛 It's sorted in different layers but I put it all together cuz yes

[undone pumice]

looks to be about 10 thousand practice problems with diff formulas and identities...

[viscid thistle]

it's identities and e-e-e-estabilishing 🤮

[undone pumice]

guys we have to learn identities next week

[sleek wolf]

10k problems are a lot it's not even 100 problems

[undone pumice]

and my teacher isn't even gonna be here

[undone pumice]

ik it was a joke

[sleek wolf]

Hm nice tho

Starting trigonometry soon after finish basic algebra

[simple tundra]

dang 💀

[undone pumice]

noice

[simple tundra]

you should lowk use like a diagram for all the trig identities

[viscid thistle]

so true

time for vectors YAYAYYAYA

I alr did polar so im skipping that

[undone pumice]

nice

[sleek wolf]

By basic algebra I mean these identities some basic inequality etc

[undone pumice]

mm nice glgl

igs like, alg2 level or so?

[sleek wolf]

For kinematics do you need calculus??

[sleek wolf]

Kinda

Kinematics 1D not 2D

[viscid thistle]

You can learn without calc pretty sure

[sleek wolf]

Oh ok

[undone pumice]

dont think so

[simple tundra]

like ap physics 1?

[undone pumice]

algebra should be fine... i think

[sleek wolf]

What do you mean by ap?

[undone pumice]

i mean you can use calculus but idt its needed, idk tho i haven't taken any like physics or calc yet so

[viscid thistle]

Theres two diff types of kinematics in high school, usually algebra or calc

so you don't need to

[undone pumice]

ap is like a high school course at "college" level

[sleek wolf]

Oh

[simple tundra]

for kinematics you likely don't need it

although its useful though

you can use it to "cheat"

[sleek wolf]

Do we need calculus in this sh

[simple tundra]

uhhhhhhhhhhhhhhh

I mean its giving equations with derivatives

[undone pumice]

i mean

its basically is calculus

[sleek wolf]

Is this calculus by any chance 😭😭 it's in the theory

[undone pumice]

yes those are integrals

uh

[simple tundra]

yep

[sleek wolf]

Never did calculus before

[undone pumice]

and the other page was differentiation. so....

uh

glgl

i mean

looks like

not terrible

like basic calc level

prolly ab type stuff in hs

[sleek wolf]

I mean idk

That why I am asking you guys

[undone pumice]

Ah. Well... er. It is kinda undeniably calc. Is my answer.

[sleek wolf]

I'm sending pictures of some exercises just tell me that it is hard or not and we require easy to mid level calc or not 😭

[simple tundra]

I think for physics you'll probably just learn like very basic calc

I think basic derivatives and integrals and just knowing what they really are should be enough

[undone pumice]

yeah seems simple enough

does say at the top, "basic formulas" so, doesn't seem like it wants to go much in depth

[sleek wolf]

I guess and I hope so

[sleek wolf]

Yes it says basic

They say it's advanced but we have lower the level

[undone pumice]

oh

looks like..

related ratess?

[sleek wolf]

Idk man because it is at the very last of the chapter

[undone pumice]

Yeah related rates I'm pretty sure. Not terrible I suppose

I mean it's not the kind of related rates where you have like three formulas and gotta chain rule taking variables as a function of time so...

[sleek wolf]

And they have like multiple exercises with basic to advanced and they said this is advanced question but we have lowered the difficulty

[undone pumice]

I see

interesting

[sleek wolf]

Oh

Its only the second chapter of physics

[undone pumice]

oh

icic

[sleek wolf]

After units and dimensions and some basic maths

[undone pumice]

im just in 9th grade so i haven't taken physics yet but

[sleek wolf]

Oh

9th grade which school

[undone pumice]

im in the us

we dont take physics till 11th here

[sleek wolf]

Yea so which school

Oh

I'm in 11th tho

[undone pumice]

ah

[sleek wolf]

Preparing for a competitive exam

[undone pumice]

jee?

[sleek wolf]

I was confused where to start from

[undone pumice]

ah

glgl

[sleek wolf]

Yup

😭

[undone pumice]

🙏

[viscid thistle]

What’s the book called?

[viscid thistle]

Ohhh ok

[sleek wolf]

Allen modules

[viscid thistle]

That makes sense then, if its a comp then its usually harder

[sleek wolf]

Yess it is quite hard

[viscid thistle]

You’re doing Olympiad?

[sleek wolf]

The hardest exam in the world

Arguably

[sleek wolf]

Can say but not entirely Olympiad syllabus

[undone pumice]

its JEE, from what i've heard its kind of like China's Gaokao or South Korea's... idk the name. Very tough and competitive college entrance exam thing? I believe (idrk, im in us so quite diff here)

[viscid thistle]

GAOKAO????

[sleek wolf]

Yes

[sleek wolf]

It's harder than gaokao

[viscid thistle]

damn, have fun😭

[undone pumice]

idk which one is harder but i supose they're comparable, likely

[viscid thistle]

HUHHH?

[sleek wolf]

If you compare sheer difficulty

[undone pumice]

i think gaokao is more ppl

and jee is harder

is what ive heard

[viscid thistle]

Yea that makes alot more sense then

[copper ledge]

in terms of sheer difficulty, JEE is not the hardest exam in the world lol. There are a lot of olympiads much tougher than that

[sleek wolf]

Gaokao = more people = more competition

[sleek wolf]

It's the hardest competitive exam

Not the hardest exam

[copper ledge]

hmm mention competitive here then

[sleek wolf]

Rmo and inmo are way harder if you compare it that way

[viscid thistle]

Idk how you guys do this😭 humbled INSTANTLY

[sleek wolf]

Hm but that doesn't mean jee is any easier

You have 3 hours to solve 75 questions

[undone pumice]

my mom and dad grew up in a country where basically... if you mess up on the single exam there is, you dont get into college. no ec's and such

[sleek wolf]

4 marks each -1 wrong

[copper ledge]

lol I know , all I am saying is its far from the hardest exam in the world

[sleek wolf]

Y s

[viscid thistle]

Jeez what the heck

[sleek wolf]

But 17 years give these exams so you can expect it to be one of the hardest in that age group except Olympiads

[undone pumice]

yeahh my mom got into her second choice college that had the department she majored in because she didn't score nearly so high as she wanted. my dad came to america for college tho.

[viscid thistle]

Well I took the hardest one here … the SAT 😱😱 ikr just put me in Caltech atp

[undone pumice]

thankfully im in america xd

so i dont have to worry about... just test scores....

[undone pumice]

xdxd

haven't taken the sat yet

[tulip fern]

i've taken it lol

i got 1430

[undone pumice]

oh

imma take it prolly this summer

[sleek wolf]

Sat is easy tbh

[tulip fern]

i feel like i scored higher this time tho

[undone pumice]

u got this trust

[tulip fern]

sat is very easy

[sleek wolf]

Yesn

[tulip fern]

lowkey don't know why i struggled the first time 💀

[viscid thistle]

Fair, I’m currently looking at international graduate schools for when I finish undergrad (ik I’m still in high school but likeeeee) and if they have graduate entrance exam (manly ETH Zurich)

But lowk after polars should I do complex plane or vectors?

[undone pumice]

mm fair fair. i see...

[undone pumice]

hmm

maybe complex

[sleek wolf]

What they ask in sat is this : 😂
In yt they said this is a hard question

[undone pumice]

yt is clickbait

i mean there are harder questions

module 2 end is a bit weird at times (or... maybe its js my mental fatigue at that point... but....)

[tulip fern]

hardest sat question ever 😨 what is 1 + 1
(a) 2
(b) 2
(c) 2
(d) 2

[sleek wolf]

Lol

[quick pagoda]

Hai

[undone pumice]

its c

trust

[sleek wolf]

Maths is easy but idk about other subjects

[tulip fern]

i answered (d) at first

[quick pagoda]

Its none of these

[sleek wolf]

They might be harder

[viscid thistle]

Idk + C

[quick pagoda]

The answer is 11

😰

[tulip fern]

twin why are we working in unary

[sleek wolf]

Heard someone wrote a proof of 300+ pages proving 1+1=2

[quick pagoda]

Cause Why not 😎

[tulip fern]

it's called set theory

[quick pagoda]

Yep you heard that right

[undone pumice]

twin ts was a definite integral, no plus c! rah

[viscid thistle]

Awww mb

Just idk

[sleek wolf]

Damn

[tulip fern]

i can do it in one line, those people were (geuninely) dumbasses ngl

[sleek wolf]

I guess

[quick pagoda]

1+1 = 11

AGAHAHAHHAHAHAH

[tulip fern]

$1+1=1+0^+=(1+0)^+=1^+=2$

[obsidian monolith]

literally anything

[copper ledge]

chat is cooked

[tulip fern]

literally by definition

[sleek wolf]

We ain't adding numbers as a string

[quick pagoda]

What are these + thingies

[viscid thistle]

String theory?

[copper ledge]

(trying to bring back order)

[tulip fern]

peano axioms + successor function

[quick pagoda]

STRING THEORY 😰

[tulip fern]

ts goes in #calculus bruv

[undone pumice]

#calculus

[quick pagoda]

What in the 💀
Gng when do we deal with these in UG?

[quick pagoda]

Real

[copper ledge]

ik lol

[sleek wolf]

Dk?

[tulip fern]

no unless you study formal set theory

[quick pagoda]

💀😰😰WAHT

[quick pagoda]

Ooo i see
Ig cs doesn't have that

[viscid thistle]

Me when I realize there’s genuinely levels to math

[tulip fern]

ts is basic set theory btw

[viscid thistle]

And I thought establishing identities w sum to product was hard

[quick pagoda]

😭lvls I'll break and jus become non existent

[quick pagoda]

Twin we on the same page

[tulip fern]

ok so basically

[undone pumice]

lol

running from scary set theory

[quick pagoda]

REAL😭😭😭

[tulip fern]

N is the natural numers

[undone pumice]

yes twin lets run away tgt

[tulip fern]

it's {0, 1, 2, 3, 4, ...}

[quick pagoda]

YES LETS GO

[tulip fern]

it's the smallest infinite ordinal

[quick pagoda]

SINCE WHEN DID NATURAL NUNBERS START HAVING 0 💀

[tulip fern]

N = omega

[tulip fern]

bro 0 is in the natural numbers in set theory

[quick pagoda]

Imma cry

[tulip fern]

you need it for it to work

[quick pagoda]

Cause

💀😭

[tulip fern]

because

when we do cardinalities

we need |{}| = 0

if 0 didn't exist, this doesn't make sense

[quick pagoda]

This is legit breaking me 💀

[tulip fern]

like the number of elements in {}

there isn't anything by definition

so there's 0 elements

[quick pagoda]

Isn't cardinalities basically the number of elements in the set

[tulip fern]

informally, set theorists count like:

"0, 1, 2, 3. There's 4 elements!"

[quick pagoda]

Hmm I seee

[tulip fern]

because 4 = {0, 1, 2, 3}

it's a set

everything is a set

[quick pagoda]

Yes

[quick pagoda]

True that

[tulip fern]

so then we want integers, right

Z = {... -2, -1, 0, 1, 2, ...}

[sleek wolf]

In set theory yes

[tulip fern]

to get this there's a very easy method

[sleek wolf]

Not normally

We don't consider 0 to be a part of natural no normally I believe

[tulip fern]

define the equivalence relation ~ on N * N

[quick pagoda]

This
Um is 0?

[tulip fern]

as (a,b) ~ (c,d) iff a + d = b + c

[sleek wolf]

Are you a maths major? @tulip fern

[tulip fern]

no im in 7th grade, 13

then we define Z = (N * N) / ~

[viscid thistle]

So Z = I times infinity divided by zeta plus beta for when zeta is to the greatest integer divided by a complex number?

[sleek wolf]

I ain't believing shit

[viscid thistle]

So it’s over for me

[sleek wolf]

Was this sarcasm

[undone pumice]

yall are we fried, 13 yr olds be knowing set theory

[tulip fern]

no, Z = (N * N) / ~ for the equivalence relation (a,b) ~ (c,d) <=> a + d = b + c

[sleek wolf]

It's fake

[tulip fern]

i'm literally 13 💀

[sleek wolf]

If it's true bro is 2nd Terence tao

[undone pumice]

wow thats um..

impressive

[tulip fern]

nowhere close 😭

[viscid thistle]

Crap, yea mb just had to compartmentalize the relationship between sin divided by Fourier transform

[sleek wolf]

Barely passed the age limit to be on discord 😭

[tulip fern]

terence tao is more orz than me

[quick pagoda]

HOW TF

[quick pagoda]

😭😭😭

EXACTLY

[copper ledge]

nope

[tulip fern]

then Q = ((Z * Z) \ {0}) / ~ for (a,b) ~ (c,d) <=> ad = bc

[sleek wolf]

Bro is getting 7 figure job

In a quant profile

[tulip fern]

this is too basic for anything special ngl

[quick pagoda]

Brah I thought since it goes from -a to a i should check out the even and odd function

Guess dint work

[undone pumice]

icl i dont understand set theory my school doesn't teach ts

[quick pagoda]

Pls enlighten us

[tulip fern]

i just do recreational math lol

[copper ledge]

there are 4 terms on the numerator, the first 3 yield a zero, but not the last one

[quick pagoda]

What is that now 💀

[sleek wolf]

You don't need his level of understanding for set theory

[quick pagoda]

Hmmmm

https://tenor.com/view/they-dont-love-you-like-i-love-you-dog-gif-12858916681645605905

[viscid thistle]

When are you meant to learn set theory

[tulip fern]

math that's "fun"?

[viscid thistle]

Like what’s the point of it

[tulip fern]

ususally never

[undone pumice]

im working on simplifying it rn

[tulip fern]

to explore the foundations of math

[quick pagoda]

Recreational math ?
Math that is fun

[quick pagoda]

This sounds interesting

[sleek wolf]

Never heard someone do maths for fun

[undone pumice]

splitting off the 1 on the right integrand and then putting the other side of

[quick pagoda]

😭I've heard

[undone pumice]

i mean i like learning calc in my free time

[viscid thistle]

Cubic formula handwritten

[undone pumice]

cus my schools math is lwk easy

[tulip fern]

so for example, there's a result known as whitehead's problem*

[viscid thistle]

Same dude

[quick pagoda]

😰

Wait

[sleek wolf]

Nicee 👍👍👍

[undone pumice]

yeah... sigh

[quick pagoda]

Are yall from Europe or like the west

[undone pumice]

im in the US

so west ..?

[tulip fern]

it's been proven that whitehead's problem has no proof, under Con(ZFC)

[quick pagoda]

Im Asian 😰💀

[quick pagoda]

Yess

[sleek wolf]

Bro first complete you class 10th

[tulip fern]

usa

[undone pumice]

im asian too

but i live in the US

[tulip fern]

asian

[sleek wolf]

Go study

[quick pagoda]

Im in freaking uni 💀

2nd sem

Rn

[viscid thistle]

My school only offers calc BC in unison with AB, so ppl end up taking the AB exam anyway

[quick pagoda]

What

[undone pumice]

oop

im in 9th grade..

[sleek wolf]

Lowkey

[viscid thistle]

Although I want to learn calc 2 by November

[undone pumice]

nice

my school makes us take ab then bc

so im taking ab next year

sigh

[tulip fern]

it's surprising because an algebraic problem has no set-theoretical solution

[viscid thistle]

R u going to high technology

[tulip fern]

idk what's that

idrc about the high eduction

[sleek wolf]

B tech?

[viscid thistle]

It’s a top stem high school

[quick pagoda]

Yesss

[tulip fern]

i'm just a random 7th grader

[sleek wolf]

Oh ok

[viscid thistle]

In the us

[tulip fern]

doing random things

[viscid thistle]

Oh yea I forgot ur not in 8th

[quick pagoda]

Quantum mechanics is fun actually 😎

🗿

[viscid thistle]

What’s 1 to the power of 0

[quick pagoda]

1

[sleek wolf]

1

[tulip fern]

1

[sleek wolf]

He will write a proof now

[undone pumice]

okay wait so now if i rewrite it as 2 (def integral from 0 to 1) 1/(x^2+2x+1) dx... then thats a perfect square... and the ln doesn't mean shi ri-

[quick pagoda]

Help

[tulip fern]

by definition, even as a cardinal

[sleek wolf]

Stop asking him

[copper ledge]

right lol, I just added it cause I felt like it

[viscid thistle]

Isn’t a cardinal a bird

[tulip fern]

formally, 1^0 is the set of functions from 0 to 1

[sleek wolf]

What is |A| when a is null

[tulip fern]

0

[viscid thistle]

0

[undone pumice]

||ur evil|| i mean, im evaluating the integral now

[viscid thistle]

IK THAT ONE

[sleek wolf]

So basically infinite

[tulip fern]

because the cartesian product is {}, the only function is the trivial function {} 😛

so 1^0 = 1

[undone pumice]

i overanalyze everything so uh ...
anyway i can't tell if im being stupid or for any value of k Isubk is 1...

[tulip fern]

in general |X|^0 = 1 lol

[copper ledge]

right

[undone pumice]

because then the sum from 1 to 4 would be 4......

[sleek wolf]

13 year olds getting sat score of 1400+

Gng we r cooked

[undone pumice]

and then the greater intenger function is ANOTHER DISTRA-

[tulip fern]

sat is waaay too easy for any college qualing ngl

not that i oppose it i lowk like my free enterance into college

[sleek wolf]

Ikr sat is easy fr

Dk why hardvard

[undone pumice]

is the answer just 4...?

[sleek wolf]

Requires sat score

[tulip fern]

all the sat does is filter out idiots ig

[copper ledge]

it is

[sleek wolf]

In our case it's jee

[undone pumice]

man...

that whole question was um..

def tested my knowledge ill say

[copper ledge]

[undone pumice]

at the edge of what i can solve

[viscid thistle]

Oh wait is set theory discrete?

[copper ledge]

oh I see

[sleek wolf]

Universal set theory is true?

[tulip fern]

no not really

there's some super continuous sets

how do you think the reals are defined?

they don't just pop out of nowhere

[undone pumice]

yeah it was kinda a struggle icl

took me a bit to work thru the left hand right hand separation integral thing

[tulip fern]

i recently learned some measure theory

apparently the lebesgue integral is much better than the riemann integral

like the dominated convergence theorem

[undone pumice]

i suppose after that beast of a probelm glares at hte ln im gonna take a clash royale break 😵‍💫

[golden storm]

Hellow, what websites should i use for practice (specifically calculus) that doesnt have me swapping thru pdfs, im currently at IBAAHL level math.

[warm oyster]

Pauls online math notes.

[golden storm]

Thanks king

[wicked hearth]

New to this bihhhhhh

currently struggling with Precal

and im like wtffff

any help would be cool

[valid topaz]

hmm

[quasi meadow]

What do you need help with?

[undone pumice]

what is your class ccurrently learning?

[viscid thistle]

IM SORRY HOW DID WE GO FROM THIS

TO THIS IN ONE PAGE???

[raw hill]

seems normal

[undone pumice]

its not that bad

[viscid thistle]

ok but like the jump is crazy

oh wait this is easy

nvm]

oh wait this is REALLY EASY

AYAYAYAYAYAIAYAYA

[undone pumice]

lol yeah its kind of like similar to the other one

[viscid thistle]

if this book tells me that the proof is left as an exercise for me one more time I will die

[undone pumice]

damn

i hate those

like..

wasn't ts alr proved, js show me how to do it alr

[viscid thistle]

litteraly, doing the work for them smh🥀

[undone pumice]

frfr proofs are one of my weak points which makes "prove this already proved proof" questions even more annoying

[valid topaz]

oh i hate those

and they show up att in the aops books

[viscid thistle]

"The proof of this theorem requires mathematical induction, which is not discussed until later on. You are asked to prove this in problem 73."

[undone pumice]

w-wow

thats um...

"It's okay! We'll just make you suffer later. Heh!"

[viscid thistle]

complex numbers is done!😛

[shut galleon]

eeeyuckkyyyy

no more complex number

[viscid thistle]

🥀

[round geyser]

Is it the one that has a^2+b^2

[raw hill]

$|a+bi|=\sqrt{a^2+b^2}$ for $a,b \in \mathbb{R}$ if that’s what you’re thinking of

[obsidian monolith]

Civil Service Pigeon

[viscid thistle]

It’s abbreviated as x^2 + y^2 in my textbook but I’m pretty sure it’s the same thing

$e$

[obsidian monolith]

SUBLAVA

[raw hill]

$x+yi$ instead of $a+bi$. They just replaced with $x$ with $a$ and $y$ with $b$, so yes it's the same thing. ($x$, $a$ are just placeholders for the real part and $y$, $b$ are placeholders for the imaginary part.)

[obsidian monolith]

Civil Service Pigeon

[raw hill]

tldr it's all different ways of writing $|z|=\sqrt{(\operatorname{Re}(z))^2+(\operatorname{Im}(z))^2}$.

[obsidian monolith]

Civil Service Pigeon

[tulip fern]

complex geometry is scary

unless you like coord bashing

[undone pumice]

My teacher gave us this story to remember the sum and difference identities …

[frail stag]

thats really impressive

[undone pumice]

lol

[swift shuttle]

Today I had some complex numbers studies and those had a very neat way of explaining trig identities

Algebraically

And geometrically actually

So the way to think about it is, cos (a+b) is the same as increasing the angle a by angle b
Geometrically on a complex plane, that's the same as multiplying two complex numbers

So you get:

• z1 = cos(a) + isin(a)
• z2 = cos(b) +isin(b)

And essentially, you just multiply them as you'd do with any other expression knowing that i² = -1

And you really just end up with a real expression that doesn't involve i, and an imaginary expression

That real side, is just cos(a+b), and the imaginary expression is just sin(a+b) multiplied by i

[tulip fern]

you prove that e^(ia)e^(ib) = e^(i(a+b)) first tho, dont you?

[swift shuttle]

You don't really need to

Because you can use the trigonometric form

And that suffices since we can interpret it visually/geometrically

Afaik exponential forms are easier for calculations yeah, but they're not obligatory

[swift shuttle]

Also that's just an exponential property, why would u need to prove it?

Or rather, why would u need to prove it on complex numbers

[tulip fern]

it's not, you need to explicitly prove it

we "use" e^ix because it works

but to prove that identity

you need to use the cosine + sine addition formulas

because that's how we define it

e^ix = cos x + i sin x is the definition

[swift shuttle]

I'm saying that you don't need e^ix at all

Because cosx +isinx suffices

But if u want to prove it using e^ix then sure ig, it's possible, just not necessary afaik

I hope I'm understanding ur statement correctly

[valid topaz]

hmm

[undone pumice]

Oh how interesting

[tulip fern]

but e^ix = cos x + i sin x by definition

i'm just using shorthand bruv

wait did i read it wrong

oops

[swift shuttle]

._."

It's easier for general computation to just take advantage of exponential properties in calculation

So yeah, it is easy to prove. But my point was that you can utilize trig forms to conclude trig identities in an easy way

That doesn't require much knowledge about exponents and complex numbers