precalculus

[rough leaf]

yeah

but idk how

[storm violet]

yea idk

i put the question in help-20

[wind lion]

@rough leaf

[rough leaf]

yo

yeah so how do you find the slope

[wind lion]

yeah so

say you have a function

[rough leaf]

yeah

[wind lion]

,,f(x) =x^2

[obsidian monolith]

calvin

[wind lion]

do you know about limits

[rough leaf]

yeah

[wind lion]

do you know about detivsti

derivatives

[rough leaf]

yeah

isn’t the derivative of this js lile

[wind lion]

do you know about limit definition of a derivative

[rough leaf]

2x

[wind lion]

yes

[rough leaf]

yeah

[wind lion]

yeah so just take the derivative

the slope function is the same everywhere

[rough leaf]

oh

so for like

wwit

[wind lion]

but

say you have two points

[rough leaf]

yeah

[wind lion]

(1,1) and (2,4)

plug in x1 (1) into 2x and that is the gradient of f(x) at x=1

[rough leaf]

oh

[wind lion]

2(1) is 2 right

[rough leaf]

yeah

[wind lion]

but plugging 2 for the next point

2(2) is different

2(2) = 4

[rough leaf]

yeah

[wind lion]

and on the graph you can visualise it too

it gets steeper

[rough leaf]

so wait

for this

you would have to take the derivative of the quadratic?

[wind lion]

yes

[rough leaf]

that’s js 2x+6

[wind lion]

take the derivative to find the slope function

yes

[rough leaf]

and now you plug in your x?

so

it js becomes 8

[wind lion]

yeah so the x value

mhm

my teacher always tells me to use $y-y_1 = m(x-x_1)$ when finding linear equations

[obsidian monolith]

calvin

[wind lion]

but personally

i use $y=mx+c$

[obsidian monolith]

calvin

[wind lion]

it’s simply easier

[thick blade]

why is this in a pre calc course

[rough leaf]

so your gonna get y-4=8(x-1)?

[wind lion]

yes

[rough leaf]

myf i’ll remove it afterwards

[rough leaf]

oh

[thick blade]

no no i’m asking why is this in your course/lesson plan

[rough leaf]

thag wasnt even that bad

[rough leaf]

it’s not

someone was doing it

[thick blade]

if it’s pre calc and it isn’t the end of the year

[thick blade]

ohh okay

[rough leaf]

and i wanted to know how to do it

i’m not even taking pre calc rn😭

[wind lion]

same

me neither

[rough leaf]

i’m an alg 2 student

[wind lion]

💀

im alg1

i think

[rough leaf]

why do you know calc in alg 1

[round geyser]

Use y=mx+b

[wind lion]

idk i self taught it

[rough leaf]

it’s the same thing

[wind lion]

same thing

[rough leaf]

whag geade

you in

[round geyser]

Formula is c=b

[wind lion]

y9 2026

[rough leaf]

i’m tryna do this tn

[thick blade]

i’m in geometry

[rough leaf]

rn*

[rough leaf]

what does this mean

[wind lion]

same thing just y intercept

[round geyser]

Cool

[rough leaf]

me too

i doubled up

[wind lion]

im in grade 9 in 2026

[rough leaf]

geometry anf alg2

[round geyser]

What about b=c=C/B

[rough leaf]

wait so 8th gr rn?

[wind lion]

australian school years start in february

[rough leaf]

oh

[wind lion]

bro what 😭

[thick blade]

ohh

[rough leaf]

wait

[thick blade]

what is this

[round geyser]

It’s from Ax+By=C

[rough leaf]

so are you like 14 or smth?

we the same geade i think

[round geyser]

m=-A/B and b=c=C/B

[rough leaf]

i’m in y9 roo

[rough leaf]

where did this come from

[round geyser]

Just solve for y

What will u see

[rough leaf]

but why

[wind lion]

these equations are the same [\begin{align*} y&=mx+b \ &= mx+c \end{align*}]

[rough leaf]

it’s js a diff variable

[obsidian monolith]

calvin
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rough leaf]

same equation

[round geyser]

Solving slope from standard form

[thick blade]

yo in algebra 1 and 2 memorize difference of squares and factoring

[round geyser]

Ax+By=C

-A/B

[rough leaf]

bro alg 2 isn’t that deep

it’s lwk easy

[thick blade]

so far in calc bc you need to have difference of squares and how to factor memorized to your core

[wind lion]

wat is bro solving for

[round geyser]

y

[wind lion]

i memorised that shit before i self taught calv

calc

[round geyser]

Cuz this formula

[rough leaf]

from my experience you need the difference of squares and stuff

in precalc

[rough leaf]

wait

what are you doing in alg

or whag have you done

[thick blade]

me too it was big in pre calc

[rough leaf]

last yewr

[wind lion]

idk my school just did algebra

[rough leaf]

yeah

[wind lion]

i mean

i mean probability

[thick blade]

alg 1 or 2?

[thick blade]

worst unit oat btw

[rough leaf]

he said he doing alg 1

but idk

[wind lion]

REAL

[rough leaf]

i i think he in 2

[rough leaf]

i agree

[round geyser]

Me?

[thick blade]

what are toy in

you

in

[wind lion]

my school hasnt done quadratics yet

[round geyser]

This chat

What’s that said

[rough leaf]

oh

so alg 1

[wind lion]

yes

[rough leaf]

bro i have to lock in and grind out calc bc

[wind lion]

i self tsught

[round geyser]

I’m in Pre-calc

[rough leaf]

i’m lwk behjnd

[thick blade]

did you do pre calc yet?

[wind lion]

what does calc ab and bc entail

[rough leaf]

i self taught

[wind lion]

because in victoria australia

we have

[thick blade]

oh up to what topics

[wind lion]

methods units 12 in y11

[rough leaf]

calc ab is like calc 1 calc bc is like calc 2

[rough leaf]

all

everything in ap pre calc

[wind lion]

then units 34 in y12

[thick blade]

when i self taught i hit parametrics and mateicies

[rough leaf]

reg precalc

[thick blade]

ok nice

[rough leaf]

and pre calc on khan

[wind lion]

are matrices easy

[rough leaf]

yes

light

[thick blade]

not light but tedious

[rough leaf]

i never hit parametrics

[wind lion]

they look really complicated

[rough leaf]

i did mattices

[rough leaf]

they aren’t

it’s js a formula

every time

[thick blade]

it’s also very easy currently because it’s very elementary operations

[wind lion]

im doing combinatrics rn

[rough leaf]

js plug and chug

[wind lion]

wow

[thick blade]

why

[wind lion]

competitions

i know its a pain

[thick blade]

some times

[rough leaf]

wait what are parametrics

i might’ve done

but it might be named diff

[wind lion]

what unis are you guys tryna go to

[thick blade]

a function bounded by time instead of x values

[wind lion]

wait what grade areuou in

[rough leaf]

mit or harvard

[thick blade]

university of michigan

[wind lion]

hmm

[rough leaf]

geade 9

[wind lion]

same as me then ig

[rough leaf]

yeah i didn’t do this

[wind lion]

wait ru 15 or 14

[rough leaf]

never encountered

[rough leaf]

14

late birthday

[wind lion]

same

[thick blade]

for example (t^2,2t-1/t)

[wind lion]

i turned 14 a couple months back

[wind lion]

interesting

[rough leaf]

me too

[wind lion]

im tryna go to unimelb

but

[rough leaf]

i’ve never done this

[wind lion]

idk if its good enough for qt

[rough leaf]

bro i kinda hated the trig part of pre calc

[wind lion]

trig is easy as shit

i learned that in a wrrk

week

like 6 months sho

ago

i finished the chapter

i bombed my pythag teat

[rough leaf]

yeah i did too but i hated solving sinsidoul equations

[thick blade]

parametrics also have direction

[wind lion]

test

[rough leaf]

and how you have to like

apply the sine rules

and cosine rules

[thick blade]

did you learn sin and cos addition rules

[rough leaf]

that’s the easy part

[thick blade]

that’s kinda important for calc sometimes

[rough leaf]

yeah never seen this

[wind lion]

i dont think so

[rough leaf]

i did like vectors or shm

sum*

[thick blade]

fairly simply

[rough leaf]

it’s like

[thick blade]

sin(a+b)=sinacosb+cosasinb

[wind lion]

wait its like $\sin(\th) = \sin(180-\th)$

[thick blade]

things like this

[obsidian monolith]

calvin

[wind lion]

oh nah i havent learned thsg

that

[rough leaf]

rhats diff

[wind lion]

i shld prolly lock in

[rough leaf]

me too

i’ll prolly grt some calc done tmtw in english class

[thick blade]

it’s good for when you have the definition of a derivative and need to find the derivative of a trig function

[wind lion]

combi is really annoying but im really eager to learn it

[wind lion]

what grade ru in

[thick blade]

that’s like what it is

when it’s used just an example

[wind lion]

interesting

[rough leaf]

yo

thanks

i’ve always wondered the proof for the derivative of sin of x

i was too lazy to do it myself

[thick blade]

yup it’s that

i went to the 3rd derivative

it goes sin cos -sin - cos

[wind lion]

wait

does this mean that

,,f^{(n)}(x) =\lim_{h\to0} \frac{f^{(n-1)}(x+h) -f^{(n-1)}(x)}{h}

[rough leaf]

i tmbr i use to prove thibgs when i was bored

that was a while ago yho

[obsidian monolith]

calvin

[thick blade]

a lot

uh

[rough leaf]

i think

[wind lion]

interesting

i wanna go to oxford but i have no chance

[rough leaf]

nah you got that

[wind lion]

they reject geniuses bro 🥀

[rough leaf]

i also lwk wanna take the gcses

idk

i js wanna

for fun

[wind lion]

gcses are deadass easy i could lowk ace them if i cbf to learn stats

[rough leaf]

i know

[wind lion]

i did stats and bombed the test in school

91% 🥀

[rough leaf]

i’m lwk doing ap stats bext year

[wind lion]

then pythag

93% 🥀

[rough leaf]

okay thays not bombing the test

[wind lion]

i lost 2 markssasss

[rough leaf]

FOR PYTHAG???

that’s bombing

[wind lion]

i rounded to 2dp instead of 1

and then

that was 1 mark

[rough leaf]

wait what even is stats

[wind lion]

then

[rough leaf]

is it js like

mean median and mode

[wind lion]

for the other mark everyone lost one

[rough leaf]

bar graphs and stuff

idk

[wind lion]

cuz wr had to be “practical “

[wind lion]

graphs data and plots

means medians and estimates

really pisses me off

[rough leaf]

oh

[wind lion]

but

qt is all about that

[rough leaf]

bruh i did ts in loke 6th gr

it was light

[wind lion]

i know i know

[thick blade]

do ap calc bc

[wind lion]

all my tests r out of ≈35-40 marks

[rough leaf]

i am

[wind lion]

so 1 mark lost is crucial

[rough leaf]

i’m doing ap calc bc

ap stats

ap euro

ap bio

[thick blade]

also for parametric this is how it shows direction (as time increases)

[rough leaf]

and ap csa

[wind lion]

interesting

[thick blade]

you can graph movement of anything really then you can differentiate a parametric to get its rate of change at any point, seems really applicable in real life

[rough leaf]

bro i ahould lwk go to bed

it’s like

12

[thick blade]

😭

[rough leaf]

i have a mid term tmtw too✌️

[thick blade]

rip

[wind lion]

gl

[rough leaf]

i’ve done exactly

[wind lion]

damm yeh you shld go to bed

[rough leaf]

zero minutes of practice for it

[wind lion]

i mean i woke up at 1pm today so

🤷‍♂️

[rough leaf]

it’s a writing mid term in french and idek what we gonna write abr so how is mans supposed to prepare

[wind lion]

💀

they dont give you a criteria?

[rough leaf]

nope

not my french teacher

[wind lion]

i got 76% hwk completion in french

[rough leaf]

we find out what we gonna write abt 2 minutes before we do

[wind lion]

my teacher never said anything to me

so i thought i was chill

[rough leaf]

bro i’m lwk locked in on french

or i was

i got the french award at my old school

[wind lion]

i wish my school had latin

[rough leaf]

mine does

but i’m not starting from the bottom

cuz i can’t take ap latin

[wind lion]

mine doesnt even have japanese or german

[rough leaf]

at least i can take ap french

[rough leaf]

i think mine might have japanese

not german tho

[wind lion]

nice

french is okay

idk

[rough leaf]

i hate it✌️

[wind lion]

not gonna take it in y12

[rough leaf]

i’m js decent at it

[rough leaf]

i’m gonna cuz i need thay ap credit

yk what ap is right

?

[wind lion]

how does the american system work

[wind lion]

like a harder version of class right

[rough leaf]

yeah

it’s essentially

[wind lion]

yh

[rough leaf]

the first yewr of college

for thay class

[wind lion]

COLLEGE??

[rough leaf]

yeah

[wind lion]

alr show me your ap maths stuff

[rough leaf]

when i get there sure😭✌️

you gotta wait till september

[wind lion]

this is undergrad level

in uni here

[rough leaf]

if i had an energy left

thid doesnt seen

seem*

THAT bad

to attempt

and do

[wind lion]

idk

ai i gotta go bye

[rough leaf]

bye bye

i ahould lwk sleep

[round geyser]

I assume z=(a+bi)

[wind lion]

idk

[round geyser]

Wait

[round geyser]

Is that you showed me the remainder theorem

Just do direct substitution

[wind lion]

i dont need help with it

it was an example

[round geyser]

Okay

[round geyser]

Though

It is divisible or it’s a root

Since it came out with 0

[rough leaf]

can you do this?

i’m looking at these problems

i could do them

[storm violet]

ngl most of the ap stuff is much easier than college but some colleges will give u credit if u do well on the ap test

[winter turtle]

Can someone help me with this

24 and 25 please 🙏

[tender quest]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[winter turtle]

1

[raw hill]

Do you know what the "One-to-One property" is?

[winter turtle]

No that’s why I’m confused

[raw hill]

If you have a one-to-one (also known as injective) function $f$ with $f(x)=f(y)$, then $x=y$

[obsidian monolith]

Civil Service Pigeon

[raw hill]

In this case, recall that exponentials $a^x$ with $a \neq 1$ and logarithmic functions are both one-to-one (or injective)

[obsidian monolith]

Civil Service Pigeon

[raw hill]

So, for example, let's say we had $6^t=6^2$. Then, if we define $f$ to be the one-to-one function given by $f(x)=6^x$, then $f(t)=f(2) \implies t=2$.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

(the easiest way to convince yourself of this on an intuitive level is to just look at the graphs)

[rough leaf]

do you still need help?

[winter turtle]

Nah I got it

I might need help with this though

2 and 3 cuz I’m really confused how to do the whole thing

[raw hill]

Don’t love this but the assumption is that $h$ is sufficiently small so that you don’t cross the domain boundary of $x=-1$. \ \
$f(x)$ is the result of inputting $x$ into $f$. So, $f(x+h)$ is the result of inputting $x+h$ into $f$. You can also think of this as replacing every $x$ in $f(x)$ with $f(x+h)$:
$$f(x)=x^2-2 \implies f(x+h)=(x+h)^2-2$$
Or you could do it as a piecewise based on whether $1+h$ is more or less than $1$ (which you’ll have to do for 3 anyway).

[obsidian monolith]

Civil Service Pigeon

[rough leaf]

uhhh

idk how to explain it

[wind lion]

not the sketching, vectors and parametrics

[rough leaf]

but replace (x-h) for every x value in the function

and rhen js aolve

[rough leaf]

i can’t do that part either

it’s 3d vectors i think

i havent done those

i could do some of the imaginary bumber stuff tho

[wind lion]

yh

[thick blade]

i could do question 2 for 7 marks

[tall bone]

what are the bases of precalculus

[willow skiff]

algebra, working with linear and quadratic equations

if you're not making dumb misconceptions like $(a + b)^2 \ne a^2 + b^2$ or $\frac{1}{x + y} = \frac{1}{x} + \frac{1}{y}$ you're on the right track

[obsidian monolith]

south

[tall bone]

ok

[rigid breach]

is this prt of precalc

https://tenor.com/view/funny-valentine-d4c-gif-23320384

pls tell

[spiral shuttle]

help please

[peak shale]

Rewrite using cos and sin

[gleaming phoenix]

I guess not but its very useful in calculus

I havent exactly done it but i'm pretty sure u'll get an upper hand at math in general with this

Dont deep dive too much into it other than quadractic equations part tho

[rough leaf]

i do some of this stuff in alg 2

at end o yewr

[echo sinew]

<@&268886789983436800>

[gleaming phoenix]

This is only based on my jee exp

Soo

If ur aiming for olympaid ye go for it

[round geyser]

Hey

[main peak]

how do I understand an integral

[torn sinew]

Which type

An integral is essentially just sum of

[round geyser]

Think it like a cake

Slice of cake

[main peak]

∫

[main peak]

huh

[main peak]

but sigma notations exist

[torn sinew]

no i know the integral symbol iwas just inquiring if there was a specific type you wanted to know like the ones below

[main peak]

oh

I thought you were asking like ∬ or ∮ or ⨋

so uhh I mean ∫ α dx

[untold sluice]

What is that symbol where the sum and the integral are merged??

[willow skiff]

$\oint$, path integral around a closed path

[obsidian monolith]

south

[willow skiff]

oh wait you didn't mean that one

I guess go search it on Detextify

[gleaming phoenix]

Integration is u taking really thing parts and adding them up for a result u gotta do it by taking elements that are basically thr small parts as a function of x and integrate with respect to x

[main peak]

idk i got it from unicode

[gleaming phoenix]

Itd basically taking really small things and adding them up a sigma notation wont work because the required element ur adding is really small

[main peak]

is this related to a riemann sum

[gleaming phoenix]

I havent learned reimann sum and i understand intehrals fine

But yes its pretty corrolated

[main peak]

oh ok

tysm

[gleaming phoenix]

If ur doing jee i can send a video on understanding how to take elements

Very useful for phy

But in jee math irs just the anti derivative of a function

[untold sluice]

Thanks for letting me know a website where I can find it

Dang it, I don’t think it’s there either

https://math.stackexchange.com/questions/4739507/what-is-⨋-u2a0b-summation-with-integral-used-for

Found info on it

[brave stirrup]

👋

[thick breach]

@modulators waver

[drowsy vessel]

curimouse

[marble quest]

hi, whats up

[drowsy vessel]

(its a bot/compromised account)

[marble quest]

oh rlly

[thick breach]

ping was no worth tbf

[knotty garden]

weirdest type of bot id say. whats the point in just waving everywhere? unless the scam comes in if you reply or something

[drowsy vessel]

no that's a good thing to mod ping over

[drowsy vessel]

its to build a record of "legitimate activity"

[winter comet]

modulators 💀

[viscid thistle]

Hi

I like limits

[rough leaf]

me too

[pearl ruin]

I’m in DE precal 2

No clue what limits r

[rough leaf]

whatd de precal

[pearl ruin]

College and high school dual credit

[rough leaf]

oh

rhen you shpuld be seeing limits at the end of the year ish

like your last unit probably

[pine snow]

GUYS OMFG

I NEED HELP I HAVE A PRECAL SUMMATIVE

TMRW

FUCK IM SO COOKED I HAVE NO IDEA WHATS GOING ON

[topaz maple]

can you show what you need help with?

i'll try

[topaz maple]

ok, what do you not understand ?

[pine snow]

i understand kinda finding vertical asymtopes and i understand y-int

and the factoring is kinda annoying like

one sec

[topaz maple]

ok

can you find vertical asymptote to f(x) = 1/(x-3)

[pine snow]

one sec let me do it on paper

[willow skiff]

the whole idea of all of this is that you can just take the 'biggest' terms in the numerator and denominator

for example, (x^5 + 2x^3) / (x^4 - x) behaves like x^5 / x^4

for x to infinity

[pine snow]

wouldn’t that just be 3?

[topaz maple]

indeed

[willow skiff]

yeah, to 1/(x - 3)

[pine snow]

like for this why was the gcf 4 and 4 and not 8 and 2

[topaz maple]

vertical asymptote to a function is just a line to a curve where y-> infinity or - infinity

[willow skiff]

,rotate

[pine snow]

thats so cool ngl

[willow skiff]

oh yeah I should have typed ,rccw

[topaz maple]

-# rcw for clockwise

[willow skiff]

ahhh, okay so x^2 - 16 = x^2 - 4^2

that's a difference of two squares

the idea is that you can do $x^2 + 4x - 4x - 4^2$

[obsidian monolith]

south

[willow skiff]

which factors as $x(x + 4) + (-4)(x + 4) = (x - 4)(x + 4)$

[obsidian monolith]

south

[pine snow]

so you need to find smth to cancel out with the denominator?

[willow skiff]

yeah

you just factored x^2 - 16 wrong

but your idea with cancelling out is spot-on

[pine snow]

OHH VECAYS

BECAUSE 8 and 2 ARENT THE GCF

4 IS

[willow skiff]

yeah you could expand it yourself and it doesn't give you the original back

[pine snow]

okay and im also so confused on holes and slant asymptotes

[topaz maple]

or you could just do $a^2- b^2 = (a+b)(a-b)$ since $16 = 4^2$

[pine snow]

would that work as well or woukd it be too complicated while solving?

[obsidian monolith]

scoob

[topaz maple]

oh south already mentioned it

[topaz maple]

yes it will

[pine snow]

okok

ill do some more practice problems

thank you guyss

[willow skiff]

yeah this is really testing your algebraic skill

if you remember that x-intercepts are when y = 0 (this is why Quizlet / Anki can be really helpful for maths), then if you want to find (2x - 5) / (x + 3) = 0, basic algebra tells you that you can multiply both sides by (x + 3) to get 2x - 5 = 0

no worries!

just making an extra point in case you find you have more algebraic difficulties

[topaz maple]

experience will help in algebra

[rough leaf]

wpuld there be a hole at x=-4

or am i geeked

nvm

there’s an asymptote there

i think this goes in geometry

[shut scroll]

Ohhh ok thanks

[ripe scarab]

highkirk

[pine snow]

OKAY @topaz maple @willow skiff GOOD NEWS AND ABD BEWS

[willow skiff]

yeah?

[topaz maple]

bad bews

[pine snow]

I FAILED MY PRE CAL TEST 1000%

BUT

I GOT FULL MARKS ON MY PHYSCIS TEST

[pine snow]

INDIDNT GET NY SCORE BACJ BUT IM GUESSING I DID BAD

[topaz maple]

dw

[pine snow]

and i have a ap chem test tmrw so more studying 😭

THEN MIDTERMS BRO

[topaz maple]

oh,

gl

why do you have mid term at this time

[pine snow]

idk cause my schools ass

but at least like ny midterms are just for my ap classes

so ap bio and ap chem but theyre still hard yk

[stiff cypress]

Gng i dont understand what they did for the second question

Where did 3x and 4y came from

[raw hill]

Take the normal vector (6,8,0) and scale it down to the scalar multiple (3,4,0)

https://web.ma.utexas.edu/users/m408m/Display12-5-3.shtml

Then use this

[stiff cypress]

Huh

D is constant?

I understand now but

It just used the value again

3x +4y

Where x is 3 and y is 4

Did they use it because the coordinates (3,4,0) are tangent of plane S

[raw hill]

$3x+4y$ is constant (aka the same value) for \textit{all} points on the plane. This includes the point $(3,4,5)$, so they used this to find the value of said constant.

[obsidian monolith]

Civil Service Pigeon

[stiff cypress]

Oh

[stiff cypress]

(3,4,0) is used in this?

And (3,4,5) are taken from the question

[raw hill]

(5)(0)=0 so the z coordinate doesn’t contribute anything

But they’re still technically using (3,4,5) and not (3,4,0)

Read what they wrote

[stiff cypress]

Oh

My bad

Thanks civil service pigeon

[raw hill]

[stiff cypress]

I can do more questions happily now 😍

[ionic wedge]

anyone got notes on the following topics:

Polynomial and Rational Functions (Combination of rational function) and Characteristics of Functions

this is for precalc culminating

[echo sinew]

Isn't there a bunch of material on this on the Internet?

[ionic wedge]

yes

[round geyser]

Okay show me plz I learned these before

Also inverses and boundedness

[brittle comet]

which country and class

?

[pine snow]

um im not saying the country but im grade 12😭

[brittle comet]

ok thanks

!

[pine snow]

why 😭?

[normal lotus]

why do logs exist im gonna crashout

[pine snow]

FUCK IM IN THAT UNIR ROO?

LOGARITHMIC SHIT AND STUFF

[normal lotus]

NO IM ACTUALLY GOING TO GO CRAZY

I do kinda get it

but I havent reached flow state yet…

[pine snow]

BRO OMFGGGGGGGG IM SO CONFUSED ON THE TOPIC

IM COOKED

[normal lotus]

I also kinda screwed myself

Im the buggest procrastinator ong

do you have finals coming up?

[round geyser]

Me too

I’m also doing logs it’s easy

[vast lava]

Logs is not easy what are you on about

[normal lotus]

real

[iron ingot]

Logs are kinda easy tho

When compared to other stuffi

[normal lotus]

Probably in the grand scheme of things but thats just what I find difficult to comprehend rn 🤷‍♀️ to each their own

[round geyser]

Logarithm outputs exponents

[vast lava]

..

[pale arch]

Chat what is an asymptote

[willow skiff]

search it up and you'll know

[pale arch]

👍

[gleaming phoenix]

Practice mlre u'll get if

[toxic nebula]

Small question

Actually

I realized it's not a small question at all

Im just going to google it

[gleaming phoenix]

?

[toxic nebula]

I wanted fo ask about partial-differential equations

[gleaming phoenix]

I shant be of any help for i have not studied that dope shit

[velvet onyx]

Whats the question

[waxen swift]

I'm looking for a study partner for probabilities any one in interested

[mental stirrup]

Hi, I can see you've posted this message across multiple channels

Please don't -- that's spam. It's best to keep your message to just relevant channels

Maybe #probability-statistics would be relevant? If not, maybe ask in #math-discussion

[waxen swift]

ok sorry

[mental stirrup]

Thank you for being understanding

[topaz maple]

who are you

haven't seen you

[viscid thistle]

integration

[raw hill]

For future reference, this belongs in #calculus, not #precalculus.

Also, when asking for help, please show what you've done so far - it gives us more context and saves time from explaining things unnecessarily. \ \

I'd do integration by parts here. Split the integral as:
$$\int \frac{\sec^2 x}{\sin^{2022} x} \dd{x}-\int \frac{2022}{\sin^{2022} x} \dd{x}$$
and do integration by parts on the first integral.

[obsidian monolith]

Civil Service Pigeon

[rough leaf]

it’s like a line the function bever touches

it gets really close

but doesn’t touch

[viscid thistle]

i multiply num and den by sec^2022x , and sec^2 = 1 +tan^2 so for example sec^2022 , we can write as (sec^2)1011= (1+tan^2)1011 , tan =t , dt= sec^2

[viscid thistle]

you cant integrate second part directly , its dx not cosxdx

whats pre calculus then ?

[raw hill]

You should've gotten that one of the integrals from your integration by parts cancels with the second integral (also idt that the pythagorean identity is relevant here)

[raw hill]

A preparation for calculus course

it's an american thing that's a grab bag of algebra review and random topics

[viscid thistle]

i cant get that , sec^2 gives tanx , second integral has no tanx

[raw hill]

Did you try writing $\tan x$ as $\frac{\sin x}{\cos x}$?

[obsidian monolith]

Civil Service Pigeon

[viscid thistle]

where will the cos go ?

[raw hill]

nvm

just show me what you have rn

[viscid thistle]

i meant second integral has no cos

[raw hill]

Yeah that shouldn't be an issue because the cos x should cancel

which is why I'm asking you to show me what you have

[viscid thistle]

i cant show , i am on pc rn

ah mb

yea its cancels out

we differentiate sin too

i took a longer approach ig

[raw hill]

[lament bear]

Js multiply by sin²⁰²²x

[lone temple]

i see that differential approximation and tangent line are having relation with each others but i dont see it clearly, can someone help me understand deeper?

[astral apex]

you can use a tangent line to make approximations

for example, suppose you’ve found the equation for the tangent line to y = sqrt(x) at x = 4

that equation is: y - 2 = 1/4 (x - 4)

now we can approximate the square root of numbers close to 4 using that tangent line

for example, to approximate sqrt(4.2), we can simply plug in x = 4.2 to the tangent line equation, to get y - 2 = 1/4 (4.2 - 4), that is y = 1/4(0.2) + 2 = 2.05

in actuality, sqrt(4.2) is 2.0493901…

and you can see the approximation is quite good

notably, this only works well (by hand) when you know a certain value exactly already and the one you want to approximate is close to that

[round geyser]

Hey is this limits

[astral apex]

sorta! limits allow us to define derivatives, and derivatives allow us to find equations of tangent lines

so in a roundabout way, yes

but typical limit calculation problems look different

[modern igloo]

can someone help me understand weeks 4 to 8?

[lone temple]

btw can i ask another question, how do we come up with the tangent line equation, like we dont exactly know which line can cut the function right at one point lol, the equation sounds like derivative but idk why

[astral apex]

it's a good question, indeed it's not obvious how to find it. That's exactly what the derivative in calculus is for!

[willow skiff]

there's actually a neat approach for the derivative of polynomials

say you have the cubic f(x) = x^3 - 2x^2 + 3x - 4

and you want this line, ax + b, to be tangent to the cubic at say, x = 1

then there must be a double root of (x^3 - 2x^2 + 3x - 4) - (ax + b) at x = 1

so that must be in the form (x - 1)^2 * (x - p)

so now compare coefficients of x^3 - 2x^2 + (3 - a)x + (-4 - b) with that form expanded, which is x^3 + (-p - 2)x^2 + (2p + 1)x - p

and you get -2 = -p - 2, 3 - a = 2p + 1, and -4 - b = -p

so find p and that allows you to find a, b

and hence the tangent line ax + b

[astral apex]

that’s very cool!

[willow skiff]

yeah I've seen this technique before somewhere

[willow skiff]

thanks for the appreciation!

also it took a lot of effort to properly type out

you can read it in 1 minute but it took much longer to write

[drowsy panther]

can somebody help me figure this out.. idk what to do after getting to (7x- ) (x+ )
what factors into 27 and gives -4 and 27x ?!?

[zenith basin]

If you want a straight answer you can put in the calculator. But if you want to solve this without the calculator you can probably start with finding the easiest which is -4 since it doesn't have a variable of x. So the possible multiplications are:

1. -1 x 4 = -4
2. 1 x -4 = -4
3. 2 x -2 = -4
4. -2 x 2 = -4

Now that we know the possibilities we can try to put it in the bracket thingy:

1. (7x - 1)(x + 4) = 0
2. (7x + 1)(x - 4) = 0
3. (7x + 2)(x - 2) = 0
4. (7x - 2)(x + 2) = 0

To know which one of these is the correct one, you could expand these four and compare it with the equation given. You should be able to find + 27x. My explanation might be complicated but I hope it helps. Mine is more about trial and error so it might be not that efficient

[drowsy panther]

Thank you, i've figured it out to be x= 1/7 , x = -4 my issue was that i couldn't see when factoring earlier that 7x in (7x-1) (x+4) multiplied to give 28x - 1x giving me the 27x. this helped! thanks

[zenith basin]

You're welcome

[round geyser]

Use ac method

Move -4

[willow skiff]

you forgot (7x - 4)(x + 1), (7x + 4)(x - 1) by the way

[round geyser]

7x^2+27x-4=0

Slide 7 into 4

[drowsy panther]

hey guys i have a new question

[willow skiff]

indeed if you write enough of them your brain should click onto 27 = 7 * 4 - 1

[drowsy panther]

how would I solve this

[round geyser]

x^2+27x-28=0

[round geyser]

Okay

Divide 2

[drowsy panther]

9x/2

idk what to do with that

[willow skiff]

no, divide everything by 2

[round geyser]

Now x^2+(9/2)x+1/2 = 0

Then move 1/2

[willow skiff]

once you have x^2 + ... , you need to divide the coefficient of x by 2

then square it

[round geyser]

Making it x^2+(9/2)x+ ? = -(1/2)+ ?

[willow skiff]

so x^2 + 9/2 x + 81/16 - 81/16 + 1/2 = 0

[zenith basin]

Yeah that one as well

[willow skiff]

x^2 + 9/2 x + 81/16 is a perfect square

[drowsy panther]

oh not together? so it wouldnt be 9x/2 but (9/2)x??

[willow skiff]

same thing

[round geyser]

I did x^2 + 9/2 x + 81/16= 81/16 -1/2

[drowsy panther]

wutttt the

[willow skiff]

$\frac{9x}{2} = \frac{9}{2} x$

[obsidian monolith]

south

[drowsy panther]

bro what in the worlddd

[round geyser]

x^2 + 9/2 x + 81/16= 81/16 -1/2

[willow skiff]

this is arithmetic on fractions

say with numbers, $\frac{2 \cdot 3}{5} = \frac{2}{5} \cdot 3$

[obsidian monolith]

south

[drowsy panther]

right that makes sense

[willow skiff]

you can think of it as 2 * 3 * 1/5 = 2 * 1/5 * 3

the order of multiplication does not matter

[round geyser]

Factor
(x+9/4)^2 = 73/16

[drowsy panther]

ah i guess i get it now, its just weird seeing it being written in different ways i guess, in my coursework the video has an easily divisible example by 2 so this 9x just threw me off

i will try to follow this video now ill be back

[round geyser]

Yes

[willow skiff]

it's called completing the square for a good reason

[drowsy panther]

okay nvm im lost already now what her example isnt helping me

how do i do (9/2x / 2 )^2

[willow skiff]

it's the coefficient of x

so (9/2 divided by 2) squared

[round geyser]

Take the sqrt

[drowsy panther]

sooo 13/2 squared?

[willow skiff]

no

9/4 squared

[drowsy panther]

9/4....??

could you perhaps draw this out for me so i can see

[willow skiff]

here

[drowsy panther]

let me see

I dont know where to start, 2x^2 +9x +1 = 0
x=9 b=1 ?

[round geyser]

9/4 is (9/2 x 1/2)

[willow skiff]

no, you need to divide everything by 2 first

it only works when you have x^2 + ... = 0

[drowsy panther]

x^2 + 9/2x + 1/2 = 0/2

and then now it goes into this square proof thing?

[willow skiff]

yes, now you can complete the square

[round geyser]

South

Ima do the work

Can you explain to her

So taking half of a fraction is multiplying by 1/2

[drowsy panther]

why did we multiply 9/2 to 1/2? the 9/2 / 2 ?

[drowsy panther]

righttt

[round geyser]

It’s the same

Do u know Keep change flip?

[drowsy panther]

yes

i think

dividing a fraction by a fraction multiply denominator with a 1 under to 9/2 right

[willow skiff]

yes, multiplying by 1/2 is the same as dividing by 2

yes so you multiply the denominators

$\frac{9/2}{2} = \frac{9}{2} \cdot \frac{1}{2} = \frac{9}{4}$

[obsidian monolith]

south

[drowsy panther]

okay so now i have (9/4)^2

[round geyser]

South can you explain this

[drowsy panther]

then i can plug this in

ah let me look at this

[round geyser]

Yea

[willow skiff]

oh that's messy

[round geyser]

Like the same base

-1/2 + 81/16

[willow skiff]

basically x^2 + 9/2 x = -1/2
x^2 + 9/2 x + 81/16 = -1/2 + 81/16

(x + 9/4)^2 = 73/16

[round geyser]

Multiply by 8 on -1/2

Yes

If you are factoring you are taking its sqrt

Take sqrt of each side

Gets

[drowsy panther]

im slowly deciphering where the numbers are coming from for 81/16

9/4 * 9/4 81/16

ok that makes sense

[willow skiff]

pause a minute to understand this:

divide 9/2 by 2 = 9/4
square 9/4 = 81/16

yeah

[round geyser]

To x+9/4=+/- sqrt(73)/4

[drowsy panther]

where does

[round geyser]

taking sqrt

[drowsy panther]

where does 8/8 come from on the right side

[round geyser]

Common base

Is 16

2 x 8 gets to 16

[willow skiff]

from x^2 + 9/2 x + 81/16 = -1/2 + 81/16

you can write x^2 + 9/2 x + 81/16 = -8/16 + 81/16

fractions need to have the same denominator to be added

[round geyser]

Yes

For me definition base=denominator

Same base for mine is same denominator

[drowsy panther]

so then we multiply -1/2 by 8/8 for the right side

then what about the left side?

[round geyser]

To continue its then x =(-9 +/- sqrt(73))/4 by subtracting 9/4

[round geyser]

It has the GCF so don’t need to do anything

Their GCF is 16

[willow skiff]

the left side is a perfect square, (x + 9/4)^2

[drowsy panther]

okay I think i get that part a little then

[round geyser]

Master more of these questions

The quicker you get

[drowsy panther]

These questions HURT my head

i think this is my first time even doing this

[round geyser]

Yea

Practice practice practice

Go on TikTok or anywhere find these similar questions

And solve them

Are you solve more

You will get it

Eventually

That’s how I learn these

[drowsy panther]

damn, may i ask if youre in college or higher education?

[willow skiff]

oh no wonder

it gets easier the more you practice

[willow skiff]

I'm at uni but any competent 9th grader will be able to explain it the way I did

[drowsy panther]

LOL i never paid attention in math

this is like my first time again in math and doing it yk

[willow skiff]

interesting

well, good luck on your maths journey!

[drowsy panther]

thank you

how did 73/16 become 73/4

bcuz we took the square root?

wait what how did this happen

[willow skiff]

yes, take the square root of both sides

[willow skiff]

$x + \frac{9}{4} = \pm \sqrt{\frac{73}{16}}$

[obsidian monolith]

south

[drowsy panther]

so 9/4 is normal but the only thing that changes about sqrt 73/16 is the denominator

when u take the sqrt?

[willow skiff]

yes, okay time for rules of exponents/roots

$\frac{\sqrt{73}}{\sqrt{16}} = \frac{\sqrt{73}}{4}$

[obsidian monolith]

south

[main peak]

𝑓(x)

[drowsy panther]

ohh i didnt notice that 16 was also sqrt'ed

[round geyser]

HS

[drowsy panther]

and then since they share the same denominator its just -9

[drowsy panther]

Wow 🫠

[willow skiff]

yes, so very importantly, don't forget the plus-minus sign

[willow skiff]

so that actually means x + 9/4 = sqrt(73)/4
or x + 9/4 = -sqrt(73)/4

[round geyser]

It’s 2 solutions

[willow skiff]

yes

x = (sqrt(73) - 9) / 4 or (- sqrt(73) - 9) / 4

[round geyser]

But I like to make it

[willow skiff]

every time you square root both sides, you need one plus-minus sign

[round geyser]

x = (-9+sqrt(73)) / 4 or (-9 - sqrt(73)) / 4

[drowsy panther]

but they write it like jake right, -9 +- sqrt 73 /4

[willow skiff]

say x^2 = 25

x = 5, but also x = -5

[round geyser]

Order doesn’t matter

[willow skiff]

we can write $x^2 = 25 \implies x = \pm 5$ to mean both solutions at once

[obsidian monolith]

south

[willow skiff]

yeah

[drowsy panther]

Okay thank you jake & south, I will definitely try to remember this

[round geyser]

Yes

[brittle comet]

is ur completeing square question solved

?

i can help if it is not solved

@round geyser

[marsh mason]

Unrelated but is Stewart's Precalculus a good book?

[brittle comet]

i m using that

its good i guess costs 200 $ , should be good

i m using a pdf !

[round geyser]

Done

[brittle comet]

ok noice

[round geyser]

Yea

[minor mica]

hi

[pine snow]

I GOT AN A ON MY PRE CAL TEST TODAY

IT WAS SUPER SUPER EASY BUT I STILL GOT AN A

[marsh mason]

Congratulations! Great job

[shrewd grove]

now, let that sink in.

no seriously whos gonna let that sink in

[toxic carbon]

https://tenor.com/view/sink-cuisine-amenagement-equipee-design-gif-8476897548120197244

[azure burrow]

Good job, really impressive

[viscid thistle]

Guys factor 2x = 4

It’s so hard only PhD can do it

[vale hill]

Anyone got good AP precalc resources or a textbook pdf?

[echo sinew]

Don't troll

[echo sinew]

#book-recommendations

[pine snow]

https://tenor.com/view/let-that-sink-in-sink-door-open-door-meme-gif-11027748423699535107

[stiff sorrel]

Do troll ❤️

[delicate knot]

2x-4=0
(1)(2x-4)=0

[willow skiff]

<@&268886789983436800> the above comment is clearly off-topic

[fossil kindle]

2(x-2)=0

thats not even precalc

[vast rivet]

Whats precalc ive never heard of it

Is it just basic calc

[viscid thistle]

my precalc teacher made me do it💀

goofy ahh ciricullum

easiest class ever

but that was at like the beggiuning of the year but still

[rough leaf]

not really

its like everything in between alg 2 and calc

so liek trig conic sections limits vectors matrices

that kinda stuff

[rough leaf]

<@&268886789983436800>

[round geyser]

Is this right

South

Ann

[uncut mulch]

careful with your signs for g(f(x))

[whole tinsel]

is limits precalculus

[willow skiff]

yes

[viscid thistle]

Does epsilon delta fall under precalc?

[marsh lantern]

Is there a good way to remember radians (unit circle)?

[astral apex]

it’s not “standard” for it, but I could imagine an ambitious teacher attempting to cover it

[marsh lantern]

I crawled my way through trig without memorizing them, but then I hit polar coordinates.

Polar and rectangular

[astral apex]

it’s recommended that you understand why 0, pi/2, pi, and 3pi/4 have the values they do, then you can always figure them out easily; then that you memorize the values for pi/6, pi/4, and pi/3 (the reason they have the values they do comes from special right triangles); then various values in other quadrants can be found from those ones by reflecting around the circle

[marsh lantern]

I understand it, and the quadrants in which they are positive/negative (ASTC)

It's just how long it takes my brain to figure it out

[astral apex]

sounds like you’re doing it right; you’ll likely get faster as you do more problems

[marsh lantern]

After sintheta/2 or sin2theta I gave up on trig

Half angle and double angle

[charred rapids]

I mean it depends for me

Not basics limits that need to be done using Taylor series are not precalculus

[willow skiff]

no, that's straight-up calculus

[rough leaf]

i js got them wirh practice

[gusty merlin]

yes also i love your mirror man pfp

[whole tinsel]

does integrals fall in precalculus

[raw hill]

no

#calculus

[whole tinsel]

oh thanks

[raw hill]

[sullen gull]

Just remember the first quadrant and subsequently put negative values and positive values respectively for cos and sin for each quadrant as it is. Like surely, x is -ve in the 2nd quadrant and y is +ve, so all values of cosine are negative, but not sine.

Also for -ve values just subtract from π/2

If less than π/2 ofc

And for greater than that, use π (obtuse) and 2π for reflex angles

Just remember π=180°

180/2=90=π/2

[bleak jacinth]

Yoooo can someone help me understand as to why certain quadrants have pi subtract or add reference angle?? Would appreciate it

I am reviewing for exam so like im tryna remember why that’s the case

[sullen gull]

Look

135° can be written as 90+45 right?

So 135 is just π/2 + π/4

which is 3π/4

So since the angle(x input) is in the 2nd quadrant, it's an obtuse angle

We can also write it as -π/4

As x is -ve in 2nd quadrant.

THAT is when we subtract -π/4 from π

As sin-x would be just -sinx

But to get proper values of other trig ratio we need such values by Adding or subtracting po

Pi

This is just my conception

It makes it ez for me to understand

Hope u find it helpful

Cheers @bleak jacinth

[bleak jacinth]

Ohhh that makes sense, tysm i appreciate the help!!

[sullen gull]

Happy to help

[round geyser]

How would u solve this one

[fiery spear]

bottom equation simplifies to a proportion

do it

[round geyser]

Okay

Can we substitute?

[sullen gull]

For the first one,y=2 and x is probs 1 (correct me if wrong)

[sullen gull]

No need

[round geyser]

Okay

Wait

[sullen gull]

The bottom is just the log property of lo(a/b) = loga-logb