precalculus

[modest bolt]

how do i get helpful role, does it need 1000 msg per day or what

[hoary iris]

You've actually helped a lot

idk why you didn't get

anyways may we ask that cursed limit to Ann

?

that tetration limit

[modest bolt]

oh

yes you can try

[hoary iris]

friends word, sure

lol

[river drift]

help in the help channels or forum

[modest bolt]

ok thx

[hoary iris]

He have helped a lot

btw

[terse pebble]

no

[modest bolt]

its automatic, i understand dw

[hoary iris]

[terse pebble]

i had to leave the server for 3 months

[hoary iris]

What?

[modest bolt]

its like bot auto assigns roles at reaching certain msg per day in help channels i think

[modest bolt]

why

[terse pebble]

idk

try it

[modest bolt]

you lost all your msg count, sad

[winter comet]

touch grass

[hoary iris]

but he got helpful role

[hoary iris]

what are you studying rn?

long time no see

[winter comet]

between linear algebra and discrete 😂

[modest bolt]

then aah maybe bot stores msg count and doesn't reset it after leaving or he really helped a lot after joining

[winter comet]

i finished the LA course but i still study a bit, and will take discrete

but rn im doin programmin :l

[terse pebble]

nah you need to leave for 3 months to get it

[modest bolt]

thats some crazy requirement

[terse pebble]

word

[winter comet]

get the green role by touching the green thing for 3 months

[terse pebble]

yep

[modest bolt]

mods really wanted us to touch grass to get the role

[winter comet]

you're very helpful when ur not on the server

[hoary iris]

Anyone ping me here when you've got an interesting limits or sum or prod

[elfin jay]

Can someone explain me this pls (supposedly this can be classified as precalculus), the only I know is that is something similar to a summatory

[raw hill]

This denotes the cardinality of the union of ${0}, {1}, {2}, \cdots {10}$

[obsidian monolith]

Civil Service Pigeon

[elfin jay]

Tysm❤️

[errant shard]

I still dont get precalc definitions

like what is d/dx, or dh/dy, ect

I get what they may mean through proxy, but I dont understand what they are trying to say

[hoary iris]

Is d/dx trig?

[errant shard]

I mistyped

[hoary iris]

maybe https://youtu.be/N2PpRnFqnqY?si=r2SrYiwGiu-G40w_

[errant shard]

ty

[hoary iris]

also there is no such thing called precalculus definitions

I sent you the concept of derivatives

like

d/dx

[errant shard]

I dont know what precalc is

I just assumed

We dont do precalculus where we live

And as there is no precalculus channel, well I assumed as I just started...

[hoary iris]

idk is derivative precalculus

https://www.khanacademy.org/math/precalculus @errant shard try this

Do we need to do "get ready for precalculus" before precalculus?

in KA

[hushed sphinx]

Derivatives are the central concept in calculus.

So it wouldn't make sense for them to be part of something sold as PREcalculus.

[hoary iris]

I see

[hoary iris]

Is this all the precalculus stuff? @hushed sphinx

[errant shard]

I have no idea

We just do calculus

[hushed sphinx]

I have no idea, "precalculus" appears to be a chiefly American topic grouping that I have no first-hand experience with. I can just deduce from the name that it has to be different from calculus itself...

[noble lava]

Precalc is actually just different subjects like trigo and stuff combined lol, if you good at that stuff you can just start calculus

Not a real thing imo

[hoary iris]

I see

Hey, executor. Do you wanna try a infinite product question?

[noble lava]

Eating rn. Maybe later

<@&268886789983436800>

[hoary iris]

ok.np!

[hoary iris]

Is L(x) factorials?

where that l extends upto the x under it

[willow bear]

... what

[hoary iris]

idk is it L

[willow bear]

can you write on paper what function you're referring to

[hoary iris]

yes

[willow bear]

oh yeah that's an old fashioned notation for factorials

in modern notation this would be $\lim_{n\to \infty} \frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}$

[obsidian monolith]

Ann

[hoary iris]

I see

Will gamma function do the same thing as factorials when the input is positive integers?

[willow bear]

almost but not quite

Gamma(n) = (n-1)!

[hoary iris]

Can I learn gamma function now?

[willow bear]

how good are you at integration

[hoary iris]

idk at which level i am

[willow bear]

hmm

[hoary iris]

I know basic integrals

[willow bear]

<@&268886789983436800> scam

[willow bear]

hm ok let's try this first: $\int\limits_{-\infty}^{+\infty}\frac{\dd{x}}{1+x^2}$

[obsidian monolith]

Ann

[willow bear]

does this look like something you're able to calculate

[hoary iris]

,, [tanx]_{-\infty}^{\infty}?

[obsidian monolith]

Monkey•D•Luffy

[drifting oyster]

arc

[hoary iris]

oh shit

[willow bear]

yeah i mean you might wanna learn not to confuse tan with arctan for starters lol

[drifting oyster]

Wow throwing shade

[hoary iris]

mmm sure!

[drifting oyster]

https://cdn.discordapp.com/attachments/465274898613534730/1339972308215009280/image0.gif

[willow bear]

no direct link to Gamma ftr i just wanted to gauge your level

[hoary iris]

Am I eligible?

[willow bear]

??

[hoary iris]

lol

[willow bear]

id say probably not yet? like don't take my words as gospel but i do think you might wanna spend time getting better at integration (and tbh also probably learning some real analysis)

[drifting oyster]

Real analysis???

Before calc?

brave...

[willow bear]

i mean

eh

line in the sand ig but i don't necessarily expect him to spend 17 years with epsilon bashing

[hoary iris]

Thank you for your suggestion! but what is real analysis?

[willow bear]

calculus concepts but rigorous

[drifting oyster]

Bros gonna let epsilon be less than zero if he learns analysis before calc 1

😭

[hoary iris]

then I am gonna do it

[drifting oyster]

I recommend the bright side of mathematics

Good view into starter stuff...

Wow that's some exciting math

What is that?

Scam analysis?

<@&268886789983436800>

[hoary iris]

calculus concepts but not calculus?

[willow bear]

im refusing to draw any line in the sand between calculus and analysis.

[hoary iris]

https://s2pnd-matematika.fkip.unpatti.ac.id/wp-content/uploads/2019/03/Real-Analysis-4th-Ed-Royden.pdf

It this book ok?

ann

enterlessguy

or this https://www.math.stonybrook.edu/~aknapp/download/b2-realanal-inside.pdf

[uncut star]

I don't think now is the best time for you to do real analysis

[hoary iris]

Where are you preparing for JEE?

[uncut star]

I don't even know

I haven't really started my preparation

Properly

[willow skiff]

try not to study for 12 hours a day challenge

[uncut star]

I don't know about him but I am definitely not studying for more than 30 mins

@hoary iris how much do you study on a daily basis

[hoary iris]

I Just don't do unecessary stuff lol

[uncut star]

Same i don't really study physics and chemistry

[hoary iris]

and study for both for my JEE and school as I am not in integrated one

[hoary iris]

Same here

it is like math (-1/12) while physics and chemistry (the probability of determining the position and momentum of an electron simultaneously)

lmao

[uncut star]

The difference from math to physics and chemistry just discourages me

[hoary iris]

Are you in integrated or normal school? @uncut star

[hoary iris]

eventhough I waste time in math in others pov

[robust pecan]

π

[noble lava]

Yeah you do you don't need to know what gamma functions are when you've barely started limits

[hoary iris]

I do know some basic integrals lmao

[noble lava]

Still, stuff like gamma isn't necessary at even jee adv level, do chem or smtg instead

[uncut star]

I am in an integrated school

Unfortunately

[robust pecan]

12th grade?

[robust pecan]

no need

[noble lava]

[robust pecan]

definitely complete integral calculus from cengage

Especially definite integration

trust

[noble lava]

What do you mean by "no need" lmao? No need to study chem?

[robust pecan]

bro

[robust pecan]

No need of stuff like gamma

[noble lava]

Ah

[robust pecan]

ill be real with you

i was cooked in Chemistry

[noble lava]

So you're agreeing with me

Nice

[robust pecan]

I am still recovering

[noble lava]

Grind hard fr, even my chemistry was a bit weak before giving jee but definitely not as bad as it used to be before i tried to actually do it properly

[robust pecan]

How can i strong my physical chem

[noble lava]

Physical chem is just grinding numericals imo

Organic is about doing ms chauhan

And inorganic i have no idea, i just studied from notes usually

[robust pecan]

Inorganic is memory based

[noble lava]

Ik

Ratta baazi hai bas

[hoary iris]

It's not unfortune

[robust pecan]

Tru

Mai abhi organic

Kar raha

[errant shard]

Is rate of change the same as the derivative?

[safe basin]

it could be if you’re talking about rate of change locally at some point

But people could also refer to the average rate of change over some interval as that

take some differentiable function f, the first one is computing f’(p) to give you the derivative at some point p

the second one is fixing some a and b in f’s domain and taking (f(a) + f(b))/(a-b)

i.e. slope of the line going through the points a and b

if f is linear then these will give you the same thing because the derivative of f will be constant

[bleak forge]

what is the derivative of 8?

[safe basin]

what do you think

[bleak forge]

I have no clue

[safe basin]

look at the definition and give it a try

[bleak forge]

définition of what

[safe basin]

the derivative

[bleak forge]

Aight

the rate of change of a fonction at a value

soooo uh I guess the answers 8?

[safe basin]

nah

so we have a function f(x) = 8

[bleak forge]

what’s that

[safe basin]

how does f change at any point x

[bleak forge]

f(x)

[safe basin]

function in a variable x

it takes a real number x and spits out 8

[bleak forge]

We haven’t covered variables yet

[safe basin]

ight I would look at that before looking at derivatives then

[bleak forge]

ok can you explain them really quick please

[safe basin]

but the answer to your question is 0

because it just looks like a flat line going through y=8

so the rate of change is 0 bc it never changes

[bleak forge]

We just finished multiplication in my class it’s a class for kids with learning disabilities

Im going to uni next year so im tryna learn it cuz im going into a math major

[safe basin]

to khanacademy you go lil bro

[bleak forge]

what’s a variable I don’t get it

Why is it not a number

it’s a letter

is it like Greek numerals like does x equal 10

[safe basin]

ts is the dumbest ahh troll I’ve ever seen vro do better

[drifting oyster]

https://cdn.discordapp.com/attachments/1155909296425545889/1374768371215892533/attachment.gif

[safe basin]

deadass

[bleak forge]

Im so cooked guys

[safe basin]

indeed you are

[bleak forge]

I think it’s to late to go for liberal arts

[safe basin]

I think step 1 is to touch some grass

[bleak forge]

« Grass » is one of my triggers so lets stay respectful please

[boreal crag]

one of the first questions i asked

now im still doing precalc

[hoary iris]

What is the use of homogenous functions?

[sullen python]

what do you mean by homogenous functions?

[hoary iris]

I just wanna know what are it's uses and I don't has any other questions!

[hoary iris]

something like this

[echo sinew]

I meant that homogeneous can have different meanings according to the context you're working with

[hoary iris]

in context of JEE

[echo sinew]

Oh ok

Then I can't help you lol

I don't know anything, even if I wished to

[hoary iris]

You can tell me about the pure mathematical homogenous equations too

I wanna know about it!!!!

[dusk forge]

cud someone explain linear differntial eqn in a simple yet definition based

[river drift]

a linear differential equation is a differential equation which is linear

[ivory fractal]

wut?

[worldly grove]

then f(x) is
a) continuous for all 1 <= x < 7 but not differentiable at x = 1
b) continuous for all -1 <= x < 7 but not differentiable at x = 1
c) neither continuous at [1,7) nor differentiable at x = 1
d) continuous and differentiable at x = 1

How can i solve this?
ive taken the left and right hand limit at x = 1 for which i got the result 3 and 6 so the function is not continuous as x = 1 which also implies its not differentiable at x = 1

should i evaluate the left and right hand limits for the intervals [-1,7) and [1,7) as well?

[noble lava]

All these options seem suspicious.

f(x) is neither continuous and hence nor differentiable at x=1

However, it is differentiable at x belongs to (1,7)

[open mason]

bro wtf is c) saying

not differentiable on [1,7) implies not differentiable at x=1

[worldly grove]

wait mb i typed the option wrongly, its
c) neither continuous at [1,7) nor differentiable at x = 1

[open mason]

ok c then!

[strange lichen]

I have a ti84 plus ce and casio fx9860, however my school wants me to get the casio fx-cg50. Would that really make a difference idk? I use the casio 9860 for math cuz it gives exact values but the ti for physics and chem for easy storing and rentry of previous answers. The fx cg50 is 100-150 dollars depending where i go for purchase

[cold vale]

can anyone integrate this

and say ans without applying limits

[shut willow]

Substitute x^2 + a^2 = k

[cold vale]

i took that

i still cant get thru it

[shut willow]

where r u stuck

[cold vale]

when i take tht = k , i get dx = dk/2x

then

when i substitute dx in the integral

can i cancel 2x and x in numerator?

..alr i got the answer

[hoary iris]

In which pattern does tan x goes?

[high pelican]

iirc tanx maclaurin series is a bit cursed

i cant imagine a scenario where you have to know more than the first couple terms by memory

[summer ruin]

$\tan(x) = \sum_{n=1}^\infty \frac{|B_{2n}| 2^{2n}(2^{2n} - 1) x^{2n - 1}}{(2n)!}$

[obsidian monolith]

Transparent Elemental

[summer ruin]

where B_2n is 2n-th bernoulli number

[high pelican]

I think 'a bit cursed' adequately describes that

[hoary iris]

Then it is no longer humane!

[river drift]

<@&268886789983436800>

[hoary iris]

Proud message with this tag lmao

yaey

[vagrant nymph]

This is what I tried but I don’t really know how do I find n from here

Like I can’t do the algebra part😭

[vagrant nymph]

<@&286206848099549185>

[spice nymph]

algebra?

you called me son.

[vagrant nymph]

how do i even solve these high exponents😭

[spice nymph]

latex it down

and ill help you

[vagrant nymph]

idk latex if u want i can write it properly and send it

$$ \frac{\left(\frac{3\left(3^n-1\right)}{2}\right)}{\frac{1}{6}\left(1-\frac{1}{3^{2n}}\right)} $$

[obsidian monolith]

TPD

[vagrant nymph]

here i did it

[hoary iris]

What do you wanna do with this? @vagrant nymph

[vagrant nymph]

Find n for which thing thing =3^10

[vagrant nymph]

this was the og question i might have made some calc mistake i tend to make a lot of those

[hoary iris]

<@&268886789983436800>

[viscid thistle]

what did he say

[hoary iris]

Who??

lmao

[viscid thistle]

The message that got deleted

[hoary iris]

It is some scamming spammer!

lol

not tpd

[viscid thistle]

Oh

[snow marlin]

Could someone please sidebar with me for fda/real zeros? I'm still pretty confused about some stuff

[drifting oyster]

pardon?

[crude zodiac]

hi

[candid condor]

prove the following
a) The sum of a rational number r andban irrational number t is irrational
b) The product of a rational number r andban irrational number t is irrational

[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

[midnight kernel]

What did you try so far?

[dry nest]

substitute x^2 + a^2 = t^2 to get xdx = tdt and the denominator becomes t^3

[void charm]

man this equation seems unsolveable

[red storm]

looks fun

ok this isn't quadratic/cubic

i a ctually can't see exponents bro

[drifting oyster]

https://cdn.discordapp.com/attachments/1165428384059379762/1353543919937388595/caption.gif

[drifting oyster]

X=3 btw...

[noble lava]

Unsolvable indeed

[red storm]

immaculate equation

[dusk magnet]

6x/10x=x/5
3/5=x/5
x=3

[echo sinew]

Not again

<@&268886789983436800>

[muted moth]

Y'all fast

[empty otter]

3

[hoary iris]

This is the reason why big shots shouldn't come here lol

[uncut star]

???

[rough zinc]

https://tenor.com/view/brain-meme-you-did-not-have-to-cut-me-off-gif-498898395089837096

[viscid thistle]

so hard

[vagrant nymph]

Can someone tell me how do I read this set E1

<@&268886789983436800>

[muted moth]

Hmm?

[drifting oyster]

$\frac{x}{x-1}>0\cap (\mbb{R}/{1}$

[rotund jewel]

Banned in different channel

[drifting oyster]

Oops

gr

[vagrant nymph]

So all they are saying is x/x-1>0?

That’s it right

[obsidian monolith]

Enterlessguy

[drifting oyster]

There we go

[drifting oyster]

That inequality + the fact that x has to be a real number thats not equal to 1

So in summary you have the set x/x-1>0 intersect R minus set of 1

[vagrant nymph]

Okay thankss these confuse me

[vagrant nymph]

There was some spam message

[late harbor]

is ap precalc bc really that hard guys

im an incoming sophemore and im lowk scared

background info, i took honors alg 2, 1 semester i got a b+ and 2 semeter i got an a-

[willow skiff]

it's just AP precalc: you mixed it up with AP Calc BC

but it's not that hard

given your background

[south oar]

There's an AP Precalc?

I'm out of the loop I think

[willow skiff]

it's fairly new but yes

no more new than the digital SAT though

[south oar]

I wasn't even aware it was digital now

Lovely

Headaches <3

[willow skiff]

out of the loop indeed

[south oar]

Very 😭

Then again my hs is very rural soooo

I'm shocked we have APs at all

[willow skiff]

damn

the rural education gap is shocking

[willow skiff]

from how you reacted you could also be Canadian or something

[south oar]

Indeed it is

I constantly look to places outside my school at this point

The math program is decent but the sciences

Hoo boy

My last bio teacher doesn't believe in dinosaurs

The one before that said 5G causes cancer

Idek anymore

But Precalc was fun <3

[deep otter]

When I took Precalculus in the senior year of high school, we just called it an Honors class, but it had IB styled problems. IB was like my school's version of AP. It was uh, weird? And british?

Don't quote me on the british part.

[willow skiff]

it's not British at all

it's very international though

British would be IGCSE then A levels

[deep otter]

I thought somebody told me it was at one point but I know the I stands for International so what you say checks out.

Truthfully I don't really remember, that was a long while agoZ

[river drift]

IB is french

[willow skiff]

did you know there's a European Baccalaureate

[south oar]

That’s how it was for me as well, it was Honors Precalc

I took it two years back

I think it may be “CHS” or whatever now

[deep otter]

Truthfully? I am not sure if it was a knowledge gap (I got into math very late, I didn't really realize I was really into math until late high school) but I took non-honors math classes until Precalc Honors and I struggled with most things. I got a lot of certain topics but others I really didn't click with, and for some of my other friends who were more academically inclined they found it rough too, so maybe it was the teacher or teaching or how things were set up, but I got a C in that class. And I was happy. It was the first time I did get a C, though.

I later went on to breeze through Calc 1, very graciously mind you, with an A. I did really well in Calc 2 as well, so I guess Precalc did its job in prepping me.

[south oar]

No I’m the exact same way. I took honors Precalc my freshman year and finished with a C average, and then got an A overall in Calculus

Idk what it is

[willow skiff]

repetition legitimises (Neely)

[south oar]

But Precalc felt so much harder

[willow skiff]

if you see precalc for the first time it's going to be hard to do well

give students a second chance and they can do much bettert

[south oar]

That’s fair yeah

[willow skiff]

truthfully, half of calc is just precalculus content applied to new situations

[deep otter]

Maybe they make it hard so they know you'll do well!

Like imagine if a giant, buff, muscular dude just clocked you in the jaw and then some really scrawny 10-year-old kid kicked your shin.

Like yes the latter did hurt, but the pain was lessened in a way because you were worried about your face not your shin.

Weird analogy maybe.

Or maybe I'm weird.

[south oar]

Calculus felt like the cool older brother to precalc

You met precalc went to his house and just were astounded by the coolness

[deep otter]

Yeah I remember in Precalc we talked a lot about domain and ranges of certain functions and the graphs of functions you don't see all the time like exponential functions and functions with radicals. You learn about those briefly in algebra 2 and then never really touch upon them again. Stuff like asymptotes, etc.

It's also where I learned the unit circle for the first time. That was something I was really happy I picked up early. I took it to heart, later in college my classmates were spending time trying to memorize it, I already had it all down.

Ah, also wear I graphed sine and cosine and tangent functions and learned how to for the first time.

Good times.

[willow skiff]

yeah there's great benefits to doing precalc

in short all of this filler, alg 1 and alg 2 can be fast-tracked if someone has the ability

really what we need to be testing is precalc for those students

to see what they don't understand and do understand, out of everything they've studied so far

[regal oar]

could someone check my answers

[noble lava]

Correct.

[regal oar]

Thank u

[hoary zephyr]

to have a more complete answer you could do start by determining the domain of the function ,then check if -x is in this domain.

[noble lava]

Wdym find if "-x" is in the domain? x is a variable.

[uncut star]

what is an even function

[noble lava]

f(x)=f(-x)

[uncut star]

oh

[noble lava]

Hm?

[hoary zephyr]

for example for (3) it would be:
$f(x) = 1/x^2$
the domain of the function (where the function is defined) is: $D_f = \left{x\in\mathbb R/ x^2 \neq 0 \right} = \left{x\in\mathbb R/ x \neq 0 \right}$= $\mathbb R^{*}$.

[obsidian monolith]

Koka

[hoary zephyr]

let $x \in D_f$.
$x \in D_f$ $\iff$ $x \in \mathbb R^{}$ $\iff$ $(x < 0 $ or $ x > 0)$ $\iff$ $(- x > 0 $ or $ -x < 0)$ $\iff$ $(- x > 0 $ or $ -x < 0)$ $\iff$ $-x \in \mathbb R^{}$ $\iff$ $-x \in D_f$.

[obsidian monolith]

Koka

[hoary zephyr]

and then you do $f(-x) = 1/(-x)^2 = 1/x^2= f(x)$.

[obsidian monolith]

Koka

[noble lava]

I see

That's cool

[hoary zephyr]

because if -x isn't in Df

you can't say it is even

[noble lava]

I can't think of a case where it wouldn't?

Maybe im brain freezing

[hoary zephyr]

let me think

it's been a long time since i did those kind of exercices

maybe for a function defined by pieces..

[noble lava]

x is still a variable so wouldn't the pieces of the function just adjust accordingly?

[hoary zephyr]

like for x > 0 f(x) = something and x < 0 f(x) = another thing

[noble lava]

Like if f=1 for x<0 and f=2x for x>0,
when we put -x,
We get f=1 for x>0 and f= 2x for x<0

[hoary zephyr]

yes

kind of

[noble lava]

Yeah that's why I can't really see the point of $D_f$

[obsidian monolith]

Executor (ask on server b4 DM)

[hoary zephyr]

but to do those kind of manipulation you should determine first where the function exists

hence the use of Df

[hoary zephyr]

do you know how to code?

[noble lava]

A bit, why?

[hoary zephyr]

Actually i want to learn how to code but i don't know where to start

i think it will be very useful to learn

[noble lava]

I see

imo you shouldn't start with something high level like python

By high level here I mean user friendly and more compile time

[noble lava]

Like all the concepts can be learned well

But when you move to something like cpp or assembly the syntax requirements will trouble you

Maybe you should start with something like Arduino.

[hoary zephyr]

arduino

[noble lava]

Yeah

It's used for circuits

[hoary zephyr]

do i need to buy it

or is it online

[noble lava]

Hm, not the compiler, but if you want to see the hardware you'd need to buy that

[hoary zephyr]

thanks

[noble lava]

Arduino mostly has applications with hardware, so if you don't want to buy that I'd suggest cpp.

That was my first language.

[hoary zephyr]

cpp , i will keep it in mind

[noble lava]

Yeah cool, it stands for c++, look it up

[hallow dew]

Does any1 here in teach uhm math like one on one

$50 for 5 hours doesnt have to be the same say

[drifting oyster]

10 dollars per hour...

https://cdn.discordapp.com/attachments/1155909296425545889/1374768371215892533/attachment.gif

[noble lava]

Fr

[willow skiff]

Min hourly wage for tutoring is double that, hun

But you can ask in the help channels for free!

[dim thistle]

Does this count as precal?

[willow skiff]

this is straight up calculus dude

also the integral is missing a +c

and the integral is in terms of which variable? that's also missing

[dim thistle]

Btw , does rational integration hard ?

[willow skiff]

yes, unless you integrate in the complex numbers

if you integrate in the complex numbers you can decompose any polynomial denominator into its linear factors

so PFD

[dim thistle]

Can someone check no.3 answer?

[willow skiff]

ask in the help channels or ask in #calculus

not here

[dim thistle]

Bet

Isn't pre cal!

[dim thistle]

It*

[willow skiff]

is what you sent before calculus? no

it's straight up calculus

anything in the us precalc curriculum goes here, examples include: trigonometry, logarithmic and exponential functions, function sketching, etc.

[dim thistle]

Thanks, I'm new to cal (I'm a high schooler)

[ionic crystal]

J wein

can u help me with geometry

im going into 8th grade

and i dont know shit

[willow skiff]

but yes your work is correct for no. 3

nice work!

[dim thistle]

Sup?

[willow skiff]

there's also a technique called the reverse chain rule that helps you integrate f(kx) where k is constant, without doing the substitution

if you just want to check your answer, not the process next time

,w integrate sin(3x) cos(3x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[dim thistle]

Thanks bro

[willow skiff]

np!

[red storm]

can't you let u = sin(3x)

so that du = 3 * cos(3x) dx

dx = 1/[3 * cos(3x)] du

also just a good tip whenever you see integrals like this with linear trigonometric functions

you can assume it's u-substitution

d/dx sin(x) = cos(x)

d/dx cos(x) = -sin(x)

d/dx sec(x) = sec(x) * tan(x)

but if it's like degree 2 and above you have to find a way to get an identity

[narrow elm]

can someone teach me calculus

[echo sinew]

Don't you feel like it's too much to ask? 😅

[noble lava]

Your textbook can.

[narrow elm]

i dont understand it

[echo sinew]

Change textbook

[narrow elm]

i cant

[echo sinew]

Or tell us why you don't understand it

You could probably have some prerequisites missing

[narrow elm]

well

what prerequisites do you need to understand it?

as far as i understand

calculus is about finding the area of a curvy graph

[echo sinew]

Precalculus, prealgebra, trigonometry

[narrow elm]

i know trignometry

idk what prealgebra is

idk what precalculus is

maybe ive done it before

[echo sinew]

https://www.cuemath.com/algebra/pre-algebra/

https://en.wikipedia.org/wiki/Precalculus

[narrow elm]

95% of pre-algebra is done

[echo sinew]

Awesome

Make sure to know how to deal with fractions very well

Both with numbers and letters

[red storm]

pre-algebra is introductory algebra

[red storm]

copious amounts of algebra and trigonometry

[narrow elm]

oof

[red storm]

calculus 2 and 3 is trigonometry-heavy

you have to learn stuff like conversion to polar form, polar coordinates, evaluating using radians, how to integrate or differentiate trigonometric functions, etc, etc

just for clarification integration is what you specified about "area under a curvy line"

it finds it

while derivatives find the rate of change at some point of a curvy line

[open mason]

No

That’s just one minor niche you can use it for

[queen hedge]

Hey dude I am new here

[noble lava]

Welcome!

[iron gate]

Hi guys, I’m taking Ap pre calculus next year, can any of you guys give me tips on how to pre study it so I can get ahead?

[red storm]

trigonometric identities, unit circle, trigonometric equations and de moivre's theorem

also equations of circle, ellipse, hyperbola and parabola

make sure you also have good algebra skill and basic trigonometry knowledge as prerequisite

[magic remnant]

Guys how do you find the interval of a trig function

Is it something set in stone

or is something you have to find?

if so how

[red storm]

t his

also you have to learn your trigonometric identities

remember tanx = sinx/cosx

if cosx = 0, then tanx will be undefined

and cotx = cosx/sinx

if sinx = 0, then cotx will be undefined

[magic remnant]

Okay so I just have to memorize them

[red storm]

kind of

you need to memorize the

domain of sinx and cosx

[magic remnant]

sinx is -pi/2 to pi/2 right?

on unit circle?

or am I being sumb

[hushed sphinx]

Both sin and cos have all the real numbers as domain.

[magic remnant]

oh yeahh

okay

[magic remnant]

Do I have to find the interval here

Scratch that HOW do I find the interval here

[noble lava]

"Interval"? Your solution is just all the values of x for which cos(5x)=0

So just find the general solution

And see which of the options fit it

[magic remnant]

How do you tell if the value represents the max or min?

would I just have to graph it and check that way?

[raw hill]

You could graph the sine function to figure it out yeah

sin has a min at 3pi/2 and a max at pi/2

[magic remnant]

so if I'm not able to graph it it's always safe to assume that when it's 3pi/2 it's talking baout minimum value

and if it's pi/2 it's max?

[drifting oyster]

sir

[raw hill]

You could learn that off for sin if you want to

[drifting oyster]

sine has its max and min at arcsin(1) and arcsin(-1)

find the general solutions to those arctrigs

and then make sure the inside value of the sine matches to those values

aka if its sin(ax+b) the ax+b inside has to be equal to the x value for sin's minimum

[open mason]

sin and cos can be analytically continued to the entire complex plane

The complex inverse trig functions attain complex values on non principle branches

And by maximum modulus principle they are technically unbounded ;)

[magic remnant]

Did I solve this right?

[digital sage]

you're wrong right at the 1st step

[magic remnant]

We don’t use the identities do we

I couldn’t subtract the cos(x)?

[digital sage]

the identity you used is wrong also

my suggestion here is convert sin^2(x) to cos^2(x)

and solve it like a quadratic

[timid widget]

can someone help me or teach me solve this problem set

[tight bobcat]

Basically you find the slope of the lines and make it pass through your desired points somehow

For example, in 1) the slope of 2x-5y+10=0 is 2/5, so the slope of the line perpendicular to it is -5/2.

[timid widget]

it says find the "equation" what that does mean? should i only find the slope and thats it or it means somethin

[tight bobcat]

It means to find a line

Since a line can be defined using an equation

For example the line y=mx+b has slope m, here we need to find b so that the line passes through the point given

1. the line we need to find has slope -5/2 so there's y=-5x/2+b
   Since it passes through (1,-2), just sub x=1 and y=-2 and solve for b

[timid widget]

ohhh i kinda get it now.. but il take my time to comprehend it more

thank you

also should i also do the same for the rest?

[tight bobcat]

It's pretty much the same, find the points the line needs to pass through as well as the slope (depends on paralel or perpendicular)

[willow bear]

@regal oar ayo

ok so when it comes to fractions in general

you can cancel things out on the num and denom if they're factors of each

[regal oar]

yoo

[willow bear]

namely, $\frac{a \cdot b}{a \cdot c} = \frac{b}{c}$

[obsidian monolith]

Ann

[willow bear]

this is the core idea of any kind of fraction cancellation

and it remains in effect no matter what

[regal oar]

yea

[willow bear]

ok right

[regal oar]

I udnerstand that part

[willow bear]

notice that if the numerator was instead something like

ab + d

then it would no longer be in the form of a * something

and so cancellation would be impossible

[regal oar]

wdym by

[willow bear]

* means multiplication as always

[dusk magnet]

is this task incorrect?(Find the maximum point of the function y=-(x²+400)/x)

[willow bear]

why do you think it's incorrect

did you find that it has no maximum point at all?

[dusk magnet]

because it's limit when x->-0 is +inf

[willow bear]

имеется в виду локальный максимум

[dusk magnet]

там не написано что локальный и не написано про промежутки

[willow bear]

про глобальный речь не идет

[dusk magnet]

обычно в заданиях егэ всегда пишут какой промежуток чтобы не было вопросов

[willow bear]

локальный максимум у этой функции вроде бы один

[dusk magnet]

так и есть

но в условии не указано что нужен локальный и на каком он должен быть промежутке

мне кажется что файл с этим заданием содержит не все данные

[dusk magnet]

и в оригинале условия были другими

[willow bear]

локальный максимум -- точка, в которой первая производная 0, а вторая -- отрицательна

[dusk magnet]

это я знаю

но математика точная наука, и когда не говорят что нужна точка локального максимума на промежутке, а говорят найти просто точку максимума у функции которая не ограничена сверху то явно что-то не так

[rotund jewel]

Hey @willow bear @dusk magnet, for moderation purposes we request that all extended non-English conversations be moved to DMs

[willow bear]

k

[rotund jewel]

I apologize for the inconvenience

[knotty copper]

im willing to help

ping me if ur up for it

[noble lava]

Multi post?

[obtuse olive]

didnt know where i was supposed to post mb

already found it tho

[noble lava]

Alr you can delete it if it's solved

[hoary iris]

Apologising to whom for what??

[hushed sphinx]

Apologizing to Ann and Uo for shooing them out to DMs.

[hoary iris]

[willow bear]

for the record, uo did not DM me

[drifting oyster]

https://tenor.com/view/deer-interview-it-goes-without-saying-gif-12669775144079688963

[hushed sphinx]

#chill

[proud raven]

to those that are out of school and training and job interviews and normal places to encounter an actual test

what is the hardest test/quiz you find yourself given in your normal life

using test/quiz loosely, obviously

[hoary iris]

[magic remnant]

How would you find the exact answer of this without a calc

Or is it already simplified enough to be considered exact?

[river drift]

,rccw

[river drift]

that's as simplified as it's going to get

[magic remnant]

Okay ty 🙏

[rugged sundial]

How do I tell what function it is exactly? I can only find the x-intercepts being x=-3, x=1, and x=5.

[willow skiff]

That's interesting

It's a rational function assuming ing the part before x = 0 goes to positive infinity

[rugged sundial]

I've been staring at this for 20 minutes and im so lost

[willow skiff]

Furthermore, the numerator must be at least of degree 3 + 1 = 4, cause the denominator is linear (only one vertical asymptote)

[rugged sundial]

x=-3 being asymtote right?

[willow skiff]

No, that's the root

My best guess based on the graph is x = -2

[whole void]

impossible, without futher information (if u want to be pedantic)

[tight bobcat]

pick a random function and pray

[rugged sundial]

ok

[tight bobcat]

At least use the roots tho

[willow skiff]

It's possible but you have to keep trying functions of this form until it matches

You must have (x - 1)^2 (x + 3) (x - 5) in the numerator cause of the roots

But 1) you don't know the vertical asymptote and 2) you don't know the vertical stretch

[tight bobcat]

Maybe vertical stretch isn't a problem here, the graph passes through (2,-5)

[willow skiff]

Ah cool

Yeah there are plenty of integer points

[rugged sundial]

i figured it out

[willow skiff]

That one looks the most exact

[rugged sundial]

its f(x)=(x+3)(x-1)^2(x-5)/(x+1)

[tight bobcat]

That looks correct

[magic remnant]

Is this correct?

[tight bobcat]

Move 4 to the other side first before taking log

[magic remnant]

So

2x=ln(11/50-4)?

Isn’t that not possible though

[tight bobcat]

Yeah...

[magic remnant]

Oh frack

Might be a problem 😓

[tight bobcat]

I see

4+e^2x =50/11

[magic remnant]

?

How

We multiply both sides by 1/50

[tight bobcat]

Then 1/(4+e^2x)=11/50

[magic remnant]

Is there still a 1 left over…

After we cross out..

The 50 😭

Oh god

I see it now

This

[tight bobcat]

alr

[magic remnant]

if we have the equation

r = 6

and it has to be graphed on a polar graph

would I plot a singular point or have to plot a circle?

[spice mica]

well r=6 means you’re graphing everything 6 units away from the origin

so a full circle

[magic remnant]

okay I was just making sure

thanks 🙏

[magic remnant]

Does this look right

[spice mica]

that should be a circle

cos graphs in polar are circles with a diameter of the coefficient, in this case 3, and the left most point is on the origin

[magic remnant]

I tried but if I need the edges to touch 1.5

I don't think making a circle would work on this graph

[spice mica]

yeah the radius is 3/2 because the diameter is 3

[magic remnant]

because then I'd hhave to change the diamters

[magic remnant]

yeh so this is probably the best I can get it

unless I'm missing somethingz?

[spice mica]

no it should definitely be a circle

[magic remnant]

Except

?

I don't get how I could make one with this grpah

[spice mica]

why not

[magic remnant]

The circles circumference has to touch 1.5 and -1.5

And isn't it doing that

[spice mica]

yeah the radius is 3/2 so that’s done

like I said

[magic remnant]

yeah and it is on the graph

[spice mica]

I don’t really get what you’re confused about

[magic remnant]

Do you think you could js draw it somewhere

[magic remnant]

I don't get what's wrong about it

[magic remnant]

yeah

[spice mica]

I was curious why cosine graphs made circles so I went ahead and proved it

[magic remnant]

Woah

That’s so cool 😭

[spice mica]

well not actually a valid proof because I would need to show more rigorously that the angle there is 2theta

kinda just hand waved that

chatgpt gave a better proof anyway

[magic remnant]

Can someone please check my graphs and what I wrote for point of intersections at poles?

[magic remnant]

I figured out the problem with my r = 3cos(theta)

It’s now a circle

[magic remnant]

Are the values of theta for which the polar graph of 3cos(theta) 0<=theta<=2pi or just pi

[magic remnant]

I have to find those for the shapes formed by the graphs here

I just don't know how to find said intervals

you mean just plug it in

and find it like that?

wait

Oh my god I'm an idiot 😭

I literally drew out the graphs for the equations

which have the innterval I need 😭

You explained it good (I watched the limits vid)

But the audio was a bit difficult to understan

but yeah it was pretty good js the audio 🔥

[spare panther]

hi guys are there any linear algebra sources you could recommend? anything to help self-study before university hits

[echo sinew]

#linear-algebra or #book-recommendations

[spare panther]

didn't notice these chats thanks

[arctic swan]

I learned sigma and product operator today and got too excited 😭😭

[tight bobcat]

I'm not sure what I'm seeing but I'm not lovin' it

[whole void]

Yes I love those. Learn how to drag sigma a bit better 🙏

[hoary iris]

This is pleasing to the eyes. Anyway, what were you studying then? I mean the topic you're going through

[noble lava]

Good luck solving that

You gonna be hella lucky if the answer is even finite

[willow bear]

yes you did

[hoary iris]

How to find the least value of n for (sqrt(3)+i)^n to become real and purely imaginary without trying every n values from 1 to some number which gives the answer?

The real and purely imaginary are separate questions

[drifting oyster]

Well least is 0 for it to be R

[hoary iris]

Sorry n should be positive mb

[drifting oyster]

Interesting question...

I would set it equal to a+0i and try to use binomial formula

Perhaps we can also use the fact that (a+b)^n>=a^n+b^n

Not sure if that will help though

[hoary iris]

What will a be?

[drifting oyster]

Any real number

[hoary iris]

How to find n in this way btw?

[drifting oyster]

not sure... but

[willow skiff]

Find the argument of sqrt3 + i then multiply by n

It's based on De Moivres

[hoary iris]

Sorry I am not taught what is argument and de moivres @willow skiff

I am only taught the arithmetic of complex numbers

[drifting oyster]

Argument is angle between z and the origin

[hoary iris]

With some properties of it

[drifting oyster]

I haven't seen that theorem though

Sounds interesting

[willow skiff]

Come back when you know it

[hoary iris]

I see

[willow skiff]

It's clearly designed for someone who knows

[hushed sphinx]

If you don’t know the geometric interpretation of the complex multiplication, then it would seem your only cance is to try every n until you find the first purely-imaginary power.
But you won't need to try very far!

[hoary iris]

But not for us

[hoary iris]

I see

I will give it a try after I have done the graphical thing

Thank you for your information!

[hushed sphinx]

The graphical thing?

[hoary iris]

um what do you mean by geometrical representation of multiplication of complex numbers? @hushed sphinx

I only know that multiplying a number by 'i' rotates the number by 90 degrees in the argand plane

[tight bobcat]

That's one example. Basically every complex number has a magnitude (absolute value) and an angle, which is the argument of the number.

Multiplying some complex numbers will multiply the magnitudes together while adding the angles up

For example, i has a magnitude of 1 and a 90° angle, while 1+i has a magnitude of √2 and a 45° angle.
Their product is -1+i, which has a magnitude of √2 and a 135° angle.

[hoary iris]

whooooaaaaaaaaaaaaaaaaa

can we represent argument of some complex number z as Arg(z)?

[tight bobcat]

Yeah I think that's correct

[hoary iris]

Can we say z=cos(arg(z))+i sin(arg(z))?

[noble lava]

Mhm

But

That's only if |z|=1

Otherwise the general formula is z=|z|(CiS)

(CiS) is a shorthand way of writing cos(argz)+isin(argz) btw

[hoary iris]

is r=|z|?

[noble lava]

Yeah

[noble lava]

This is the polar form of complex numbers

[hoary iris]

we can find the arg of some number z if we represent them in polar form. right?

[noble lava]

You'll also learn the euler form eventually

[hoary iris]

it is e^(i arg(z)). right?

[noble lava]

The polar form is just a representation like the normal z=x+iy, in the polar form if you factor out the common multiple, that will just be your 'r'

[noble lava]

Mhm

[hoary iris]

I have a doubt regarding r=|z|

is it really true?

can you give me an example on this?

axe cutter

@noble lava

[noble lava]

Wdym?

[drifting oyster]

if you repesent a+bi

as a triangle

[noble lava]

r is just a representation for |z|

[drifting oyster]

r is the hypot

right?

[noble lava]

Yeah

[drifting oyster]

and the magnitude of z denotes the distance of z from 0

and thats the same as the hypot

hence r=mag(z)

[hoary iris]

yes it is but........

[drifting oyster]

but?

[hoary iris]

what does this mean?

[drifting oyster]

so

$a+bi=re^{i\theta}$

[hoary iris]

Is cis(argz) the unit thing?

[obsidian monolith]

Enterlessguy

[drifting oyster]

$z=re^{i\theta}$

[noble lava]

.

[obsidian monolith]

Enterlessguy

[drifting oyster]

$\abs{z}=\abs{re^{i\theta}}$

[obsidian monolith]

Enterlessguy

[hoary iris]

ye bro but is cos(arg z)+ i sin(arg z) the unit thing of that number?

[drifting oyster]

$\forall z \in \mbb{C}: r\ge 0$ hence $\abs{z}=r\abs{e^{i\theta}}$

[obsidian monolith]

Enterlessguy

[drifting oyster]

yes because thats r=1

[tight bobcat]

That's the angle part, the magnitude is the r

[hoary iris]

How to represent z=1+i as in this form btw?

[noble lava]

Firstly find |z|

Then find argz

And write it in that form

[hoary iris]

[noble lava]

What part's not clear?

[hoary iris]

How to find arg z?

[noble lava]

sqrt(x^2+y^2)

Where z=x+iy

[hoary iris]

ik how to find |z|

but not arg z

[drifting oyster]

$\arg(z)=\arctan{\frac{b}{a}}$

[obsidian monolith]

Enterlessguy

[drifting oyster]

(but)

[hoary iris]

What are b and a here?

[drifting oyster]

you need to make adjustments based on the quadrant of z

[tight bobcat]

z=a+bi.

[drifting oyster]

but here since both of your a and b are positive

[drifting oyster]

you can just use this formula

[hoary iris]

wdym by adjust here

astc?

[tight bobcat]

The range of arctan is (-90°,90°) iirc

[hoary iris]

yes

[tight bobcat]

The argument's range is [0°,360°)
-# i was wrong oops

[drifting oyster]

so for some quadrants,

you need to consider starting from 180 degrees

thats what I mean

[drifting oyster]

negative pi to positive pi

[hoary iris]

not 0 to pi??

[drifting oyster]

no...

clockwise and anti clockwise...

[noble lava]

(]

[tight bobcat]

yeah I don't really remember things correctly so I'm not sure

[drifting oyster]

both can be open...

doesn't really matter

[noble lava]

Conventional principal argument is defined that way

[drifting oyster]

yes

[hoary iris]

but why not 0 to 2pi?

[tight bobcat]

Because everyone sure loves seeing other people suffer 🥰

[hoary iris]

lessguy and cutterr

whyyyy nottt?

they're gone without telling it 😭

[drifting oyster]

from - pi to pi is more symmetrical...

and nicer...

[noble lava]

It's just how it's defined

[drifting oyster]

its just nicer to define it the other way

so when you don't slightly move under the positive reals

you immediately don't jump to 2pi

[tight bobcat]

From this I conclude that I'm not nice. □

[hoary iris]

Can anyone explain how this works?

i can guess the quadrants quite easily

[drifting oyster]

for quadrant 1 arg(z) is just theta

for quad 2 arg(z) is theta +pi

etc...

[hoary iris]

[drifting oyster]

and you have the formula for theta...

whats the issue...

[hoary iris]

How the formula came??

[tight bobcat]

Quadrants 1 and 4 are quite easy to see

[drifting oyster]

math

its trigonometry...

I think you can derive it yourself...

[hoary iris]

I want to know the math behind it!

[tight bobcat]

For 2 and 3 you just throw in a pi and pray it works

[drifting oyster]

just pay attention to the domain restriction on tangent

[hoary iris]

whooaaa yeah

I still don't get it sowwy

everyone

[drifting oyster]

draw a triangle...

to z

where a is the adjacent side to theta

and b is the opposite

you have that tan(theta) = opp/adj =b/a

hence theta= arctan(b/a)

pretty simple...

[hoary iris]

bruhh not this

how theta + pi and -pi for 2nd and 4th quad

[tight bobcat]

Hmm

[drifting oyster]

I think you can understand this better visually...

[tight bobcat]

For 2 and 3 try reflecting z over the y axis and find the supplementary angle of the argument of the new point

Explanation: trust me bro

[drifting oyster]

notice that for the 3rd quadrant

we have -pi rotation already?

so the argument is theta-pi

[hoary iris]

oh yes

do we need to take a and b with signs?

or just the magnitude

[drifting oyster]

yes...

with signs

[hoary iris]

and use that adjustments according to the quadrants

right?

[drifting oyster]

yes...

well

only needed for 2 and 3

[hoary iris]

Thank you so much!!

[drifting oyster]

also to write z in its polar form

you just need to calculate arg(z) and |z|

and then plug it into $|z|e^{i\arg(z)}$

[obsidian monolith]

Enterlessguy

[drifting oyster]

(|z|) is r

[noble lava]

euler form*

[drifting oyster]

euler

yes

[river drift]

that's usually called polar form at least in my experience

[drifting oyster]

well

technically polar is the cos(theta)+isin(theta) one

no?

[noble lava]

really?

[river drift]

you could define it that way but we always just used e^(i theta)

[noble lava]

Eh it's just names

Doesn't really matter

[echo sinew]

In Italy we call it exponential form lol

[echo sinew]

Amd this one trigonometric form

And z = a + ib algebraic form

There are so many names 🙈

[small solar]

In France it's the same. But we also can call |z|e^(iarg(z)) the exponential form.

By the way if you like the exponential form, you can solve : $$\arg(z)\equiv\arg(z^2+i)\ [2\pi]$$

[obsidian monolith]

gottawakup

[hoary iris]

In India(especially in tamil nadu) too

[magic remnant]

what do I right for the limit as x approaches infinity for the sin, cos and tan functions?

i know it has no limit because y never reaches a certain point but I just wrote

lim x -> inf, y = NL

and at the top wrote NL = no limit

Is tehre a formal way to write this

[river drift]

they way i've seen it written is $\lim_{x \to \infty} \sin x$ does not exist'' or $\lim_{x \to \infty} \sin x$ DNE'' but how you write it isn't super important

[obsidian monolith]

cloud

[magic remnant]

okay, thanks 🙏

[magic remnant]

How would you find the interval of a piecewise function

Like how do I find it for this graph

(I’m talking about increasing/decreasing interval)

[dry lantern]

Increasing = positive slope
Decreasing = negative slope

[magic remnant]

Yeah but for piecewise functions what would that look like

Because this one has 3 functions

So 3 diff intervals right

[dry lantern]

It works the same for analytic functions