precalculus

[magic owl]

you can use the geometic series

[hoary iris]

here in the second line how does the a^n-1 taken inside the summation?

yes but if it is a constant why does it change when it is taken inside the summation?

[magic owl]

a^(n-1)*a^(-k)

[magic owl]

it doesnt change

[hoary iris]

oh yes lol i haven't seen it

[hoary iris]

did he mean not to use L'Hospital rule?

[magic owl]

yep

[hoary iris]

it's one of the easy proof i think

[magic owl]

but there some limits that need to use L'Hospital

[hoary iris]

my book used some kinda binomial expansion lol

[hoary iris]

L'Hospital can only be used to certain limits you mean?

[magic owl]

normal limits

see this limit

this is not normal limit

you need to use L'Hospital

[hoary iris]

we can't do it directly by any means other than L'Hospital rule?

[magic owl]

no

[magic owl]

i can show you how to solve this limit if you wanted

to know how to use L'Hospital in this cases

[hoary iris]

but I don't know about gamma functions clearly. If you can explain me, go ahead.

[magic owl]

btw do you know mascheroni constant ?

[hoary iris]

nope

@magic owl what is the branch of math of Gamma function?

i think gamma function is quite interesting to learn

[magic owl]

gamma(x) = (x-1)!

x! =x(x-1)(x-2)....2x1

by other way

[hoary iris]

you mean euler's constant gamma

[magic owl]

the gamma function can be defined by an integral

[magic owl]

yes

that constant is near 0.577

[hoary iris]

is this proof without the use of L'Hospital rule?

[magic owl]

its with the L'Hospital

you can see the third line

[hoary iris]

ohh

[hoary iris]

differentiating the integral of gamma or by some other methods?

[magic owl]

no need

the dérivative of gamma(x) is gamma'(x)

[hoary iris]

just direct differentiation

the derivative of gamma of 1 is -gamma?

can't we prove it without L'Hop?

[magic owl]

we can do it

but its not easy

i proved it with without L'Hopital ( i mean the limit)

you need to turn it into integral

[magic owl]

yes , gamma'(1) = -mascheroni constant

[winter comet]

you can always solve a limit without using l'hopital, it just may not be practical

[winter comet]

it's not in a specific branch of math, but you might see it in calc 2 or later classes

[pulsar patrol]

mathematics

yessyessyess

mathematics

🐵

[exotic barn]

precalc

[magic owl]

just showing him 😅

[lofty granite]

whats the first derivative version of the inflection point called? i forgot whats its name in english

the maximum minimum thingy... what's its name?

oh it's extremum/extrema

[willow skiff]

Or turning points, or critical point (if that isn't discontinuous)

[lofty granite]

thankuuu

[rocky wind]

this is a precalc channel
your question suits #calculus better

[lofty granite]

lol mv

mb

[hoary iris]

ohh you found the equation of a chip

[arctic dagger]

what's it called

a (bounded) parabolic hyperboloid?

[viscid thistle]

yes

why is my gender female

[viscid thistle]

absolutely

[willow bear]

you must have misclicked during onboarding

go to "channels and roles" and untick she/her pronouns and tick he/him instead

[hoary iris]

...

[next cloud]

Get ur papers from tyrion papers .

[lunar elbow]

Someone here knows any way to start working on formulas from existing ones to better ones ?

[willow skiff]

what do you mean by better formulas?

[viscid thistle]

thx

[lunar elbow]

Some formulas give some estimates, i would like to make one that is 100% correct

[willow skiff]

What kinds of formulas aren't 100% correct?

You're best off sending a picture of your question or whatever it is you're investigating

[lunar elbow]

Partitions

[willow skiff]

Ah partitions of integers

There is a recurrence relation for them

[lunar elbow]

Yea

[willow skiff]

There's no exact closed form solution though

[willow skiff]

But this is exact

You could easily code it if you have some programming experience

[lunar elbow]

I wuold have liked a formula, it would be helpfull for all of mathematics

[willow skiff]

Maths isn't that neat all the time

[lunar elbow]

Unlucky, is there a proof that says there isn't an exact formula or it could be discovered ?

[willow skiff]

Um I don't know about that

[willow bear]

what is PSPSDzps supposed to mean btw

[arctic meteor]

How did $\sum_{k=1}^{n} \frac{2}{2k+(2n-1)}$=$\sum_{k=1}^{n} \frac{2}{2(2k-1)}$ ???

[obsidian monolith]

wolly5114

[arctic meteor]

How did $\sum_{k=1}^{n} \frac{2}{2k+(2n-1)}$=$\sum_{k=1}^{n} \frac{2}{2(2k-1)}$ ???

[obsidian monolith]

wolly5114

[arctic meteor]

wrong type

sorry

[boreal wharf]

idk

if lim_b -> infity b!
will b just be infinity

[magic owl]

by the "King's Rule"

[arctic meteor]

@magic owl which is?

[magic owl]

try this

[rocky wind]

1. show attempt to your own question
2. wrong channel. this channel is for precalculus questions. yours belongs to #calculus

[boreal wharf]

oh ok

[sturdy hound]

how do you find the median on a sine function or trig function like cos of theta?

[willow bear]

wdym by median

!xy

[tender quest]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[rancid bluff]

I have a questionnnn why does 1/2 turn into -1/2 when I derive it?

Why does it not drop out?

[upbeat tundra]

it doesn't

https://tenor.com/view/i-hope-that-was-helpful-corey-vidal-i-hope-that-helps-you-hope-that-was-useful-to-you-hope-that-was-of-value-gif-20766062

[willow bear]

!xy

[tender quest]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[idle frost]

can anyone explain to me about partial integration method and when to use it?

because i confused about how it works hehee

[uncut mulch]

that's in calculus territory,
or better to just claim your own channel
and ideally post a specific example

[willow skiff]

do you understand the power rule now?

[quick hound]

Hello, could someone support me with this

[winter comet]

<@&268886789983436800>

<@&268886789983436800> again

lol

[river drift]

<@&268886789983436800>

[sturdy hound]

nvm i figured it out it is a line equidistant from the minimum and maximum for example on the graph y=sin theta the median is at y =0

[willow bear]

midline?

[bright abyss]

tbh

precalc is soooooo. easy

[willow skiff]

https://math.stackexchange.com/questions/1617961/polar-coordinates-of-an-egg-shaped-curve

the polar equations are definitely not obvious

you only learn about special cases such as flowers, cardioids, and limacons for good reason

oh and lemniscates (the figure 8s)

[normal gale]

i need to learn the proof of why the derivative of e^x is e^x by the end of tomorrow please help 🙏

[willow skiff]

#math-discussion message

try following this thread

ah, starts from around here: #math-discussion message

[normal gale]

thanks 🙂

[willow skiff]

@viscid thistle

Kepe helped you so I used that to help someone else, yay

[viscid thistle]

Sigma

[viscid thistle]

Basically you need 2 formulas/identities for it: the identity(or formula?) of f'(x) which is (f(x+h) - f(x))/h and the identity of e itself which is lim (x > ±∞) (1 +1/h)^h = e which is 1

So uh

The end part its gonna be e^x • 1

[rancid bluff]

I am not sure what you mean exactly ^^"

Here is the example we did in
school and I do not get how it comes to x^-(1/2) when I derive it.
Why isn't the it f'(x)=(3/2)x^(1/2)+7(1/2)*x
instead?

[summer ruin]

1/2 - 1 = -1/2

[eternal crater]

Is there a convenient way to remember the cross product? My book tells me that besides v w sin(theta),

[azure jay]

the king's rule is also appliable for sigmas?

i mean integrals are basically sums but yeah anyway

[winter comet]

its the determinant of this matrix, which equals the sum of these smaller determinants

i was running outta room lol

[river drift]

you can also expand it out in terms of basis vectors

in which case you have
i × j = k
j × k = i
k × i = j

• if you swap the order you get a negative sign, and the cross product of a vector with itself is 0

[arctic dagger]

cloud suits yellow

[night belfry]

how hard is precalc

im gonna take it this summer

[sturdy hound]

normal or honors?

[winter comet]

what's the difference?

[sturdy hound]

well for my school honors is way harder than normal

for normal precalculus all assessments are take home quizzes

and also

well i havent taken normal so i cant give a good comparison

but quite literally all of the assessments we've taken the teacher has had to curve the scores

[sharp hawk]

i feeling scared of calculus

how should i start learning calculus
which books

[rancid bluff]

OOOOOH I SEE THANK YOU SO MUCH! 😄

[hollow widget]

briggs

[stuck rock]

don't be scared calculus is probably the coolest thing you gonna learn

[buoyant fern]

bound integration makes me nut

[somber jay]

Hey um i'm really struggling with verifying identities, can anyone help out?

[viscid thistle]

ya lemme help

[eternal crater]

Thank Viper!

[viscid thistle]

{sqrt(4x+5) + 3/x-2 = 5} can someone confirm that x is 7 😭

[echo sinew]

$$\sqrt{4x + 5} + \frac{3}{x} - 2 = 5$$ this?

[obsidian monolith]

Alberto Z.

[echo sinew]

Or you meant 3/(x - 2)?

[viscid thistle]

yez

[viscid thistle]

its sqrt(4x+5) + (3/x-2) = 5

mb

[fierce viper]

hi could anyone help me with this one problem, I think I understand it, but no I don’t. It’s verifying identity

[supple sleet]

Whats the problem?

[sharp hawk]

well I mean it do look sick
but it probably going to be a pain to learn

[sharp hawk]

that's a book right?

[viscid thistle]

i solved it, it is 7, i believe

it used the quadratic formula and some factoring

[willow skiff]

,w sqrt(4x + 5) + 3/(x - 2) = 5

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by sooouth.

[viscid thistle]

shit

im so chopped

[willow skiff]

what kind of problem even is that lmao

[viscid thistle]

we havent learned this in school

[willow skiff]

yeah so after rearranging and squaring both sides

[viscid thistle]

where does the sqrt(-1) come from

[willow skiff]

ah you get a cubic

[viscid thistle]

oh i see

this allat of work

[willow skiff]

no real solutions

[viscid thistle]

ohhh

approximate value then?

[willow skiff]

also you could just sub in x = 7 to check

[viscid thistle]

dtm

[willow skiff]

https://www.desmos.com/calculator/6twbvoniwf

[viscid thistle]

man ure so much better

[willow skiff]

better graph but yeah the solutions are all complex numbers

since they don't intersect in real space

they intersect in some higher-dimensional complex space

[viscid thistle]

beyond

?

[willow skiff]

basically you have sqrt(4x + 5) = (linear)/(linear)
linear = (quadratic)/(quadratic)

quadratic * linear = cubic
so a cubic = quadratic equation is cubic - quadratic = 0

or just cubic = 0

[willow skiff]

yes you can extend all the operations you know to complex numbers

e.g if you wanted to multiply $(3 + 2i)(5 - i)$

[obsidian monolith]

south

[willow skiff]

multiply normally first using distributive law

then use the fact that i^2 = -1

[viscid thistle]

btw, im a little new to this. what does the $ mean?

[willow skiff]

it's how you type maths on this server! (and many others)

guide: https://en.wikibooks.org/wiki/LaTeX/Mathematics

[viscid thistle]

wow

im gna check that out

ty

[willow skiff]

np!!

[viscid thistle]

i think i may have gotten x = 7 because i set up the equation wrong

[willow skiff]

https://www.youtube.com/watch?v=T647CGsuOVU

also this is what I mean

[willow skiff]

but you discovered a completely new area of maths right

lol

[viscid thistle]

yes lollz

im buns at math but i still find it fun

i dont read test question and if a question says evaluate i forget to

😭

[viscid thistle]

are you in university?

[willow skiff]

yep

[viscid thistle]

shit

😭

how did you lock in if u dont mind me asking

[willow skiff]

never said I'm a mathematics major

but I am a former maths major

everything I said wouldn't be university knowledge in many countries (12th grade usually)

[viscid thistle]

ya bc ure good at math

[willow skiff]

but learning more advanced material and being forced to revise and apply more basic concepts from high school

[willow skiff]

definitely

[willow skiff]

really helps you understand and explain

[viscid thistle]

i think my math teacher hates me

bc

idk she js hates me in general

i do lua, typescript, javascript, css, html, some c# (not too much) since 9

so i think that definitely played a pivot in my relationship with maths

[whole void]

where do u go to school

just wondering

[willow skiff]

down under

[willow skiff]

okay that's jacked

never met a HSer who does Lua

[viscid thistle]

😭

my experience in almost all of those languages varies from 5 months to 5 years

[alpine bolt]

is it possible to write the equation for a function with a hole/point discontinuity directly next to another hole discontinuity?

like how (x-3)(x-1)/(x-1) has a hole at x=1

but with a hole directly adjacent to iot

[winter comet]

define "directly adjacent"

[alpine bolt]

like the next point over

ig it would be infinitesimally close

so maybe no answer

[winter comet]

exactly

💀

[pastel shard]

yes

[storm lodge]

yes

[boreal wharf]

Is this integral correct for the are in the top right.?

[willow skiff]

#calculus next time

[boreal wharf]

Oh yeah

I always forget sorry

[willow skiff]

but yes that does indeed give you the corner area

[boreal wharf]

Thanks

[willow skiff]

integrating 5 - sqrt(25 - x^2) from 0 to 5 gives the same

[willow skiff]

np!

[hoary iris]

is this a factoid? lol

[whole void]

alright but why would u use calculus to make things more complicated than they need to be

cause it’s just a square minus a quarter circle

[boreal wharf]

Oh I didn’t know that

[left anvil]

If anyone has any ways on how to self study calculus please let me know thanks

[dry verge]

I've been learning through Khan Academy.

[rocky wind]

i self-studied calculus when i was in Form 3 (Grade 9)

it's 15 years ago

i was using traditional methods

with a thick book with about 300 pages

i did/learnt by heart all derivations

it's very important to master the basics (trigonometry and precalculus) first
it's also important to know how to do every exercise question in your textbook
i used online CAS to check my calculations, back in 15 years ago
now you have easier to use tools

[glass flare]

is anyone here that can help

[honest pulsar]

yeah so I got a 40% this quarter in precal, last semester I got a 64%, I need to get at least a 78 to pass this course

[willow skiff]

no I'm going one step back and setting up the intended integral

then you can split apart the 5 dx from 0 to 5 = 25

[willow skiff]

@pulsar cradle so

the highest degree term is x^2 * x * x^3 = x^6, and it's concave up (-x^6 would be concave down)

x^2, x^4, x^6.. all look the same

and so on x^3, x^5, x^7...

from that it's a matter of drawing the right shapes that fit, so draw a cubic graph around x = -5, a quadratic graph around x = 0, and then around x = 3 it will just look like a curved line

[willow skiff]

and keep in mind that the overall shape is a big U due to the +x^6

that's how you can curve sketch

you can draw in the x = -5 and x = 3 parts first to figure out that it's concave down at x = 0

fill in the middle

[pulsar cradle]

Doesn’t seem to difficult thank you bro

[willow skiff]

yes you definitely need to watch worked examples and practice questions to understand this further

but at an intuitive level, locally (around a certain root) there are only 6 kinds of shapes
1, 4) linear
2, 5) like x^2
3, 6) like x^3

and each can be increasing or decreasing

so you just focus on each root

the proper way to do this is to check the first and second derivatives immediately before and after the root, which will tell you the same info

well, as long as you choose values between two of the roots it also works

np!!!

[whole void]

can u explain perhaps on an a more advanced level why the three (distinguishable) types of behavior around its linear, x^2 and x^3?

@willow skiff

[willow skiff]

x^2, x^4, x^6.. all look the same
so do x^3, x^5, x^7......

the first type has positive (or negative concavity) and the second type has zero concavity

at the root

and so all of these except for x also have a zero first derivative

[viscid thistle]

14 years olD??!

[willow skiff]

there is younger.

like if you know the power rule, product rule, quotient and chain rules

[viscid thistle]

learning calc at my age is diabolical

[viscid thistle]

ez

[willow skiff]

that to many people would count as having studied it

[willow skiff]

told you

[viscid thistle]

ik all of my exponent laws

im so cool

[willow skiff]

LMAO?

[viscid thistle]

no joke

those who know: 💀

[willow skiff]

calling them that is dumb then

[viscid thistle]

Whom?

[willow skiff]

power rule and product rule, but for exponents

[willow skiff]

.

[stuck rock]

actually am not that good at algebra i still able to learn it fine
just think that everything will become easy if u effort into learning it

[uncut star]

How do we prove that gcd(a,b)=gcd(a-b,b)

I have proved if g divides a and b then g divides a-b => g| gcd (a-b,b)

How do I prove that this is the gcd

[viscid thistle]

Oh mb 😭

[viscid thistle]

What do you call logarithm laws then?

I'm new to math like this, lol! Please correct me if I'm wrong. I'm just a bit of a grade h grader who loves math, and I enjoy being curious.

[rocky wind]

15 yrs old

That's b/c I didn't understand the definition of "derivative" when I read the graphical description from the book a few months ago for the first time

and I didn't know how to find YouTube at that time

and my (Form 3 maths) teacher wouldn't answer me such (calculus) questions
Another teacher knew this subject matter, and I heard that she held many degrees. That's why I asked her a little bit

[sharp hawk]

ok thanks

[warped shuttle]

teachers that don't answer your questions because it's for "higher levels" are so annoying

[willow skiff]

exactly they could just refer you to some textbook

[rocky wind]

after i grew up, i could understand their mindset of "fairness to everybody"

and after i learnt deeper math, and i looked back, i didn't even needa be sad

even though i can neither like such mindset nor change what's already happened
i can look forward and try to change what's gonna happen

[willow skiff]

no joke international school kids in HK learn basic differentiation in f3

[rocky wind]

by giving my opinions here, with the help of tech

[willow skiff]

that's the extended track where you do IGCSE then IGCSE Add Maths

[rocky wind]

u r lucky
i attended local school like the great majority of the local school kids

[willow skiff]

surprised they didn't teach it then for you

did you do M1 or M2 for DSE?

[rocky wind]

sch teachers work as a team
they're preoccupied to admin paperwork more than educational work

they had to teach according to a syllabus

[rocky wind]

M2

they "downgrade" it from a "subject" to an "extension module"

a "packaging" that discourages many local students from studying #calculus

the "M" stands for "module"

[willow skiff]

yeah this part really sucks

[willow skiff]

that's every school system for ya

[rocky wind]

that's planned

[willow skiff]

but aren't like local school teachers really passionate sometimes?

they regularly organise group chats and students text them about homework questions at 10pm at night or even later

[rocky wind]

the "grandpa" has a "script" pre-written

[willow skiff]

ah I see

yeah I think pedagogically international school teachers definitely are more experienced

they have to undergo a lot of training and professional development too

[rocky wind]

not in my class or era, back in 15 yrs ag

ago*

[willow skiff]

yeah it may have been a bit more formal then, I see

imagine doing form 7...

[rocky wind]

that's why i said u r lucky

[willow skiff]

I want to know your experiences of the 3 year uni system

before all of this 3322 bullshit (cls)

[rocky wind]

local school class size is around 40

[willow skiff]

oh wait did you go to uni overseas

I just assumed

cool

[rocky wind]

local public univ

i went overseas for master

partly cuz i'm traumatized by local edu sys

[willow skiff]

yeah I guess your family didn't have enough money for both UG and masters overseas

[willow skiff]

oh?

[rocky wind]

they won't pay for int'l sch, but local ones were still affordable for them

i saw some classmates in public univ applied gov's grant loan

[willow skiff]

yeah it's like only 30% of all f6 students even today can go to uni

the sub-degree market is a big scam

[rocky wind]

in my era the figure is 18%

[willow skiff]

yeah it was even lower back then

[rocky wind]

many wealthy parents try to send their kids to intl sch to avoid that system
or send kids for overseas studies after DSE

[willow skiff]

in particular there's one common trend if families have enough money

UK boarding school

I seriously don't understand why

how about Canada or Australia, if it has to be boarding school (cause parents gotta work and take care of their elders lah)

[willow skiff]

you literally don't have to explain it to me

dai lou I grew up in HK and only left when I was 18

[rocky wind]

one possible reason: at least one of their parents has a British passport, another factor would be reputation?

[willow skiff]

yes and yes

definitely colonialism is why

[left anvil]

Thanks for telling me would khan academy be a good option as well or just traditional textbook ways?

[left anvil]

How is it working for you do you learn stuff

[dry verge]

Yes, I've been learning stuff on there, like how to integrate and how to find the derivative of a function.

[rocky wind]

also try many exercises until you're confident

[viscid thistle]

I forgot the bracket at the end 😭

[pseudo zealot]

im a rising junior in high school if this changes anything

im taking calc bc next year for math and im deciding between taking ap physics 2 or c. how did taking ap physics c with calc bc concurrently work out for anyone that did it

specifcially im asking people that have done pretty well in their classes beforehand (Straight As) and not just anyone who decided to pick up the class

[winter comet]

have you taken ab?

[pseudo zealot]

nope i took pre calc

but its like a pre calc course that will prep you for calc bc

[winter comet]

as someone who hasn't taken ap,
I would recommend just doing the physics with the calculus lol

[pseudo zealot]

because?

keep in mind im taking it concurrently with calc bc

[winter comet]

because you don't need to be a master of calculus to do the introductory physics with calculus, and because personally I believe that physics without calculus is like bread without butter

💀

[pseudo zealot]

alr

[winter comet]

if you can I would learn the fundamental concepts of calculus ahead of time

differentiation and (relatively basic) integration

[pseudo zealot]

alr good to know

thanks

[hoary iris]

what do you really mean, south?(I don't really understand)

[half sinew]

Hey

[worn totem]

hey

[woeful mountain]

Hey guys! I'm a Paramedic Student thats struggling with Precalculus, but I need to pass in order to stay in Paramedic School. I have a quiz monday on:

Quadratic Functions

Polynomial Functions

Polynomial Division & Factor Theorems

Zeros of a Polynomial

Rational Function

Nonlinear Inequalities

My professor uses videos, but I don't grasp his learning. Any tips??

[gusty galleon]

Learn basics of calculus and take them congruently

[arctic dagger]

isn't calculus more advanced than those?

[winter comet]

wdym?

[arctic dagger]

calculus is more advanced than these. studied later than these. like these stuff are more basic than calculus

[arctic dagger]

cuz these are algebra

[river drift]

that's why this is in the precalculus channel?

[unreal osprey]

What grade is precalculus?

[willow skiff]

Start from integrating upper - lower

You know your stuff but I'm just pointing out a step you skipped without realising it

[pearl hinge]

how would you find the inverse function of more complex functions

[willow bear]

1. lie down
2. try not to cry
3. cry a lot

but in seriousness, there isn't really an answer anyone could possibly give you

with such generality

[pearl hinge]

are there any other methods other than y=f(x) and solve for x

[willow bear]

is there a question you're looking at specifically rn

[pearl hinge]

nothing specific but something for example containing e^x and x

[winter comet]

[summer ruin]

there are, but none of them would classify as precalculus

[pearl hinge]

what would they classify as

[winter comet]

math 👌

[summer ruin]

second year university and later

[pearl hinge]

idm asking in the appropriate channel, I am just not sure where that is

[summer ruin]

something like this

if you can't solve the equation y = f(x) for x, there's not much you can do at this level

[pearl hinge]

I am so glad I'm going to computer science and not math

[pearl hinge]

"it is possible" refers to step 3, I assume

[winter comet]

"create a program to find the inverse function of any one-to-one function"

[pearl hinge]

Wolfram alpha got u covered

[willow bear]

when you go to a restaurant do you ask for just "food"

[winter comet]

that definitely sounds like something I would do 💀💀

[sharp gulch]

can someone help me please 😇

i am in year 10

[willow bear]

!da2a

[tender quest]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[winter comet]

what with?

[sharp gulch]

aysmptotes

[willow bear]

just post your question mate

[sharp gulch]

oh sorry mate

[winter comet]

i am in year 2025, did you create a time travelling machine?

[sharp gulch]

no i mean i am in grade 10

sorry sir

[winter comet]

i know i'm joking 😂

[sharp gulch]

oh sorry sir

[winter comet]

its funny when people say it like that

[sharp gulch]

oh laugh out loud

[winter comet]

i am

[sharp gulch]

please help me doe vicious viper

[winter comet]

with what?

wait i misread

WAIT WHAT

💀💀

im jk but seriously post your problem lol

[sharp gulch]

okay vicious viper

this one is tricky

@winter comet any thoughts?

[winter comet]

i am thinking that is not related to asymptotes :l

[sharp gulch]

what about graphing these things

[winter comet]

what about graphing those things

[sharp gulch]

how do i do

please papa

and what is a desmos

someone told me to use it

but idk the formulae

@every1

[winter comet]

https://www.desmos.com/calculator

[sharp gulch]

thank u

[winter comet]

do you know the general shape of an exponential function?

[sharp gulch]

is it a curve?

like going from left to top right

📈

like this but a little smoother

like this baba?

[willow skiff]

yes that's the graph of y = 2^x

[winter comet]

yup

[sharp gulch]

okay thjank u

[willow skiff]

how you get there is to calculate 2^(-2), 2^(-1), 2^1, 2^3

[winter comet]

did i accidentally give him the ultimate cheat program that he wasnt supposed to know about yet :l

[willow skiff]

1. fill in the missing values by calculation
2. plot the points on the graph, for each function
3. join with a smooth curve

[winter comet]

☠️

[willow skiff]

that's how you graph by hand in general btw ^

[sharp gulch]

my teacher say we can use desmosus

[willow bear]

desmos is a graphing calculator

[uncut star]

Just a question that came to my mind

[willow bear]

you can type an equation into it and it'll graph it for you

[uncut star]

We learnt that sinx'= cosx

But why is that the case

[sharp gulch]

are you transgendered?

[willow bear]

might wanna slide over to #calculus for this one

[sharp gulch]

i support ur transition

[winter comet]

plug it into the definition of a derivative

[willow bear]

i am a trans woman, yes.

[sharp gulch]

oh congratulations Ann mate

[willow bear]

but also that was just a tiny bit weird to bring up in the middle of a convo like that.

[sharp gulch]

oh sorry Ann 🧦

[sharp gulch]

I think there's a misunderstanding of the basic steps involved. First, it's important to recognize that in mathematical analysis, 'filling in missing values' isn't just an arbitrary task – it's about using the appropriate method for the function, whether it's interpolation, solving equations, or simply using given formulas. Plotting and connecting points aren't just about random placement, but about understanding the behavior of the function and representing it clearly. Would you like help with any specific part of this?

[winter comet]

well at least he fits his name

[winter comet]

chat GPT ahh response

[sharp gulch]

nahh i type quick

[sharp gulch]

Ah, calling someone 'Goofball'—I guess it takes one to know one, right? But hey, I’d rather be a 'Goofball' than someone who gets their kicks from making fun of others. At least my name’s memorable, unlike some people's sense of humor.

haha AI roasted u

[winter comet]

haha your personality is just AI

[sharp gulch]

haha!"""dfej2

530.1/xn4 2333 @winter comet ----21n a znzhg{}zz{ZE}Z{{32]3[2] ^&8z

[winter comet]

maybe you should move to #chill 💀

[sharp gulch]

44zm 5n xnsb ))(x th n y ga

i moved

[willow bear]

!nogpt

[tender quest]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[sharp gulch]

how was i using it to answer other people questions

[willow bear]

you weren't in this moment, but consider this as a kind of warning shot.

[past spear]

😂😂

[willow bear]

eh?

[viscid thistle]

Does anyone know why B is considered the correct answer? I tried to solve it but all of them seemed like they werent differentiable at x=3?

[willow bear]

,rccw

[willow bear]

why are you saying $\sqrt{x-3}$ and $\sqrt{(x-3)^3}$ are discontinuous at $x=3$?

[obsidian monolith]

Ann

[viscid thistle]

I did left and right hand limit and they were undefined whenever i used the left hand limit

Wiat let me try it again

Oh wait i dont need to use left snd right hand limit if its not 0/0 right?

[willow bear]

i think you misunderstand somewhat.

the domain of both sqrt(x-3) and (x-3)^(3/2) is [3, +∞)

so when looking at continuity at the endpoint, you consider only the one 1-sided limit that even makes sense at all

so these things are in fact continuous

the difference lies in what happens when you use the formal limit definition on each one

for (x-3)^(1/2) you will end up with +∞ but for (x-3)^(3/2) the limit of the difference quotient actually works out to 0.

[viscid thistle]

Thank you

[pseudo zealot]

for anyone that took calc bc/calc 2 concurrently with ap physics c how was it

[willow skiff]

<@&268886789983436800>

[terse pebble]

i took calc bc and both physics c classes simultaneously and i didn’t find it bad

but again it depends on you

if you don’t particularly enjoy math/physics you might struggle

[half sinew]

I want to take Bc, but my school doesn’t offer.

Or physics

[terse pebble]

mine didn't offer physics c e&m or physics 2 so i just had them buy me the exam and i self studied for it

well i mean i bought it but they ordered it for me

[winter comet]

a.k.a., they did nothing for you

[terse pebble]

yes

couldn’t even get me ap classroom exercises

and the videos were dogshit for those two courses too

[half sinew]

How do you Self study

Strategy or motivation?

[terse pebble]

by reading books and watching videos

[terse pebble]

wdym

[half sinew]

So textbooks and videos?

Got it

[terse pebble]

yea

[half sinew]

So like

Motivation to discipline yourself

To study

[terse pebble]

calc bc is like the easiest possible subject to self study

[half sinew]

And set aside distractions

[half sinew]

Depends did you take calc 1 before

I know calc bc is a mix of calc 1 & 2

[terse pebble]

i enjoy math but there was a time when i just liked the idea of math more than actually doing math and to get out of that shithole i had to stop playing video games and doomscrolling on my phone

[half sinew]

I’m currently in that time

Do you recommend deleting social media

Expect YouTube obviously

Or changing your accounts and search history

[terse pebble]

yea i haven't used instagram, snapchat, tiktok etc in ages now

[half sinew]

Tiktok is where I learn information

[terse pebble]

lmao

[half sinew]

History

[terse pebble]

"educational tiktok"

[half sinew]

I might just switch the account

[terse pebble]

don't lie to yourself bro

just because you're not watching dance videos or women doesn't mean your brain isn't rotting

[half sinew]

I wouldnt say that

I’m see useless videos on my feed

Like movies

Fortnite

Etc

The algorithm feeds me into it

[terse pebble]

yea get off that shit asap

[half sinew]

Where else do I learn history

?

[terse pebble]

just don't use your phone like that

[terse pebble]

nowhere that shits ass

[half sinew]

I have Twitter and X

No LMAO

I mean

Instagram and X

[terse pebble]

lmao

[half sinew]

I could delete those right of the bat

[terse pebble]

people fr use twitter?

[half sinew]

Since I’ve been getting Imposter syndrome.

And bias

[terse pebble]

some old head shit

[half sinew]

It’s filled with racism

I should delete it before I get indoctrinated.

[terse pebble]

uhh

[half sinew]

I’m one step close

[terse pebble]

are you preparing for next year?

[half sinew]

Yeah im. A sophomore

But to be honest

[terse pebble]

what math are you in now

[half sinew]

Algebra 2

I’m taking accelerated courses

Summer

For pre calc

Then Junior year calc

[terse pebble]

through a local college?

[half sinew]

I mean yeah

There’s a local college

But I better apply before deadlines close

[terse pebble]

you probably have like a month

[half sinew]

Ok

Social media made me lose most of my personality

[terse pebble]

right about when spring semester ends for the college kids

[half sinew]

I’m trying to build it back.

[terse pebble]

then delete it

[half sinew]

I am

But Im stuck between Tiktok

[terse pebble]

work through khan academy or something

[half sinew]

Since it’s the quickest way to get shorts for history

💀

[terse pebble]

bro if you want to learn history just look into books

😭

[half sinew]

I do both

But tiktok is more in depth

[terse pebble]

it's not

[half sinew]

I could use YT shorts

[terse pebble]

just condensed giving you the main points

brief

[terse pebble]

you're trolling right

[winter comet]

when you don't have an attention span so you need to include educational content into your brainrot feed:

[half sinew]

No I swear

[half sinew]

I use to do that.

But my feed got a lot worse.

I’m seeing random

Phonks

[terse pebble]

lol what

[half sinew]

I somehow got interested and brainwashed by a Basketball creator.

I need to fix that asap.

[half sinew]

YouTube shorts isn’t bad.

It’s filled with history content on there

I just don’t use it.

[terse pebble]

https://tenor.com/view/copium-meme-pepe-frog-gif-26117735

[half sinew]

Can you block certain creators on YouTube?

[winter comet]

yes

[winter comet]

there are more effective ways to learn ._.

[terse pebble]

youtube is close to the bottom for learning in depth

good for learning to the test

in a short time span

or as a supplement for understanding

like you're probably much more likely to remember what you learned if you were using a book/doing exercises

[half sinew]

Obviously

But

[half sinew]

I remember what I learn from doing an active recall strategy known as blurting

[terse pebble]

bro what

[half sinew]

I would watch Heimler’s history videos

And take a piece of paper and try to recall everything

I just listened to

[winter comet]

that's good

[half sinew]

Repetitively

Incorporating space repetition

[winter comet]

in preparation for a test?

[half sinew]

• practice problems

Yeah

My new strategy

[terse pebble]

are you in ap world or some shit

10th grade was the only time i enjoyed history

then i came to my senses

[half sinew]

I enjoy every subject

[terse pebble]

cap

english?

[half sinew]

Yeah

I read literature

[terse pebble]

bye

[half sinew]

English isn’t even that hard

You can argue essays

But just adapt

To the meta

[half sinew]

Please come back

I was joking

[winter comet]

I never enjoyed history

[terse pebble]

good for you

[half sinew]

😦

Why

[terse pebble]

its horrible

so boring

[half sinew]

But you enjoy math

[terse pebble]

math is stimulating

and interesting

history is so dry

[winter comet]

its pointless for me

[terse pebble]

and pointless

[half sinew]

It’s not

[terse pebble]

ok use history to build me a car

[half sinew]

Ok

[winter comet]

bad argument but i don't disagree 😂

[half sinew]

You take inspiration from Henry Ford

[terse pebble]

he is a naz

[half sinew]

Which progressed us through society.

[terse pebble]

ford island

[half sinew]

Nazi.

[winter comet]

theres a difference between learning ABOUT a thing, and learning a thing

you can learn about the history of cars but thats not gonna help you

[terse pebble]

yep

[winter comet]

you wanna learn how to build a car

[terse pebble]

fordlandia

[half sinew]

How do you think we innovated from agricultural to industrial?

[terse pebble]

steam engine

[half sinew]

I see what you mean

But

[winter comet]

looking at previous data doesn't count as history 💀

[half sinew]

Urbanization

[terse pebble]

bro you didn't pay attention in ap world

steam engine

[winter comet]

💀

[terse pebble]

what was his name

british dude

james something

james watt

[winter comet]

wait watt?

[terse pebble]

yea

like watts

[winter comet]

bad joke :l

[terse pebble]

oh

lmao

[winter comet]

🔥

[half sinew]

I’ve deleted every social media

Expect

YouTube

[terse pebble]

youtube is next

[winter comet]

i feel the POWAH

[terse pebble]

expect youtube

yea you dont like english bro

💀

[half sinew]

You still have Youtube

[terse pebble]

right over your head

[half sinew]

Says the guy who doesn’t like literature.

[terse pebble]

https://tenor.com/view/joke-missed-over-your-head-gif-8604199

[half sinew]

Odyssey was also fun.

Back in 8th grade.

[terse pebble]

alright lets see how you do on the exam in a month bro

tell me about king leopold in the congo

[winter comet]

I would say youtube will consume you and your loved ones
except eventually you won't have loved ones because you didn't go outside

[terse pebble]

fire leq

[terse pebble]

or maybe it was an saq i forgot

[half sinew]

Can you write an Ap lit essay.

If you want right now?

[terse pebble]

nah fuck that

[half sinew]

Cohesive.

[terse pebble]

fuck hamlet

shakespeare is ass

[half sinew]

YouTube is a learning resource

Let me guess you use Khan Academy

….

[terse pebble]

videos on khan academy are too long for you?

[half sinew]

• problem attic
• Crack ab

[half sinew]

Let me guess you prefer IXL

💀

[terse pebble]

ixl sucks

[half sinew]

Khan Academy is perfectly fine

[winter comet]

understandeth me you can no,
thou doth telleth me to awaith i go,
pleaseth readeth me for centuryeth aftereth my deatheth,
or I shall turn matheth into metheth

[half sinew]

I pay a $15 subscription for IXL

….

[winter comet]

direct shakespeare quote 100%

[terse pebble]

gross bro

th

[half sinew]

@terse pebble I might need to exit the door.

BUT WAIT

TIKTOK HAS A STEM SECTION

FOR SAT problems

Their might be something extremely wrong with me

[terse pebble]

yea i used to watch those and get my comments taken down because i'd shit on their video and approach to the problems

[half sinew]

Why?

[terse pebble]

because why solve a problem in 10 steps when you can solve it in 2

[half sinew]

I KNOW

[half sinew]

Mentality

[half sinew]

Most problems require more steps

So therefore your logic is invalid

[terse pebble]

if it takes more than a step to solve an SAT math problem you're probably wrong

[winter comet]

problem
if x = 5, what is x^2?
them:
first lets look at all the answer options
a)13
b)16
c)25
e) 12
ok now we will take the square root of each option
the square root of 13 is... hmm, i don't know this one (NOT LIKE I DONT HAVE A FREAKIN CALCULATOR). maybe we should try the next one
the square root or 16 is 4! oh but wait, they said that x must equal 5. so that can't be right
the square root of 25 if 5, which does allign with our answer choices. But lets test the next one just in case
the square root of 12. well if we factor 12 into 4*3 = 2^2 * 3, we can take the square root of 2^2 * 3 and get 2sqrt(3)... that doesn't seem to be equal to 5
so therefore c must be the correct answer

thats what they would do 100% 🔥

[half sinew]

Hmmm

[terse pebble]

this might be too swift of an approach lmao

[winter comet]

yeah i was being generous

💀

I couldn't think of something that would take longer but somehow they do

[terse pebble]

it was always the quadratic questions

they'd do the shittiest approach

[winter comet]

me when i didn't know the vertex was at (-b/2a, f(-b/2a)) but i knew differentiation

[terse pebble]

lmao

i remember when i first came to that realization

like wait differentiating just gave me the same shit

[winter comet]

I learned differentiation before literally 💀

wacky order

[terse pebble]

before vertex form??

[winter comet]

yeah

[terse pebble]

do you have older siblings or some shit

wtf

[winter comet]

what?? 💀💀

[terse pebble]

how would you know differentiation before vertex form

did you know differentiation before slope of a line too?

[winter comet]

no i knew the slope of a line

[half sinew]

Wow

[winter comet]

either I learned in algebra and didnt pay attention or... idk

[half sinew]

College?

Jesus Christ

[winter comet]

no

[terse pebble]

hes a freshman

in hs

[winter comet]

i'm not a freshman???

💀

[terse pebble]

lmao

junior

[half sinew]

Sophomore*

Viper is a college student

[terse pebble]

right

[half sinew]

I’m also athletic.

10.8 100m dash

4.44 40 yard dash

[terse pebble]

you're slow asf bro

[winter comet]

💀

[half sinew]

Excuse me what do you run?

[terse pebble]

4.40

[half sinew]

I’m close

And I’m a sophomore

Logically, im faster

[terse pebble]

logic isn't your thing

[half sinew]

In other words, potentially becoming faster.

[winter comet]

😂

[terse pebble]

so what are you good at

history right

[half sinew]

What are you good at

[terse pebble]

hard to count

[half sinew]

Everything

Expect for art

[winter comet]

watching youtube/tiktok probably

[half sinew]

Math, science, history, and English

Everything

Expect for Spanish + Art

[terse pebble]

help me with my homework bro

[winter comet]

man is being generous with himself

[half sinew]

Not really

[winter comet]

impossible

[half sinew]

My Spanish teacher makes me want to commit suicide.

[terse pebble]

i might need to ask axkyn then

[winter comet]

what is your basis for being good at something

[winter comet]

yea bro he might know

XD

[half sinew]

High grades + Memorization + problem solving skills

Well grades are just discipline.

[terse pebble]

do you want to test those skills?

[half sinew]

You could be extremely gifted at history, but have terrible grades.

[sacred egret]

precalc is harder than calc III

[winter comet]

could be

[terse pebble]

"gifted at history"

[half sinew]

You could have terrible grades while being gifted obviously not on tests, but missing assignments

Am I wrong?

[terse pebble]

how does that address that

how can you be gifted at history lmao

it's just memorizing facts

there's no critical thinking

or hardly any at least

[half sinew]

History requires critical thinking to right an essay.

DBQ

[winter comet]

bro just inherently figures out facts from thin air

[terse pebble]

not really

spawned in knowing who wrote the declaration of independence

[half sinew]

Math is also memorizing a bunch of facts.

[terse pebble]

eh

what problem solving is there in history

you certainly memorize things in math

[winter comet]

the main purpose of math is to use facts with critical thinking lol

not the facts themselves

[half sinew]

Analysis + argument evaluations.

[terse pebble]

but being good at math isn't the same as being able to recite definitions

[terse pebble]

this is so lame bro

[half sinew]

Memorization leads to critical thinking.

[winter comet]

in what universe

[half sinew]

I could name one person.

[half sinew]

….

.

Are we being serious?

[terse pebble]

when you were born?

[winter comet]

now i know there are ties but really that sounds like the english part, not the history part 💀

[half sinew]

William
James Sidis

Tell that to him.

[winter comet]

thats a weird date

[terse pebble]

lmao

[half sinew]

@winter comet answering history short response questions is based on memorizing facts?

You know you need to read the document

[terse pebble]

he did not know who thomas jefferson was when he was born

[half sinew]

I’m just trolling

It is

[terse pebble]

he was a child prodigy though

[half sinew]

Exactly

He could memorizing every day of the past

BCE

[terse pebble]

bro you're missing the entire argument

[half sinew]

dates

[half sinew]

Alright back to the argument if

If

Ig

I hâte typing on phone.

[terse pebble]

do you want to test your superior problem solving skills

[half sinew]

Hmm

In what subject?

[terse pebble]

math

[half sinew]

I take everything as a learning process

Sure

[terse pebble]

what topic

[winter comet]

W take

[half sinew]

Hmmm

Lets try Geometry/Algebra 2

[winter comet]

for 1 brownie point, 10 brownie points, or 50 brownie points?

[half sinew]

Hmm

[terse pebble]

alright let me find a problem

[half sinew]

I’ll show my work

[winter comet]

not sure what the point of this is but

can't complain about MATH

[half sinew]

He’s trying to find an AMC Question

[winter comet]

oh nice 🔥

[terse pebble]

ok

[terse pebble]

nah im being generous

show that $n^2$ divides $(n + 1)^n - 1$ for $n \in \mathbb{Z}^+$

[obsidian monolith]

knief

[terse pebble]

@half sinew

[half sinew]

Ok

[terse pebble]

should be fairly straightforward

[half sinew]

How am I suppose to show?

Its long

[winter comet]

what's long?

[terse pebble]

lmao

my guy is trying to show it for every n by cases

😭

oh

no he means the solution?

just type it

you dont need advanced latex for this

[terse pebble]

what are the odds its in his chatgpt history rn

[half sinew]

Let me show a picture

[half sinew]

I swear I’m not using CHATGPT

[winter comet]

dw if its chat GPT it would probably be blatantly obvious 💀

[half sinew]

Show???

[terse pebble]

yo your handwriting could be better

[half sinew]

Obviously my desk is cramped

[terse pebble]

what is this

[half sinew]

The work is suppose to show

[winter comet]

"show" means prove

[half sinew]

That n^2 divide sinto

(N+1)^n-1

I just proved it

[winter comet]

it seems to me that you're missing a key detail, maybe its implicit to you but 💀

[terse pebble]

what is the first line?

[winter comet]

well actually nvm the question isnt that specific

[half sinew]

The first line indicates the expression in the brackets

On thé boom

Wait

The first step of the problem would be to use Binomial theorem

[terse pebble]

explain your work sir

[half sinew]

Which I did

I did not learnt that

But whatever

In school

[winter comet]

then how did you use it?

[terse pebble]

so how did you know to use it

[winter comet]

did you invent it just now

[half sinew]

I self study math.

[winter comet]

oh 💀

[terse pebble]

bro i put the prompt into chatgpt and your work looks similar i can't lie

[winter comet]

the work just looks..vague