precalculus

[tender crest]

Sister ann

👊👊

[willow bear]

you are acting way too familiar with me. don't.

[tender crest]

🙈🙈

[fading monolith]

Bad habits for just typing fast lol, or should I take the time I dont have to type it in latex? If you are happier being the only helping in those channels its all yours

[willow bear]

typing fast
saves 2 characters in a 12 character long expression

[fading monolith]

👍

[obtuse dagger]

That's what I figured, but wouldn't you just square each term individually? (What is the point of treating both terms as one quantity, and then squaring that quantity?)

[willow bear]

no you would not square each term individually

[keen wharf]

help

ok so

how do i do command thinggy

anyways i need to find the derivative of $(3x^(2)-2x)/(x^(2)+5)$

[obsidian monolith]

timmiee

[keen wharf]

nevermind uhm

lemme redo

$\frac (3x^2-2x)/(x^2+5)$

[obsidian monolith]

timmiee

[keen wharf]

WHAT

[stark vale]

$\frac {3x^2-2x}/{x^2+5}$

[obsidian monolith]

hk

[keen wharf]

HELP

[stark vale]

oops didnt see that

[keen wharf]

hahaha

[stark vale]

$\frac {3x^2-2x}{x^2+5}$

[obsidian monolith]

hk

[keen wharf]

yess

can someone help me find the derivative of that

but like

without using shortcuts like chain rule quotient rule thingy

like we legit need to like

plug it as x+Δx

[stark vale]

did u do that

[keen wharf]

i did but my answers varied

like erm

I have to use this SOBS

[stark vale]

it might be a bit messy but just plug it in, you'll have to expand a bunch of quadratics out but do so carefully

[keen wharf]

i cant use the gf'-fg'/g^2 thingy

[lament gorge]

why would you want to compute the derivative with the limit definition

[stark vale]

^

[keen wharf]

i did that like three times and my answers were all different

[stark vale]

it is a very pointless exercise

[stark vale]

pick the one that agrees with the one u got with the quotient rule

[keen wharf]

ikr but we have to do that for some reason

our teacher assigned it

like

i wanna use quotient rule so bad

im itching

[stark vale]

use it

[keen wharf]

we cant

[stark vale]

and just follow limit definition knowing what the right answer should be

if you're getting a bunch of varied answers, you have a concrete, much easier way to see which one is correct

which your teacher doesn't need to see since its irrelevant to the actual limit definition computation

[hidden remnant]

Im not sure if i should ask this question here since i am a bit unsure if it is precalculus but ill let u guys judge.

Solve the problem with a calculator.

A wolf has been shot by a poacher. Your mission is to determine the time of the deed. To determine the time of the wolf's death, you measure its body temperature on two occasions. You take the first measurement at 21.00 on the day the wolf was shot, and the wolf's temperature is then 28.0 °C.

Three hours later, you measure the wolf's temperature to be 25.6 °C. The ambient temperature is always around 0 °C. You assume that the body temperature after the death of the wolf decreases exponentially with time and that the body temperature of a living wolf is 36.9 °C.
Answer in the form hh.mm

I began doing what i would go for but my answer just gets wrong. I subract 12h and 48m to 21h and get 8h and 12 min but that is still wrong. I have done something wrong in the process but im not sure what. Or possibly i have just gone for the wrong approach

[willow bear]

alright so let's see

[hidden remnant]

Omg i solved it

[willow bear]

your measurements are:

Time | Temp
-----+-----
??:??| 39.0
21:00| 28.0
00:00| 25.6

yes?

[hidden remnant]

It was so much easier doing all the work on paper rather than geogebra

[willow bear]

oh

but you want y = 36.9

not x = 36.9

your x-axis is time

[hidden remnant]

Yeah sorry, i am really tired i havent slept for 22 hours

[willow bear]

what the fuck

go slep

sleep*

[hidden remnant]

i cant, then im gonna be tired for school tomorrow

[willow bear]

dont see the logic

you would rather go even MORE sleep-dep than get a nonzero amt of sleep

is that what you're saying?

[hidden remnant]

If i sleep now. I will wake up like 5 hours before school begins. If i sleep in like 3 hours i kind "fix" my sleeping routine

Because on monday i would go to sleep normally

If that makes sense

[chilly stone]

How do you all build discipline? I get distracted way too easily.

[leaden wind]

Having the same problem too

[obtuse dagger]

Why? (Is there a mathematical rule that explains why?)

[willow bear]

a + b = c + d does not imply a^2 + b^2 = c^2 + d^2

(plus or minus some generalization)

[obtuse dagger]

So, in general, if you want to eliminate a square root on one side of an equation, you must square both sides of the equation. However, if there are two terms on the side opposite to the root, you have to treat them/square them as one quantity (even though the two terms appear as if they are separate quantities)?

[willow bear]

you always have to treat the entire left/right hand side as one quantity.

no matter what you do.

[obtuse dagger]

Ooooh

Interesting, ok.

Do you know why? Like, is there some kind of mathematical rule or law that explans why?

[pure lily]

lim x->x0 f(x) - f(x0) / x - x0 is like
Beyond pointless when you know x^n

[pure lily]

that would take forever to do it with limit definition

[willow bear]

missing parenthses

[viscid thistle]

Wtf is calculus

When will I take it?

Man I am grade 10 and I am alrdy suffering

Now imagine the suffering that will come in uni year 1

The reason I hate math isnt bcz its complicated, infact its fun for me! But the problem is that it WILL never help me in my future as a doctor

[willow bear]

But the problem is that it WILL never help me in my future as a doctor
debatable

[hallow tide]

are you SURE knowledge of "Calculus" will not help you as a doctor

https://en.wikipedia.org/wiki/Calculus_(medicine)

[viscid thistle]

BRO

THATS LITERALLY-

OMDs

NAH BRO YOU GOTTA BE TROLLING 💀

I really meant like THE MATH itself not this food or whatever this is 💀💀💀

[hallow tide]

the main takeaway here is:

study calculus 👍

[viscid thistle]

For the sake of getting accepted nothing else ✅

[split pelican]

calculus is very useful for finaces ive heard

[swift widget]

Isn't pre calculus different from calculus? But i guess all mathematics branches are interconnected depending on the problem (i could be wrong)

[viscid thistle]

Wait is calculus abt algebra?

Or what is it abt really

[swift widget]

As far as i know there are limitations, derivative, integrals and many more.

[river drift]

pre-calculus is a preparatory class for calculus, covering any topics needed for calculus (review of algebra, elementary functions: polynomials, rational functions, algebraic functions, trigonometric, exponential, logarithmic)

[winter comet]

precalculus usually doesn't talk about limits, derivatives, or integrals

and those are the 3 basic concepts of calculus, although there are a lot of applications and rules that come with those concepts

i'm pretty sure

precalc occasionally goes into limits but i consider limits to be a calc concept

[winter comet]

its not about algebra, but it does use algebra

its kind of about rates of change (derivatives) and areas of weird shapes and stuff (integrals) and infintesimally small numbers (limits)

hard to broadly explain, especially cuz i don't know it well 💀

[swift widget]

Thank you, anyway what are topics or specific lessons should i consider studying for precalculus besides geometry and Trigonometry. i feel like i still need to dig a little more deeper in geometry.

[winter comet]

you might want to look at conic sections...

uhh

[swift widget]

Thats the one were studying currently in pre calculus, though what are topics before that, coordinate geometry perhaps?

[winter comet]

you may want to look at complex numbers/ polar coordinates

[swift widget]

Oh i have bare minimum knowledge in complex number, and i haven't seen about the other, i will look into it. Thanks

[winter comet]

yeah

especially like complex roots

de'mourivers theorem

pretend i spelled that correctly

[simple urchin]

Quick question: If I have a + and - sign combined and I negate it, does it then turn into - and plus or would a plus and minus sign just absorb the negation?

If I negate the one on the left does it turn into the one on the right?

[winter comet]

um

the one on the left means plus or minus

if you negate plus or minus

its still plus or minus

that makes no sense

you add and/or subtract the thing

you do both or you don't know which one you do

you can't negate that

unless i'm wrong

but i have no idea what the thing on the right is

i would assume its the same thing

that or i have no idea what im talking about and its something i never studied

[simple urchin]

so does it stay the same even if you negate it with a minus in front?

[winter comet]

yes

the thing on the left means plus or minus

5 plus or minus 3 = 8 or 2

5 plus or minus (-3) = 8 or 2

[simple urchin]

So it just stays the same, you don't "flip" the order from +- to -+

[winter comet]

the order doesn't matter

however

-5 plus or minus (3) is different from 5 plus or minus 3

but you negated the 5, not the plus or minus 3

ngl its more of a plus and minus

[river drift]

$\pm$ and $\mp$ both mean "take either positive or negative value", the main use is that if you have multiple in one equation, then they mean "take the opposite sign", i.e. $\pm 5 \mp 4$ means both $+5-4$ or $-5+4$

[obsidian monolith]

cloud

[winter comet]

oh yeah

it only makes sense when you have both, then its opposites

i guess i was specifically thinking of an example where theres only one plus or minus lol

mb

[sleek path]

for the sake of development too, studying in school is a general sense to get a grasp to study

even if it may seem unnecesary

[sleek path]

so if i am a pre uni student and basically all of my questions are about limits derivatives integrals differential equations where should i post them?

[hallow tide]

in a calculus channel lol

most calc that pre-uni students cover falls under #calculus

[sleek path]

fair, i wasnt aware of that stuff as i just took pre uni role when i joined

now i just enabled those channels seperately

[hallow tide]

valid

[runic light]

me and math have had a rocky relationship since day one but man do i love precal <3

i started studying precal on kahn academy the summer leading up to this year and it really helped me, now im the token person people ask for help from in class and i feel so powerful lol

also its just really fun

i mean i would assume math gets more fun when you understand it lol

well its also that i have really good foundational algebra skills, i think thats another factor

my high school credits were really weird so i took alg 2 and alg 1 in the same year (last year)

so i think i retained that knowledge well enough to have a good start in precal

[pine geyser]

Calculus is even more fun! You will see...

[runic light]

i look forward to it!

[pine geyser]

🔥

[viscid thistle]

“For the same of development too” brother what the fuck will algebra help me in?

What about calculus

The only important chapter in whole math is shapes and trigonometry

Thats the only thing engineers need

When it comes to modelling and stuff

But for example calculus and algebra are just super annoying and useless

[stable gull]

mmm nuh uh

alg and calc help if u want to be an engineer as well, you also need a similar level of math for accounting, economics, physics based jobs, and a majority of scientific jobs

[willow bear]

idk man even if you talk engineering you can't design any kind of motor or machine without an understanding of diffeqs and control theory

[river drift]

you want to say how calculus will be useless for you then chose one of the professions that makes use of calculus the most

the computer does most of the computations but you still need to understand what they mean

[royal gust]

Anyone know any good videos or methods on understanding implicit differentiation?

[stable gull]

tbh i just go on khan academy when idk smth

but ppl here are nice so just ask 1 of the ppl with the helpful tag

https://www.youtube.com/watch?v=M0SMSWM2oZA

[sleek path]

buddy u are brainwashed by social media

[winter comet]

i mean honestly

[winter comet]

part of calculus is literally calculating shapes at an advanced level

which is definitely part of engineering

but also like if you're building a rocket

you'd want to calculate the velocity it's going

not just a rocket

engineering is so broad you make different things lol

i dont even know all the applications

but i can see that its necesary

and math is all sort of interconnected ish

for instance, calculus is kinda just geometry, trigonometry, algebra, and stuff in precalc woven in together

except they add concepts to make previously impossible problems more possible

[royal gust]

thanks ill check this out

[winter comet]

I would argue the math engineers do not need to know is stuff like number theory and advanced proofs and more abstract math, which is mostly used just to prove more math, not to actually solve real world problems

why am i still yappin

[sleek path]

also maths increases ur problem solving skills

which is literally necessary for each and every human being

[winter comet]

true

unless you're that one guy who sits on the couch and watches tv

and even then you have to problem solve of how to get up when ur so fat 🤔

completely joking btw 🤣

[sleek path]

idk why media has made it so that whatever school teaches is completely unnecessary

[winter comet]

well

probably because people in school don't see why its relevant

until they do

most people dont use sin, cos, tangent in their life to the point where its a meme about how useless it is

except it isn't if you're doing things bigger than daily life lol

[winter comet]

so i can sorta see why

[sleek path]

even then as i mentioned its not just direct application

u need to learn things

[winter comet]

true, but thats more of a psychology thing

[sleek path]

so u wanna be a doctor, lets only teach you biology from when u are 5 years old

sounds right?

[winter comet]

social media isn't good at psychology 😔

[winter comet]

i mean

sure

i see that its not

but i also kinda agree

[sleek path]

huh

[winter comet]

you shouldnt JUST learn biology

but you can MAINLY learn biology

[sleek path]

what if the person just doesnt wanna be a doctor later in life

[winter comet]

biology includes other stuff though so...

[sleek path]

like in highschool

[winter comet]

ah that is true as well

[sleek path]

maths is basic and needed throughout the world

[winter comet]

math isn't necesarily basic

basic math is basic

[sleek path]

ye

[winter comet]

unless you meant basic as in used as a base for everything else

☠️

[sleek path]

like atleast teach the basics till 9th 10th

then u can decide what u wanna be

[winter comet]

true

or like

12th

make it an even high school graduation

...

[sleek path]

but peopl crying about subjects in like 8th grade is funny

[winter comet]

lol

its cuz

they don't think they're ever gonna use it

because they don't know

they dont believe it

they haven't seen any indication of how its actually useful

[sleek path]

even if u dont use it ever again, its part of basic education smh

[winter comet]

tru...

theres also the part where most people have a bad mindset about school

i mean everyone does to some extent i guess

[sleek path]

like if u dont wanna be a historian doesnt mean u wont ever study history

[sleek path]

for me its chemistry 😭

[winter comet]

im taking a history class rn i dont like

i mean i dont hate

its just uninteresting ish

[sleek path]

ikr

[winter comet]

i like math tho

i'm not great at it but i want to be

i could be better

tryna get better

[sleek path]

history is something one should know especially about their nation, doesnt mean u have to be a historian to know history

same goes for world affairs, u must know whats happening even if u arent going to use it in your profession

[winter comet]

i mean i can see that its relatively important, at least "good to know" but it still isn't the most exciting thing...

like okay, something happened somewhere, idrc

[sleek path]

yea but u must have an idea

[winter comet]

sure it started a butterfly effect that created some widely used thing, or something

but yea

[winter comet]

i can see how its important

i would argue its less important than some other subjects

but i also just simply don't particularly enjoy the class as much as the math class

[sleek path]

importance is subjective

[winter comet]

i mean i dont HATE it, just don't love it

[tropic eagle]

Yo I’m new to pre cal and I’m like really confused on what is going on can someone help me?

[winter comet]

important to development of modern day or creation of idk, technology?

[winter comet]

what are you learning

[tropic eagle]

Rn we learning graphs and like the cheater before we had like roots radicals and all that and I’m lost in both of them I haven’t done goof on my quizzes

[sleek path]

history ig still teachers us stuff, we learn from their mistakes or whatever i am not a history enthusiast

i just studied till 10th

from 11th i had phy chem math computer science english only

[tropic eagle]

This is my first time taking pre cal so there’s a lot that might be new for me

[sleek path]

now imma go for engineering

[winter comet]

you mean like sqrt(9) for radicals?

[winter comet]

do you wanna shoot us a problem or something and tell us as best as you can what you already understand, so that we can help you with what you don't understand

[tropic eagle]

Yeah lemme get a screen shot of what I’m doing

It’s this

[winter comet]

ah

they're kind of vague

[tropic eagle]

Like I’m trying to catch up so I’m. Starting from the first choater but tbh I’m like lost

[winter comet]

do you have any idea what to do?

or like

where to start

[tropic eagle]

Not really

[winter comet]

would you know how to multiply, say, the numerators of (a)

so like

(9x^2 - 4)(9x^4-6x^3+4x^2)

that looks confusing but just read it out lol

i'm trying to get a sense of what you already know and what you don't know

[tropic eagle]

What ik is that you have to factor out

[winter comet]

yeah

so like

i'm going to go simple

(5x + 2)(2x + 3)

you want to multiply the first term in the first parenthesis by each term of the second parenthesis

[tropic eagle]

So if you multiply it it would be 10x2 and 15

[winter comet]

ah but don't forget the variable

5x * 2x

is 10 * x * x

and x * x = x^2

so the first term is 10x^2

but then you'd have to add the first term by the next term in the second parenthesis

so 5x * 3

= 15x

then you finished with the first term in the first parenthesis, because you multiplied by all the terms in the second parenthesis

so you move on to the second term in the first parenthesis

so you take the second term in the first parenthesis (2) and multiply it by the first term in the second parenthesis (2x), so 2 * 2x = 4x

then you take the second term in the first parenthesis (2) and multiply it by the second term in the second parenthesis (3) and get 2*3 = 6

then you add up all your results

10x^2 + 15x + 4x + 6

but wait, the 15x + 4x can add together ,because they have the same term

so you have 10x^2 + 19x + 6

yea that looks really confusing on discord, maybe you should watch a video on factoring

things generally look more confusing than they actually are

[tropic eagle]

I see i kinds get it a bit but imma watch more videos thanks

[honest aurora]

you could try factoring the thingies then see if there are any evident simplifications

oh wait some of those expressions have the 4th power nvm factorizing everything wouldnt be the best way

[viscid thistle]

Oh damn but yeah am talking about these chapters/lessons, like why make me waste time studying them when literally they have 0 value in life

Other than that, yes math is obviously important but there r few chapters that arent important LIKE VECTORS, SETS, ALGEBRA, and more

[viscid thistle]

Wellll yes thats what I am talking abt, and the thing is I will NEVER use math even after university as I am willing to become a doctor

[winter comet]

just looking at it briefly, i dont think you can simplify it

[viscid thistle]

But yes I agree with 99% of what u said

[winter comet]

vectors are important

algebra is important

[viscid thistle]

Give me one use of alegbra

Not the basic algebra

I mean the hard algebra

[winter comet]

do you agree this problem is important (its a calc 1 problem that im doing)

i can type it out if u cant see

its tiny

💀

im also stuck on it

if anyone wants to

yk

...

[honest aurora]

isnt that like physics

[viscid thistle]

How does that have to do with anything? 😅

Thats not algebra

[winter comet]

its calc 1

[viscid thistle]

^^^^

[winter comet]

you use algebra, i can explain the process if you want

[honest aurora]

do u know what you're supposed to use in order to solve the problem?

from calc 1, i mean

[viscid thistle]

Welll yes calculus is actually important

[winter comet]

the latter is falling down at a rate of 0.375 meters per second

thats the rate of change

the rate of change of the horizontal side is 0.9 meters per second

these are vectors, you can draw them as vectors

[honest aurora]

oooh so like

a function?

oh vectors 💀

[viscid thistle]

Wait uhh how do I answer this question anyway

[winter comet]

then when the horizontal side is at 5, you can calculate what the vertical side is

and then you can use pythagorean theorem to calculate the length of the latter

with algebra

actually this is not the one i was stuck on

but anyway

[honest aurora]

do u have like

[winter comet]

the algebra on a piece of paper that i can send a picture

if thats what u were gonna say

the answer is maybe

brb

[viscid thistle]

What the frick 😭

So basically this is calculus? A question which is about group of chapters/lessons?

[winter comet]

i could also just type out the process

[winter comet]

this is a part of calculus

[honest aurora]

yea please do if u can

the problem seems interesting

[winter comet]

you have to use derivatives, a.k.a rate of change

[viscid thistle]

Ohhh alr alr

[honest aurora]

what do u have to derive tho

rip we dont have the same problems related to derivatives here

they only give us like analytical problems (with limits and functions etc)

[viscid thistle]

I am glad I dont even have calculus xd

[honest aurora]

not with actual real life problems

[viscid thistle]

I am 10th grade

[honest aurora]

I am 11th

wait but whats the relation between vectors and derivatives here

im just gonna wait for him to type out the answer then ill read the whole thing

thanks btw this is probably super annoying to type as one message

NAHH AINT NO WAY BRO'S STILL TYPING

[viscid thistle]

Man I could have done that question with just physics, no need for vectors sets and these stuff

[honest aurora]

bro you're awesome

[viscid thistle]

But when I saw the “horizontal” is where the problem rlly is…

[winter comet]

i'm going to call y the vertical length, and x the horizontal length, and z the length of the latter.
we know that the change in y with respect to t is -0.375 m/s. This means dy/dt = -0.375.
We also know that dx/dt = 0.9 m/s.
We want to know: when x = 5, what is z?
We have to use a relationship formula:
x^2 + y^2 = z^2
We know the rates of change, so we have to take the derivative of the entire formula. If you dont know calculus, you won't understand how i did this, its kinda hard to explain. Also, z is a constant, so the derivative is 0.
2x * dx/dt + 2y * dy/dt = 0
can be rewritten as:
2x * dx/dt = -2y * dy/dt
You know x = 5, dx/dt = 0.9, dy/dt = -0.375, yoúre trying to find y.
Plug in:
2(5) * 0.9 = -2y * (-0.375)
y = (2(5)*0.9)/(-2)(-0.375)
using a calculator, y = 12.
BUT the problem isn't asking for y, its asking for z
So, we use the pythagorean theorem which is z^2 = x^2 + y^2.
we plug in x = 5, y = 12, and solving for z we get z = 13.

[honest aurora]

The problem is so vague how would u be able to do it

[viscid thistle]

I hope u are in ur laptop/pc

[winter comet]

you only need vectors in order to make a visual representation, you dont actually NEED vectors here

[winter comet]

yes 🤣

[honest aurora]

oooo I kinda get it

ok ill be fr I dont get it

[winter comet]

💀

[honest aurora]

N

[winter comet]

its hard to explain

[honest aurora]

O*

[winter comet]

its not hard to understand

[honest aurora]

T

[viscid thistle]

Yeah everything here is fine but the question remains… how I know what lesson I use or method thats the hard part rlly

[winter comet]

you mean, how do you know to use the method that i just used ?

[viscid thistle]

Literally there r 4 different methods

[winter comet]

you mean steps?

there are four steps...

[viscid thistle]

Yessss

4 steps which ARE SO DIFFERENT

Pythagros theorm, deriv, rate of whatever, algebra

At this point

[winter comet]

but SO RELATED

[winter comet]

derivative and rates of change are the same thing

but yes

[viscid thistle]

I KNOW BUT LIKE HOW I KNOW if I am in the exam rn how I know what lesson i should use

[winter comet]

i assume you aren't supposed to come up with this

[viscid thistle]

Other than that the question itself is actually easy

[winter comet]

isaac newton came up with this

i didnt come up with this

i saw it before

i've done it many times

thats how u can do it on a test

[viscid thistle]

So the questions rlly differ in lessons

Or they r the same lessons used

Like r these 4 steps the only needed

[winter comet]

umm

[viscid thistle]

Or they differ

[winter comet]

they differ depending on the problem

this type of problem is called related rates

[honest aurora]

yo vicious viper

you got any problems related to limits?

[winter comet]

in which you take the derivative of a formula and plug in what you know to solve what you don't know

[honest aurora]

not problem like word problem

maybe smth like

computing

[viscid thistle]

I am glad I dont have these otherwise I would have been dead by now

[honest aurora]

just beginner stuff

[viscid thistle]

Anyways viper cya gtg

[winter comet]

🤣

[winter comet]

ill see

[honest aurora]

okay thanks

wait see as in see now or see as in see later

[winter comet]

see as in im looking for it 💀

[honest aurora]

ooh okayy

thankss

[winter comet]

heres one

[honest aurora]

okayy

[winter comet]

heres another

[honest aurora]

okayy thankss

[winter comet]

heck heres one more

🤣

[honest aurora]

they all have the same idea tho

[winter comet]

yeah

basic limits

[honest aurora]

do u have anything else?

less basic?

NAH I GOT A FLASHBACK OF THAT REEL OF CINDERELLA SAYIN SHE'LL BE TURNIN BACK TO A BASIC B AS SOON AS IT HITS MIDNIGHT

I CANT ESCAPE IT

[winter comet]

☠️

[winter comet]

what kind of less basic are you looking for

idk what i have

[honest aurora]

Hmm

[winter comet]

you mean like harder algebra or more like l'hop rule and stuff

cuz i havent done l'hop rule yet lol

[honest aurora]

nah we don't use l'hôpital's rule in our country

it's considered SHAMEFUL

[winter comet]

why, is it against the law 💀

[winter comet]

LOL

[honest aurora]

no

it just

oversimplifies stuff in some cases

like it'll either get you nowhere

or will make the problem too easy

and they don't want the problem to be too easy

so they forbid us from using it altogether

[winter comet]

thats like not using the derivative rules

and just calculating derivatives using the definition of a derivative every. single. time.

[honest aurora]

yea it's pretty dumb

[winter comet]

💀

[honest aurora]

LOL IMAGINE

YOU HAVE TO CALCULATE A LIMIT

[winter comet]

ikr 🤣 🤣

[honest aurora]

EVERY TIME YOU HAVE TO DERIVE SHIT

LMAO

[winter comet]

🤣

thats literally what i thought i had to do for the rest of my life

until out from the heavens came the derivative rules

☠️

[honest aurora]

yea but banning l'hôpital's rule is pretty dumb

but i gotta get used to not using it

plus most of the limits that can be solved using it can be used without it

[winter comet]

i'm not entirely sure, is it lim as x approaches... something? (f(x)/g(x)) = f'(x)/g'(x)

or something?

[honest aurora]

yup

[winter comet]

can x approach anything?

[honest aurora]

yea

[winter comet]

you don't have to plug in x on the other side?

[honest aurora]

what other side?

[winter comet]

say x is approaching 5

[honest aurora]

ooh like derive 5 too so it becomes 0?

[winter comet]

it doesnt necearily have to equal f'(5) /g'(5)

[honest aurora]

nah

[winter comet]

nah i mean like

what happened to the number the limit was approaching

[honest aurora]

nothing happens to it

[winter comet]

ok 💀

[honest aurora]

l'hôpital's rule can be proven by just calculating the limit using the derivation's definition I think

I'm not too sure tho I have never actually studied the rule

[winter comet]

calculating the limit of what...

[honest aurora]

just seen it on youtube videos

[winter comet]

ah 🤣

[honest aurora]

of f(x)/g(x) and f'(x)/g'(x)

and finding they're the same

[winter comet]

wait

[honest aurora]

or at least I think

[winter comet]

calculating the limit of ( f(x)/g(x) ) and proving its the same to the limit of ( f'(x)/g'(x) ) ?

[honest aurora]

nono

like

[winter comet]

or taking the limit of ( f(x)/g(x) ) and proving its the same as f'(x)/g'(x)?

that prolly maeks more sense but maybe idk what im talking about

[honest aurora]

wait I gotta look the proof up instead of spreading more misinformation

[winter comet]

LOL 🤣

[winter comet]

its probably ok, i'm not taking it as guarenteed i just think it doesnt hurt to learn things ahead of time, cuz i havent learned it yet

besides seeing the formula

i've never used it or proven it

i've just seen it

lol

[honest aurora]

the problem is

i've seen a simplified proof of it

but i forgor

💀

[winter comet]

💀

[honest aurora]

anyways enough of this forbidden rule

do u have a limit related to trigonometry?

[winter comet]

only forbidden in your country 🤔

[honest aurora]

I'm working on one too but it gave me a super duper bad headache

[honest aurora]

ik ik 😭

[winter comet]

hm i dont... think so?

maybe?

ill check tho

💀

[honest aurora]

don't give me ones with inverses of trig functions tho

i hate them

especially arctan

[winter comet]

what do you have against my boy arctan 😡

i memorized the derivatives of inverse trig functions even tho my teacher was like "eh u dont need to learn"

i took that as a "eh u gotta learn it RIGHT NOW GO LEARN IT"

💀

[honest aurora]

💀

I mean we're not supposed to be learning abt them rn

we're not supposed to see them until next year

[winter comet]

i don't know if this is what you're looking for 💀

[honest aurora]

oh god what is that 💀

[winter comet]

are you in an ap class or are you not actually taking it rn

or why next year 💀

[winter comet]

btw it exists

[honest aurora]

it's 0 then

[winter comet]

i don't remember how i even did it

unless

[winter comet]

LOL

yeah

☠️

how did u do it

i dont even remember

besides if you use the squeeze theorem maybe?

[honest aurora]

yup

[winter comet]

💀

[honest aurora]

dayum u still remember

[winter comet]

i only did it a few weeks ago 🤣

[honest aurora]

A FEW WEEKS AGO

[winter comet]

nah but

[honest aurora]

AND YOU STILL REMEMBER

[winter comet]

i dont remember exactly

[honest aurora]

I did a limit yesterday and I forgor the solution

[winter comet]

im just guessing its the squeeze theorem because you can't solve it by plugging it in

or factoring

[honest aurora]

yea it was the squeeze theorem INDEED

do u have another one?

[winter comet]

i dont even know exactly how you would use the squeeze theorem unless you used estimated values though...

[honest aurora]

nop

so basically

[winter comet]

i actually dont know how to algebraically solve it

[honest aurora]

I set X = 1/x

[winter comet]

tell meh XD

OHH right

[honest aurora]

so when x goes to 0

[winter comet]

-1 < cos < 1

[honest aurora]

the absolute value of X goes to positive infinity

[winter comet]

then add all the trash?

[honest aurora]

yea

[winter comet]

wait

-1 < cosx < 1

how do you get the 2x

sorry the 2/x

[honest aurora]

it doesnt matter

[winter comet]

um

[honest aurora]

cosine of anything real

is between -1 and 1

[winter comet]

oh

[honest aurora]

so what's inside the cosine doesnt matter

[winter comet]

-x^6 < x^6 cos (all reals) < x^6

[honest aurora]

the xˆ6 in the denominator

[winter comet]

wdym

ur multiplying?

[honest aurora]

oh wait yea nvm we changed it to 1/x

but wait

WE DID CHANGE IT TO 1/X

which means it will be 1/Xˆ6 now

[winter comet]

wdym? how??

[winter comet]

inside the cos?

wait no

[honest aurora]

inside the limit

[winter comet]

oh

[honest aurora]

wait was i dumb by changing it

[winter comet]

do you take the lim -x^6 = lim x^6 = 0

as x approaches 0?

[honest aurora]

nvm nvm

[winter comet]

oh no

[honest aurora]

yes yes

[winter comet]

not the limit

[winter comet]

after that

you take

[honest aurora]

after that you substitute

and you get that it's between 0 and 0

[winter comet]

-x^6 = x^6 = L, then x^6cos(all reals) has to = L

[honest aurora]

so it must be 0

yayayayay

[winter comet]

and the only way -x^6 = x^6

is if x = 0

cuz negative has to be positive

so yeah

:D

[honest aurora]

😄

EW

[winter comet]

i need to review this more

[honest aurora]

WHY DID IT GIVE YOU A CUTE TEXT BUT GIVE ME A BIG EMOJI

[pine geyser]

Also consider that their "limits" are equal, not themselves

[honest aurora]

send more limits

[winter comet]

br what 💀

[winter comet]

ohh thanks

[honest aurora]

yea

[winter comet]

i was wondering that

[honest aurora]

you just pretty much substitute

[winter comet]

but limit as x approaches what?

[honest aurora]

x approaches 0

in the limit

[winter comet]

how do you know its 0?

[honest aurora]

remember?

[honest aurora]

.

[winter comet]

the answer is 0 but you havent gotten to that yet

oh

im dumb

[honest aurora]

wdym

[winter comet]

💀

the og was 0

of course

[honest aurora]

yea

[winter comet]

so back to

[honest aurora]

alr send more limits

[winter comet]

here

you actually have to take the limit of all three things

and THEN do what we did

alr

lemme find

[honest aurora]

so r u in college rn?

or in hs?

[winter comet]

dual enrollment

taking a college class

[honest aurora]

send the hardest one u got we can solve it using the power of friendship (and wolfram alpha)

[winter comet]

but still technically in hs

[winter comet]

🤣

im just finding easier ones

like

obviously squeeze theorem

[honest aurora]

0

[winter comet]

idk how many ones that they gave with trig

[honest aurora]

can u find the hardest one?

[winter comet]

no

[honest aurora]

yes 💀

[winter comet]

nu

💀

its 3

cuz u plug in 3

[honest aurora]

oh wait

[winter comet]

yea

XD

[honest aurora]

oh shit mb

💀

[winter comet]

🤣

ANYWAY

that didnt happen

im gonna see if theres a harder problem

[honest aurora]

lMAO WHY DID I SEE 3 TIMES 3 AND INSTANTLY WENT LIKE SIXXX

[winter comet]

i could also look at other problems cuz there might not be that many of these

[winter comet]

fr fr

but theres prolly more lemme look

this is my old homework 💀

[honest aurora]

dayum that was one confident booster

CONFIDENCE

omg

my confidence got boosted so high it broke

[winter comet]

how?🤣

[winter comet]

🤣 🤣

btw what are u taking

[honest aurora]

I aint takin shi

[winter comet]

YOOOO

[honest aurora]

basically in my country

[winter comet]

i see what u mean now

🤣

u self studying?

[honest aurora]

IM NOT A DROPOUT

[winter comet]

naw naw not what i meant ☠️

[honest aurora]

nono

so in my country

you only have one curriculum

(in public / private national schools)

like a fixed one

and there's a bit of everything every year in our math curriculum

this year we had

logic

sets

applications

sequences

limits

derivatives

number theory (??? idk what it's called in English)

[winter comet]

number theory is a thing

💀

[honest aurora]

yea ik

[winter comet]

but thats cool

what kind of applications

[honest aurora]

i WAS TALKING IN THE WRONG CHANNEL LOL

I meant arithmetic not number theory

[honest aurora]

um regular ones?

[winter comet]

LOL

[honest aurora]

#calculus

and some geometry (2 lessons)

[winter comet]

ah

[honest aurora]

not too simple but not too hard

[winter comet]

arithmetic as in just like multiplying dividing adding subtracting big numbers?

[honest aurora]

the only thing that shocked us is when they introduced us to Cauchy Shwarz IN ELEVENTH GRADE

[winter comet]

what were you learning in geometry

[winter comet]

who the heck 💀

[honest aurora]

we didnt see it in exams BUT SRSLY THAT WAS TRAUMATIC

and no we didn't get the integral definition of Cauchy Shwarz

(idk if im writing Shwarz correctly if im not sorry)

[winter comet]

ahh its probably a calc 2 thing

or calc 1 but farther along then i am

when it actually goes into integrals

[winter comet]

☠️

[honest aurora]

yea we only learn abt integrals next year

[winter comet]

ah

wait

next year as in

[honest aurora]

twelvth grade

wtf did i write that correctly

[winter comet]

ah

twelfth

[honest aurora]

twelvth

[winter comet]

🤣

its a weird word

twelfth

wth is twelfth

[honest aurora]

EWWW WHY IS IT WITH AN F

[winter comet]

looks liek a doctor seus thing fr

[honest aurora]

bye im gonna start writing it with a v idgaf

so

in twelvth grade

[winter comet]

🤣

[honest aurora]

we start learnin abt the good stuff

integrals

complex numbers

differential equations

[winter comet]

ah

[honest aurora]

continuity (yea they taught us limits but not continuity)

[winter comet]

complex numbers as in like with polar coordinates?

[winter comet]

LOL

are you self studying as well

[honest aurora]

yea thats the part with algebra

[honest aurora]

I used to

not anymore tho

[winter comet]

ahh

[winter comet]

why?

[honest aurora]

idk just wanted to focus on what was alrdy on my plate

[winter comet]

ahh that makes sense

[honest aurora]

while I was self studying I learned that I already have enough nice stuff i can learn about that is already like ya know my level typa stuff

like limits and shi

[winter comet]

yea 🤣

[honest aurora]

so why go to the harmonic series and its relation with the natural log and allat

[winter comet]

what is harmonic series 💀💀

how is it related to the natural log 💀

[honest aurora]

it's that

[winter comet]

i actually dont know 🤣

[honest aurora]

sum of 1/k when k goes from 1 to infinity

[winter comet]

oh is it the summation thing?

[honest aurora]

yea

it's a sum

[winter comet]

with sigma notation i think its called?

[honest aurora]

yup

[winter comet]

ahh

yeah im a bit foggy on that

[honest aurora]

we have a lot of sigma notations in our limits

[winter comet]

you do???

bruh

im missing out ☠️

[honest aurora]

not explicitly

that'd be considered a limit of a series (we have em next year)

but while working on some limits

you might wanna factorize some things

and while factorizing you can use the sigma notation coz it helps

[winter comet]

huh

i probably need to review that 💀

[honest aurora]

yea I'm working on a limit involving the pi notation rn

(sigma for repeated sum and pi for repeated product)

[winter comet]

i never officially took precalc, just some self studying, and i almost took precalc but i decided to transfer to calc because precalc looked like it was covering all the stuff i already knew

i dont think it was gonna go over polar coordinates or matrices or stuff

[honest aurora]

nahhh shoulda stayed bruh

even if it seemed like a waste of time or learning stuff u alrdy learned

[winter comet]

nahh im glad i went 🤣

[honest aurora]

you coulda at least learned one or two new things

[winter comet]

learning one or two new things vs learning a lot of new things and self studying those one or two new things...

[honest aurora]

that's how you view things

[winter comet]

i know practice is good but i can practice while im taking calc 1

[honest aurora]

maybe you can actually 100% understand the stuff u self study

[winter comet]

i'm looking for rapid progression while also reviewing a lot so that i can be a master at everything i can do

[honest aurora]

for me I only learn like 60% and the rest goes down the drain

[winter comet]

i keep reviewing

i try to review things every day

and going back to things i learned before

im not even going to lie

i had completely forgotten most of the trig identities before calc

now i have a lot of them memorized

[honest aurora]

wait rn r u an 11th or a 12th grader?

[winter comet]

i memorized them the next day 💀

[winter comet]

10th

[honest aurora]

TENTH

[winter comet]

🤣

[honest aurora]

so a sophomore yea?

[winter comet]

i guess

i was homeschooled

a.k.a online classes + self studying

im still homeschooled

[honest aurora]

oooh okay

[winter comet]

a.k.a online classes + going to campus classes, but those classes arent high school so...

technically still homeschooled?

lol

[honest aurora]

ugh amazing life

[winter comet]

🤣

i am really lucky ngl

[honest aurora]

I WANNA GO TO COLLEGE ALRDY AJHGCHFVGL

where do u go for the calc 1 classes?

[winter comet]

you will get there 🤣

[honest aurora]

hopefully

[winter comet]

bro i just lost connection lol

[honest aurora]

ME TOO WHAT

[winter comet]

bro what really?

wth

maybe its like the server clogging or something

[honest aurora]

maybe

ANWYAYS u got any more limits?

[winter comet]

lemme look 🤣

[honest aurora]

send one that looks difficult

[winter comet]

i think i ran out of hard ones before they went to derivatives 💀

you know how to do limits approaching infinity right?

[honest aurora]

yup

[winter comet]

maybe theres some on like khan academy or sum

lemme look lol

[honest aurora]

okay thankss

[winter comet]

the khan academy ones are basic too 💀

unless

maybe they go over limits after derivatives as well

maybe those would be harder, hopefully not involving hard concepts

[honest aurora]

hopefully

[winter comet]

oh

theres something

[honest aurora]

👀

[winter comet]

idk if this is easy or hard i gotta think about it 💀

[honest aurora]

😔

this is like

[winter comet]

wait

[honest aurora]

concerning continuity

it's basic if u know continuity

[winter comet]

i think continuity just means

the thing that the limit approaches

is part of the function

basically the solid dot

means its continuous at that point

if it has a hole

its discontinuous at that point

but i dont think its relevant

actually it probably is

[honest aurora]

yea it is

[winter comet]

i think f(x) doesn't have a limit

neither does g(x)

[honest aurora]

coz when u try doing the limit of f and g seperately

they dont exist

[winter comet]

yeah

i dont think the limit exists

thats an optino

lemme see if its correct

[honest aurora]

me either

[winter comet]

nope

its not correct

[honest aurora]

but it might exist

yea

[winter comet]

ok uhhhhhhhh

[honest aurora]

it's probably 3

[winter comet]

oh yeah cuz limits are probably not

distributive...

[honest aurora]

they are

[winter comet]

thats an option as well

:l

how do we prove its three

[honest aurora]

when the limits of f and g both exist

[honest aurora]

we dont

idk it's just a guess

[winter comet]

🤣

i mean

[honest aurora]

it's just coz i saw both graphs

approaching 3 from a side

so I said it could be 3

[winter comet]

yeah

[honest aurora]

so is it correct?

[winter comet]

you know how limits approach a number

they may not get there

but they may

you know?

[honest aurora]

yea ik

[winter comet]

if they get there

its continuous

if they dont

its discontinuous

[honest aurora]

yea ik

[winter comet]

of course you have to look at intervals

but yea...

[honest aurora]

like for example both f and g here ar discontinuous at

1

anyways whats the answer is it 3

[winter comet]

wait no its actually not

wth 💀

[honest aurora]

💀

[winter comet]

the other options are 0, 1, and 4

💀

[honest aurora]

nah lets stop

[winter comet]

waaaiait

[honest aurora]

get us a limit we can compute

[winter comet]

WAAIT

[honest aurora]

not smth abt graphs

and coninuity

pwease?

[winter comet]

yea ok

[honest aurora]

thanks

[winter comet]

💀

wait

[honest aurora]

did u find anything?

[winter comet]

do you know the proof for lim as x approaches 0 [sinx/x] = 1?

[honest aurora]

well you could use l'hôpital's

[winter comet]

now we're going into things I don't know 😔

i read some geometric proof that used the squeeze theorem that i half understood

[honest aurora]

in our country it's smth just given to u like just says yea limit of sinx/x when x approaches 0 is 1

[honest aurora]

I seen one too

OOOOH YEA FROM BRI THE MATH GUY I THINK

it graphed the circle

[winter comet]

oh yeah bro naw you cant prove that with l'hop remember

its illegal

💀

[honest aurora]

💀

NAAA I CAN HEAR SIRENS THEY'RE COMING FOR ME

BRO I GOTTA HIDE

[winter comet]

NOOO

🤣 🤣

[honest aurora]

im gone they caught me

they say they're gonna TAKE MY DERIVATIVE

and throw it in jail 😔

[winter comet]

💀💀💀

[honest aurora]

well i'm a constant so my derivative is 0 therefore they aint throwin shit in jail

[winter comet]

NAAAAAAWWWWW

[honest aurora]

HAHAHAHA I AINT GOIN TO JAIL BABY YALL DONT GOT PROOF OF MY TAX EVASION YET LOLOLOLOL

[winter comet]

you know you've hit ground 0 when you're spouting math jokes 🤣 🤣 😭 ☠️

[honest aurora]

yea 😭

[winter comet]

bro just use the anti-derivative to TAKE BACK YOUR DERIVATIVE

[honest aurora]

NAAAH THE NEW PRESIDENT SAYS HE'LL MAKE ANTI DERIVATIVES ILLEGAL TOO

BRO THAT'S WILDDDD

[winter comet]

BRO

[honest aurora]

anyways do u have any other limits to solve?

[winter comet]

LOL

let me see

[honest aurora]

at some point he's gonna make math illegal