precalculus

[tender mist]

Pre-calc curriculum is the most diverse thing across the planet

[winter comet]

yea

[tender mist]

[supple sky]

Well that ain’t gonna help me prepare me for college calc

If it’s so dang diverse

What would these introductory courses for calc and linear algebra be

Because I don’t want to be wasting time going over stuff I already know

[winter comet]

matrices, polar coordinates, maybe limits off the top of my head

not all precalc courses cover limits but yeh

[supple sky]

Me wishing I could hack into the college website and just find the stuff I would be learning in the class before having to wait till fall

If I could just see the names of the units

But instead I have to wait till September to get the books lol

[winter comet]

lol

i mean

uhh

[supple sky]

I mean it makes sense haha.

[winter comet]

you can't look at like previous class syllabus or anything?

[supple sky]

It wasn’t as easy as highschool lol

Because when I graduated middle school I knew like the next math class I would have to take which was geometry

So I would just look up the subject matter on YouTube and khan and all of it would teach practically the same thing

So I was able to get a little bit of a head start

[winter comet]

oh yea and series

[supple sky]

I could see

All I know is the names of the classes

[winter comet]

i think khan academy has a decent overview of precalc, but it may not apply to all precalc classes...

it still seems like it probably covers mostly everything that could be considered "precalc"

[strong epoch]

What is f(0)

As a limit

With both open corcles

Please someone tell me

[winter comet]

doesnt exist

they approach different places from both sides

[supple sky]

Right now I’m only working a few hours a week so I’m trying to manage my time by going to the gym, trying to get a head start on subject matters I might take in college next year while looking for a new job that I will enjoy this summer and that will give me a lot of hours.

[winter comet]

wait

[winter comet]

what exactly is ur question

[supple sky]

I’m legit putting all my hope in this channel since it seems really legit

https://youtube.com/@ProfessorLeonard?si=7Nmtxos0222Y3yQF

Don’t know if he’s legit or not

But he makes calc and calc 2 and diverential equations

[strong epoch]

What is f(0)

Like in the middle

What’s the limit

Would it be undefined

?

[winter comet]

you mean the limit of f(x) as x approaches 0?

[strong epoch]

Because there is an open circle

[supple sky]

I see f(0) as well

[winter comet]

you can't take the limit of f(0)

[strong epoch]

I mean

The y value

Is it undefined

?

F(0)

[winter comet]

the limit of f(x) as x approaches 0 is undefined

f(0) is not the same

but it is also undefined

[strong epoch]

Wouldn’t it be dne

[winter comet]

yes

[supple sky]

Also why is there g(x) and h(x) and f(x)

Aren’t those all the same exact thing

[winter comet]

different functions

[winter comet]

pretty much

they're just used when ur working with different functions

like

g(x) = 2x
h(x) = 5x

they different functions, but they both mean functions

[supple sky]

So it’s like the equations stuff

[winter comet]

uhh

[supple sky]

Where they add like 2x+3y+4z=3

[winter comet]

if by equation you mean function then sure

[supple sky]

Or something along those lines

Just a way to separate each variable

[winter comet]

you mean different variables?

[supple sky]

Yeah

[winter comet]

yeah

this is

a way to seperate functions

[strong epoch]

I’m asking what f(0) is

Not the limit

[winter comet]

f(0), having nothing to do with the limit, is undefined

[strong epoch]

Like this

[strong epoch]

I know

[winter comet]

ok

[strong epoch]

I’m asking what f(0) is

What I sent on the loose leaf paper

Not on this

That’s just an example of what I’m saying

[winter comet]

you get that f(0) is different from lim f(x) as x -> 0, right?

they both do not exist

for different reasons

[strong epoch]

Yea

100%

[strong epoch]

Wouldn’t f(0) be undefined

Because the open circle

[supple sky]

Seems like the first unit is evaluating functions

[strong epoch]

I know how they work I didn’t mean to say limit

[supple sky]

Is this a good place to start for pre calc

[strong epoch]

Wdym

This is my last unit

Its derivatives after this

[supple sky]

Oh 💀

[winter comet]

sure, i forgot the very slight difference between dne and undefined but im pretty sure they're practically the same

[winter comet]

he was talkin about himself not u 💀

[strong epoch]

Yea it’s just you can’t say undefined when it’s a limit

Dne

[supple sky]

Wait so I should do something else first

[winter comet]

oh, why not?

[strong epoch]

Oh

[strong epoch]

I said it on a test it was wrong

[winter comet]

starting with functions and composite functions is fine

[strong epoch]

It said error on my calculator so I did undefined

But I forgot it’s a limit and as the limit approaches it is dne

[winter comet]

if you completely understand/have no problem doing them, move on. until that, keep practicing

[strong epoch]

I was just wondering because I just retook that skill in that test

Hopefully I get a 3 or a 4

Skills based grading weirdd

The f(0) question was on my test so that’s why I was worried I did it wrong

Even though open circles I did say it was undefined tho

[winter comet]

i think you can say does not exist or undefined in every context in limits except with infinity limits. if the limit approaches infinity then its undefined but does exist

any other time they are interchangeable

[strong epoch]

Oh idk why we don’t do it like that

If I didn’t put undefined on the test I would’ve got an a

[winter comet]

🗿

thats kinda dumb tho

[strong epoch]

Instead I got a c

[winter comet]

oh yeah its that grading scale thing ig

breh

[supple sky]

It’s weird because it goes from evaluating functions to domains of functions to graphing functions to solving quadratics to polynomials to trig to rational functions to inverse functions to log to more trig to graphing trig to composite to polar

It’s in a weird order which I dunno why

[winter comet]

composite at the end????

composite functions?

[supple sky]

Yeah it’s weird

It’s close to the end

[winter comet]

._.

[supple sky]

I dunno Pre calc stuff is confusing

All of them have different orders

[winter comet]

fr 💀

if you look at khan academy

i think that curriculum is decent

like good

[supple sky]

I just don’t like how short the videos are

[winter comet]

why not?

not enough explanation you feel?

[supple sky]

Doesn’t explain like a full 30 min video would

[winter comet]

you can at least look at the topics they cover

[supple sky]

That’s one thing I don’t like about this Pre calc stuff

Is it’s not like regular math where

You go from like addition to subtracting to multiplication to division

But instead it’s like in this wacky order

[winter comet]

the order u just said is more wacky than usual 💀

[supple sky]

I know

Lol

[winter comet]

lol

this the khan academy order, better imo

[supple sky]

But I’m gonna start at evaluating then go to converse

Composite I mean

[winter comet]

you can look at the topics without looking at the videos just to get a sense here, if u want

[winter comet]

yea

[supple sky]

Some of this stuff seems super easy ngl

[strong epoch]

Yea in order to get a 100 you need to get the level 4 right if you don’t it’s a 90

And if you miss one question and get the level 4 right you still get a 2

I got the level 4 right 😔

[winter comet]

thats good

[supple sky]

Is this right?

With the F(0)

I got 0,0

[winter comet]

idk, i don't have the context

like whats F(x), what does the problem ask for, ect. 💀

what is answer number C

is it 10?

or -10 ☠️

i think the answer is C

and also thats not true

the fact that nobody in the world could do a multiple choice problem

💀

my name isn't C

the answer is C

[willow bear]

don't troll. <@&268886789983436800>

also don't capslock.

@winter comet don't feed the troll.

[winter comet]

Don't really think that's considered a troll ☠️

trolling would be if ur tricking or confusing people

this would be obvious to ppl who understand english and addition

obvious that it's a joke

[supple sky]

I ran into a problem lol

Would I just leave it as undefined

Because like 11/0 ain’t a real number

[supple sky]

What’s fx

F(x)= square root of (x)^2 -3(x)

It’s kinda hard to write it on discord text lol

[willow bear]

f(x) = sqrt(x^2 - 3x)

if you put parentheses in the right places, it is not that hard

also sqrt for square root

[viscid thistle]

f(4) = 9(16) - 3(4) + 1

is that it?

[willow bear]

2^2 isn't 16

[viscid thistle]

sorry for the time, I was working

[willow bear]

f(4) = f(g(2)) = 9*2^2 - 3*2 + 1

[viscid thistle]

lmao sorry

[willow bear]

9*16 - 3*4 + 1 would be f(g(4)) not f(4)

[viscid thistle]

it was a dumb mistake

f(4) = f(g(2)) = 36 - 6 + 1 = 31

man, it sucks

[tranquil inlet]

i have no idea where to start

can someone teach me

[supple sky]

but it was with zero

[clear scarab]

Can someone tell me how to integrate 1

I have exam in 2 hr so help rn would be good

[supple sky]

some of this pre calc stuff is pretty easy

[winter comet]

thats good

[viscid thistle]

Integrate separetely

[viscid thistle]

gl buddy

[winter comet]

wdym

[shut monolith]

Hint: use the identities sin^2(x) = 1/2(1 - cos(2x)) and cos^2(2x) = 1/2(1 + cos(2x))

oh wait, I now realize you said you had an exam in two hours, two hours ago, nevermind then

[tranquil inlet]

For 6 do i still use Pythagorean identity

[willow skiff]

Yes

You are going to have to multiply x or y by something to make it work out

9 again uses the Pythagorean identity

[hallow lodge]

anyone got videos for differentiations and antidifferentiations/integration (including their chain rules) please send me good youtube teachers

[near sentinel]

PW English

Mathsmerising

[thin surge]

https://youtu.be/fYyARMqiaag?si=mmrWp-RuPInZLGAo

he is good

hope it helps

[languid linden]

Professor Leonard love!!

[thin surge]

yes!

[agile sparrow]

Goated fr

But he doesn't teach basics

[viscid thistle]

are we differentiating?

[willow bear]

that's an apostrophe, not a comma

and it means derivative

f' is the derivative of f

no, not the same thing. a comma sits on the bottom, an apostrophe at the top

no

$\int f(x)\dd{x}$ isn't the same thing at all as $f'(x)$

[obsidian monolith]

|Ann⟩

[willow bear]

<@&268886789983436800> we got a troll over here

i'm a she.

<@&268886789983436800> transphobia

[hushed sphinx]

Timed out pending further investigation.

[supple sky]

I’m using him to learn Pre calc right now

He’s legit really good

[thin surge]

True

[agile sparrow]

What about integral of f'(x)= f(x)

True for limits from 0 to anything

According to lebinitz rule

@willow bear

[willow bear]

i mean

what are you even asking

[agile sparrow]

alright

no worries

Nothing much

[proven void]

what is that leibnitz rule you and transparent elemental keep mentioning

some integration trick?

[agile sparrow]

I think I only mentioned that shit twice

But alright

Use to find derivative of an integral

[neon island]

Is it alright to ask precalc questions in here? Just wanted to make sure this was not just a discussion place before I post cause I'm super stuck on a problem lol

[winter comet]

yes

[agile sparrow]

Ask whatever wherever

nobody cares what channel

[neon island]

Gotcha

So the problem is this

Nvm apologies I'll have to upload a picture of it once I get home since it's not sending

[agile sparrow]

alright

[strange saddle]

Someone up for a challange? I’ve got some really spicy homework

[winter comet]

what kind

[strange saddle]

Definite integrals

I’ll send a pic, 1 minute

[winter comet]

wth ☠️

[strange saddle]

I tried and I got the answer 0 -9/2 log|2| after plugging in the limits log(0)log(1+0^2+……+0^9) = -9/2log|2|

[winter comet]

what method did u use?

oh

i cant read 💀

[strange saddle]

Well, first u rewrited the integral, then integrate by parts, then polynomial long division, substitution and then finally i evaluated (entering lower and upper bonds into the expression)

I*

[winter comet]

uhh

ohhh im dumb

[strange saddle]

But i think the answer is 13 π^2/144

After redoing it

[winter comet]

me taking 8 years to do ibp over here ☠️

also why you put this in precalc channel 💀

[strange saddle]

Yeah I guess, sorry lmao

[mellow tapir]

Write that sum as a finite geometric series then use properties of logs

[tranquil inlet]

Anyone know how to do this???

(53-56)

[midnight trench]

MIT integration bee

That ain’t homework

[viscid thistle]

LOOOOOOOL

[viscid thistle]

im in 8th grade and i can do this com on

[winter comet]

then...help?

[viscid thistle]

you know at sum point sin and cos do reset so 54 and 56 go with 1 and 4 thats a hint

also i thing 53 gose with 3

so that means 55 gose with 2

[tranquil inlet]

makes sense

[tranquil inlet]

why

[tranquil inlet]

bruh self studying is hard but i am in 9th grade so

good luck in high school next year :)

[midnight trench]

I’ll help you out

[midnight trench]

When it comes to parametric, I like to get points, but unfortunately you graphs doesn’t exactly have neat points lol

[tranquil inlet]

fr

i tried eliminating parameter but didnt work out

[midnight trench]

If you want to find an easy answer to I, plug in for 0. Clearly 53 doesn’t work, 54 doesn’t work, and 55 doesn’t work.

Because sin(0) is always 0 sooo

56 would be your answer

If you really want to find something graphically, you have to eliminate the parameter

[tranquil inlet]

how would i do that with like these equations

does factoring work?

[midnight trench]

Tbh i just like plugging in points lmao

To solve for 53, you can easily eliminate the parameter

[tranquil inlet]

wait how

[midnight trench]

Wait. I’m dumb. Can’t do that for these shit lmfao

I guess just try to hand draw is the only option

Plug in for t = -2 and get. (-4,-6)
t = -1 and get (1,0)
t = 0 and get (0,0)

Wait shit it’s ^2 not ^3

It still looks like the 3rd graph tho tbh

It doesn’t exactly repeat

[tranquil inlet]

2 and 4 repeat, and 1 repeats because it's closed and the graph maps back onto itself

right?

[midnight trench]

Yup. Just plug in tbh

I plugged in wrong

But for many problems you can sometimes just eliminate t

[tranquil inlet]

.-.

ok so 1. eliminate parameter 2. try and determine behavior of graph

3. plug points

[midnight trench]

Plugging is only solution

[midnight trench]

Range t = [-2,2]

[tranquil inlet]

got it

[midnight trench]

Yup

[tranquil inlet]

how would u plug in points for the other problems then

like 54. if t=1, x=sin (3), y= sin (4)

[viscid thistle]

i can fell it in my bones

also in t =1 x = -1 and y = 0 so it has to be 3 cuz 2 nerver it negitves

[midnight trench]

It’s difficult. Use ranges

Understand that sin’s range is [-1,1]

In equations parametrics with just sin, it will never go out of that range, maybe even domain

I’ll show you with that problem

[tranquil inlet]

wow never thought about that

[midnight trench]

Just as I thought

Of course, x values with change. For example, if I make the x = t instead of sin(3t)

I’d get a completely different, but clearly similar, answer

Lmfao you’re gonna love this

[tranquil inlet]

would the graph still be the same, but the tables different

[midnight trench]

X coordinate will be different

Look at this

Recording

[tranquil inlet]

straight 🔥

sorry gtg for like 30-40 min

i'll talk to you later

thx !

[midnight trench]

Added you

[midnight trench]

Still sin(4t) and graph is sin(4x)

But making the domain the same as sin(x)’s range

Think about that the next time you look at a graph. 54 is literally a sin graph within itself

It looks like an atom

The other ones will come on their own. 56 clearly is graph I because it will never touch 0,0

Process of elimination is key. Using simple tricks like understanding domain and range of functions is always useful. There’s a point where parametrics need graphing functionality and point plotting. Nobody can do x = sin^5(t) + t^2-t+3cos(t^2) without plugging in points a lot of times, but understanding that its range is -inf,inf and around the origin will look strange will give an understanding of the graph

[stray lynx]

I don't know if this is the right channel to ask but is there a book, website or anything in general that help me understand vectors?

[midnight trench]

I can try to explain it to you. If you want YouTube tutorials/videos, khan academy has some basics

Are you doing it for comp sci or just learning vectors for linear algebra

[stray lynx]

Khan academy as you said explain it in general.

[midnight trench]

So you’re looking for something more complex?

[stray lynx]

Doing it since it is slowing me down in Physics, Algebra. (Engineering)

[midnight trench]

Gotcha

I can explain it simply

Imagine a table with data. Input, output. Vectors are essentially just holding that data in place

[stray lynx]

If you mean complex by providing some proprieties that are ignored (for example trigonometry proprieties sin(2theta)=...etc) then I wouldn't say no.

[stray lynx]

Go on.

[midnight trench]

Imagine a coordinate plain. We can use normal math to essentially understand how many units are in height or length

But using vectors, we can understand magnitude and direction

On a simple space, we have a line. The start is known as the tail then leads to the head.

I’ll make a diagram for u

[stray lynx]

Alright.

[midnight trench]

In this data, we can hold quite literally anything we want

And we can tell it what direction we’re going

We can tell it the speed it’s going

In physics, this basically can be described as a velocity or point systems

I’ll give you an example

Any questions specifically though?

[stray lynx]

For now no, you are covering the basics.

[midnight trench]

Then let’s get into some of the more complex stuff

[stray lynx]

My issue is when you start playing with vectors, especially if we are in physics for example:

[midnight trench]

Unit vectors are denoted by a^ (^ on top of the a)

It tells you the direction of the vector

Imagine it as a slope

The magnitude can be measured in speed in kilometers and directions could be north or south

If you’re doing something in all 3 directions, we can say up and down, but for now, let’s visualize a simple plain

[stray lynx]

(Polar coordinates vectors, Spherical Coordinates vectors, how to switch between each one (+ Cartesian)) Moreover the relation between angles and vectors. For example a angle between ox and a vector and (theta is 45°) we add X angle to find that same angle but between the vector and iy(some sort of translation by angle)

In the previous example, when you decompose your vector(you use the vectors i and J) and you use sin and cos since you have an angle, my issue is manipulating the angle.

[midnight trench]

Polar coordinates are simple, we have our distance r from the origin and the angle that makes it positive with the x axis

So if we’re converting Cartesian coordinates to polar coordinates, we have (r,angle)

So r = sqrt(x^2+y^2) and angle = arctan(y/x)

We essentially have rcos(theta) and y = rsin(theta)

For spherical coordinates, it’s the same principal, expect now we’re using our z axis. We have (x,y,z) which are now spherical coordinates (p,theta,phi)

Now it’s just sqrt(x^2+y^2+x^2), theta = arctan(y/x) and phi = arccos(z/p)

If you’re converting back, it’s x = psin(phi)cos(theta), y = psin(phi)sin(theta) and z = pcos(phi)

[stray lynx]

Why phi is arccos(z/P)?

And how did you do the converting?

[midnight trench]

Because cos(phi symbol) = z/p

[midnight trench]

I’ll do a proof

Take sin inverse or cos inverse of sqrt(x^2+y^2) and get arctan

It’s still tan(theta) = y/x

That’s also another way to get arctan(y/x)

Next is x = rcos(theta), y = rsin(theta)

Idk if I’m teaching you well

I’m not a great teacher with this kind of stuff

Sorry

[stray lynx]

It is alright mate. You are just not hitting the right corner of the topic.

[midnight trench]

Sorry man. I tried

I can try to help you find resources if you’d like

[stray lynx]

And I agree since I'm confused too since I don't even know the issue I'm facing specifically

[midnight trench]

Perhaps the issue isn’t understanding how they work. Perhaps you just have to think differently

[stray lynx]

It sounds like something about vectors + trigonometry.

[midnight trench]

Trig I can help with

I can tutor that well lol

Or teach

It’s fun

And usually effective

[stray lynx]

Trigonometry is fun when you remember all the proprieties NGL.

[midnight trench]

Real

I have great memory

Math people call it a curse

[stray lynx]

Haha.

[midnight trench]

Unfortunately, it helps me remember every identity

[stray lynx]

So, do you know any book where I can find all the proprieties in trigonometry?

[midnight trench]

Not exactly. I’d go over formula sheets and prove identities

[stray lynx]

Wdym prove identities?

[midnight trench]

https://www.cambridgeinternational.org/Images/417318-list-of-formulae-and-statistical-tables.pdf

Second and third pages have identities and integrals

And some vector math lol

[midnight trench]

I like proofs. It’s fun to see how things work. There are some complex formulas to remember. Like complex vector geometry

z1 = x1 + iy1

You have to memorize adding and subtracting. Scalar multi platoon, magnitude, angles, conjugates, bleh

[stray lynx]

Man, the imaginary numbers aren't supposed to exist.

[midnight trench]

0 exists

e^ipi exists

We have an entire elliptic function (E) because we cant get the arc length of cos lol

Or sin

Literally every trig function lmfao

[stray lynx]

Isn't there a source where it teaches me to mastery trigonometry?

[midnight trench]

It depends on what you want

[stray lynx]

So I shortcut my way threw Cartesian coordinates system.

[midnight trench]

I guess just understand cos, sin, tan

[stray lynx]

You know simplify and manipulate the.

[midnight trench]

Yeah

Do you know matrices?atricies

[stray lynx]

What I know is shallow, really shallow level.

[stray lynx]

Yes but let's don't dive into that lmao.

[midnight trench]

lol

Gonna have to

Important for coordinate expression

[stray lynx]

Oh, I thought we talking about Matrices in Algebra 4 (University level)

[midnight trench]

I can give you a crash course in what they mean if you want

[midnight trench]

Way above what I know then lol

I thought you meant you didnt like them

[stray lynx]

Who said I do lol?

[midnight trench]

Lmfao

[stray lynx]

Bro, keep your love for math in you, you will need it in University.

[midnight trench]

https://tenor.com/view/connor-mcgregor-gif-20436904

[midnight trench]

I’m mostly self-taught

My parents didn’t put me in higher level math as a kid because we didn’t know how the education system worked

I had to learn from YouTube, khan academy, library books

I was America’s equal to a depressed Russian citizen

The only words I know in Russian are hello and suka blyad lmfao

[stray lynx]

Lol, I might be talking with future Olympic math guy.

[midnight trench]

Nah

I’m 16

Too late for me

I’m only good at integrals

And don’t be discouraged because I know things in math and am trying to explain to you. I don’t know nearly enough to be considered an “olimpyad”

I had a shelf full of math books

To be fair, memory is a big thing for me. Memory is my everything

[stray lynx]

The #1 in my Engineering University also complains like you.

[midnight trench]

He’s a nerd

I am not a nerd

I also don’t study

I study the test after I take it to never make the same mistake again

[stray lynx]

The difference is he is focused on his life goal. So you have to do.

[midnight trench]

I wanna go into mechanical engineering and break into something specific

I already have a full scholarship to anywhere in my state, I plan on going to a state university for my bachelors then trying for an Ivy for my masters

[stray lynx]

Let chat in DMS it not chatting channel.

[midnight trench]

True

Added u

[worn bridge]

Help

[midnight trench]

What do you need help with?

The table has each coordinate. For the first one, add all the Y coordinates -3 the amount of times it comes up

So just Ynumber - number(3)

Number in this case is just 10

So do Y1 + Y2 + Y3… + Y10 and then - 30

Similar can be done with Z

And 4

I don’t get a notification when pinged. If you need some help add me and message so I’ll see it

[worn bridge]

What about 3 and 5

[midnight trench]

3 is adding up all the Xs and adding 10 at the end

[strange saddle]

Really? I was just doing my homework sheet

[willow bear]

no actually

not "the next 6"

but down to the 6th

and dont forget to multiply them all by 3 bc the sum says 3y_i and not just y_i

$\sum_{i=3}^6 3y_i = 3y_3+3y_4+3y_5+3y_6$

[obsidian monolith]

|Ann⟩

[strange saddle]

Ey brahs, how do you use the commands and such

To illustrate

[thin surge]

your pfp💀

[worn bridge]

@willow bear this would be the simplified answer?

[hushed sphinx]

No, she was just explaining what the notation means, not actually doing the computation.

[worn bridge]

Oh mb

[willow bear]

what tropo said

[willow bear]

whose pfp?

[thin surge]

@strange saddle

[midnight trench]

I think so… can’t remember

[supple fjord]

why do we use a -sqr x⁶

and not just use sqr x⁶

please help

[willow skiff]

Cause the limit is as x approaches negative infinity

So the square root of any number is positive or 0

[supple fjord]

but

why here its not - in front?

[willow skiff]

And as for the denominator, it will be negative, as 6x^3 goes to -infinity

[willow skiff]

Ah okay so the behaviour of even powers is different from odd powers

x^2, x^4, x^6, x^8 etc go to +infinity as x goes to -infinity

But x, x^3, x^5, x^7 etc go to -infinity

[willow skiff]

Yeah I feel this isn't very well explained too

[summer ruin]

there's no such real x for which equality x^2 = -sqrt(x^4) holds

[willow skiff]

You need a few examples to see that oh, $\sqrt{(-2)^2} = 2 = -(-2)$

[obsidian monolith]

south

[willow skiff]

But $\sqrt[3] {(-5)^3} = -5 = -5$

[obsidian monolith]

south

[willow skiff]

Of course it's easy when you have a positive number instead of say -2 and -5

What happens when x is negative usually isn't explained too well

[supple fjord]

okay I think I got it

thank you

[willow skiff]

Yeah no worries

[hushed sphinx]

Because we know x² is never negative.

(Oof, off by 1 hour).

[fair ibex]

#calculus

[midnight socket]

hello, I am having a hard time with Inverse of Trigonometric Functions huhuhu... like, I get the gist of it, but I still manage to stumble on some steps..

[willow bear]

show the problem(s) that you are struggling with

[midnight socket]

sure, hold on

I have a solution for it, although I am not too confident about it. [cry]

[willow bear]

well show it anyway

that way we can tell you what you did wrong and you will know better next time

which is how you learn

[midnight socket]

as u see, there's a question mark next to it LOL

[willow bear]

replacing tan(x) with x is not good...

also misused = signs that should have been =>, in a lot of places

[midnight socket]

my teacher used the "let x" trick on some equations so I just did the same thing lol

[willow bear]

for #1 you could have fixed it by letting tan(x) be literally any letter other than x

because x is taken

any other letter would have been fine

i am serious

why are you rofl reacting me

[midnight socket]

mb mb

anyway, I'm just used to x

[willow bear]

it will do you good to break this habit and be more flexible

what you just told me amounts to saying "i would be fine solving an equation if its unknown was called x, but call it by any other letter and i risk getting lost"

which is, again, not good

[midnight socket]

yea, I should fix that

[willow bear]

anyway, so you got tan(x) = -1 => x = -pi/4 -- were you expected to find the solutions only between -pi/2 and pi/2?

or were you expected to give all real solutions

[midnight socket]

I'm not sure tbh, sorry T-T they just gave me this assignment

[willow bear]

ok let's move on to #2 then

... what is "1e + cos(x) = x"?

where did the variable e come from

[midnight socket]

that's "let" T-T

[willow bear]

oh god. ok.

you need to write your t's so they don't look like plus signs mate

[midnight socket]

mb T-T

[willow bear]

and make your l's and 1's distinct from each other as well

[midnight socket]

for sure

[willow bear]

and that equals sign right before it should have been erased entirely

(not even a =>)

and again the same overloading of x

[willow bear]

is that question mark your own doing? or your teacher's?

[midnight socket]

mine, I ain't sure w/ my answer T-T

[willow bear]

what are you unsure about? that cos(x)=1 => x=0?

[midnight socket]

yea

[willow bear]

does cos(0) = 1?

[midnight socket]

it's 3 AM here I am so sorry oh god T-T

[willow bear]

why are you doing math at 3 in the morning?

are you on a due-yesterday deadline?

[midnight socket]

nope, I just have a tight schedule

[willow bear]

(that also doesn't answer my question, but that seems to be a lesser issue)

a schedule so tight it leaves you with like 3 hours of sleep every day at most???

[midnight socket]

kinda, yea, I'm forced to be in an advanced section

[willow bear]

augh.

[midnight socket]

i know right

[willow bear]

anyway, we went off track and you didn't answer my question

does cos(0) = 1?

[midnight socket]

i think so T-T

[willow bear]

why do you only "think so" instead of being certain of it?

do you also merely "think" that 7*8=56 instead of knowing it for a fact?

[midnight socket]

i only started learning abt this so i'm very rusty mb T-T

[willow bear]

you have a unit circle chart right here. do you know how to read it?

[midnight socket]

yeah

[sterile rapids]

someone explain the the surface area of a sphere is exactly 4 times the area of a circle

[willow bear]

ok, how do you find the cosine of an angle using the chart?

[willow bear]

https://youtu.be/GNcFjFmqEc8

this is a bit calculus-y but hopefully a little more insightful than "that's just what the formula is" or "that's what happens if you take the derivative of the volume formula"

[midnight socket]

I'm so bad at explaining, but, you use the y function or sum..

[willow bear]

"the y function"?

ok let's try this

put the unit circle chart in front of you

using that chart, find cos(5pi/6), and tell me how you got it.

[sterile rapids]

i dont need a chart to solve that

[midnight socket]

I do HSDFHSDF

[sterile rapids]

-(√3/2)

[willow bear]

was not asking you!!!

[sterile rapids]

sorry

[midnight socket]

bro, they were asking me

[willow bear]

i am trying to teach dowsy so she (a) knows how to do it and (b) knows how to explain what she's doing

[midnight socket]

so, um, from what I can explain is that you could find the cosine if the degree was given, right

[willow bear]

you can do it only with degrees? not with radians?

... i have to go but i think you may want to go review the unit circle & how to use it properly

cause you need to be able to explain

[hallow lodge]

how do i do the line graph here

[coarse prawn]

just plot it right?

[worn bridge]

Need help w checking my answers

[willow bear]

well, send us your answers to check then

[worn bridge]

1. 57
2. 94
3. IDK
4. 92
   5.Idk
   6.55
   7.105
5. 36
6. 78
7. 45

[willow bear]

for mine and everybody else's benefit, here are the data and problems in one place

give me some time to check these

ok so all of them are correct except for the two unanswered ones

what is confusing you about #3 and #5?

@worn bridge

[worn bridge]

I dont know how to deal with subsets for 5, and for 3, im not really sure what to do but i believe, the answer would be the sum of X plus 10?

[willow bear]

yes, #3 is just $\paren{\sum X} + 10$

[obsidian monolith]

|Ann⟩

[worn bridge]

For 3 i think its 79

[willow bear]

show your work?

my answer does not match yours.

[worn bridge]

82?

[willow bear]

show your work, i won't accept answers without working

[worn bridge]

I mustve put the wrong numbrrs

Okk

What i did was add all the x values (i only used calculator) then i added 10

[willow bear]

ok thats correct

82 is the correct answer, so it was probably a typo on your part.

now for #5, i remember that i said this: #precalculus message

in which i explained to you what the notation meant

$\sum_{i=3}^6 3y_i = 3y_3+3y_4+3y_5+3y_6$

[obsidian monolith]

|Ann⟩

[willow bear]

do you understand the meaning of the RHS here? y/n

[worn bridge]

What does rhs mean

[willow bear]

right-hand side.

(left-hand side is abbreviated to LHS, just fyi)

[worn bridge]

Well its just the summation of 3yi from 3 to 6 but idk how to do operations on subsets

[willow bear]

what do you mean by "subsets"

did you maybe mean subscripts? the little numbers below?

[worn bridge]

Oh ye mb

[willow bear]

those aren't an operation

not in the same sense as superscripts are for exponents

$y_3$ means the 3rd value in the $y$ column (in the order that they're written, top to bottom)

[obsidian monolith]

|Ann⟩

[willow bear]

so from the table, $y_1 = 4, y_2 = 12, y_3 = 8$, etc.

[obsidian monolith]

|Ann⟩

[willow bear]

@worn bridge do you understand now?

[worn bridge]

So i would write 3(8) + 3(11) + 3(6)+ 3(7)?

[willow bear]

yes

of course, you can also factor the 3 out to make your calculation a little easier

so 3(8 + 11 + 6 + 7)

[worn bridge]

Hey @willow bear, about numbers 1 to 4, why do i have to multiply the integers with how many values a variable has? I never fully grasped the explanation of another person, but he showed me how to solve it

[willow bear]

??

i don't understand what you're saying here, can you show where exactly the multiplication you're talking about happens?

[worn bridge]

Im referring to this

Below the reply is his explanation

[willow bear]

well that's easy

you're adding 10 copies of -3 along with your y values

which is 10*(-3)

does that make sense to you?

[agile sparrow]

how's all that under calculus

[worn bridge]

But why do we add 10 copies of -3

[agile sparrow]

Isn't that stats or some shit

[worn bridge]

Precal

[daring tapir]

Lmaoooo

[agile sparrow]

why u most of the time here

also boards results soon

[daring tapir]

Waiting for someone to clear up a doubt in trig (you can check if you are free)

[daring tapir]

20th may is farr away

[agile sparrow]

Oh yea you're from cbse

Im from isc

[daring tapir]

Hm

Isee

[agile sparrow]

It's about perspective

For me it's tommrow

Every day feels like a minute these days

Until 26th

[daring tapir]

Fuck lol i can imagine the stress
Confident for 75?

[agile sparrow]

what nah

[daring tapir]

Rip

[agile sparrow]

Not stress about boards

Strreesed about advanced

[daring tapir]

True true

[agile sparrow]

Scoring 75 is ez pz

[daring tapir]

Have fun 💀

[willow bear]

because we add a -3 for each y value

and we have ten of those

[agile sparrow]

Sadly I won't score full in math

As I wished to

[daring tapir]

(Doesnt look like so considering how ppl were crying after phy board)

[agile sparrow]

Somewhat around 95 if (-1 or -2 for viva / practical)

[agile sparrow]

Fuck it

I'm from isc

Also the physics paper was not that tough just conceptual

[daring tapir]

Lmaooo fr
(Help plz for trig-)

[daring tapir]

Imean there is no way for me to know that 💀

[agile sparrow]

Seeing it

[worn bridge]

Does the parentheses determine that? If you look at number 1, it has parentheses, but 3 doesnt, so why do we not add 10 copies to 10?

For number 3 btw

[willow bear]

yes for number 3 the ten is not in parentheses and so isn't inside the sum, and so only gets added once.

and for #1, #2 and #4 the extra number is inside the sum and so is added as many times as there are values in the y column

[worn bridge]

Alr that makes senses

Sense*

[old bane]

how do we use the chain rule

[willow skiff]

Watch a YouTube video on it

[hallow lodge]

do yall have any tips for integration/antiderivatives and chain rule for antider? like is there a study trick to it? mnemonics? anything?

[willow skiff]

it's just practice

You need to see enough examples and practice them in order to develop the pattern recognition you need for integration

I agree that it takes a long time to learn all the different types of integrals

There's no hack to learning maths quickly unfortunately

Without sacrificing on understanding

[hallow lodge]

you think i can master derivatives to antiderivatives with their chain rules in half a day?

i have exams in 3 days

and im hella unconfident

[daring tapir]

no.

[hallow lodge]

i mean i found it easy when discussed, i js forgot how to di everytying

[daring tapir]

ah then yea you can revise it in a few hours

[hallow lodge]

thx man

[winter comet]

if you have a log in the exponent with the same base as your base, it cancels out

by rule of logs

i like saying things confusingly

jk i don't but idk how else to say it 💀

number 7

[feral tulip]

why

why is that

[winter comet]

um

lets just say log_b(k) = a

then k = b^a

then if you replace a = log_b(k) in og expression

you get b^a = ?

well we already know its k XD

[feral tulip]

k

[winter comet]

yeh

[daring tapir]

by definition xD

xD

[golden cairn]

How did my teacher replace log10 with a 1?

I don’t get it

[shut monolith]

log(10) = 1

because 10^1 = 10

The reason is because “log(10)” is read “log base 10 of 10”, and its value is determined by asking:

“What power do I raise (the first) 10 to get (the second) 10?”

Well that power would be 1 because 10^1 = 10. So log(10) = 1

[golden cairn]

Ahh okay

Doesn’t that apply to anything though?

Yeah

My teacher like just straight up changed log10 to 1 without even telling us anything so I was confused

But now I get it

[past meadow]

no, in lots of highschool math classes (your included) the base of every log is assumed to be 10 if not stated otherwise

[pure sable]

hi could anyone help me with graphing parabolas ?

[midnight trench]

Sure

What do you wanna know?

[pure sable]

here like where do i start, not even sure if it’s a parabola or not

like how do i start this problem and maybe i can figure out from there

[midnight trench]

Ah, those

That’s a circle

The first thing I’d do is refresh on completing the square

You remember how to complete the square?

[pure sable]

yes

even with those coefficients of 2? do i factor those out

[pure sable]

thank you 🙂 i was confused because of the 2 in front of x and y

usually she gives us problems with no coefficients

[midnight trench]

You can just divide te whole thing by 2 lol

[midnight trench]

No problem

[pure sable]

what about the 17?

[midnight trench]

I’d just divide the whole thing by two and solve like a normal circle

[midnight trench]

Just becomes 17/2

You’ll have to add more fractions anyway

not drawn to scale

but that’s the steps

I did the fraction adding in my head. If it’s wrong it’s still the right idea lol

[pure sable]

ahhhh

thank you soooo much

that helps a lot cuz i was confused on the steps

[midnight trench]

Yurr

If u need anything try to ping but i wont reply for hours

If u need help just send a dm

[agile sparrow]

It's a circle

with center x= -1/2 , y= -7/2

[winter comet]

they uh

^

[agile sparrow]

nuh uh

[winter comet]

mmhmm

[agile sparrow]

and radius 2

[winter comet]

☠️

[agile sparrow]

@shut wraith wanna do some math

fuck wrong guy

@winter comet

[winter comet]

what kind of math

[agile sparrow]

idk u decide

[winter comet]

i have to find problems? 💀

[agile sparrow]

yes

Or no if u don't want to

[winter comet]

i honestly don't know where to look 💀

im thinkin sum integral or smthn

i dont know partial fractions or trig sub very well maybe sum with that

would prob be easy for u lol

[warped shuttle]

would 2 months be enough to finish percalc ?

[hollow widget]

Depends on what level of precal

[winter comet]

depends on quite a lot of stuff that we don't know XD

[golden cairn]

This guy said something and then deleted it. He said something like “math is easier when you understand it”

[chrome tinsel]

Same eqn. Diff calculators r giving diff values

Plus the ans should be 6.20 smt

[shadow summit]

To do it by hand simply make y=0

[chrome tinsel]

See the eqn

[shadow summit]

Yes I see it

[chrome tinsel]

I cant possibly sit and solve that

[shadow summit]

Why not?

[chrome tinsel]

It will take too much time

And i tried it, i wasnt able to

[shadow summit]

Can you post the original question?

[chrome tinsel]

Ok

last part

[shadow summit]

,,F’(t)=20+15\sin(\frac{\pi t}{6})-0.2x2^{0.1t^{2}}

[obsidian monolith]

TheLord26

[shadow summit]

You missed the sine function in desmos

[chrome tinsel]

Ohh

Ohk

Thx

[warped shuttle]

Different type of functions (One to one, …)

Graphing functions

Logarithmic functions

Trigonometry (Radians, graphing sine waves etc)

Inverse of a function

Limit and continuity

[daring tapir]

i mean it depends on your dedication+ current skill too, could take entire two months, could be done in a week or two

[proven void]

$\lim_{n \to \infty} \frac{5^{2n} - 4^{2n+2} \cdot \sin(n)}{5^{2n+3} - 3^{2n+1} \cdot \cos(n)}$

[obsidian monolith]

milanesa de pollo

[daring tapir]

divide numerator and denominator by 5^2n

try to get the power of all numbers to equal 2 n

[proven void]

wait

looked hard but was easy

thanks ender

[warped shuttle]

so it's totaly possible ?

[daring tapir]

extremely possible some might even say it is ez but it depends on you after all

[warped shuttle]

alright thanks, i had a glance at those topics and it looked easy just wanted to make sure

could i get to derivatives in maybe 3 months if i have consistency then ?

[daring tapir]

you could do it in a lot less

[warped shuttle]

alright then, it looks promising

[whole perch]

I need help. None of my math test grades have been good and although i have been trying to fix them nothing really works. This test I studied 6hrs+ the day before and even more cumulatively. I did every single practice problem did the study guide as well. I tried to find questions on google... didn't work. Although being honest I was absent on one of the most important day of the unit but I was able to clear up all of my doubts and my friends helped me out a lot too. During the test I was extremely confident that I would get an A but instead got much lower and piling up with my preivous test grades I don't think I can legitimately get an A in the class and as a freshman in HS im cooked. I have recently realized that up till now I have either brute forced my way through units (not working) or just naturaly getting the topic. I don't really think I even know how to study for math anymore and with My parent asian background brute force seems to be the way. Please educate me on how to study for math someone (none of the youtube vids help). I'm in precalc btw.

[winter comet]

why do you get lower grades?

is it because you make mistakes, or you don't understand the concepts?

i mean i would suggest making sure you completely understand the concept of each topic, and the process used to solve types of problems within the topics

then practice and be really careful to try to not make mistakes, and learn from your mistakes, and be patient

thats what i try to do usually

[whole perch]

im not sure what I did wrong this time but tbh i thought i knew all the concepts and all the problems I did were right so idk how i fucked up on the test

[winter comet]

maybe you made some mistakes

or smthn

[whole perch]

usually its either silly mistakes or not being able to attempt questions because I don't know how to solve it

[winter comet]

ah lol

[tranquil inlet]

maybe try paying attention in class

i never pay attention in c lass

lol

[winter comet]

difficulty level: infinite

[whole perch]

lol I do and I take notes as well

[winter comet]

nah jk 💀

[whole perch]

lol

[tranquil inlet]

what topic

[whole perch]

its almost as if my own brain is sabotaging

me

I did everything right outside of the test

maybe the test questions were harder?

[tranquil inlet]

for sure

[whole perch]

or i mixed up concepts

[tranquil inlet]

unit tests tend to be much harder than a final or quiz or whatnot

[whole perch]

yeah i see that a lot

[tranquil inlet]

cuz they go in depth into the topic

[whole perch]

yup

[tranquil inlet]

youtube videos prob dont help you

[whole perch]

yeah they dont

[tranquil inlet]

cuz they dont cover as deep as the teacher will

[whole perch]

yeh

[tranquil inlet]

anyways i think try to actually understand concept very well and rizz up teacher

maybe u might be able to save ur gpa

[winter comet]

🗿

[whole perch]

including this ima have 3 B's

;-;

im cooked

[tranquil inlet]

🫡

[whole perch]

5 A's

4.1 GPA

[tranquil inlet]

bro my friend got a b in math last semester and his mom took away his phone insce

[whole perch]

terrible

i dont use my phone anyway

its nonexsistent

[tranquil inlet]

XD i only use my phone for gmail and discord and text

[whole perch]

exactly

[winter comet]

that's very dumb

[whole perch]

and brawlstars on the bus

lol

[winter comet]

fax 😂

[tranquil inlet]

clash royale 2v2 during lunch

[whole perch]

real

[tranquil inlet]

12 evo recruits the back

[whole perch]

i dont even use tiktok or snap or insta

[winter comet]

🗿

[tranquil inlet]

SAME

LOL

[whole perch]

only brawl stars and clash

[winter comet]

who does 💀

[tranquil inlet]

• monk and battle healer

[whole perch]

litterally everyone else in the school

😂

[winter comet]

☠️

[tranquil inlet]

fr they always scrolling insta reels or some sht

[whole perch]

"use insta reels" - random kid

[winter comet]

+clone 😂

[tranquil inlet]

like hell nah id rather study and get into college

[tranquil inlet]

perfect

[whole perch]

not with 3 B's no 💀

[tranquil inlet]

bro im genuinely curious how you have 3 b's and still have a 4.1

[whole perch]

5 a's

[tranquil inlet]

8 classes??

[whole perch]

yeah

AK HS

[winter comet]

🗿

[tranquil inlet]

bro ig my school is just sht

[winter comet]

nah bro its all different 🤣

[whole perch]

PE, ELA, Math, Bio, CS, Spanish, B.E. , History

[tranquil inlet]

NAH my school forces all freshmen to take STUDY HALL AND NO AP

[whole perch]

oh they let ppl take 2 APs

[tranquil inlet]

BROOOOO

[whole perch]

i took none

ela 1 cooked me hard tho

and precalc

bio i had a 89

[winter comet]

what B.E.?

[tranquil inlet]

and the only aps u can take in sophomore is ap chem calc physics language and comp sci

[whole perch]

business essentials 💀

[winter comet]

☠️

[tranquil inlet]

oh hell nah

[whole perch]

im taking the most free and useless classes this year

[tranquil inlet]

...

[whole perch]

idk how im in precalc bro

its that bad

how can I get 3 Bs

[winter comet]

💀

[whole perch]

with those classes

[tranquil inlet]

im taking english (fcking stupid) intro to engineering, biomed, sports (xc and tennis), math 2, study hall (forced)

im self studying precalc to skip to calc next year

[whole perch]

precalc finna be an AP in our school

[tranquil inlet]

bro 💀 our school doesnt have ap precalc OR ap world

[whole perch]

why the hell is HS ELA so hard bro

[whole perch]

💀

ppl are taking ap world as freshmen

[tranquil inlet]

no way wtf

[whole perch]

our school is sweaty asf

[tranquil inlet]

private?

[whole perch]

all our clubs pretty much make nationals or states every time

[whole perch]

public

[tranquil inlet]

english is not too difficult but the teachers are just terrible

[tranquil inlet]

dam

thats impressive ngl

[whole perch]

yeah my teacher was known for harsh grading and answering questions with questions 💀

"is this paragraph good?" - me

"idk is it?" - teach

[tranquil inlet]

my teacher was known for yapping the entire time and not letting us play games on computer

[tranquil inlet]

im sorry for your loss

[whole perch]

we dont use computers in ELA for the most part 💀

[whole perch]

lol

[whole perch]

what grade r u in

[tranquil inlet]

man are there a lot of asians at ur school

[whole perch]

thats true

[tranquil inlet]

freshie too but im really young

[whole perch]

even the white kids

[whole perch]

oh

same

im not young tho

[tranquil inlet]

i turn 15 in 7 months

[whole perch]

i turn 15 this month

[tranquil inlet]

lol

it must be hard competing with the other kids at ur school

[whole perch]

yeah

i mean 3 B's bro

it would be hard at any school with that

only thing special abt me is that im in precalc

[tranquil inlet]

freshman year at our school is stupidly easy

[whole perch]

so everyone thinks that im a math nerd

[tranquil inlet]

they baby feed you

[whole perch]

nah

[tranquil inlet]

💀 aint nothing special about me