precalculus

[frail lion]

I understood like 90 percent of that

[sweet hearth]

thanks

[frail lion]

No need to thanks me i guess

I should be thanking you

[sweet hearth]

I am not necessarily thanking you because you helped me,I am just thanking because people nowadays barely have it in them to read a full paragraph. Even about enjoyable stuff like I have made long anime theories and most of the comments are like "I ain't readin allat".

[frail lion]

Anime theories

[sweet hearth]

yeah

[frail lion]

Ok man cool

I guess

Small thing

Infinitesimally small

Is dx

Continuously adding dx gives us big thing

And that continuous adding is integral

[lone temple]

so integration is integral but limited?

[frail lion]

Integration is the method

Integral is the answer

[lone temple]

no i mean thats obvious but im telling about the meaning of integral and stuffs

if i understand dx i think i might understand integration using subsitution xd

[frail lion]

Integration might not be limited

Don't give limits to it

Write c constant after integral

[trim shard]

this is a very nice (and loaded) question

[frail lion]

Lucy gonna be typin sum crazy explaination about dx probably

[trim shard]

you probably already know this, but in an integral, dx mostly just tells us that we are integrating with respect to the variable x. however, what dx really represents is this really infinitesimally small change (smaller than delta x and for that we represent it as dx) in x. when we sum up the product of some functions height by the infinitesimally small widths (dx), we get the total area under the curve which is our integral

[trim shard]

where there is maths there is some cool history too

[lone temple]

f(x) as height and the symbol of integral is sum so its sum of infinite rectangles with each area is f(x)*dx with dx extremely small to make the area more accurate?

[trim shard]

exactly that!

[lone temple]

i understood it, thanks!

[trim shard]

area of each rectangle would be f(x)*dx where f(x) represents h and dx represents width

[trim shard]

ofc

[forest sleet]

Say you have a function f(x), you can stretch it, invert it, change the x and y position of the index, but how do you rotate it by theta degrees upon the origin?

[summer ruin]

apply the rotation matrix to the graph, if that's your intent

[forest sleet]

Thanks

[uncut star]

But I am one of them

[frail lion]

I want information about this parabola

How can I deduce things about a tilted parabola ?

Like axis , directrix and all

[raw hill]

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/10%3A_Analytic_Geometry/10.04%3A_Rotation_of_Axes

Rotate the axes

Then rotate everything back

[frail lion]

Man rotation of axis is

Very gruesome unpaid labour

Ya got something else

[raw hill]

Eh this is a kinda special case tbf

$(x+y)^2=4x-2$

[obsidian monolith]

Civil Service Pigeon

[frail lion]

It's not only about this

This is sorta an example

[proud tangle]

What do the $ signs mean?

[frail lion]

$wassup$

[obsidian monolith]

Sam

[proud tangle]

Ah

$cool$

[obsidian monolith]

nomnom15

[fair minnow]

I have a multivarible system question. Ik it's more algebra, but these have 4 varibles. Does anyone have a method for solving these?

[uncut star]

Gaussian elimination or just long substituting

[uncut star]

I am assuming linear equations here

[fair minnow]

Well, 4D systems i guess.

[uncut star]

Can you show the equations

[frail lion]

Bro what is gaussian

Elimination

[uncut star]

It is simplifying a matrix to find solutions

Similar to elimination in 2 variables

[frail lion]

Hmm idk about matrices

[frail lion]

But yeah send once

Send the

Equations

[fair minnow]

It's not one specifically, but more of an algorithm i could follow

to keep the numbers straight.

[frail lion]

What question do you wanna solve bro

Or you're jus randomly asking

No specific question

[fair minnow]

nothing specific. sorry. nvm

[uncut star]

Certain equations involving logs are unsolvable using elementary algebra

[faint sail]

Anyone got files for amplitudes?

[frail lion]

What wym

[celest lantern]

Can someone tell me what I’ve done wrong?

[upbeat vine]

Sin inverse -1 is -π/2

[ornate mist]

what the hell kinda pre cal are u taking

cos starts from the top, sin starts from the bottom

from the origin

if its -cos and - sin just flip them

[willow bear]

this is definitely not pre-calculus

but definitely calculus calculus

[obtuse narwhal]

hello everyone, someone can recommend me a good book for precalculus? i need theory, not the problems

like "precalculus from stewart" or something like that

https://tenor.com/view/monkey-thinking-monkey-thinking-think-money-gif-9734025314392564509

[molten hearth]

can someone explain how to graph trig functions, specifically cot/sec/csc? i need some practice problems/example problems

[timid spruce]

why does $real(e^{ix}) = \cos(x)$ and $imag(e^{ix}) = \sin(x)$?

[obsidian monolith]

esoij

[timid spruce]

please ping btw

[river drift]

are you familiar with taylor series?

[frail lion]

It's actually by Taylor series

[timid spruce]

nope

[frail lion]

Basically expansions

If cos theta, sin theta , e^x expansions?

@timid spruce ?

[timid spruce]

what

i dont understand

[frail lion]

Yeah actually bro the thing is that

[river drift]

well do you know any calculus?

[frail lion]

Yeh exactly my question too

[timid spruce]

yeah

i like just started calculus class a few month ago

im still learning derivatives in my class

[river drift]

https://www.youtube.com/watch?v=v0YEaeIClKY

not sure if this is at your level yet but you can try watching it

[timid spruce]

thank you

makes sense to me

[fallow hemlock]

better to ask in #book-recommendations

[raw hill]

In the future, please use the ,rotate command.

,rotate

[raw hill]

https://math.stackexchange.com/questions/1618039/show-that-2n-n-12n-2-fracn-2n-322n-4-n1

[frail lion]

I don't understand the solution can ya explain?

[frail lion]

@raw hill bro wot

[neon ingot]

which is 3pi/2

[limber holly]

which book's questions is this? i want.to buy it

[frail lion]

It's in no book

[limber holly]

so what it is?

[raw hill]

Which solution? What specifically don’t you understand? We need some more context to help you out here.

[frail lion]

Some assignment that I got

[frail lion]

Yeah I got it

No problem

[upbeat vine]

Yh

[limber holly]

so which class or some exam's assignment is it?

[frail lion]

Class 11th

Jee advanced pattern

[bitter shoal]

hello

Help me understand this if I’m doing it wrong because my precalc teacher can’t teach properly she just give us a packet

For the first property the x->4^-is the hole in the graph and the -5 is what the solution of the function should be once the hole is put into x in the equation

The second property the x->2^+ is the vertical asymptote and the negative infinity is how the graph behaves from the right side

And the last property is the horizontal asymptote

[raw hill]

The first property doesn't necessarily mean that there's a hole at $x=4$. The graph could just pass through $(4,-5)$.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

your second and third ones are fine

[limber holly]

can u please dm it to me?

[azure mist]

Ok now how do we do these

As a tenth-grader, I'm curious

[limber holly]

its much easy brother,its just an a binomial function

[azure mist]

Explain

[raw hill]

@azure mist

[azure mist]

Ty I'll view that later

Also where is the calc section

[raw hill]

#calculus

[frail lion]

No

[limber holly]

why?

:/

[frail lion]

Too lazy

[uncut star]

But where are you getting these from

The question looks insanely hard

[limber holly]

bro do challanges and thrills of precollege mathematics 4th edition book,then u will know the real meaning of "hard"

[uncut star]

Isn't that hard

Except geometry

Well it is known for geometry

[limber holly]

did u done tht book?

[uncut star]

So what am I even doing

[uncut star]

Only the combinatorics part

[limber holly]

so is it a good book?

[limber holly]

Why not the whole?

[uncut star]

I never got the time to complete it

But the combinatorics wasn't too bad

[cinder heron]

looks like something related to the binomial theorem

[limber holly]

why did u evn just did the combinatorics part then?

[uncut star]

Uh I like combinatorics

That is the only reason

And then I gave up on mo

[uncut star]

Excursion was much harder though

[limber holly]

means?say clearly

[limber holly]

in that book? well,which book did u may prefer me to do for deeper understanding in mathematics?

[uncut star]

Whichever book you like

It depends on the reader

Pretty much any standard book does the trick

Excursion is good though

[limber holly]

and did u do That book for whom's saying or by whom u get to know Abt tht book)?

[limber holly]

in tht book?

[uncut star]

I saw it online

It was recommended by pretty much everyone

[limber holly]

So which book r u doing now? and did u choose tht book for exam or self study?

[uncut star]

I am not doing any book now

As I said I quit mo

[limber holly]

oh olympiad prep ,noice ,so wht r u doing now? drinking juice?

[uncut star]

Nothing really

[limber holly]

well ,u probably tlking to me

[uncut star]

Wasting time

Anyways you can go through any number of books you like but most competition math books do not have a lot of theory

So it is better to just search up competition math problems online

[limber holly]

\documentclass[12pt]{article}
\usepackage{amsmath, amssymb}

\begin{document}

\section*{Elite-Level Challenge Problem}

Let (a, b, c) be positive integers such that
[
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1
]
and (a \le b \le c).

\begin{enumerate}
\item Find \textbf{all possible triples} ((a, b, c)).
\item Prove that there are \textbf{exactly finitely many solutions}.
\end{enumerate}

\end{document}

[obsidian monolith]

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

[limber holly]

done this qstion

[uncut star]

I have seen it somewhere

[limber holly]

its in the tht book

its toooooop esy

[uncut star]

?

[limber holly]

sorry its from number theory so...

but still ,

Good!

bye

gn

[uncut star]

Have a nice day mate

[arctic raptor]

hi

i dont understand the unit circle thing in precalc

anyone know of any good ytbers for precalc bc i wasnt there for my teachers lectures

[haughty spoke]

The Organic chemistry tutor is best

He explains it very well

[arctic raptor]

tyyy

[craggy canyon]

hi

chat

[frail lion]

Hi

[willow breach]

<@&268886789983436800>

scammer

hacked account

[raw hill]

<@&268886789983436800> spammed amongst multiple channels

[stuck dagger]

https://youtu.be/e2kzTfNM7hU

This guy is pretty good

Darn

His name is Michel Van Bizen

[raw hill]

<@&268886789983436800> multiple channel spam

[cedar garnet]

How to

K

[unkempt lodge]

I'd assume "gradient of 1" means that y = 1 if x = 2, so you can just substitute y with 1 and x with 2, then evaluate for k

[cedar garnet]

I think its dy/dx = 1

But i dont know how to differentiate with fractions

[unkempt lodge]

oh wait sorry, gradient means slope i forgot huhu

[unkempt lodge]

use quotient rule

[hard kernel]

can soemone expalin triangular numbers and the bionomial theorem to me

[willow skiff]

do you still need help?

[acoustic apex]

Whats a gradient

[acoustic apex]

Triangular numbers are numbers that are triangular

[hushed sphinx]

An analogue of "slope" that works for linear functions of several variables.

[acoustic apex]

Oh ok

[willow skiff]

imagine you are climbing up some hill

the direction where you gain elevation the fastest is the gradient

[acoustic apex]

Ok

[hard kernel]

na ty though

[lethal lion]

4

[neon herald]

How do I know what to do first (stretch flip etc)

[dense zealot]

🤔 what exactly do you mean by this

What are you trying to do?

[neon herald]

We have to identify the parent function, then graph it, then graph the changes.

[dense zealot]

Im not sure where the confusion is here

Are you concerned with the manual graphing?

[neon herald]

Ye

I just don’t know in what order to do the things

Specifically the things outfrount

[dense zealot]

Oh well something nice about this parabola is that it’s in vertex form

[dense zealot]

Well I like to start with getting the important stuff down like your plotting a point for ur vertex

Do yk how to find the vertex?

[neon herald]

We already have it? I’m just trying to do transformations.

[dense zealot]

Well I thought the confusion was the order of transformations

[neon herald]

Ye?

[dense zealot]

You only have shifts in the horizontal and vertical axis

No stretches no compressions

Those are the only transformations

[neon herald]

I think I’m just gonna ask my teacher tomorrow

[dense zealot]

there’s a negative sign infront of (x+5) which suggests a downwards parabola…

💔

[willow breach]

you too have adhd?

i also, always, even now, have a video running in the background, when im doing something else.

[fallow hemlock]

yay transformations

translations come last

work from the inside-out

[neon herald]

Nah I’m just bored and wanted to watch a tornado vid while doing my hw

[willow breach]

can you help me in dms

[neon herald]

No sorry

[fallow hemlock]

correct me if i am wrong, but this should be the order:

\begin{enumerate}
\item horizontal shift: replace $x$ with $x - h$ (right $h > 0$)
\item horizontal reflection: replace with $-(x - h)$
\item horizontal stretch/compress: $b \cdot (\pm (x - h))$ (stretch by $1/|b|$)
\item input absolute: $|b \cdot (\pm (x - h))|$ (erase/reflect left of y-axis)
\item apply base $f$: $f(|b \cdot (\pm (x - h))|)$
\item output absolute: $|f(\cdot)|$ (reflect below x-axis up)
\item vertical stretch/compress: $a \cdot |\cdot|$ (stretch by $|a|$)
\item vertical reflection: $-a \cdot |\cdot|$
\item vertical shift: $\pm a \cdot |\cdot| + k$ (up $k > 0$)
\end{enumerate}

*for the form

[
y = \pm a \left| f\left( \pm b \left| x - h \right| \right) \right| + k
]

[obsidian monolith]

∫_M dω = ∫_∂M ω

[heady bluff]

This might be a bit vague but can anyone give me a basic overview of the essential topic areas to know about exponential and logarithmic functions?(I have a test tomorrow) and I’m doing a last minute review

Thanks!

[fallow hemlock]

firstly, do you know the definition of an exponential and logarithmic function?

[heady bluff]

Yes

[fallow hemlock]

what are they?

and also make sure you know your properties of exponents/logarithms too

aside from that do exponential growth/decay problems

you should be familiar with the limit and series definitions of e and e^x also

[heady bluff]

Exponential function is of the form y= b^x / y = a•b^x or f(x) whtever and b can never be negative if I’m correct

[heady bluff]

Yup

[heady bluff]

I’m working on tht tonight too lol

[heady bluff]

Kk

For logarithms it’s of the form log in base 10 usually X = Y

And X also cannot be negative too I forgot

And ik the basic stuff like how to convert between exponential and logarithmic form already so im pretty good with tht

[fallow hemlock]

how about telling me what the domain and range of log(x) are?

that should answer your question lol

[fallow hemlock]

there is another restriction on b

can you tell me what that is?

[heady bluff]

All real numbers?

[fallow hemlock]

oh if you didn't cover that in class, don't worry about it

they'll likely show up later in precalculus

[heady bluff]

Yea we didn’t cover limits U-U

So ig I’ll ignore tht part

[heady bluff]

Oh shoot wait no

The uh

Domain is

All positive numbers

Cuz since the domain can’t be negative

The graph doesn’t go below the x axis into the negative

[fallow hemlock]

nope

[heady bluff]

Mb I corrected myself here I was thinking of the range probably

Idk

Is that right?

[fallow hemlock]

range is all real numbers

domain is all positive real numbers

do you know interval notation?

you can write this as (0, ∞) for the domain and (-∞, ∞) for the range

( means greater than
[ means greater than or equal to
) means less than
] means less than or equal to

or do you use set-builder notation?

[heady bluff]

I do

[heady bluff]

Yes

[heady bluff]

We use interval notation

So when solving for equations of logs and exponential functions would I use the same properties of logs to rearrange and solve them?

[grim magnet]

Could someone please help me with this?
I don’t know if this is right 😭

[slow zinc]

@grim magnet so that cant actually be factored further from 2x(2x^2-x+3)

but your method is still wrong, the way you tried to do it is called slide and divide factoring

https://valenciacollege.edu/locations/lake-nona/documents/Method3-SlideandDivide.pdf

above is just a random pdf i found online on the correct method

[grim magnet]

Thank you but all three numbers have an X….🤔

[slow zinc]

?

2x(2x^2-x+3) cannot be further factored

the (2x^2-x+3) does not have x on all the terms

[fallow hemlock]

example?

[obsidian monolith]

Couldn't find an attached image in the last 10 messages.

Nov 12, 2025, 6:09 AM

[hidden birch]

,rccw

[heady bluff]

e^2x+1 = 200

How would I go about solving it?

[willow skiff]

do you mean e^(2x + 1) = 200?

$e^{2x+1} = 200$?

[obsidian monolith]

south

[heady bluff]

Yes

[willow skiff]

alright, what happens when you take ln of both sides?

[heady bluff]

Would the e and the ln cancel on the left and then the ln stays on the 200 on the right?

After I put the exponent infront of the ln infront of the e?

[willow skiff]

yep! the e and ln undo each other

[heady bluff]

Okay!

[willow skiff]

so can you write out the new equation you get then?

[heady bluff]

Yeah

(2x + 1) = ln 200

Right?

[willow skiff]

yep!

so then remember that ln(200) is just a number, like any other number

2x = ln(200) - 1

and so on

[heady bluff]

Oh ok

Ok I’m lost

[heady bluff]

Wht do I do from here on?

Divide?

By 2?

[willow skiff]

yep!

so to write this online you need brackets around the (ln(200) - 1)

on paper you don't need brackets cause you can write it as a fraction

[heady bluff]

So X = ln (200) -1/2 and then I simply to a decimal if needed?

[willow skiff]

careful

x = (ln(200) - 1)/2

[heady bluff]

Oh whoops mb!

[willow skiff]

no worries!

[heady bluff]

Tyy

For helping me

:)

[jagged dust]

Hi I'm new to pre calc any tips

[uncut mulch]

make sure you're 100% good with basic algebra

[heady bluff]

Hey

Is anyone available?

[tame elk]

hello

[hushed sphinx]

It is unlikely that anyone will promise to answer your question before you even ask it. The most reliably way to find out whether anyone is willing and able to answer a question from you is to ask it. That will give readers a chance to figure out whether they have an answer before they make any rash claims.

[tame elk]

hello troposphere how are you my friend

[hushed sphinx]

Do I know you?

[dapper harbor]

LOL😂

[hardy igloo]

I’m planning to start an electronics engineering university next year, not a native english speaker (though I’m at C1 level), and I’m looking for a good book to learn pre-calculus. Could anyone recommend one?

[fallow hemlock]

aops precalculus

if that's too difficult, read aops intermediate algebra first

or if you want something a bit more challenging, "basic mathematics" by serge lang

[fallow hemlock]

<@&268886789983436800> think this classifies as cheating

:)

[celest minnow]

Dude got reported

Lol

https://tenor.com/view/dancing-boy-cowboy-gotcha-finger-guns-gif-17948078

(in @fallow hemlock's mind)

[desert shadow]

Heyy, good night from my country.
Im looking for a book that clearly explains limits, functions and graphs. Do you know of any? 👀

[willow skiff]

yes, James Stewart's Precalculus

[bronze sorrel]

yes or no

[desert shadow]

Thank you✨️

[raw hill]

The idea is fine, but your use of the implication symbol and dropping the limit notation is off

\begin{align*}
\lim_{x \to 0} \frac{1 - \cos(3x)}{x^2 + 2x} &= \lim_{x \to 0} \frac{1 - \cos(3x)}{x(x + 2)} \
&= \lim_{x \to 0} \frac{1 - \cos(3x)}{(3x)^2} \cdot \frac{(3x)^2}{x(x+2)} \
&= \lim_{x \to 0} \frac{1 - \cos(3x)}{(3x)^2} \cdot \lim_{x \to 0} \frac{9x^2}{x(x+2)} \
&= \frac{1}{2} \cdot \lim_{x \to 0} \frac{9x}{x+2} \
&= \frac{1}{2} \cdot \frac{9(0)}{0+2} \
&= \frac{1}{2} \cdot \frac{0}{2} \
&= \frac{1}{2} \cdot 0 \
&= 0
\end{align*}

[obsidian monolith]

Civil Service Pigeon

[raw hill]

Something like this would be better

[bronze sorrel]

ok thanks

[void pine]

I just bombed my test -_-

[woven thicket]

everyone does, not many don't

[brisk mica]

Bro i feel like i couldve just skipped ap precalc, it feels so ez

[bronze sorrel]

u js like me fr

why do u use if and only if? ( <=> )

[hazy delta]

Manditory by our school and teachers

Because the propositions are correct in both ways

[bronze sorrel]

i guess

[hazy delta]

Not using an equivalency arrow is a wrong notation, they say

[bronze sorrel]

u can just exapand (x-1)(x+1)......

and say vx³

will be dominant

or does that not

if x € R and not N

[hazy delta]

It’s a rational inequation

the denominator can’t be 0

[bronze sorrel]

let me get my pen and paper

[hazy delta]

All the factors in the denominator must be ≠

[bronze sorrel]

and try to solve it myself

[hazy delta]

Okayy

[bronze sorrel]

@hazy delta

sorry for my messy writing

im on 2 hours of sleep

but see how the terms are +,-,+,-/-,+,-,+

that means that k/v ≤ 0

the other cases are just what ifs

pretty sure they will never be dominant unless maybe with x=1

i forgot

that its all Real numbers

maybe this doesnt if its all real numbers

[hazy delta]

Why are you expanding all of this

[fallow hemlock]

works but nobody does that lol it's kinda bloated

in solving inequalities, it's not strictly necessary unless you're emphasizing that each transformation preserves the solution set

you can simply use "→" or proceed step-by-step without any symbol, as long as each manipulation is valid

@hazy delta i can show you how i'd solve this

[echo kraken]

Im not sure if this is the right thread: But how do you find the last 2 digits of 7^3^2^(1/3)^(-1)^9^2^i^6? Saw this online (lost the source)

And another question: How should I solve x(4^x)=80? Online calculators work, but im not sure what are the steps and working.

[woven thicket]

From right to left you should be able to simplify the last 6 exponents

[echo kraken]

Which gives 7^3^8, right?

[woven thicket]

Yeah

From here probably some number theory tricks

[echo kraken]

... Like what? The issue is that 7^3^8 is... extremely large and the laws of indices dont help much from here.

[woven thicket]

Hm

7^3 end with 3

wait

[echo kraken]

I think we should look at the 3^8 part - given that its 7^(3^8)

[woven thicket]

I am, but haven't found anything useful

[hushed sphinx]

You only want the last 2 digits, so 7^(3^8) mod 100, and phi(100)=40, so by Euler's theorem you want 3^8 mod 40.

However 3^4=81 which is 1 modulo 40, so 3^8 is also 1 modulo 40, and you're now looking for 7^1 mod 100.

[echo kraken]

Which is 7.

[hushed sphinx]

Explicit calculation with a bignum calculator confirms that 7^(3^8) is a 5545-digit number that ends with ...,741,152,007

[echo kraken]

I see, thanks! Sorry for the trouble.

[hushed sphinx]

Was no trouble.

[hushed sphinx]

There's no good general symbolic method for that.
If we look for integer and then rational solutions by trial and error, it doesn't take long to find x=5/2 -- but if there had not been such a nice solution, there wouldn't really be anything to do but to approximate it numerically (say, by more trial and error, or bisection, or Newton-Raphson).
You can get tools like Wolfram Alpha to create a symbolic expression for the solution that involves the Lambert W function -- but for most practical purposes that is just a cop-out that says if you want actual digits you'll have to find them numerically anyway.

[dreamy basin]

Yo

I'm taking AP calculus

Next year 🥵

[lusty light]

hello

[runic dew]

is it difficult

[autumn spire]

no

[viscid thistle]

what does precalculus mean

[hushed sphinx]

It's a group of loosely connected topics that in American school systems are named for the fact that they are taught before calculus.
(Silly naming if you ask me, but what can you do?)

[viscid thistle]

ohh, mhm thanks. weird but then ok

[harsh rune]

highschool calculus

[woven thicket]

Okay I'm not sure what category this question is, so I just ask here. I remember a theorem states that there's always at least [I think] a prime between p and 2p, does anyone know what's it called?

[hushed sphinx]

Bertrand's postulate.

[magic wyvern]

anyone here a teacher that i can interview?

[jagged badge]

So im in middle school but i really like math and physics and i know basic differential and integral calculas but i always have this doubt that how is the differentiation of sinx = cosx
all yt teachers just said like its a formula i have to learn it but i want to know how it was like derived pls dont include too high level stuff

[modern wedge]

you can use the definition of a derivative

f'(x) = f((x+h)-f(x))/h as h approaches 0

put in f(x) = sin x

use a few identities and the fact that sin h/h approaches 1 as h tends to 0

[jagged badge]

oh thanks

and can u also tell a like a good yt channel that explains calculas from the basics in a interesting way language english

@modern wedge

[modern wedge]

no idea

the organic chem tutor maybe

[hazy delta]

Hello

I made somewhere an error

Can someone help me please ?

[woven thicket]

You can't conclude 2^x=12 or 2^x-1=12 from the line above

Or even not at all in this problem

[hazy delta]

Why?

They are both briggs log

Can’t you just cancel them ?

[woven thicket]

Wydm cancel them

[hazy delta]

there are log on both sides of the equations

OWWW

i see it

[woven thicket]

If x(x-1)=12 does that imply x=12 and/or x-1=12

[hazy delta]

it isn’t = 0

I’m stupid

My bad

Sorry

[stray lynx]

hey can someone help rq. I keep trying to so this and I get similar answers but never right on.

[hushed sphinx]

Could you explain what you're doing and which wrong answers you get?

(Also: weird bizarro world where interest rates stay constant for 15 years at a time and the interest is compounded continuously).

[winter comet]

Hey I wouldn't complain

[shadow mantle]

use the compound interest formula

[dusky oxide]

is this deltamath

[dreamy basin]

yes

[dreamy basin]

HELLLLLLLLLLLL NAHHHHHHHHHHH

I actually took it last year

I mean, this year but :v

🤡

its hard as hell

[magic mist]

Good luck soldier

[dry sierra]

I don't understand lmvt properly,what is it's main uses

[hushed sphinx]

"lmvt"?

[woeful cosmos]

i believe he means lagrange mean value theorem

[dry sierra]

yes

[stiff elk]

is the answer 2?

[raw hill]

You can check this yourself in #bots

,w remainder when x^10 + x^8 is divided by x-1

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[hushed sphinx]

In general, when you divide any polynomial p(x) by x-a, the remainder is always p(a).

(And here f(1) is obviously 2).

[stiff elk]

,w remainder when X^6-10 is divided by x-2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 1__shiny__1

[stiff elk]

is this how you use it?

[hushed sphinx]

Weird that it doesn't deign to show any result; it shouldn't be all that bad.

Ah, it's confused because you mixed X and x.

[stiff elk]

oh

[hushed sphinx]

https://www.wolframalpha.com/input?i=remainder+when+x^6-10+is+divided+by+x-2 gives an answer.

[stiff elk]

nice thank you

what I do is for the x - 2 I set it equal to 0 then use the 2 and plug it into f(x)

is this the right way or are there other ways?

[hushed sphinx]

That's generally the quickest if your divisor is of degree 1 and you just want the remainder.

[stiff elk]

alright thank you

[hushed sphinx]

It's not the only way, of course -- for example, you could use the generic polynomial long division method.

[stiff elk]

ok nothing to complicated thanks

[ancient kelp]

guys i just started into calculus can any of yall explain what its abt

[tender hare]

There are two parts of calculus. One is differential calculus and another is integral calculus. In differentiatial calculus i.e. derivatives u have to find slope of a line and its intercept point on respect to x axis. More clearly The derivative measures the instantaneous rate of change of a quantity with respect to another. It tells you how much a function's value is changing at a specific point.and in integral calculus u have to find areas of curve ,rectangles that represents a function in a graph. It's the inverse method of derivative. Thats it .Good luck

[honest canyon]

Any good lecture video of differential and integral calculus where they teach from basic also

[slow solstice]

I might need help later if I can’t do this homework right😭

This class is making me break down😭

[magic void]

Pre calculus

[sonic hill]

I find it makes more sense in terms of differentials, but yea

[slow solstice]

I think I got it finnaly😭

[storm halo]

Pre calc ts so easy 😭😭

yall tripping if you can’t get an A in this class forreal

[thorn leaf]

matrices are scary

[lone temple]

i havent known much about it yet but indeed it looks scary lol

[thorn leaf]

they terrify me

[lone temple]

also can someone explain me about chain rule, why is
[f(g(x))]'=f'(g(x))*g'(x)????

[drowsy citrus]

Well it isn't

[f(g(x))]' is equal to f'(g(x))*g'(x)

[sonic hill]

I mean, just kind of intuitively, whatever ypu change about the inputs of a function like f(x + 5), or f(5x) or f(g(x)), those operations transform the graph that's shown sure, but think about it like they're transforming the xaxis itself, and all the points on the graph follow along with it. So for f(g(x)), the function f is of course going to change at a rate f'(g(x)), but then you habe to also multiply it by the rate that the x axis changes now because of g, so you multiply by g'(x).

And this surely isn't precalc...

[lone temple]

sorry i wrote it wrong lol

[lone temple]

i find this channel to ask calculus only

[sonic hill]

Thats what #calculus is for

[sonic hill]

Does this make sense?

[modern zodiac]

Wanted to confirm if this question is correct or not?

If it helps, this question was taken from the UNSW Integration Bee 2022 Knockout Round-3 Question 2

https://assets.ctfassets.net/xv1hr0zszyo1/1Bui41TER2cQ6aUqTIuHbO/cd46c2114f0b5083102d5cdfef6b0536/Integration_Bee_Questions_and_Answers.pdf

[arctic prism]

does calculus help distracting me

[storm halo]

bitfh that’s not even pre calc

that’s like multi variable on steroids

[modern zodiac]

😭 but it's only 2 variables...

[storm halo]

oh!

well idk what type of pre calc YOURE learning but that’s like so complicated and im in honors pre calc

[modern zodiac]

I'm just a JEE aspirant that likes to tackle Olympiad problems i guess

[storm halo]

oh clock it

[left laurel]

What is 1+1

[hushed sphinx]

A fairly reliable recipe for being thrown out of a math server if that's all you appear to want to use it for.

[echo sinew]

10

[left laurel]

Ohhh

[echo sinew]

Or 1 of you prefer

Definitely not 2

[modern zodiac]

Everyone gangsta until you need to prove it

[hardy crypt]

1+1
1+succ(0)
succ(1+0)
succ(1)
2

[slow solstice]

Anybody know what the heck question 6 and beyond talking about😭 why does it have sin and cos😭

[swift sequoia]

the question asks you to solve the inequality of (2cos -1)(sin +1) < 0 then ig

[patent barn]

At least one side is already 0
So just use your tricks and summon the answer

[slow solstice]

😭

[woeful widget]

Somebody help me I got a test tmr …

[modern zodiac]

Can you send a more complete photo? I can't see the whole problem...

[honest marlin]

Can someone hop on a call with me and explain integration?

Kindly DM me, any help is appreciated

[gaunt sleet]

Someone teach me differentation

[echo sinew]

Be more specific

Do you have an exercise?

[gaunt sleet]

Like first principles

And what is ?

[echo sinew]

Also, differentiation is part of #calculus

[gaunt sleet]

Yh

[echo sinew]

Go watch Khanacademy or Organic Chemistry Tutor on YouTube

They explain everything from scratch

[gaunt sleet]

Ok

[muted widget]

Is this college algebra in your country?

[gaunt sleet]

What are topology

[echo sinew]

It's almost impossible and too many things to be taught here in Discord

[echo sinew]

! redir

[tender quest]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[hallow tartan]

id love someone to be my study partner that is doing atleast 3 out of the 5: maths, computer science, biology, chemistry, physics. I am currently in yr11 but im already learning as-level at home. I just finished as pure maths and am doing as physics and chem. I am actually decently smart. add me if u wanna be my partner and message me

[sonic hill]

I'm also doing those / have done them already :p

[hallow tartan]

Nice

[still brook]

what is 0.5% as a fraction

[winter comet]

what does % mean

[still brook]

percentage 💔

[winter comet]

what does that mean mathematically

💀

[still brook]

oh

1/100

[winter comet]

yeah, if its a percent you multiply it by 1/100

[still brook]

ok

so 5/10 x 1/100

[winter comet]

yes

[prisma ferry]

hi gang im severely uneducated in the world of calculus may i ask how do i start learning and what do i need to know before learning

im a 9th grader idk if that helps and i just like math and want to learn in advance

[gloomy vector]

I think if you have a solid grasp of these 3 then you’ll be good

[prisma ferry]

thank you!!

https://tenor.com/view/dance-yenkim-ivory-jokebear-nagano-gif-17607741496208810987

[gloomy vector]

I’m also in 9th grade but I’ve seen some visualization videos of calculus through YouTube and it’s really interesting

[gloomy vector]

You’re welcome! I hope that helped

[swift sphinx]

i just got a question, why do we sometimes add +C in different integration equations

[dense zealot]

integration is just the opposite of differentiation

whenever u differentiate a function that has a constant u just leave it out

we factor in that constant whenever we integrate

[swift sphinx]

oh ok

[somber void]

Alternatively, because to find area under a curve from an antiderivative you have to find F(x_2) - F(x_1), so if you have a constant there it's going to cancel out

[woeful widget]

Yes

[pearl hinge]

would anyone be able to hop in a vc and explain how to find limits and prove continuity using the epsilon-delta definition of a limit?

[normal saffron]

anyone got tips for learning permutations and combinations? really need some

[red ivy]

If you just want to learn integrals and derivates then go Source: Pauls Online Math Notes https://share.google/7C2503dXaoXcn7bN4

If you want to understand the concept behind calculus then watch some youtube videos
But i shud tell you that you should first learn limits and series before starting to integrate and derive as this will make it easier later on when u need to combine them

[red ivy]

There are like 4 theories for them

No point to get tips

[prisma ferry]

tysm!!!

[whole void]

wdym?

[red ivy]

Like there are only 4 theorems for those 2 stuff

[whole void]

I think there’s more than that, but it depends on what u want to do

[red ivy]

What are there
The formulas for both
Einsteins thingymajig and something im probably forgetting so thats 4

[whole void]

Einsteins?

I mean there are things like (n choose 0) + (n choose 1) + … + (n choose n) = 2^n

[somber void]

Yeah cuz that's the expansion of (1+1)^n

[red ivy]

Yeah

That

[whole void]

Sure, if u prove the binomial theorem

But the binomial theorem is harder to prove

[hushed sphinx]

It's so useful that it has to be proved anyway.

[whole void]

Yeah

another classic proof is thinking about making a choice of choosing or not choosing each of n objects

[magic juniper]

I just like to think of it as percent meaning over 100

that is it

[somber void]

I just like to think of it as a number % = 1/100

[sterile thorn]

Per cent means per hundred

So /100

[wispy widget]

Does the points where a function and its inverse meet always lies on y=x?

[somber void]

I don't think so

[echo sinew]

I'd say it's either on y = x or they're symmetric about that line

[somber void]

It has symmetry about y=x, but that just means any point that already were at y=x would map to itself by reflection, if it weren't on y=x it could conceivably map to some other part of the graph

[echo sinew]

For example y = -x which is its own inverse as well

[somber void]

On the other hand, I can't immediately think of a counterexample

Ok, y = -x and y = 1/x are counterexamples, but are there counterexamples that aren't their own inverses

Yes

y = 1/x^2 - x^2

So the answer to your question is no, but it does surprisingly often

[wispy widget]

Yeah you are right, but it's only false in case a function is same as its inverse , otherwise the statement is true

[somber void]

Wrong

This is a clean function, there is no multiple branches shenanigans or anything, and it isn't its own inverse

But it intersects its own inverse infinitely many times, and only one of those intersections lies at y=x

So if you want to try salvaging this conjecture, maybe consider limiting it to only polynomials, or saying that if it intersects itself, then there is at least one intersection at y=x or some other form of making it weaker

[willow skiff]

I'm pretty sure this works for polynomials as a consequence of FTA

[hushed sphinx]

How about 1-x³? It is invertible, but (0,1) and (1,0) are in the intersection between the graph and its inverse.

[willow skiff]

oh, good catch

yeah if you think about FTA, that implies that there can be a maximum of 2n intersections for a polynomial with degree n and its inverse, I hope

frankly there are just too many exam questions where they only intersect where y = x

cause those exam questions are contrived

[quiet juniper]

theres no calculus channel so idk if i can ask this here

dont need help just curiosity

but could anyone well versed in calc tell me if an infinite taylor series is actually "equal" to the function youre trying to "approximate"?

even if you cover the entire domain of the function hence the infinite part are there any small inaccuracies whatsoever throughout the curve of say sin(x)? or does it perfectly match sin(x) for every input of x?

im thinking that it isn't completely exact because we dont take the derivative at every value but maybe my understanding is wrong

[winter comet]

#calculus

[winter comet]

it is

the approximation is only for finite taylor series

[quiet juniper]

thanks idk why it doesnt show for me

[winter comet]

but an infinite taylor series is exactly the function

[quiet juniper]

good to know

[winter comet]

just like an integral is exactly the value of the area

[quiet juniper]

so if its finite it'll have inaccuracies

[winter comet]

not an approximation anymore

[winter comet]

yes

[winter comet]

if you grab the undergrad role you should be able to access all the channels

you don't need to actually be an undergrad to take the role you can have it if you're doing that type of math or just really if you want to lol

[quiet juniper]

alright i can see it now

[hushed sphinx]

#calculus is in the Early University category which is accessible even without any of the math-level roles.

It might not be shown in the channel list unless your choices in Channels & Roles select it, though.

[tough lake]

I am in grade 12 and learning pre calculus 12

I have found a new branch of mathematics called discrete math, set theory and mathematical logic

Pre calculus 12 never covers these topics

How important are these topics from a mathematical standpoint

I plan on taking calculus and learning lots of maths

[deft jetty]

set theory is a requirement for most math so thats very useful

the others can be useful as well

[round geyser]

You are in a similar situation with me

[modern zodiac]

The feeling when you apply Integral by parts and reach the original question again after 5 steps

[sonic hill]

??

[opaque spire]

Hlo

[signal crypt]

bye

[opaque spire]

Are you a maths expert

[signal crypt]

no

[opaque spire]

How much maths you know

[signal crypt]

how do yo measure it?

[sonic hill]

What's up

Do you need help with something?

[opaque spire]

Yes I am starting maths

After a long time

How much time it will take to master integration and calculus

[sonic hill]

It will depend on how much time you put toward it, but you could probably get through Calculus 1 through Calculus 4 in a 8-10 months to a year maybe if you go fast?

Maybe even faster than that, I'm not really sure. Why?

[opaque spire]

I have to give a exam for master which requires maths for entrance

😭8months

[sonic hill]

How much calculus do you need to know?

[spice aurora]

that should be a calc question

[tender quest]

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

[spice aurora]

1

[woven thicket]

Given side lengths of both square for example a and b, how can you find the shaded area?

Let just ignore the increase/decrease rate of those sides for now

[spice aurora]

okay let me try

[spice aurora]

yea i totally faild i dont know from where to start

[woven thicket]

We can get the shaded are by subtract the smaller triangle from the bigger one if you know what I mean

The base of both triangle are the same and heights can be found using Pythagore

[spice aurora]

oh i see it now

[spice aurora]

but i have to get the area in terms of a and b not numbers right?

[woven thicket]

Yeah

[spice aurora]

if a is small square Length and b big square then it should be A= 1/2 ab - 1/2 a^2

yea i guess it is wrong

[spice aurora]

is this right or not?

[round geyser]

Hey

There is 2 formulas you will use

Difference of cubes and Quadratic formula

[hidden birch]

quadratic formula is for finding roots

the original problem seems to be about factoring, not finding roots

it was a polynomial expression but not an equation (doesn't equate anything)

,rccw

[somber drum]

hi
say i had a line $y=-\frac{b}{a}x+b$ and i wanted the equation of a line parallel to it, thats offset by a vector of (a,b), how would i find it

[obsidian monolith]

Vq!

[willow skiff]

it would be easiest to use point slope form

[sonic hill]

Offset by a vector?

[willow skiff]

so just $y - 2b = -\frac{b}{a} (x - a)$ cause that passes through $(a, 2b)$ automatically

[sonic hill]

Do you mean it passes through (a,b) or that the line is somehow displaced some distance relative to one of its points?

[somber drum]

displaced

[willow skiff]

I'm assuming that they mean to translate every point on the line by the vector (a, b)

[somber drum]

yeah this

[sonic hill]

Then the line wouldn't necessarily pass through (a,b)

[willow skiff]

oh wait I did it slightly wrong

[willow skiff]

this originally goes through (0, b)

[somber drum]

whats that?

[willow skiff]

so you would want the line to go through (0, b) + (a, b) = (a, 2b)

[willow skiff]

search it up

[somber drum]

oh ok

[willow skiff]

the equation for a line with slope m to pass through a given point

[obsidian monolith]

south

[sonic hill]

uh

y - y1 = m(x - x1)

where (x1,y1) is the point you want the line to pass through and m is the slope

[somber drum]

ty :)

okay problem its not doing what i want it to do 😭

[willow skiff]

what do you want it to do?

[somber drum]

okay so i was trying to make a graph thats basically the pythagorean theorem, the squares a and b work fine but whenever a≠b the purple square (c squared) gets.. funky
the graph for reference

[sonic hill]

y = m(x - x1) + b + y1

Hmm

Shouldn't it be this?

Before the transformation it passes through (0,b), after the transformation it passes through (x1, b + y1), so point slope gives you y = m(x - x1) + b + y1

[willow skiff]

except that the vector is already (a, b)

[somber drum]

so like.. got any fixes 😭

[sonic hill]

Yeah?

The vector is always (a,b)

[willow skiff]

after the transformation it passes through (0, b) + (a, b)

[sonic hill]

y = m(x - x1) + b + y1 = m(x - a) + 2b

I just generalized

[sonic hill]

What I'm saying is that you wrote it wrong

It's not $y - 2b = -\frac{b}{a}(x-a)+b$

[obsidian monolith]

pebble

[willow skiff]

oh lol, corrected

[sonic hill]

it's supposed to be $y=-\frac{b}{a}(x-a)+2b$

[obsidian monolith]

pebble

[sonic hill]

lol

Assuming that -b/a is the correc tslope

[willow skiff]

yeah I edited my message too fast and it came out wrong

hopefully the most recent one works

[somber drum]

oh okay

[sonic hill]

Give this a try

[somber drum]

😭

[somber drum]

it infact did not guys

[sonic hill]

hmm, let me think

[willow skiff]

could you send the link to the Desmos graph?

[sonic hill]

What's the specification of this triangle?

Is it axis aligned, right triangle, what about the angles?

[somber drum]

here

[sonic hill]

Or do you just specify the a and b length

and a is the length along the x axis toward the right, b is the length along the y axis upward?

[somber drum]

a is the base length, b is the height

yes

[sonic hill]

That's it?

[somber drum]

yeah

[sonic hill]

Alright, so the slope would in fact be -b/a.

[somber drum]

everything ive done has worked up until finding the parallel line which is for c^2

[willow skiff]

I know why

you're not translating the line by a perpendicular distance of sqrt(a^2 + b^2)

[sonic hill]

$-\frac{b}{a}\left(x-\left(a+b\right)\right)+a$

[obsidian monolith]

pebble

[somber drum]

whagt

should i try that?

[sonic hill]

wait

hold on

[somber drum]

kk

[sonic hill]

I'm making a diagram to show you

[willow skiff]

https://www.desmos.com/calculator/2laklirhnp

I fixed it for you

[willow skiff]

$y-\left(a+b\right) = -\frac{b}{a}\left(x-b\right)$

yep!

[obsidian monolith]

south

[sonic hill]

You see, I've just taken the same triangle and moved it

[willow skiff]

they work out to the same thing

[somber drum]

oh

thank you 😭

[willow skiff]

no worries!

[somber drum]

thanks guys :>

[somber drum]

hi guys im confused again 😭

so i was labelling right, i was putting the values in the middle of the square but um, how do i get the coordinate for the middle of c²

[sonic hill]

You could average the four corners of c

[somber drum]

?

[sonic hill]

Like

[hushed sphinx]

@woven thicket please don't delete modpings -- that does not make the ping itself go away, and just makes it more difficult to have to look around to "why was there a ping in this channel".

[sonic hill]

The square c has four corners right? So add up the x components for each corner, and divide by 4 to get the center of the square in the x. Then do the same for the y components

[woven thicket]

Oops my bad, there was a scammer here but I pinged mod a bit late

[sonic hill]

$x_{\text{center}}=\frac{1}{4}(x_1+x_2+x_3+x_4)$

[obsidian monolith]

pebble

[somber drum]

oh

[somber drum]

it ended up being $\left(\frac{\left(2a+2b\right)}{4},\frac{\left(2a+2b\right)}{4}\right)$

[obsidian monolith]

Vq!

[somber drum]

or just

$\left(\frac{a+b}{2},\frac{a+b}{2}\right)$

[obsidian monolith]

Vq!

[sonic hill]

For c^2?

Or

the center of it?

[somber drum]

the centre

[sonic hill]

Interesting

yeah

makes sense

[somber drum]

its cause the points are
0,b
a,0
b,a+b
a+b,a

so for x its 2a+2b all over 4 and y is 2a+2b all over 4

[sonic hill]

yep

[somber drum]

this is probably just a desmos thing now but how could i display the actual area of a², b², or c²

[woven thicket]

hmm

[somber drum]

huh

[sonic hill]

Uhh

[woven thicket]

I was finding the center... just want to post another approach

[somber drum]

oh

[round geyser]

This is Pythagorean theorem

You sum the two squares and it will give you c^2

[somber drum]

ty

[hushed sphinx]

Interesting that the line to the center of the square on the hypotenuse always bisects the right angle.

[somber drum]

oh wait really

[sonic hill]

arctan(y/x) = 45 deg

very interesting indeed

[somber drum]

hi dude what if i wanted to show an angle on a graph from like any point

[sonic hill]

uh

probably use a circle

[somber drum]

what if like the angle changes....

frick im gonna have to use a bunch of stupid trig

[somber drum]

i finished it :) https://www.desmos.com/calculator/yfzogcjmbp

[ember ore]

hi

@everyone

oh mb wrong chat

[last pecan]

guys whats harder, Alg 2 or precalc

[icy verge]

precalc is harder i just moved to it from alg 2 anyway i like precalc more than alg2

[last pecan]

i hate alg 2

i hate pascals triangle

and dividing and subtracting and adding rational equations

[lost helm]

Can anyone help me qith calc

[willow bear]

you should post your question(s); and also we have a #calculus channel where you may have better luck.

[viscid thistle]

3

[sick crystal]

Guys can anyine help on this $y=\frac{1}{\ln^{2}\left(2x-1\right)}$

[obsidian monolith]

nomaidens

[sick crystal]

This is screwed

why is it shaped like that? how can i know how to sketch it on exam, for which x are y values positive..

[hidden coyote]

thats how it should look like on a graph

[signal crypt]

-4

[hidden coyote]

oh shoot yes

forgot to make it negative

[sick crystal]

so you used some derivation, on end it looks worse, and how do you still know how the graph looks?

the usual log graph looks very differently

[signal crypt]

,w differentiate (1/(ln^2(2x-1)))

[obsidian monolith]

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[round geyser]

,w graph log(x)

[obsidian monolith]

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[round geyser]

,w graph e(x)

[obsidian monolith]

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[round geyser]

,w graph e^(x)

[obsidian monolith]

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[round geyser]

,w graph ln(x)

[obsidian monolith]

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[dense mango]

how do one-sided derivatives work? in the original definition of the derivative, there's lim as h (growth) approaches 0. so how does h -> 0+ or h -> 0- make sense? I can't wrap my head around this

[somber void]

in normal derivative you pick point (x, f(x)) on the curve and then consider points (x+h, f(x+h)) where h is small (and approaches 0), but could be negative or positive.
For one sided it is either only positive or only negative. afaik

[grave flame]

Is there a book that could help me study pre calculus on my own

Do you guys know any?

[lost helm]

@grave flame use khan academy, books i don't know any that could help

Or actually use college prep books from the official website

[hushed sphinx]

This is #calculus rather than pre-calculus, but:
If the derivative exists at some point, the one-sided derivatives will also exists and have the same value. So they're not very interesting in that case.
It becomes more interesting then the full derivative doesn't exist. Then we might still be lucky enough that the one-sided derivatives do exist and can capture at least something about how the function behaves, even if it's not as nice as an actual derivative would be.

[celest lantern]

For question 9 what do I do after this?

I found the roc but how do I continue

[uncut mulch]

,rotate

[celest lantern]

???

[placid pebble]

,w graph log(x)

,w graph x^2+secx-1=y

[obsidian monolith]

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[placid pebble]

,w graph log(x)sin^-1(y)

[obsidian monolith]

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[bitter pier]

i am doing right guys?

[willow skiff]

the problem is that 1 - sin(pi/2) is still 0

but you can multiply $\frac{1}{1 - \sin x}$ by $\frac{?}{?}$ to make the denominator not have that problem anymore

[obsidian monolith]

south

[willow skiff]

and 0 * infinity is an indeterminate form

[bitter pier]

I just do this instead

i use pythagorean identities in the 4th line

[willow skiff]

that's wrong

$\sin^2 x (1 - \sin x) = \sin^2 x - \sin^3 x$

[obsidian monolith]

south

[bitter pier]

what part i got wrong?

[willow skiff]

you need to fix the denominator of your line 4

[willow skiff]

(ping)

[round geyser]

Can you distribute

[round geyser]

What I plug 0 in

[paper thistle]

fix here

[dense zealot]

<@&268886789983436800>

[tepid widget]

So it's 2 right?

[river drift]

@grizzled jewel this is a channel for on topic conversation about math. please keep memes in #chill

[echo sinew]

It's 4! - 5

Now stop trolling

#precalculus message @grizzled jewel

<@&268886789983436800>

[paper thistle]

Yes

[willow breach]

L'Hôpítal

[willow skiff]

#calculus

[modern zodiac]

Actually someone in #discussion wanted a question so I just posted it here for them

They didn't want to go to dms

[willow skiff]

I know but this is still the wrong channel

[modern zodiac]

Sorry, I'll use the correct channel from now on.

[unborn dune]

how do i find all theta this is what i have rn

i know sin theta can be 1/2 but that cancels out all cosines

and isnt the only solution

[red storm]

try using power reduction formula to write cos(t) in terms of sin(t)

i think it would help to add 0 inside the argument so it turns into a multiple of 2

[viscid thistle]

how to learn precalculus

[muted widget]

Go to school

[viscid thistle]

i do

[willow skiff]

Khan Academy

[viscid thistle]

https://tenor.com/view/sad-cat-cat-in-front-of-sea-gif-16930437336998530733

[viscid thistle]

aiht

[errant shard]

Erm why can't I access the calculus channel??

Pre uni thing, no?

[acoustic apex]

Can you see #calculus? You may need to enable it in id:browse

[errant shard]

Ah, ic

My mistake

[pine geyser]

Interesting method but there is actually an easier way to do this problem. See how those 4theta and 2theta are basically "3theta + theta" and "3theta - theta"? Use this type of prespective to solve the problem!

[umbral dew]

godayumm

ong genius

[willow skiff]

who can spell prosthaphaeresis without looking it up

[pine geyser]

😭😭

[umbral dew]

thinking out of the box bro

[main bone]

I can spell pneumoultramicroscopicsilicovolcaniosys without looking it up yet I have never heard of that word

[median spear]

even I can do it!

it's easy to spell and the only time I heard it was in a TV show

[fading iris]

I love adding prefixes and suffixed to make words

Priorianticircumnavigationalisticians

[autumn harness]

i mean i guess bro

[thick blade]

huh..

same answer different approaches

[round geyser]

How can a trig equation relate to unit circles

[willow skiff]

by definition, cos theta is the x-coordinate of a point on the unit circle, and sin theta is the y-coordinate

[tepid widget]

It originates from circles

[somber void]

because trig is about angles, and angles are defined as paths along a circle

[round geyser]

That’s linear

And I get 0.71…

[sonic hill]

What's linear?

[round geyser]

That rim that touched (cos,sin)

[sonic hill]

.71 for what?

[round geyser]

Sqrt(2)/2

[sonic hill]

Mhm

What's the issue?

[round geyser]

I wonder is that the invention of trig

Like as radical

Like linear graph goes through 30 degree and 210 degree

I wonder how many degrees does quadratic goes through

[sonic hill]

Uh

Well the idea is kind of a ray that rotates about the origin

not a parabola

[silver mason]

how is this the same