precalculus

[winter comet]

fr fr

[honest aurora]

um

0

[winter comet]

wait

no

thats too easy LOL

also its not 0 ☠️

[honest aurora]

OH ITS NEGATIVE ONE

[winter comet]

🤣

[honest aurora]

OMG BYE I CANT CALCULATE SHIT TO SAVE MY LIFE

[honest aurora]

in my defense im computing limits and listening to Mr Vampire simultaneously

[winter comet]

🤣

[winter comet]

mr vampire?

[honest aurora]

it's a song

[winter comet]

ah

[honest aurora]

DNE

[winter comet]

uhhhhhh

[honest aurora]

yea im pretty sure it doesnt exist

[winter comet]

oh

because

if its more than 2

approaching 2 from the...right

then its 4ln(2)

[honest aurora]

yea

[winter comet]

and if its approaching from the left

its ln2

[honest aurora]

and from the left it's just ln(2)

[winter comet]

right

i mean left,

but correct

💀

yea

[honest aurora]

more limits?

[winter comet]

ahh

conjugates

ehh this ones easierish but yea

paper time

[honest aurora]

2/5

[winter comet]

bruh

[honest aurora]

conjugate the top

[winter comet]

i literally just went to get a piece of paper

[honest aurora]

u get 2x - 6

factor using 2

simpify the x-3 s

[winter comet]

i get 1/2...

[honest aurora]

you get 2/ (the stuff on the nominator but with a +1 instead of a -1)

[winter comet]

oh

wait

[honest aurora]

I mean I did it in my head while listening to NOT OKAY so you might have the correct answer

but I dont see any mistakes in what I did so

[winter comet]

im doing paper math, wait 2 hours while i complete this problem that you did in ur head in like .2 seconds

anyway

💀

[honest aurora]

so is it 1/2?

[winter comet]

im still doing it

[honest aurora]

shit

wait

yea it's 1/2

why did I think that square root expression was equal to 3 💀

[winter comet]

no its 1

💀

the denominator is 2

[honest aurora]

EVEN IF IT DID WHY DID I THINK 3 + 1 IS 5

[winter comet]

but dont forget the numerator also 2

[honest aurora]

💀

[winter comet]

oh

wait what

[honest aurora]

oh yea

yea it's 1

bro im so slow

[winter comet]

yeah its 1

its correct when i put it in

[honest aurora]

UGH LISTENING TO MUSIC AND DOING MATH AT THE SAME TIME IS NOT A GOOD IDEA

[winter comet]

🤣

[winter comet]

IN UR HEAD

[honest aurora]

ok send another limit and I'll try solving it in my head too

[winter comet]

we both got it wrong in head

until we didnt

[honest aurora]

with music too

[winter comet]

its probably good

for

brain

brain exercise

[honest aurora]

yay brain workout$

[winter comet]

https://tenor.com/view/spongebob-squarepants-chest-bust-rip-shirt-gif-18233808676138016499

💀

[honest aurora]

this my brain rn

[honest aurora]

💀

[winter comet]

do THAT in ur head

[honest aurora]

I can one sec

[winter comet]

💀

br

[honest aurora]

1/4

oh wait

or 4

lemme redo it

yea it's 4

100%

4

limit is equal to 4

basically the same thing

conjugate the bottom

simplify the x-3 s

[winter comet]

yea

4

ur right

💀

[honest aurora]

YAYAYAY BRAIN WORKOUT

[winter comet]

i forgot to cancel out numerator and denominator bruh

i was like whaaaaaa

🤣

[honest aurora]

what can i say

[winter comet]

wait its not 4??

[honest aurora]

IT ISSS PLEASEEEE BE FOURRR

[winter comet]

naw its wrong

💀

[honest aurora]

no yea no it's four 100%

[winter comet]

its the answer i got on paper

[honest aurora]

HUHHHHHH

[winter comet]

but its not right

😔

we made boo boo

[honest aurora]

no it is

whats the answer then

[winter comet]

idk im figuring it out

[honest aurora]

lemme plug it in wolfram alpha

im like 100% sure it's 4

[winter comet]

🤣

oh

its -4

💀

i bet

lemme plug it in

yeah 💀

cuz the denominator is 3-x

bruh 💀

[honest aurora]

HUHHHH ITS NEGATIVE FOUR?????

[winter comet]

yea

[honest aurora]

ooooooh yea

💀

[winter comet]

(x-3)( 2 + sqrt(x + 1))/(3-x)

yea

💀

[honest aurora]

BRUHHHHH WHY AM I LIKE THIS

[winter comet]

🤣

[honest aurora]

UGH I WAS SO CLOSE TO A SUCCESSFUL BRAIN WORKOUT

send another one

this one will be the one

[winter comet]

bro like did a pull up but didnt get his chin over the bar fr fr

great analogy

[honest aurora]

💀

I GOT EVERYTHING OVER THE BAR

[honest aurora]

LIKE MY WHOLE BODY

EXCEPT THE CHIN

[winter comet]

bro did a flip over the bar except he kept his chin under 💀

[honest aurora]

-5

wait

that was a guess wait lemme actuaklly do it in my head

no yea

-5

same thing as the previous one

YAY SUCCESSFUL BRAIN WORKOUT

ugh I feel my brain gettin dat pump

[winter comet]

no

💀

[honest aurora]

💀

im gonna literally 🔪

[winter comet]

🤣

lets be fair

im doing this on paper

ur doing it in ur head

like 5x likelier to maek a mistake

☠️

likelier is a word??

bro i may gtg soon

if u want accept dm

if u dare.... 🫡

[honest aurora]

okay im goin on paper

[winter comet]

🤣

[honest aurora]

I dare

[winter comet]

https://tenor.com/view/luke-gif-20623705

[honest aurora]

I added u

[winter comet]

🤣

alr

[pure apex]

This is my fav precalc question ever. I found it to be beautiful and thought you would like it. Note- I am not asking for help, just sharing it.

[obsidian monolith]

ethan_m_c

[pure apex]

Solution marked as spoiler below:

||Note that $\operatorname{lcm}(18,48) = 144.$ So, [(zw)^{144} = z^{144} w^{144} = (z^{18})^8 \cdot (w^{48})^3 = 1.]Hence, every element in $C$ is a 144th root of unity. Conversely, consider an arbitrary 144th root of unity, say [\operatorname{cis} \frac{2 \pi k}{144}.]Note that $\operatorname{cis} \frac{2 \pi (2k)}{18} \in A$ and $\operatorname{cis} \frac{2 \pi (-5k)}{48} \in B,$ and their product is [\operatorname{cis} \frac{2 \pi (2k)}{18} \cdot \operatorname{cis} \frac{2 \pi (-5k)}{48} = \operatorname{cis} \frac{2 \pi (16k)}{144} \cdot \operatorname{cis} \frac{2 \pi (-15k)}{144} = \operatorname{cis} \frac{2 \pi k}{144}.]Therefore, every 144th root of unity lies in $C,$ which means $C$ is precisely the set of 144th roots of unity. It follows that $C$ contains $\boxed{144}$ elements.||

[ember garden]

help in this

[willow bear]

these black bands were like 2 times taller than the image itself

does the problem say that [ ] denotes the floor function? @tender crest

[tender crest]

Yes it is greater integee fubction floor function sorry for not writing jnti english

[willow bear]

ok

so, progress?

also what's the lower boundary on the integral? i can't read it and i can't tell if it's 0, pi or something else.

[tender crest]

It is π

And upper one is 2π

[willow bear]

the upper boundary was legible enough.

ok.

[tender crest]

Sorry for bad picture

[willow bear]

so, progress?

[tender crest]

Soooo i guess i have to make some partition wherre it changes values

At π sinx is 0

And at 2π it is alos 0 but it will be below x axis

[willow bear]

what range of values does 2sin(x) take on the interval [pi, 2pi]?

[soft swallow]

why is it in some other lang

[zealous mango]

can someone help me with precal parabolas

[tender crest]

[0,-2]

I dont know how to find the point where it cross -1

[sleek path]

plot the graph of 2sinx first, its a good first step, then try to figure out on ur own from there

just remember the definition of greatest integer function

and what definite integration means

[willow bear]

2sin(x) = -1, x = ?

[tender crest]

Ohh lol
5π/4

[willow bear]

2 sin(5pi/4) = ?

[tender crest]

Noo

[sleek path]

plot the graph

[willow bear]

2 sin(5pi/4) is -sqrt(2), not -1.

[sleek path]

plot the graph of 2sinx

then try to understand what gif means on applying on that function

honestly i feel like if you are asking some of these questions its better you first understand how gif is used and its applications

[tender crest]

Yes it is done

[sleek path]

i feel like u are skipping topics

[tender crest]

True

[sleek path]

this q is a mix of functions trigo, functionn and integration

u cant just skip steps

if u wanna do integration complete ur NCERT textbook

do the basics first

[willow bear]

what?

[tender crest]

Sinx=-1/2
Sin(π+π/6)

So 7π/6 will be -1

[supple fjord]

are limits precalculus?

[willow bear]

bad wording.

also 7pi/6 is not the only point.

[tender crest]

11π/6 also

[willow bear]

and you tell this only after i ask like 4 times, why?

[tender crest]

I was drawing this...ahh my bad

Slow learner 😝

[willow bear]

slow learner ≠ slow responder

also your fingerwriting is almost illegible.

[tender crest]

By solving i got -5π/3

[river anvil]

I honestly dont understand the mark scheme, so some how from (i) they've gotten the value of 3root3, which in my understanding they've factored out 4/rootx and then multiplied by R, but I dont see the method, how did you cancel, how was R brought into it?

The second part is just to find the value of a which ironically is easier than the first part as it's necassarily quite straight forward

[raw hill]

$\frac{4}{\sqrt{3x}}=\frac{4}{\sqrt{3}\sqrt{x}}=\frac{1}{\sqrt 3} \cdot \frac{4}{\sqrt x}$

[obsidian monolith]

Civil Service Pigeon

[river anvil]

So they split the fraction giving the original curve and a new 1/3x, now how did they multiply it by 9

where did that come from I understand it's the area but how is it related to 1/root3

[river anvil]

I'm trying really hard to understand, but why, how have they related that area to this enitrely different cruve even if its bound by the same x coordinates

becasue my immediate instinct is to solve for a with the given curve given R is 9 and then solve for part a, and yet they dont do that?

the seperate the fraction and multiply by 9

[primal girder]

Is it just me or are they explaining the domain wrong? i got the right notation but it's saying that the domain is all real number less than -4, even though the notation says x=>-4, x not 4

also this other homework answer

I'm not wrong for saying that f(4) = 34 correct?

could u ping me if ur able to answer :')

[pine geyser]

Yeah they probably have made mistake, if the question is to find the domain of 1/sqrt(x+4), then your answer should be bigger than -4 and not -4 itself

[pine geyser]

Yes f(4)=34, I guess the writer was high while writing the answers 💀

By Making two mistakes...

[tranquil inlet]

Can someone explain real nth roots to me (ping plz)

[chrome ether]

what is there to explain? be specific

[willow bear]

what is up with the numerator?

[tender crest]

I differentiated and put the limits

[willow bear]

did you use l'hôpital??

the integral looks easy to calculate directly...

and how did you get 0 on the bottom then?

[tender crest]

Yes

Sin(π-π)

[willow bear]

you didnt use l'hôpital properly

[tender crest]

I got it

Hang on

[willow bear]

setting aside the fact that i think it's unnecessary here

you should have differentiated the denominator as well

and you didnt do that

[tender crest]

So first i have to put the value of limit before L'Hospital

[willow bear]

...

no, that's even worse.

or

ok wait

NOW i get what you're talking about.

took me a minute.

[tender crest]

When i integrated

I found numberator is not going to 0

[willow bear]

... your work is still wrong, but this limit actually doesnt exist.

from putting $x = \pi/2$ directly, you'd get $\frac{1}{2}\pi^2 - \frac{1}{8}\pi^2$ in the numerator

[obsidian monolith]

Ann

[tender crest]

Yes that is what i was saying

Which is not 0 and we can't use l'hopital?

[willow bear]

not pi - pi/2

but yes, we:

• can't use l'hop
• and don't need l'hop anyway

[tender crest]

So limit doesn't exist as it goes to infinity

It should be
(π^2/4 - π^2/16 )/0

[tender crest]

Am I right?

[willow bear]

i don't know where you got the extra 1/2 factor from on the top

but yes you're right the limit doesnt exist

the one-sided limits will be +∞ and -∞ (but dont ask me which is which. i dont care)

[tender crest]

I first integrated then i put π/2

[willow bear]

do you want to go over the same limit 19 more times

[tender crest]

Please check each step

[tender crest]

I don't know how you got this maybe you put the limit after l'hopital which is incorrect

[willow bear]

no

i did not use l'hôpital

[tender crest]

How you removed integration?

[willow bear]

oh

wait hold on

x goes to pi/2 not pi. my bad. got confused over all this shit.

[tender crest]

May I ask another question?

[willow bear]

you did, just now.

[tender crest]

How to compare logrithm?

[willow bear]

$\log_a(b) = \frac{\ln(b)}{\ln(a)}$, and $\ln$ is an increasing function.

[obsidian monolith]

Ann

[willow bear]

so you are asked to sort the list $\frac{\ln(\alpha)}{\ln(10)}$, $\frac{\ln(\alpha)}{\ln(3)}$, $\frac{\ln(\alpha)}{\ln(2)}$, $\frac{\ln(\alpha)}{\ln(e)}$

[obsidian monolith]

Ann

[tender crest]

Damn

You made it too easy for me thanks for lighting my brain 🙄

[tender crest]

If we have 3 letters and 3 address envelopes then what is the probability one envelope goes to its correct envelope letter

So here i made this
Letters ABC and envelope 123
So
a1,b2,c3
a1,b3,c2
a2,b3,c1
a2,b3,c1
a3,b1,c2
a3,b2,c3

[willow bear]

do you want exactly one correct envelope, or at least one?

[sleek path]

limit doesnt exist, also make sure to always check the condition before applying l'hopital

[tender crest]

At least one

[willow bear]

a1,b2,c3
a1,b3,c2
a2,b3,c1
a2,b3,c1
a3,b1,c2
a3,b2,c3

[tender crest]

I did that's why my answer is correct

[willow bear]

from this list, count the arrangements in which at least one letter is put in the right envelope.

[sleek path]

the fact u applied l'hopital on 1/0 form proves u didnt 😭

[tender crest]

What envelope is right place?

I am stuck at this counting actually

[willow bear]

So here i made this
Letters ABC and envelope 123

presumably, letter A belongs in envelope 1, letter B in 2, and C in 3.

[tender crest]

Thank you ann

[primal girder]

okay thank you 🥲 !!

[tender crest]

#help-46 message

I didn't get any answer

[ocean briar]

Guys how can I ask math question

Do I just ask here

[obtuse dagger]

@steady sun I just saw your reply; figuring out how 1/4 was extracted from 1 - x^2/4 (and then multiplying 4 by √1/4) required a little bit of abstract thinking on my part. Nevertheless, I understand how the final answer came to be.

Thank you

[earnest crystal]

Can someone explain what I’m missing here?

[summer ruin]

it's not even clear what you're trying to do and what is your final answer

[earnest crystal]

My bad

[earnest crystal]

The goal was to find the values which satisfy the inequality

I’ll have to redo it more neatly and post again

[winter comet]

you're missing the prompt 💀

[shrewd oyster]

when solving for slant asymptotes we have to simplify fully first right ?

[proven void]

what does supremum infimum mean

[exotic barn]

when it comes to seq. supremum is defined as the lowest upper barrier and infimum as the biggest lower barrier

[willow bear]

!xy

[tender quest]

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

[willow bear]

"supremum" and "infimum" on their own mean "lowest upper bound" and "highest lower bound" respectively, but you HAVE to show us where you saw these words in direct succession.

[obsidian monolith]

xbz24

[willow bear]

show me where you saw the words

upper bound implies ≥ 1

(or triple-check the questions that you ask, in order to ensure that you are asking exactly the thing you want to ask about, and not some nonsense)

...

why are you deleting everything now

@proven void what is this

why are you on a deletion spree

[proven void]

I am just confused how to start "a)"

[willow bear]

but why did you delete your entire half of the convo there??

???

how does this "not disturb" it???

???

?????

[proven void]

sorry

[willow bear]

you're literally causing MORE disturbance by doing this deletion thing

dont

dont delete any of your msgs for this convo

please

[proven void]

im sorry

[willow bear]

the statement "1 is an upper bound of A" is, by definition, the same as "every element of A is ≤ 1".

[proven void]

how do I check that?

we know that n is in N

[willow bear]

what form do all the elements of A have?

this is your chance not to miss parentheses

[proven void]

sorry

[willow bear]

dont apologize

answer my question

[proven void]

they are in natural form

[willow bear]

no, that's not what i'm asking. no, that's not what "form" means.

i was expecting you to read the other part of the set notation

n/(n+1)

[proven void]

. . .

[willow bear]

your set A consists of all values taken by this expression as n ranges over the naturals.

[willow bear]

is something wrong?

[proven void]

mmm

[willow bear]

yes/no/can't say?

[proven void]

how can we use the fact that n is a natural number, i.e. non zero

?

[willow bear]

is something wrong? yes/no/can't say

[proven void]

yes.

[willow bear]

... are you agreeing with the replied-to message? or are you saying "yes, something is wrong"

<@&268886789983436800> scam

[proven void]

mmm

[willow bear]

ignore that one

they are a scammer

i want to know two things:

1. why are you acting so avoidant around me?
2. why won't you tell me what is wrong?

[proven void]

avoidant. . .?

I just want to know how can we use the fact that n is a natural 😁

[willow bear]

you were deleting your messages left and right earlier

and now you are not answering my y/n questions

which i find strange

[edgy flare]

Drama

[willow bear]

why would you not do that

[proven void]

mmm sorry I missed one of them, can you resend it

[proven void]

sorry.

[willow bear]

im not looking for apologies

when i sent this, you said "..." (pictured here)

was this because something was wrong?

yes/no/can't say

[proven void]

no.

[willow bear]

ok then why was it?

[proven void]

?

[willow bear]

???

i am more confuseed than ever now.

ok whatever.

let's try to get back to the problem

you want to show that for every n ∈ N it is true that n/(n+1) ≤ 1.

this should not be hard if you don't overthink it.

[proven void]

mmmm

[edgy flare]

Take the limit when n goes to infinity , is 1

[proven void]

we know that n is nonzero

we can do some algebraic manipulations to this inequality

[edgy flare]

Suppouse the contrary , that is >= 1

Multipky by n + 1 both sides

[willow bear]

yes that is exactly what you can and should do

[willow bear]

unnecessary

[edgy flare]

There are different approach

[willow bear]

you do not need to assume anything towards a contradiction when the exact same argument that follows can be done directly.

[exotic barn]

this doesnt prove 1 is and upper bound

[willow bear]

so it is just silly.

we know n is natural, thus we know n ≥ 0, and thus n + 1 ≥ 1.

so multiplying both sides by (n+1) produces an inequality equivalent to the original.

and the new inequality is n ≤ n+1, which is obvious.

[proven void]

... is n <= n+1 true?

[edgy flare]

I was proving that n / n+ 1 <= 1 and that is one way

[willow bear]

is it?

do you doubt it?

"yes i doubt it"/"no i don't doubt it"

[proven void]

can't say

i.e.
n = 2
2 <= 3 .

but this is only true for naturals maybe

[willow bear]

i mean, n is natural, so even if this happened to be false for non-natural n, it wouldn't bother us.

(but n ≤ n+1 is true even if n is allowed to be real)

[edgy flare]

n <= n + 1 <=> 0<=1

[willow bear]

(as should be clear if you, again, don't overthink)

[proven void]

now what?

b?

[willow bear]

you first have to confirm that you are OK with part a) and have no further questions

[edgy flare]

How can you write so fast

🫠

[proven void]

its ok

I think i understood a)

its OK and i have no more questions for a)

for*

is there an element a from A which satisfies 0.9 < a < 1?

no

since naturals start from 1

[willow bear]

many years of practice?

i've got like 90 wpm in english

[willow bear]

you are confusing n with n/(n+1)

it is n/(n+1) that needs to lie between 0 and 1. NOT n itself.

make sure to read the entire question carefully.

such misunderstandings can only really arise from misreads.

[proven void]

how do I check
0 < n/(n+1) < 1
inequaility holds?

whaat?

[proven void]

mmm

[edgy flare]

n / n + 1 = 0.99 , n = 0.99n + 0.99 , 0.01n = 0.99 , n = 99

[willow bear]

er. sorry, 0.9 and 1, not 0 and 1

[willow bear]

missing parentheses.

also you were lucky to pick 0.99 and not some other value.

[edgy flare]

I know girl but i am on phone

[willow bear]

so this is bad.

also being on your phone is NOT an excuse not to type parentheses.

your keyboard most certainly has them.

[edgy flare]

It is

[willow bear]

but ok i'll just let you handle it if you think you can help better than me

[edgy flare]

I am not familiar with writting good as you

[edgy flare]

No i am not trying to. , i like how you explain

[exotic barn]

maybe you shouldnt write then and let the professionals work

[willow bear]

i'm gonna be honest like

[exotic barn]

😎

[willow bear]

it's not that you shouldnt be trying

but right now you are getting in my way

and making it harder for me to deliver my explanations and address @proven void's doubts

[edgy flare]

I understamd , thnx for being honest

[edgy flare]

Tf dude get a life

[willow bear]

anyway, where were we

since you know by part (a) that every element of A is ≤ 1

for part b, you need to find at least one value of n which satisfies n/(n+1) > 0.9

which again is a matter of algebra

and i will reiterate that you should not overthink it

you are currently overthinking it a lot

[proven void]

$ \frac{9}{10} \times (n+1) < n $

[willow bear]

\frac

also drop the <1

$\frac{9}{10} \times (n+1) < n$

[obsidian monolith]

Ann

[willow bear]

im gonna leave for now bc i would rather not indulge in your algebraic overthink habit

[proven void]

$\left(\frac{9n}{10} + \frac{9}{10}\right) < n$

[obsidian monolith]

xbz24

[proven void]

$\left(\frac{9n}{10} - n \right) < -\frac{9}{10}$

[obsidian monolith]

xbz24

[proven void]

$\left(9n - 10n \right) < -9$

[obsidian monolith]

xbz24

[proven void]

,,\left(-n < -9\right)

[obsidian monolith]

xbz24

[proven void]

,,\left(n > 9\right)

[obsidian monolith]

xbz24

[proven void]

wtf

[exotic barn]

nice

also funny how you did everything here

see there are infinite many solutions

[proven void]

interesting

let me check

,w 0.9 < 10/11 < 1

[exotic barn]

for very big n you still get a number below 1

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by xbz24

[proven void]

thats so great.

[zealous mango]

can someone help me with an ellipse equation

36x^2+9y^2+48x-36y+43=0

i just have to put it into standard form

[exotic barn]

try to group the terms and then you need to complete the square, do you know this method?

[steady sun]

np man, happy to help, its a little unusual but it just needs a little gettin used to.

[zealous mango]

yes, this is what i did but i’m sure i did something wrong i just don’t know what

[worthy ocean]

dont you use de moivre's theorem to find the foci if it is complex

[compact spade]

Help 💀

So obviously u = v (no shit) but what's the process for proving it

[edgy flare]

Find coordinates

If given two points , the start and end of a vector

You can find it's coordinates with formula

[compact spade]

I know the coordinates - it says them

But I'm just unsure how to structure it as a proof

Or in any mathematical way

[river drift]

two vectors are equal if and only if each of their components are equal

[compact spade]

Yes

I understand that

But how do I write it down?? What process do I go through to prove that on paper?

[river drift]

find the components of u and v individually, then if each component is equal that shows that u and v are equal

[compact spade]

Ok got it tysm

[edgy flare]

they have same coordinates so they are equal

[exotic barn]

The good thing is you completed the square almost, you need to add the terms from the left side also on the right side, otherwise you lose the previous equality and equivalence and things go wrong.

So basically, you are missing a

+36 • (4/9) on the right

and a

• 9 • 4 on the right

[broken ermine]

need help with finding answersss

[exotic barn]

bro just did his homework lmao

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[steady mesa]

Hello! I'm new to Pre-Calculus, does anyone have tips about what to do? I just got accepted into the class not too long ago.

[tranquil inlet]

For ellipses is A always on the x axis and B on the y axis?

[icy solstice]

No, they can be in any pair of ortogonal lines

[broken ermine]

thank you kind sir

[broken ermine]

🤫🤫🤫🤫

[lethal palm]

What exactly is the dx in an integral? More precisely, why is it the same as in dy/dx? because when we do a change of variable, we get dx = something, and on our integral we replace that dx with that something, and I don't really understand it, I've been told it is just a notation, but if it is, then why do we multiply by it

been trying to look into it but didn't understand

[summer ruin]

why is it the same as in dy/dx?
because there's not enough letters in the alphabet and we use same letters to denote completely unrelated things

then why do we multiply by it
because it's easier to remember this way

$\int f(g(x)) g'(x) \dd x = \int f(u) \dd u$, this is all there is to $u-$substitution

[obsidian monolith]

Transparent Elemental

[lethal palm]

hmmm

so the multiplying by dx is just a trick?

there is no deeper meaning?

[willow bear]

it is a notational device, i'd say.

[summer ruin]

dx in the integral doesn't even mean anything in particular

[lethal palm]

in a definite integral, is it not like a very small change in the x values? because it is the sum of infinite rectangles, and dx is the base?

[summer ruin]

well if you say each base has a finite length, then you don't recover exact area under the curve, but only approximate it

if you say each base is "infinitely small" then it's not possible in the first place

and it doesn't participate in actual computation of the integral either (unless you're doing it by definition at which point dx doesn't even appear anyway)

[river drift]

the notation (both for derivatives and integrals) was developed by leibniz, who used "dx" to refer to an "infinitesimal change". modern definitions of calculus no longer relies on "infinitesimals", so they don't really mean anything anymore, although it can sometimes still help intuition to think of it that way

[zealous mango]

i did do that and then i got a 9 on the right

[exotic barn]

ok

well then the rest looks fine by me

btw b = 1/2 not 1/16

1/4 = (1/2)²

[broken ermine]

guys I also need help with these

[blissful dune]

hello

[vestal bison]

are u a high schooler?

[tender crest]

If there is any other good short method for rational function monima maxima please suggest

[hallow tide]

other methods exist i guess

but the one you used here is the standard method... and it is already fairly fast

so there is not much to complain about imo

though. smth i can think of that makes this fairly simple is
consider D ≥ (x^2 + x + 1)/(x^2 - x + 1) ≥ C
then, C and D are the roots of the discriminant of (1 - C)x^2 + (1 + C)x + (1 - C)
the discriminant is (1 + C)^2 - 4(1 - C)^2, whose roots are 1/3 and 3
therefore the rational function has a minimum of 1/3 and a maximum of 3

[tender crest]

how did you get it? (1 - C)x^2 + (1 + C)x + (1 - C)

@hallow tide

[sleek path]

in the second term

divide num and denominator by

x

apply AM GM

u can get one of the extremes

[tender crest]

?????

how?

[sleek path]

it becomes 1+[(2)/(x+(1/x)-1)]

u would need to modify AM GM a little tho, but its the price to make the q shorter

theres actually another way

which directly gives u the whole range

[sleek path]

ghost ping??

[silk needle]

hiya guys

is there any way I can slove the following polynomial by factoring?

6x^3 - 23x^2+ 9x + 18

[warped cipher]

factor by grouping

or you could do rational root theorem if you learned it

[silk needle]

how do I factor by grouping if 23 is prime?

thats where im held up

[silk needle]

the original eq is

[silk needle]

this reduced one I found thru synthetic division

[warped cipher]

sorry just finished dinner

[warped cipher]

careful there's gcf

in group 6x^3-23x^2

[warped cipher]

what did you divide it by? -3?

[silk needle]

x(6x^2-23x)?

[silk needle]

yeah, by 3. this is how i (blurrily) did it

[warped cipher]

yeah looks correct

[warped cipher]

nice gg

[silk needle]

but then if I group 9 and 18 as 9(x+2) I can't then separate them and solve for x :((

sorry if I am confusing stuff, I'm not very good at explaining

from what I've been taught you can get both parentheses to be the same

then solve the parentheses and the coefficients

for x

either way I solved it but ty for your help

I am still p new to this lol

[warped cipher]

i think you better try with rational root theorem

I found it easier

[silk needle]

yeah the way our teach taught us was to first do the rational root theorem

independent term / leading coefficient

then find all the possible solutions

[warped cipher]

yep

[silk needle]

and from then on try out each solution with synthetic division

yada yada

is that generally the quickest way?

[warped cipher]

ye

[silk needle]

ok cool

thanks man

https://media.discordapp.net/attachments/942870809096101918/945529066189099078/ezgif.com-gif-maker_11-1.gif

[warped cipher]

no worries

[broken ermine]

can someone help me with theseeeee

I need answers

but I don't know how to od

[hoary iris]

Hey guys!
What is the the meaning of pre calculus ?????

[willow bear]

in America a bunch of different topics in math are organized into one class by that name, such as trig, exponentials, sometimes combinatorics

varies a lot what goes into it

[hoary iris]

Combinactories?? What's that?

[lone zodiac]

study of counting

[lone zodiac]

list of topics may differ from country to country, in mine it does not include combinatorics and exponentials/logarithms

[hoary iris]

Can you give me a question from this topic?

[lone zodiac]

how many ways can you arrange a deck of cards? like this type of stuff

[hoary iris]

In mine i don't know what is precalculus

[hoary iris]

Ok

[lone zodiac]

basically a collection of topics that is supposed to “prepare” you for computational calculus

[hoary iris]

What is calculus though?

[lone zodiac]

study of continuous change

like your dealing with quantities that approach nearer and nearer to a certain value but never reach it

[hoary iris]

Ok thank you

[tender mist]

Yeah, I've seen people's pre-calculus include complex numbers, whereas I never had any exposure to that, lol

[winter comet]

It's literally so many things, basically review and deeper understanding of everything before calculus, some new things you'll need for calculus, and sometimes even a preview of some calculus.

[chrome ether]

half life is how long it takes half of the sample to decay

but radioactive samples continuously decay, hence exponential

there are a couple ways to find the amount remaining

one option is to set $y=a\cdot e^{bx},$ plug in $a=100$ (since they want it as a percent) $x=5730$ and $y=50$ and then solve for $b$

[obsidian monolith]

elrichardo1337

[sage willow]

I have a test
who can help me

[kindred verge]

Anyone wanna study maths with me?

[limber mason]

I’ll study math with u

[obtuse island]

Hey y’all if I’m planning to take precalc in the summer and then calculus for 12th grade will it be too much? Is the summer enough time to prepare for calculus ?

[limber mason]

Whoever is down to study algebra with me dm me

[proud elk]

what is the limit method to find end behavior near a vertical asymptote

,help

[obsidian monolith]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[winter comet]

very dependent on how well you can learn it

precalc has a lot of possible topics, even the classes don't cover all the topics

[hoary iris]

Does any of the topics contain precalculus???

[tranquil inlet]

Not really sequences and series are part of precalc tho

[hoary iris]

Any other of the eight topics?

Is

In

Precalculus???

[tranquil inlet]

I’ve been studying precalc for about 3 months now (on my own) and I’m about halfway through. If u focus up and spend a lot of time then u can for sure do it

[tranquil inlet]

Besides series precalc is kinda just more advanced material of these topics

Like more advanced functions and geometry extensions (trig)

[hoary iris]

Then nothing here is in precalculus

There's are topics in my 10 th grade mathematics

[tranquil inlet]

Pretty much :/

Oof

[hoary iris]

After my final examinations I'll learn many more math stuff

[tranquil inlet]

I learned that in 8th grade .-.

[river drift]

precalculus is a very vague topic (since it amounts to "prerequisite knowledge for a calculus class", which varies by the calculus class). so anything asking "is this precalculus" doesn't have an objective answer (especially since topics may be covered in a different order)

[hoary iris]

Because in my state the 10 th grade is the very basic for the advanced mathematics

I think in my 11 th and 12 th grade contain precalculus

[hoary iris]

Ohh thank you

Then in precalculus nothing can be determined exactly. Right?

[hoary iris]

Which grade are you studying now?

[languid plank]

Lfg guys

4 percent done with teaching myself pre calc

Finished composite functions

[winter comet]

"nothing here is in precalculus" is wrong. those things are part of precalc, just not all of it. precalc is very generic, but it is usually includes a deeper understanding of algebra/geometry/trigonometry (usually with harder problems), also they may add concepts that you may not have seen before that are still technically algebra/geometry/trigonometry, and it sometimes introduced concepts from calculus (1 or 2 or 3) or higher mathematics on a relatively simple level.
If you don't want to read all that, math subjects really overlap, so precalc is basically a bit of everything before it, a few new things, and a preview of what's to come. basically.

sometimes people don't even get the preview, so....

honestly i'd say look at topics and understand them, and get good at doing problems for them. khan academy can help with this but yea

[compact spade]

How might I go about doing this

[willow bear]

is this happening on the plane?

@compact spade

[compact spade]

nah i'm in my house

i'm kidding, yes it is

[willow bear]

ok

do you know how to get the component form of a vector from its length and direction?

[compact spade]

yes

i think so

[willow bear]

ok then do it

[compact spade]

so as it happens you've perfectly described the part i'm struggling with

[willow bear]

ok in that case

tell me, in your own words, how to find the component form of a vector using its length and direction angle.

[compact spade]

uhhh

this will probably be wrong

...wait fuck i have no idea

[compact spade]

use triangle?

[willow bear]

that's it?

how come you answered "yes" to my question

[compact spade]

because i thought i did

[willow bear]

it is actually not terribly hard unless you overthink or never saw it before

[compact spade]

i'm exhausted right now and cant think straight

[willow bear]

and why are you trying to do math while exhausted?

are you on a deadline that's due yesterday?

[compact spade]

it's due tomorrow

[willow bear]

anyway:

the component form of a vector $\bd{v}$ with length $r$ and direction angle $\theta$ is given by $$\bd{v} = r \cos(\theta) \bd{i} + r \sin(\theta) \bd{j}$$

[obsidian monolith]

Ann

[compact spade]

yes, i should have done it earlier

[compact spade]

thank you

i think that will help

[empty zenith]

No more hesitation

[hoary iris]

Ohhh ok thank you so much

[hoary iris]

What kind of topic is this?

[tranquil inlet]

My middle school is really advanced so when freshman come to the high school, they relearn the same topics. So I’m relearning geometry/algebra but self studying precalc to take calc next year

I think of precalc as transformations, rational functions, logarithms, trig, polar and parametrics, vectors and matrices, sequences and series, and basic calc

So yeah

[winter comet]

transformations??

[tranquil inlet]

Of functions

[tender mist]

Like translations and stretches/compressions

[winter comet]

oh

i was thinking like left/right/up/down and flipping over x and y axis lol

[tender mist]

That is what that is. I was just using the "technical terms", lol

[idle flicker]

Why are odd square roots defined for all real numbers but even square roots are only for positive real numbers

[hoary iris]

Because the square of any number can't be negative so it is.

It will be always positive

For example, what is the square of 2 and -2?

[idle flicker]

It's 4

Hmmm

I kind of get it I guess

[hoary iris]

Do you understood? Completely

If you take square root of 2 you will get +2,-2 but if you take square root of -2 that doesn't exist it won't be possible. So all the square root are defined for all positive real numbers.

[willow bear]

If you take square root of 2 you will get +2,-2
no you won't

sqrt(2) ≠ 2

also $\sqrt{x}$ and ``the square root\textbf{s} of $x$'' arent the same thing. the symbol $\sqrt{x}$ always refers only to the positive root

[obsidian monolith]

Ann

[hoary iris]

?🤔

[hoary iris]

How

Ms.Ann

[chrome ether]

this is simply established mathematical convention

a function should only generate one output thus it is nonsense to say stuff like $\sqrt{4}=\pm 2$

[obsidian monolith]

elrichardo1337

[fierce basin]

Yo can someone factor, 6uv+21+8v+28 by grouping I've asked chat gpt brainly Photomath they all gave the same answer but it's wrong😭

[chrome ether]

!nogpt

[tender quest]

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

[chrome ether]

your first mistake was asking gpt

[fierce basin]

Oh

[obsidian monolith]

ry44an

[lapis crown]

why is dx cos(pix) = sin(pix)/pi and not just sin(pix)

is it chain rule? how would you integrate it

[chrome ether]

GPT gets even simple questions wrong frequently 😭

it has no consistency, no actual knowledge, no actual reasoning

[charred fiber]

I have a quick question about phase shift. for 2cos5(x-2) would I set the insides of the parentheses to 0 so I would do x-2 = 0, or do I have to include the 5 in there?

[winter comet]

you would ignore the 5

the 5 is the period, and you would use x-2 = 0 to find the phase shift

[twilit quartz]

I have yet to study for my exam

And it’s tomorrow

I’m cooked

[viscid thistle]

I have problems with calculus, can anyone provide me basic calculus questions so I can practice them cuz the ones from the book are just outta this world

I have problems with differentiation, like the ones with the rules and stuff (chain rule, product rule)

[willow bear]

why not ask in #calculus lol

but ok how many questions do you want

[exotic barn]

$$\frac{\dd}{\dd x} \ln \bigg ( \frac{\sin x \cos x }{e^x}\bigg ) = ...?$$

[obsidian monolith]

adonhs

[viscid thistle]

Alright I will work it through

[viscid thistle]

Oo this is actually kinda tricky for me since I never did this kinda but imma try

Is it cosx(-sinx) /e-x?

I never really did Ln single the ones I did were always lnX

Man, I am afraid of calculus

Tbh, it's the most important aspect of maths isn't it?

[swift widget]

Nvm im fine now. Anyway yes i also do believe that it is important and im also feel intimidated by it

[viscid thistle]

I am pre grad so it wasn't showing in my channels

[willow bear]

my offer to generate a bunch of derivative questions for you is still up regardless

how many do you want?

[viscid thistle]

How many can you do comfortably?

Just give me as many as you like without it being a hassle.

I will check it out as soon as I finish classes.

[willow bear]

ok sure, i'll give you like 10 probably

[exotic barn]

You can use these log tricks:

log(a/b) = log(a)-log(b)

log(ab) = log(a)+log(b)

[viscid thistle]

Back

[viscid thistle]

Woah

Arc tan?

That's new

[willow bear]

a.k.a. tan^-1 sometimes.

[viscid thistle]

Ahh I see

Alr i will probably only be able to do half to these correctly

I will still try

I will get back to you when I do finish

[willow bear]

ok sure

make sure to remind me that i gave you these problems or just repost them

[swift widget]

Hey guys just wanna quickly confirm something, what are the two points closest to each other is the vertex and center or vertex and focal

Wait maybe it depends on the given i guess??

[willow bear]

... context?

with what?

do you just want answers or do you want help understanding something?

[swift widget]

Sorry to interrupt This is the problem but i just wanna know what could be most likely to be the closest point to each other ill take care of the answer

Oh wait

[willow bear]

@tawdry grove the stuff under the integral is a quadratic in x. it's messy, and it's got some scary looking logs in it, but all those logs are actually just numbers.

[swift widget]

I know its basic stuff but just wanna know cuz im forgetting stuff

[willow bear]

sorry, who's this addressed to?

[primal girder]

Hi guys, **would anyone know a good easy video to listen to when it comes to Trigonometry = graph (period 2pi - circles) one that explains soh cah toa in graphs? **I pretty much read/took the time to work on everything our teacher left us to do for, well for last weeks lecture (im late 😩) and am now just finishing up with the extra material he left us with. I'm kind of confused. I mean it kind of makes sense. But our teacher just left us these graphs without explaining anything, pretty much how 80% of our university works :)

Or a youtube channel that you guys like that might cover this

ping me if you reply to this!!

i have to move on and do this weeks lecture :''')

[chrome ether]

"explains SOHCAHTOA in graphs" is rather counterintuitive

the graphs of the trig functions extend the notion of SOHCAHTOA to non acute angles

[icy solstice]

it's the vertex of each branch

[viscid thistle]

Hey, I am really late but do you have to use the quotient rule on maths on the 5/x in Q:2?

[viscid thistle]

Alr i will keep that in mind

[little sonnet]

can someone help me out on a homework problem

im stuck and cant find it on youtube

[winter comet]

what's the homework problem

[smoky sphinx]

Anyone in here want to helo me study with pre calc?

[winter comet]

you don't HAVE to. you can technically say 1/x = x^(-1), then take the derivative of x^(-1), which is easier.

[little sonnet]

im down

[little sonnet]

is there like a vc in this discord server?

if not, i'll send it to you right now

I don’t know how to arrive at the answer

#17 and the answer

Here’s the work I did.

[viscid thistle]

I actually think I have problems with the basics. Most probably gonna be better for me to know the basics then touch these cuz i can barely make sense out of em

Can anyone give me something like a page or whatever

On the basics of differciation

[willow bear]

you could, but there's also a different way

[viscid thistle]

This?

Like one thing I still don't understand is what are cos, tan, sin, arctan, e^x, sec^2,ln, log

[winter comet]

what are they or what are their derivatives?

[viscid thistle]

What are they

[winter comet]

yes but you'd probably like ann to confirm that lol

[winter comet]

uhh...

they are functions of trigonometry

[viscid thistle]

Like what's that?

[winter comet]

hmm

it's hard to just openly explain

i don't really know how to define trigonometry

[viscid thistle]

Ahh

That's the problem

[winter comet]

you could look at trigonometry for khan academy

or smthn

[viscid thistle]

I don't understand this 😭

[winter comet]

yeah

you might want to look at trigonometry

[viscid thistle]

Anyhow, I will have to do smth about it.

[winter comet]

its very important

[winter comet]

yeah

[viscid thistle]

Or else i feel like I might fail next year

[winter comet]

fail what class?

[viscid thistle]

O levels

Am in class 9

[winter comet]

oh

[viscid thistle]

O levels in may/june

[winter comet]

what were you learning recently?

[winter comet]

i dont really know what that means

[viscid thistle]

I was learning functions idk how I got into trigonometry

[winter comet]

oh...

[viscid thistle]

Like that's just the session of my exam

[viscid thistle]

I am mediocre at maths

[winter comet]

you may not want to be doing derivatives right now then

[viscid thistle]

Never practiced seriously tbh

Now am just suffering

[winter comet]

lol 🤣

[winter comet]

nah

[dusky shadow]

<@&286206848099549185>

[winter comet]

are you getting derivatives in class or...?

[viscid thistle]

Yep

Well so basically I would have to go into my past a bit

[winter comet]

that's really weird

[viscid thistle]

To make sense out of ir

I was in like a different exam board

Edexcel

I switched to cambridge

Which is actually harder then edexcel

[winter comet]

ah...

[viscid thistle]

But it provides better conceptual maturity

[winter comet]

it seems like you're taking calculus but you haven't learned trigonometry

[viscid thistle]

Wait, isn't trigonometry a part of calculus?

[winter comet]

no...

[viscid thistle]

Oh...

Differentiation?

[winter comet]

differentiation is calculus

[viscid thistle]

Yeah that's what I am doing

[winter comet]

ah

[viscid thistle]

But why is there so much trigonometry in it?

Wait actually I have a idea

You are undergrad right?

[winter comet]

kinda

[viscid thistle]

First year?

[winter comet]

i'm in high school but i'm taking a class at a college

[viscid thistle]

Which class)?

[winter comet]

calculus 1

[viscid thistle]

Ahh

I see

Alright I think you would still be able to help

If i gave you the list of chapters

Can you tell me what I need to practice on

[winter comet]

i mean i don't know what you already know

[viscid thistle]

Like just names, not the whole chapter

[winter comet]

but you can try

are the chapters from calc or before or what?

[viscid thistle]

What are the basic chapters I should study

I starred the ones I thought would be important

But I wanna know your opinion

Give me 3 chapters

[winter comet]

ok that looks like a really weird precalc class that also has calc or something lol

anyway

[viscid thistle]

Nah it's not calulus

It's just maths chapters

Like the entire book

Out of these which should I study to get better and things like differentiation and trigonometry?

Just suggest 3

[winter comet]

hmm

if i had to pick three i would probably say 1,2,10

are you trying to get ahead?

[viscid thistle]

Yep

Well

Fell back

[winter comet]

ahh

[viscid thistle]

Trying to get up to be precise lol

[winter comet]

what chapter are they on?

[viscid thistle]

Intregration

[winter comet]

oh

i see the problem

💀

[shadow summit]

Chapter 13, doesn’t show up much in calculus, but is required for linear algebra.

[viscid thistle]

Is that a part of trigonometry?

[shadow summit]

No, but you will need to know trig beforehand

[winter comet]

that's true, but i think he should focus more on the bases

[viscid thistle]

Yeah

I have a weak base

[winter comet]

exactly, but he doesn't really know it so he should do trig way before that....

[shadow summit]

Vectors are part of what I consider “the basics”

[winter comet]

i think trig is more important than vectors

function is more important than vectors

imo

[viscid thistle]

Man, I started studying maths this year. Don't be so harsh damn....

[viscid thistle]

Seriously studying*

[shadow summit]

Obviously, but vectors are as fundamental as differentiation and integration.

[viscid thistle]

Wait lemme check out vector

[winter comet]

but he's going to be studying differentiation and integration in the near future, whereas linear algebra i'm assuming is going to be much later

[viscid thistle]

Hey

[winter comet]

wsp

[viscid thistle]

Vector doesn't look too har-

Woah

Nah

Am done

[shadow summit]

I mean, might as well know the basics of vectors in case he ends up doing physics or linear algebra.

[viscid thistle]

Am literally cooked

[winter comet]

yeah but we're thinking a bit more short term here

[shadow summit]

Nah vectors aren’t that bad

[winter comet]

they aren't too hard

things look a lot harder when you don't understand them

then you understand them later and its ez lol

the better you get, the easier it looks

[viscid thistle]

Holy, reminded me of the light chapter in physics

I have diagram-phobia

[winter comet]

💀

[shadow summit]

Haha fair enough

[winter comet]

i want to be really really good at math

unfortunately

im not

💀

the thing is