precalculus

[last palm]

I hope this helpsss

Answer to this👆

[keen delta]

honestly doing this rigorously would be hell I can only suggest using obvious quadratic equations that follow a and b since a would essentially always be true(in this case) and u have to find a function such that b is true

[fresh jay]

that one is made by me btw

[keen delta]

make the y positive
whatever is the direction of the x(+ or -) indicates if it goes upwards or downwards

[keen delta]

perchance is it 2

[fresh jay]

Correct

[keen delta]

😔
A can't be true because if c is always real, it is already proven false by b

since either f(x) or g(x) would have non-real roots which means f(c) can have c as non-real

[fresh jay]

👍

C is actually the main reason why I made that

[keen delta]

I have no idea what a leading term is

[fresh jay]

I actually made that in Korean first

And asked Gemini to translate

sooo

[keen delta]

shhh it's a common math term I'm just trying to ragebait people

[fresh jay]

🤔

[silver robin]

Why are normal and tangents important in Conics?

Need an intuitive answer

[raw hill]

In a rough sense, normals and tangents describe how a curve interacts with a line at a point. When a light beam strikes a conic (parabola/ellipse/hyperbola), the beam reflects according to the law of reflection (which is measured with respect to the normal). For instance, a parabolic mirror can send incoming parallel light beams to a single focus. An elliptical mirror can reflect light from one focus to the other. So tangents help describe the local direction of the curve whereas normals give the direction used to predict how light beams bounce.

[silver robin]

What about orthogonal trajectories in differential equations?

[raw hill]

Orthogonal trajectories are just finding where the tangent of the first curve acts as the normal to the second curve (and vice versa) where the curves cross

ex. if you have curves representing lines of constant temperature in a room, then heat always flows along the orthogonal trajectories (hot to cold)

[eager meteor]

Doubt chat:

We know that e is a constant. So e raised to any power, say, x, will also be a constant. If I am correct, then why is the derivative of e^x with respect to x is e^x again? Shouldn’t it be 0, given the derivative of a constant is always 0? If there is, please show me the wrong in my thinking. Thanks 🙏

[uncut mulch]

x is a variable

the value of e^x depends on the value of x

taking the derivative of e^x wrt x,
you're considering how e^x changes as x changes

that won't be 0

d/dx e^x = e^x
is one of the definitions of e

,w graph e^x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by ramonov

[uncut mulch]

,w graph e

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by ramonov

[sonic hill]

So like, yeah, you're conflating two ideas. If you had e^c, d/dx(e^c) = 0

(assuming c is not a function of x)

[hushed sphinx]

The same reasoning would lead to the derivative of 2x being 0, since "2 is a constant, so 2 multiplied by any factor, say x, will also be a constant" .

(On the other hand, since this is #precalculus, derivatives don't exist yet at all).

[eager meteor]

Thx

[eager meteor]

Sorry…I’ll post such questions next time…Thanks. Again.

[hushed sphinx]

The appropriate channel would be #calculus.

[eager meteor]

Thanks a lot

[round geyser]

In angles of depre. and elevation, why is it (sqrt(6)-sqrt(2))

[raw hill]

https://math.stackexchange.com/questions/881210/trigonometry-find-the-exact-value-of-sin15-circ

[haughty crown]

That isn’t English! I was really confused for a second!

[round geyser]

That’s Portuguese

[gentle lantern]

Use desmos 🙂

[snow elm]

ull get circle equation just substitute x values and get y

[round geyser]

Is that a min or max word problem

[rough leaf]

How would you do this

Wirhout using derivative

[undone pumice]

sub 3 and 4 into the equation, get (3,4) and (4,3)

3x+4y=25, 4x+3y=25. x-y=0, x=y. 3x+4x=25, 7x=25, x=25/7

then calculate the mutual inclination using the slopes

to get... arctan(7/24). i think

[round geyser]

What are some exponents rules that is outside of this

[eager meteor]

Then you have loga(0) = 1 for any a ig

[uncut mulch]

log(0) is undefined

you swapped the 0 and the 1

also not any a,
a>0 and not 1

[charred breach]

If x > 0

[dreamy flicker]

Yeah but I feel like that doesn't need to be said

[charred breach]

But is should…. lol

[dreamy flicker]

Alr.

Well then, input of log in all these should never be 0 or -ve

And I think that's all there is to log

[charred breach]

LMAO

[karmic crow]

I wouldn't be alble to ,probably .

[round geyser]

How about log_a b^c^d u multiply I think

[uncut mulch]

multiply what

[round geyser]

Like a to c

[uncut mulch]

wdym

Can you write out the whole thing

[round geyser]

Like this

[uncut mulch]

is this an equation you're trying to solve or something else

[round geyser]

That’s the only one I remember with the law of exponents

[uncut mulch]

where'd that come from

that made no sense whatsoever

[echo sinew]

This is the law of exponents (with logs): $\log_a b^c = c \log_a b$

[obsidian monolith]

Alberto Z.

[echo sinew]

If you want to apply it here you will have: $$\log_a{(b^{c^d})} = {c^d}\log_a b$$

[obsidian monolith]

Alberto Z.

[round geyser]

I found a good one

[neon comet]

guys can someone help me

[toxic bluff]

If you draw a picture it might give you some ideas.

[neon comet]

no i tried ts shit 10 million times confused asf

[echo sinew]

And?

[white imp]

Guys

[fossil kindle]

looks like pythagorean to me

[round geyser]

Sure

I’m also doing that too

[round geyser]

Find x

[echo sinew]

Ok, and what's the issue you're facing in solving it?

[grand inlet]

does anyone know how to find range and domain??? i've been struggling on it recently and i want to know how since i believe it's fairly simple

[cunning dust]

You should try lectures in of professor leonard on YouTube, he got a playlist of precalculus.

[grand inlet]

okay, thanks!

[plush carbon]

Does anyone know any good videos or websites that can teach inverse trig functions?

[obsidian slate]

https://www.youtube.com/watch?v=KqNGetDiix4

[hushed sphinx]

<@&268886789983436800> mrbeast

[plush carbon]

Thanks

[haughty crown]

Mr who

Why was he here

[hushed sphinx]

There's a persistent group of scammers who use subverted Discord accounts to post false claims that the youtuber (I think?) MrBeast has opened an online casino and is giving away large amounts of money as sign-up bonuses. All lies, of course, just the bait for an advance-fee scam.

[haughty crown]

Ohhhh I remember that

Post screenshots of his Twitter or something?

I’m never sure if it’s a bunch of scammers or a virus that infects accounts

[hushed sphinx]

Well, screenshots that purport to be that.

[haughty crown]

Right right right

[hushed sphinx]

Definitely scammers. Most likely they buy the subverted accounts from someone else who farms them with cruder bait (in the vein of steam giveaways etc) -- at least one should hope there's less than one person falling for the casino scam each time they post it, so they'll need an additional source. But this is not really known.

[haughty crown]

Cruder bait lmao

Man I hope I don’t fall for stuff like that when I’m geriatric

[round geyser]

I’m struggling how to find other 8 roots

[raw hill]

me when roots of unity again

[bold carbon]

i dont think -1/2 is a root

there should be 9 complex roots and 1 real root

[brisk raft]

just learn how to do polar

its a lot easier like that

you would get $\left(\frac{x}{x - 1}\right)^{10} = 1$

[round geyser]

Ye

[round geyser]

I mean it’s no solutions

It’s 1 real and 8 complex roots

[brisk raft]

there are 10 roots by ftoa

so you made a mistake

[round geyser]

One no solution

1≠0

Okay

[brisk raft]

i am still quite confident you solved it wrong

$$\frac{x}{x - 1} = {\exp(i 2\pi k / 10)}_{k = 0}^{9}$$

[brisk raft]

this should yield 1 real and 9 imaginary

wait

i see my bad

because exp(0) = 1 but x/(1-1) isnt defined

sorry 😅

[round geyser]

Okay

[exotic barn]

tryhard

[tough flare]

$ln (y)$ just means what power of e equals y?

[obsidian monolith]

Ujjawal Gupta

[tough flare]

Like $e^{?} = y$

[obsidian monolith]

Ujjawal Gupta

[tough flare]

?

[exotic barn]

yes

[tropic fossil]

yo whats the chain rule?

[undone pumice]

its how you differentiate functions with inside functions eg e^x^2 = f(g(x)) where g(x)=x^2 and f = e^x. It belongs in #calculus

[tropic fossil]

ohh right wrong channel mb

[undone pumice]

ye

isok

[haughty crown]

Chain rule.

Chain rule is pain.

https://tenor.com/view/omni-man-blackhole-gif-8271324335240180549

[orchid urchin]

what??

wym by that

[haughty crown]

What’s confusing

[orchid urchin]

how is it painful its super easy no?

[haughty crown]

If I’m js casually differentiating my ass ALWAYS forgets chain rule

It is super easy

I js forget it

[orchid urchin]

so if u say cos(2x) youd get -sin(2x)

[haughty crown]

No

Because now I’m thinking about it

[orchid urchin]

but if u forgot

[haughty crown]

But normally like a 25/75 wrong/right

[orchid urchin]

in what way do u forget it

do u just differentiate ln(3x^2 + 9) into 1/(3x^2 + 9)

[orchid urchin]

im very curious

[haughty crown]

Yes bro

[orchid urchin]

hmm

[haughty crown]

It just slips my mind

I’m better now

[orchid urchin]

thats good

[orchid urchin]

what if u just always apply chain rule on anything

because it does work on everything

ln(x) using chain is still 1/x

[haughty crown]

Too much thinky thinky

[orchid urchin]

or sin(x) is still cos(x)

[orchid urchin]

itd get automatic no?

[haughty crown]

At some point

[round geyser]

Hey, I heard there is a inverse pythagorean theorem

Which is 1/a^2 + 1/b^2 = 1/c^2

Does that work

[orchid urchin]

would u do it tho?

for the sake of it being automatic?

[haughty crown]

Nah

Enough normal practice will get me there

[orchid urchin]

fair enough

[haughty crown]

Never heard of it

[round geyser]

But Ik or everyone knows

[orchid urchin]

also yes because a^2 + b^2 = c^2 is the pythag theorem and if you raise everything to the power of -1 then you get the equation you have there,

its just the reciprocal

[round geyser]

Okay is that useful

[haughty crown]

But

345

[round geyser]

And where would u use it

[orchid urchin]

although, a b and c cannot be zero

cuz division by zero is a no no

[haughty crown]

What abt a 345 triangle

[round geyser]

Ik there is sin^-1, cos^-1, and tan^-1

[haughty crown]

It’s not a triangle atp 😐

But wait wait

For a triangle with legs of 3 and 4, hypotenuse has to be 5

[round geyser]

Ohhh

[orchid urchin]

keep in mind when you apply the power of -1 you may get a contradiction if you have 1/9 + 1/16 = 1/25, but if you have 1/9 + 1/16 = 1/c then thats okay

for normal numbers its fine tho

[round geyser]

It’s not this it’s
1/a^2 + 1/b^2 = 1/h^2

[orchid urchin]

actually wait i lied

[orchid urchin]

trhat was a bad example

[haughty crown]

https://tenor.com/view/sus-rock-gif-23559354

[round geyser]

a and b are legs and h is the altitude

[haughty crown]

Are we SURE here

The numbers do not seem like there working out

[round geyser]

Look

It looks like this

[orchid urchin]

yes because 1/h^2 = 1/a^2 + 1/b^2, youd just find a common denominator for 1/9 and 1/16 which is 144 and get 25/144, and then use comparison.

[round geyser]

3-4-5 triangle and want to find the height

[haughty crown]

Oh I see now

[round geyser]

Would it be 144/25

h^2=144/25

[haughty crown]

It would be the least distance between the right angle and the hypotenuse

[round geyser]

h=12/5

[haughty crown]

I was misreading that

[orchid urchin]

its not for c^2 its for h^2 which is the altitude

[haughty crown]

This feels like the wrong channel for ts tho

[round geyser]

Okay

[orchid urchin]

the picture explains it

[round geyser]

Yea

Is it a good formula to remember

[orchid urchin]

3 * 4 = 5h -> 12 = 5h -> h = 2.4

[round geyser]

You can do that?

[orchid urchin]

its from the area = 1/2 base times height, and you know for specifically a 3-4-5 triangle that 1/2 * a * b = 1/2 * c * h, giving a * b = c * h

[round geyser]

Ohhh

Can I use that for bearing problems

[orchid urchin]

no its a bit more complicated than that

[orchid urchin]

if the two legs a and b are already perpendicular to each other then you can treat leg b as the base and leg a as the height, which gives 1/2 * a * b. then now imagine rotating the triangle so it sits on its longest side, the hyp c, in this orientation the altitude h is the height giving 1/2 * c * h, and then you set them equal which implies a * b = c * h or h = (a * b)/c

[round geyser]

Okay

Since I’m doing bearing type 2

The direction is now N/S (degrees) E/W

[orchid urchin]

i would search up a visual proof

[round geyser]

Since I’m a visual learner I’ll do yhay

That

[long bane]

chat idk how to do law of sines- ambiguous cases can someone help
like how do i find how many solutions from just B=36degrees, a=5, b=8 😭

[round geyser]

That’s what I’m doing

[undone pumice]

like solve for the first angle using law of sines regularly

then do 180 - first possible angle

and if that plus the other possible angle is less than 180 2 solutions

i think its kinda been a while since i did it

[haughty crown]

From that you can find the angle of A, then it’s 180-A-B=C.

Then you can use angle C to find side C

[fringe quarry]

Hello I'm new here.

https://klipy.com/gifs/rabbit-cry--k01KQCKGX3WQEP8ZAM4CYEHJR8T

I think I chose wrong subject, I'm gonna change it.

Ok bye!

[tough flare]

Hi new

[shut tangle]

What's precalculus

[gentle lantern]

Stuff before calculus

[flat crystal]

(I haven't studied in the US so this might not be 100% accurate)
Calculus is a very big subject that use alot of concept that you didnt even heard about before
And pre-calculus will prepare you for that

You will see alot of new mathematic objects such as log, limits, trigonometry identities
You will also go over alot of new functions (trigonometry functions, log, expo, rational)
You should also see vectors (which are very useful in physics by the way)
I've heard that you also see matrix but I'm not sure
And more things about trigonometry because it's so useful

(Sorry for the big message)

[round geyser]

How about 180-(A+B)=C

[haughty crown]

Same thing

[round geyser]

That’s what I did

[viscid thistle]

Somebody give me I question, I wanna solve one real bad

[tame shard]

Sure prove that for all $n > 2$ and positive integer $a,b,c,n$ ; there exist no $a,b,c,n$ that satisfy the equation $a^n+b^n=c^n$

[obsidian monolith]

multiplexer

[tame shard]

[viscid thistle]

Thanks, give me 5 mins

Or 10..

[viscid thistle]

Interesting

[tame shard]

https://tenor.com/view/riddler-paul-dano-new-rockstars-thumbnail-does-he-know-he-doesnt-know-gif-27552850

[viscid thistle]

Yup completely lost...

[tame shard]

Congrats

[viscid thistle]

How are you supposed to solve that?

[tame shard]

It took andrew wiles (someone with a PhD in math) 7 years to prove this

:3

[viscid thistle]

What the... You really gave me a question that took 7 years to prove xd

[tame shard]

And that is with a PhD

[viscid thistle]

I got no PhD

[tame shard]

And works from multiple other mathematicians

[tame shard]

Ofc i was joking

[viscid thistle]

XD

Ok pal

[urban kernel]

(Bullying pre-unis)

[round geyser]

What

[astral apex]

more like 350 years

[lucid trench]

helloo?

[undone pumice]

hello

[lucid trench]

hi i dont really have a math problem but id like to ask for some advice regarding math.. lol is that ok?

[undone pumice]

sure

[lucid trench]

ok so its also abt gpa

ok so

[undone pumice]

kk

[lucid trench]

i have a question what are the best AP's to take that would like significantly boost my gpa

[undone pumice]

....err

All AP classes are weighted the same (5s on a 4 point GPA scale)

[lucid trench]

ooh

[undone pumice]

for example: i have 2 AP classes, 2 honors, 2 regular

[lucid trench]

mmm

[undone pumice]

so 5+5+4+4+4+4=10+16=26. 26/6=4.3... ish

[lucid trench]

ooh thats thats good

[undone pumice]

Well my school weights honors as 5s

but I believe universities do not

[lucid trench]

ooh

[undone pumice]

(So I have like a 4.6... ish >.< still not val cus of PE and Chinese, which do not count as honors)

[lucid trench]

wow nice

can i ask what AP's u take?

[undone pumice]

Precalc

And Comp Sci Principles

(I'm a freshman, so I can't take others.)

[lucid trench]

oh man are they hard?

FRESHMAN OH no im cooked

[undone pumice]

not really

Next year I'll be taking AP World and Calc AB

[lucid trench]

oohh

see

i was thinking

im not sure if you know what this is

[cyan quiver]

can someone help me with this

[lucid trench]

can i dm you if thats fine lol?

[undone pumice]

sure

[fossil kindle]

What

[haughty crown]

https://tenor.com/view/jerry-meme-tom-and-jerry-meme-jerry-points-get-a-load-of-this-guy-this-guy-gif-11384860625931393733

Chat you ain’t seen nothing until you take AP macro/microeconomics with a teacher that knows less than you do

[undone pumice]

fahh

sounds um...

amazing

[haughty crown]

Awful

Exam is Monday

Haven’t finished content

Coulda finished it like last month if we locked in

Instead we did push ups

[undone pumice]

🥀

im suddenly grateful we finished course content in both my ap classes

[haughty crown]

Always be grateful

[undone pumice]

macro/micro are senior classes at my school so thats a future me problem

[haughty crown]

Bc got done earlier this week but I’m behind

So I still gotta learn the hard stuff

My physics class has been done but she lowkey js neglected to teach some stuff…

[undone pumice]

oop

[haughty crown]

Nah it’s fine tho I’m gonna get a 6

[undone pumice]

lol

[haughty crown]

https://tenor.com/view/me-atrapaste-es-cine-its-cinema-cinema-esto-es-cine-gif-17729711691959966457

[fossil kindle]

skull

[tough flare]

Lets say that we have time and position axes, and we plot the movement of a fly, so it's random data, now let $f : t \to p$, so is $f$ a perfectly defined function?

[obsidian monolith]

Ujjawal Gupta

[raw hill]

I assume you meant to ask this:
\begin{tcolorbox}
Suppose we plot the movement of a fly on a coordinate system with time $(t)$ and position $(p)$ axes. If we define a mapping $f$ from time to position ($f:t \to p$), is $f$ a well-defined function?
\end{tcolorbox}
\vspace{0.3cm}

In this case, the answer is yes. Recall a function is well-defined if every input from its domain maps to \textit{exactly} one unique output. A physical object can cannot be in multiple places simultaneously but still must exist, so the fly occupies exactly one specific $p$ at any given time $t$.

[obsidian monolith]

Civil Service Pigeon

[tough flare]

Yes, but we don't have a mathematical expression to define random data right? So how f is well defined?

[tough flare]

Ok then, whats equal to f(t)?

[raw hill]

$f(t)$ is simply the physical position of the fly at time $t$, as you said. A function doesn't have to possess some neat, explicit algebraic equation like $f(t)=t^2+3$ to be valid. As I said earlier, a function is strictly defined as any rule or mapping that assigns exactly one output to every input. So the rule doesn't have to be an equation, but can also be an empirical data set, a lookup table, or just physical reality. For example, if the fly was at the point coordinates $(2,4,1)$ at time $t=5$, then you'd simply have $f(5)=(2,4,1)$. \

Tldr: The reality of the fly's location \textit{is} the function.

[obsidian monolith]

Civil Service Pigeon

[tough flare]

Didn't know that, cool

[raw hill]

[tough flare]

Btw $f(5) = (2,4,1)$ can also be represented as $2x + 4y + z = 5$?

[obsidian monolith]

Ujjawal Gupta

[raw hill]

(2,4,1) are coordinates in 3d space

Not the coefficients of a normal vector or smt

Idk where the =5 comes from in any conceptual sense

[tough flare]

How can I represent this data as a linear equation?

[raw hill]

You … don’t? There’s no reason why the fly has to follow a linear path.

I think you’re doing too much to escape from the abstraction to the point where it’s wrong

[tough flare]

Agreed, but these points can give linear equations ig

Which then can be solved and one can also find best solution possible through projection

Like 3 points (4,2,8), (2,4,1), (3,7,1) can be represented as $\begin{bmatrix}4 & 2 & 3 \ 2 & 4 & 7 \ 8 & 1 & 1\end{bmatrix}$?

[obsidian monolith]

Ujjawal Gupta

[raw hill]

You can write 3D coordinate vectors as columns of a matrix, but this is more of an organisation tool than anything unless you're atually going to do something with the matrix. In fact, putting the coordinates in the matrix has completely dropped $t$ (the domain of your function $f$). So if you wanted to use projections to find a line or plane of best fit (that's my best possible guess for what you want, it's very unclear), you'd no longer have the corresponding times to model the movement. And again, the matrix is just an organisational tool -- it doesn't magically force a fly's highly erratic (typically non-linear flight path) into a "nice" linear system.

[obsidian monolith]

Civil Service Pigeon

[tough flare]

Your guess is correct, I think projection can give a nice estimate of the fly's path through linear regression?

[tough flare]

$t$ can also be involved as the 4th axis ig, making it an m by 4 system

[obsidian monolith]

Ujjawal Gupta

[raw hill]

ehhhh idk about "nice"

Like I said, flies are famous for moving in highly erratic and non-linear paths

forcing a line/plane of best fit through that chaotic data is probably going to give you a largely meaningless trajectory

[tough flare]

Estimate with more than 50% accuracy

[raw hill]

....

idk how that's happening

[tough flare]

Ah ok

[fresh prawn]

Hello guys! Can someone help me with the "properties" of integrals?

[raw hill]

wrong channel

#calculus

[fresh prawn]

Ohhh tanks! sorry

[raw hill]

[green crown]

I need a bit help with the task below. I am just wondering - would there be infinitely many solutions for this problem?

The task:
Two planes are parallel to the xy-plane and have a distance of 6 from this plane. Find an equation and a parametric representation for each of these planes.

[tame shard]

it may or may not help to consider the 2d version of this with lines

[green crown]

This would be the xz-plane: y = 0

[green crown]

What do you mean?

[tame shard]

nvm

iw as tripping

i was thinking of 2 parallel lines to x = 0

[green crown]

Okai

Ohh

But maybe i need to first find the parametric equation for the xz-plane?

In order to find the two other planes

But if these two planes are parallel to the xz-plane, would they have the same normal vector as the normal vector to the xz-plane?

<@&286206848099549185>

[heavy pewter]

yes

they don't have a fixed let's just say y intercept

like you can fix two parallel planes of distance 6, and move them about the y axis

[green crown]

Okai

[pale void]

DO NOT PING HELPERS HERE

[heavy pewter]

because they still satisfy the condition, that means that there are infinite solutions

to your condition

[green crown]

Ohh i didnt know, i am sorry

[green crown]

But do i need to find the parametric equation to the xz-plane first in order to find the two other planes?

[heavy pewter]

what? no

[green crown]

Oh okei

[heavy pewter]

well what do you mean exactly

there's a really easy method with vectors and it is quite illustrative

but i'm not sure if that is applicable for your case

but if you want to like definitely prove it then sure use equations

[green crown]

Okei wait, so in order to find a parametric equation for the two planes i need to find a point it passes and two vectors (non-parallel vectors) that are parallel to the plane

I believe

[gilded scaffold]

Is Pre-Calculus just Functions and Trigonometry? Is Algebra is also involved here?

[green crown]

I think soo

I think it includes algebra too

[undone pumice]

it goes over algebra as well

in my class, we have these 4 units

[gilded scaffold]

I see

[exotic barn]

Yes

[exotic barn]

Also for parallel planes to the xy, xz or yz planes, you can simply consider simpler equations like x=c, or y=c, or z=c. And then for the xy plane you really have only two choices, a plane with points where just (x,y,z=6) or (x,y,z=-6) or shortly the planes z=±6

any other construction would either fail to be parallel to the xy axis or not have distance 6 anyway

[green crown]

Oh silly mee, i meant "Two planes are parallel to the xz-plane and have a distance of 6 from this plane. Find an equation and a parametric representation for each of these planes"

[green crown]

But i think i understand. A plane parallel to the xz-plane must also have a constant y, and in this case it can only be y = 6 or y = -6.

[green crown]

Yess

And the xz-plane would have this equation: y = 0

[exotic barn]

yes

[exotic barn]

yes

[exotic barn]

Two distinct lines that are parallel I suppose

Though even with one line, there would be only one plane associated with it anyway

[green crown]

I apologize, i meant planes not lines, so two planes that are parallel to the **xz-plane **

[exotic barn]

Then the same applies what I had said before

[exotic barn]

.

[green crown]

Okiee

I will try to solvee it noww

[exotic barn]

And yeah as the task says, 2 planes at most is only possible

[green crown]

Understood

Let mee try

Soo the equations for the two planes that are parallel to the xz-plane (the plane in the middle) would be y = 6 and y = -6

And noww i just need to find the parametric equation

[exotic barn]

yes

You can easily pick 3 points A,B and C and set up E : x = A+sAB+tAC

Since any point with y=6 for example, is just (x,6,z)

[green crown]

So plane y = 6 passes this point (0, 6, 0) while plane y = -6 passes this point (0, -6, 0)

Right?

[green crown]

Yesss

[exotic barn]

yes

[green crown]

And noww i need to find the direction vector. Since they are all parallel, they would all have the same direction vector, which would be (1, 0, 1), or as long as it is on the form (a, 0, b).

[exotic barn]

What do you mean by

Since they are all parallel

[green crown]

$l: \begin{cases} x=s\y=6\z=t\end{cases}$

[obsidian monolith]

dream

[green crown]

I think this would be correct for the plane y=6

[exotic barn]

works

you just picked (1,0,0) and (0,0,1) which are trivially perp to (0,1,0)

[green crown]

Well the task says that the planes are parallel to the xz-plane

[exotic barn]

Oh you meant that

[green crown]

Bahaha yess

[exotic barn]

Also usually planes are denoted with capital letters e.g. E

[green crown]

Ohh okie

$E: \begin{cases} x=s\y=6\z=t\end{cases}$

[exotic barn]

but nothing to be concerened of mathematically

[obsidian monolith]

dream

[green crown]

Like this?

[exotic barn]

you can't copy directly as it omits the double backslah

yea

[green crown]

I seee

[green crown]

Cant we use alpha as well

$\alpha$

[obsidian monolith]

dream

[exotic barn]

you can use any letter

[green crown]

Oh okai

Got it

[exotic barn]

any letter to your liking

[green crown]

Haha okiee

$\alpha: \begin{cases} x=s\y=6\z=t\end{cases}$

Ohh

Wait

[exotic barn]

fell twice for it

[obsidian monolith]

dream

[green crown]

And the second one would be

$\beta: \begin{cases} x=s\y=-6\z=t\end{cases}$

[obsidian monolith]

dream

[green crown]

For instance

[exotic barn]

yea

[green crown]

Thank youuu

[exotic barn]

No problem

[rustic cobalt]

Guys is it encouraged to use log differentiation when approaching questions with e^x? I just started and I always use the basic chain rule and quotient rules

[exotic barn]

<@&268886789983436800> sus behavior

[gilded steppe]

e^x is a special case in differentiation

[rustic cobalt]

Do I jsut just add a ln ?

[rustic cobalt]

?

[tame shard]

e^x is the only function whose derivative is itself

[rustic cobalt]

Makes sense

[rustic cobalt]

But to solve one a derivative of a function with e^x can ln both sides?

And use log rules?

[green crown]

What do you mean? It depends on the assignment - for instance if you want to solve for x in this equation e^x = 2 then you can apply ln (the natural logarithm) to both sides in order to solve for x, which would give x = ln(2).

[rustic cobalt]

Nah let’s say we have have f(x) = cos(x) plus 5x / 2x^2 * e^2x and we got to find f prime of 1. Instead of using chain rule and quotient rule can we add logs to make it simpler?

[dim oyster]

guys any book recommendations for precalc self study

[rustic cobalt]

Liek are u allowed to add ln to both sides in a function?

[rustic cobalt]

Skip pre calc, take college algebra instead

I mean just take the basics of college algebra

I don’t have pre calc in our country, but our units are functions, then calculus

[green crown]

Ohh

I am not suree

I dont think i have ever done that

[rustic cobalt]

K

[rustic cobalt]

I’m just horrible at differentiating

[green crown]

Hmm well i would recommend learning how to differentiate, because even though one is allowed to use logarithms to make it simpler or some other rules, in the end you have to differentiate i believe.

[mossy quiver]

what have you tried?

[round geyser]

I used x^3+y^3=(x+y)(x^2-xy+y^2)

Then got x^2-xy+y^2=3

[mossy quiver]

you mean y^2?

[round geyser]

Yes

[mossy quiver]

okay, next?

[round geyser]

Can i use (x+y)^2=x^2+2xy+y^2

For plugging x^2-xy+y^2

[mossy quiver]

i don't see why not

[round geyser]

When I did that it’s 9=x^2+2xy+y^2

x^2-xy+y^2=3
x^2+2xy+y^2=9

[mossy quiver]

that works, but a bit overcomplicated

[round geyser]

I’ll do elimination

[mossy quiver]

just note that x^2 - xy + y^2 = x^2 + 2xy + y^2 - 3xy = (x + y)^2 - 3xy = 3

you can easily calculate xy

since you have the exact values of x + y and xy, the next steps are easy

[exotic barn]

lograthmitic differntiation in the context of implicit differentiation, for example y=x^x then applying log to get log(y)=xlog(x)

[round geyser]

Okay

xy=1

[green crown]

Soo one can use logarithmic differentiation to simplify the expression?

[exotic barn]

simplify differentiation yes

[green crown]

Staaar

[green crown]

Okiee

Got it

Nooo

Not that emoji bahahaha

[candid kite]

guys help 😭

for c, i know what to do, but theres too much i need to differentiate so idk what order to do

[pale void]

please do not ping helpers here

[pale void]

chain rule applies here

[candid kite]

OMG IM SORRY

[pale void]

ill give you a hint

[candid kite]

i know i need to use chain rule but ive just started trig, so im kinda confused on where to start with chain rule

[pale void]

$\frac{d\cos^4(5x)}{dx} = \frac{d\cos^4(5x)}{d\cos(5x)}\times \frac{d\cos(5x)}{d(5x)}\times \frac{d(5x)}{dx}$

[obsidian monolith]

Annie Maqionde

[pale void]

1. power of the function
2. look at the argument, you have the form for derviative of cos y, right?
3. argument w.r.t. x

[candid kite]

i dont understant how its become a fraction now

i dont get it 😭

[floral barn]

Do you know chain rule?

[candid kite]

yes

[floral barn]

Use that

[candid kite]

but dont i have to derive the cos too?

[mint sequoia]

No need.

It is in term of f o g.

[floral barn]

You have to do this much

[candid kite]

so would it come to 60 cos^3(5x)?

[round geyser]

I thought this is graphing

[floral barn]

You have to keep doing it until the derivative becomes 1

[candid kite]

no it asked to find the derivatives with respect to x

[mint sequoia]

Basically derivative of cos(5x) and multiply with derivative of cos^4(5x).

[round geyser]

Ok

[candid kite]

i feel like i did these wrong

[candid kite]

OHHHHH

wait lemme retry

[mint sequoia]

That explanation written by Annie was correct, but quite long.

And do not forget the constant 3.

[candid kite]

12 (cos^3(5x)*-sin^3(5x))?

bro im so cooked

[undone pumice]

no this is calculus work

[candid kite]

i really dont understand this

[undone pumice]

ummm try to think of it like

double chain rule? i think

[candid kite]

this is what i got from doing chain rule

but not double

[undone pumice]

idk if double is the right word exactly

like when u do chain the first time

you take the inner function as cos5x

[candid kite]

yeah

[mint sequoia]

D/dx is just apply derivatives.

[undone pumice]

and u have to differentiate the inner function for the chain rule right? well the inner function's derivative is found with the chain rule

[mint sequoia]

No that is wrong.

[undone pumice]

for d/dx(cos5x) basically the outer function cos x and inner 5x

[candid kite]

wouldnt derivative of cos(5x) be -sin(5x)?

[undone pumice]

not quite

remember the inner function is 5x

[mint sequoia]

You missed 5x inside.

Chain rule again.

[candid kite]

what is the final answer so i can try figure out how to get there

[ancient inlet]

Differentiate the inside

[undone pumice]

your answer is very close ||if you do want a hint, the coefficient of the answer is -60||

think about how to apply chain rule to d/dx(cos(5x))... the inside... the outside...

[ancient inlet]

Yeah

If use try integrating sin5x you wouldn't get cos5x right?

[undone pumice]

oh this is the precalc channel..

[ancient inlet]

LOL

[undone pumice]

fah i just remembered i have ap classroom work

for precal

🥀 im sure i can speedrun like half of a practice exam

[undone pumice]

hopefully you're not too confused, if u need more help ill try to answer ur questions while i speedrun my own hw

[ancient inlet]

What do u learn?

[undone pumice]

🥀

[undone pumice]

cus of the ap exam its just practice exams now. im in precal so its easy but its a bit tedious

[ancient inlet]

I love no claculator yay

[undone pumice]

xd

[candid kite]

OMG I THINK I GOT IT

[ancient inlet]

I do love mental math

[undone pumice]

im gonna crash out if i make one more algebraic error on frq4

[ancient inlet]

What's FRQ?

[undone pumice]

yay

frq = free response question

[candid kite]

is it because of the -sin() from the derivative of cos()

[undone pumice]

when u do chain rule

u multiply by teh derivative of the inside function

the isnide function is 5x

d/dx(5x)=5

5*-sin(5x)

d/dx(cos5x)=-5sin(5x)

[candid kite]

but yes i need to add the sin(5x)

[undone pumice]

mmhm, remember the negative sign

rest of it looks good

[candid kite]

thank you

[undone pumice]

like this is our frq 4 (but this one doesn't really have word problems its just solving)

[undone pumice]

you're welcome, glad to help ^.^

[undone pumice]

time to grind this take home practicce exam calc mcq igs

[candid kite]

if theres a coefficient inside the sin() does that count as another different function?

[ancient inlet]

I love calculus so much

[undone pumice]

yes

outer function as sin(x) and inner function as (whatever it is inside sin)

[candid kite]

cuz the next question is y=(sin 3x)(1 - 2 cos x)

[undone pumice]

ah

[undone pumice]

i hate precallll ackkkk

[candid kite]

when deriving sin(3x) would it be 3cos(3x)?

[undone pumice]

uhh

i think so

[ancient inlet]

Yes

[candid kite]

thanks

[undone pumice]

similar to the 5x one, you take derivative of 3x as 3 and multiply

[candid kite]

yeha

[undone pumice]

wait i have a possibly silly question how do i know the concavity

[candid kite]

double derivative

[undone pumice]

like after i graph is there a way to find inflection points cus i can't find a way in desmos and my calculator is lowkgenuinely dead

[undone pumice]

errr i dont think my precalc teacher would like that

im not too keen of that idea either cus with the 2pi/365(t+15) i think thatd be chain rule

[candid kite]

but i dont really know any other way to find concavity other than double der

[undone pumice]

idk either

💀

maybe i just plug in at 299 and 301 and see if its increasing or decreasing, then guess with a 50/50

[candid kite]

lemme try it on calc

wait maybe you can do the sign test

[undone pumice]

well its a decreasing function at 300 so theres that

[cerulean cape]

I mean u can graph it lol

[undone pumice]

oops

[cerulean cape]

if u dont wanna do double deriv

[undone pumice]

ya but how do i find concavity from there

i have it graphed in desmos cus thats how i was looking at it at 300 but

[ancient inlet]

Function is not that complicated if u look at the qn

[candid kite]

if the double der is negative, its like a sad face/decreasing and positive is happy face/increasing

[cerulean cape]

just at 300 is it decreasing or increasing

[candid kite]

😭

[undone pumice]

ye ik the double derivative test

[cerulean cape]

if u graph

[candid kite]

sorry

[cerulean cape]

lowk dont remember if they taught us this in 9th

[undone pumice]

i just feel like my precalc teacher will chew me out if she sees me doing that (cus we have to submit our work :c)

[undone pumice]

im in 9th 🥀

[cerulean cape]

yea I dont remember if we did this I think we were alr doing linear alg

jk

[scarlet cedar]

Bro is a fast learner

[undone pumice]

thx

[candid kite]

NINTH?

[undone pumice]

ykw what looks concave up imma call it a day and move on 🥀

[candid kite]

bro im in 12th and we just started ts 😭

[undone pumice]

ye

[scarlet cedar]

Wut

[undone pumice]

im teaching myself calc

[scarlet cedar]

Derivative is year 10

[undone pumice]

but im in precal

[undone pumice]

varies

here at my school

precal is standard 12th

11th advanced

[ancient inlet]

Same

[undone pumice]

10th advanced honors

[scarlet cedar]

Interesting

[undone pumice]

but im in the US so my classmates are slow tbf

[scarlet cedar]

The word "US" explained it all

[candid kite]

im in australia so we started calculus/derivatives in year 11

im in year 12 now

[undone pumice]

and the advanced honors track is calc in 11th

[candid kite]

so we're going into expos and trig calculus

[undone pumice]

ah interesting

u didn't learn trig calc in 11th?

[candid kite]

no

just normal differentiation

and the first thing we did in year 12 was double derivatives

[scarlet cedar]

Trig calc supposed to be taught in lat yr 10

then they will revise it in uni

[undone pumice]

ic ic

[cerulean cape]

I alr graduated so

I lowk forget

how it was

[candid kite]

im graduating in october

[undone pumice]

my school has like calc ab and bc

[cerulean cape]

I think we did calc 3 senior yr

[undone pumice]

oh wow

[cerulean cape]

or calc 2 idk

Im doing ee rn

[candid kite]

bro this math test is on friday and i cant even do simple shi 😭 im so cooked

[undone pumice]

🥀 nunu u got this

just remember like the basic derivative rules and such

grind any practice problems u find 🥀

[candid kite]

yeah thats what im trynna do rn

ive got 4 days

[undone pumice]

🙏 i got math finals tuesday, wednesday, friday. and then ap exam on tuesday and then my math teacher said shes gonna make us learn calc until june

[candid kite]

i didnt go to school today (mostly because i overslept my alarm) so i can study for this

[ancient inlet]

Its okay we will help u

[undone pumice]

i missed one day of math class which happened to be when we learned polar

[candid kite]

am i getting somewhere

[ancient inlet]

2nd derivative is wrong

[undone pumice]

the second part

the 1 shouldn't be there

i think

[ancient inlet]

Differentiate 1 - 2cosx

If you differentiate constant what would it be?

[candid kite]

i rearranged it to be easier for my brain so i wrote -2cosx+1

[candid kite]

nothing

[ancient inlet]

Yes

[scarlet cedar]

Not until complex polar

[undone pumice]

right but when you d/dx(-2cosx+1) the 1 shouldn't remain, its like if you were differentiating -2x+1 you'd say its -2 whether or not you have 1-2x or -2x+1, not that the one matters or that the placement matters

[candid kite]

how would i multiply cos3x with cosx

[undone pumice]

just leave it as cos3xcosx

or well -6cos3xcosx

[candid kite]

yeah

thanks

[ancient inlet]

Need help with logarithms?

[undone pumice]

er...not really

but im confused on um

k(x)

is it supposed to be like

1-cos^2x/cos^2x instead of tan^2x and such or like

[ancient inlet]

It said cosine appears once only

[undone pumice]

oops nvm

[undone pumice]

could i rewrite it as like

1/(cos^2(x))

[candid kite]

im cooked

im gonna fail this test bro

[ancient inlet]

Factor?

[candid kite]

idk i take that step back, idk why i did that lol

[candid kite]

idk what to do after simplifying it

[undone pumice]

i think its right on the second line

[ancient inlet]

2nd line

Is your final answer

[candid kite]

yeah i know, ignore the 3rd

[candid kite]

ohhh okayy

thank youuu

[ancient inlet]

Would this be correct?

[undone pumice]

Ummm my approach was

Csc^2-cot^2 is 1

Tan^2x is sec^2x -1

Sec^2x is 1/cos^2x

Idk if that’s right tho

lwkgenuinely im bouta just hop on brawl stars trig work is kinda ragebaiting me

[ancient inlet]

No way

[undone pumice]

erm

[candid kite]

bro i gave up, im palying roblox

[undone pumice]

Fr bro math can go crawl in a hole

[ancient inlet]

Everyone lazy rn

[undone pumice]

Absolutelyyyy

And I still have math finals to study for but who cares

[candid kite]

the academic stress isnt worrying me, whats worrying me is how im straight up ignoring it

💀

[undone pumice]

😔

[ancient inlet]

Then lock in man stop playing lmao

[undone pumice]

🥀

[candid kite]

no its like physically impossible

i can not lock in

[undone pumice]

nunu u can do it (says while continuing to grind brawl stars)

[candid kite]

LOL

chat?

[undone pumice]

uh

y' should be the slope

then calculate how much um... y intercept? to add

i think..

[candid kite]

yeah but

if m is 2cosx

lik

[undone pumice]

plug in

pi/3

[ancient inlet]

Ez

[candid kite]

but if m is 2cosx and the equation would be y=mx+c wouldnt it be y=2cosx(x) + c?

[undone pumice]

it says

calculate the equation of the tangent

at x=pi/3

so we want the specific slope at pi/3

so we need to plug in for that

[candid kite]

the equation of the tangent is y=mx+c

like plus pi/3 in the 2cosx?

[undone pumice]

2cos(pi/3) = m

[candid kite]

i did that befpre

but then how do we get the +c

[undone pumice]

if you think about it

[candid kite]

2cos(pi/3) = 1

[undone pumice]

2sin(pi/3) is

sqrt3

right?

and right now with a slope of 1

what would the tangent line evaluate to at pi/3?

before adding a intercept

don't overthink it

[fossil kindle]

is brawl stars fun

[undone pumice]

i like it

[candid kite]

i used to like it

[candid kite]

pi/3?

[undone pumice]

yup

cus rn we have basically y=x

so the difference between the values of sin(x) and y=x

would be... (dont need to simplify)

[tulip fern]

another helper ping

[candid kite]

0?

[undone pumice]

ah...

well

if you have 2sin(pi/3) as sqrt3

and y=x at pi/3 as pi/3

whats the amount you need to add to make the tangent line go up to touch the curve?

[candid kite]

im so confused

sorry

[undone pumice]

as you can see we want the line to move up a certain distance to touch the graph

(btw, 1.73... number is sqrt3)

so that distancce

is sqrt3 - pi/3

as such

sorry idrk how to explain it

back to brawl

[candid kite]

its okay

i'll try and figure it out

[undone pumice]

gl... the second pic above is my final answer with the tangent line so igs u can look at that

[weary flower]

Can anyone help me on this question? Im not good at matricies or vectors so its confusing.

[wicked vapor]

I found this bullcrap question

I'm not asking for an answer but like it's so weird

[weary flower]

What is this 🥀

[devout bone]

take r as a column matrix of (x y z) and then multiply the matrices to get the equations of plane and the line

and the angle between a plane and a line is the angle between the normal of the plane and the line

[weary flower]

thanks for the help!

[fossil kindle]

no way this is precalc

[hardy raft]

Bro what the hell is this how do I even approach this😭🙏🏻

[hardy raft]

As someone who is just starting precalc this is terrifying

[wicked vapor]

It actually dosent have any calculus in it

It's arithmetic but clunky

[wicked vapor]

Lagrange interpolation formula

[glad sun]

and here i am taking precalc 12 in canada where the worst thing i would see is trig

[undone pumice]

🥀

[glad sun]

chatgpt says its infinite

[wicked vapor]

It is

[glad sun]

yeah bc of lagrange interpolation, whatever the flippers that is

[weary flower]

Whats that

[bold crag]

-1/12

[next moat]

now who is pinging me in PRECALC/

[jade scaffold]

any1 explain me this i just strted calculus

or deravatives

[earnest marsh]

substitute a = e^(loga)

[jade scaffold]

i have not studied logarithms so i guess i wont get it

[earnest marsh]

have not??

[jade scaffold]

yeshh why do i skip words in sentence :<

mb

[earnest marsh]

then i think it is time to study logarithms ig

[jade scaffold]

yessss

i will

[gentle lantern]

#calculus

[fossil kindle]

ye its just a ton of products

[keen delta]

take the natural logarithm of y=a^x
that gives us lny=lna^x=xlna which gives us lny=xlna
now I'm pretty sure this is implicit differentiation(same thing basically) but you find y'(same thing as dy/dx) after multiplying, this is also basically chain rule as y is a function of x and y' is the derivative
so this gives us: y'/y=lna
which can then be done as y'=lna * y=lna * (a^x)

in case you're wondering what a logarithm is

ionknow

[undone pumice]

a/c

the degrees are equal

[round geyser]

Yes

[keen delta]

unless b and d are 0 or a/b=c/d

I think

oh yeah that's it

[round geyser]

Ye

The domain is x≠-d/c

[smoky mural]

Hi everyone

Can l post a question

[tender quest]

Asking the actual question right away is more likely to get responses.

Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.

[orchid urchin]

You need to write and do somethig like this:
$$a^x = e^{(ln(a))^x} = e^{x ln(a)} $$
$$\frac{d}{dx}[a^x] = \frac{d}{dx} [e^{x ln(a)}]$$

[obsidian monolith]

text book

[orchid urchin]

e an ln are inverses and that is why that works

and then you use the chain rule

since its not in the standard e^x form

[orchid urchin]

also if you don't know your logs and ln's then you shouldn't be doing calculus at all

they are quite simple though

[jade scaffold]

yea h they are im just learning deravatives rn log is my next topic

[wicked vapor]

Tf

Logarithms should be taught before differential calculus

[jade scaffold]

idk ill learn it

in next class (lecture)

[hoary zephyr]

shouldn't differential calculus and integration be taught first , bc ln(x) is the integral of 1/x

[uncut mulch]

logs are the inverse of exponents

and first appear in that topic

[jagged dust]

are they? or are they a completely diff thing im confused

[undone pumice]

Like log with a base of 2 with argument 8 is basically saying

2 to what power js 8

[jagged dust]

oh ye

i geddit

[undone pumice]

That’s the opposite of 2 to the power of 3 is 8

[jagged dust]

but expo was before log or was log before expo

[undone pumice]

So log is an operation that can undo exponents. like multiplying and dividing

[undone pumice]

Wdym by before?

[jagged dust]

i see

[jagged dust]

like which came first in discovery or were they found together

and later differentiated

[undone pumice]

Exponents I believe logs were calculated

[jagged dust]

i see thats what i felt would be

was logs discovered to counter issues of math in which alg cant enter?

[undone pumice]

Actually idk if exponents were first but yeah people would like publish log tables to solve problems

[jagged dust]

hm

yes

[undone pumice]

I’m not sure when the calculus implementation of exponents and logs was tho

[jagged dust]

exponents should be before because they come naturally not saying log is artificial but exponents are moe out there in human and space logic than log

[jagged dust]

could be when calculus branched into things where alg couldnt enter?

[undone pumice]

Probably

Idrk math history

[jagged dust]

hm

im going off intuit here

[wicked vapor]

Exponents have 2 inverses

Roots and logarithms

[jagged dust]

Ohh

So log is the longer more accurate one?

[wicked vapor]

No

They do different things

You can't compare them, they're used for different scenarios

[wet ingot]

hi

[round geyser]

Can you do factor with x^pi =1

[echo sinew]

Idts

[astral apex]

it appears that while basic facts about exponents were known since antiquity, the modern concept of an exponential function and its derivative didn’t come until after people noticed the area under a hyperbola is related to logarithm tables.

Napier/Briggs: logarithms as computational tools
Saint-Vincent/Sarasa: natural log as hyperbola area
Newton/Leibniz: calculus makes d/dx[ln x] = 1/x
Bernoulli/Euler: e, exponentials, inverse-function viewpoint, and d/dx[e^x] = e^x

the thing is it took a long time for people to formalize what a function is and what should count as a function

[undone pumice]

hmm i see, interesting

[jagged dust]

Alright

[jagged dust]

As these quantities were more radical?

[astral apex]

I'm not sure what you mean

but something like $2^{\pi}$ took a while for people to come to grips with

[obsidian monolith]

ManifoldCuriosity

[astral apex]

or $\sqrt{2}^\pi$

[obsidian monolith]

ManifoldCuriosity

[fair garden]

yo guys, what on earth is Limit?

[undone pumice]

a limit defines what a function approaches at some x value

also one sided limit, from the left/right

[fair garden]

alright thanks
but that's not quite what I am lookin for

[undone pumice]

what are you looking for...?

[fair garden]

sorry, I asked the wrong question

where does limit comes from?

[astral apex]

it's calculus

though you get a quick intro to the idea at the end of precalc

[fair garden]

oh, so that's not the question to be asked in this chat

I'll go to calc chat

if there's such

[astral apex]

there is one, I think it's fine to ask here though

I'm not quite sure what you mean about where limit comes from

do you mean what motivates the concept of limit?

[undone pumice]

my teahcer taught us diff quotient in the first week of school 🥀

[astral apex]

in precalc?

[undone pumice]

ye

[fair garden]

nay, what I am asking is the formal definition of Limit

[fair garden]

that's tuff bro

[undone pumice]

<@&268886789983436800>

[undone pumice]

it was kinda silly tho cus the kid next to me was like rlly confused

bcs

[orchid urchin]

so many ppl asking about calc 1

[undone pumice]

the video we watched said f(x) and our worksheet used g(x) and they told me "its not the same function" with a straight face

[orchid urchin]

why they say that?

[undone pumice]

probably because they didn't have good enough foundations to understand that f(x) is just a name for a function..

[fair garden]

of course they're not the same

[astral apex]

ah, sure. Well there are a couple types. There's limit of a sequence of real numbers, and there's limit of a function f(x) as x -> a or x -> infinity. It also looks a little different if the value of the limit is infinity

[orchid urchin]

seem about right

[undone pumice]

they were a senior btw like a full grown adult with a mustache

[orchid urchin]

the formal definition of the limit is

[fair garden]

if f(x)=x² and g(x)=x³, they're different functions

[undone pumice]

not like that

it was a formula

[astral apex]

yeah, that's the case of a function limit, with the variable approaching a finite number, and the value being finite

[undone pumice]

which used f(x) as an example

and the worksheet had us calculate it with a function g(x)

[orchid urchin]

i think what @undone pumice was talking about was two functions that have the same set of input numbers and output numbers

like f(x) = x^2 and g(x) = x^2