precalculus

[shadow summit]

It’s easy to be “good at math”

[winter comet]

i can do the stuff in my class no problem

[viscid thistle]

Differentiate 2x in two dimensions.

[winter comet]

but anything else is much harder

[shadow summit]

It’s hard to apply topics to real world scenarios.

[winter comet]

um.... wouldn't i just graph y = 2?

xD

[viscid thistle]

Lol

[winter comet]

yeah but like

[viscid thistle]

What are dimensions btw?

[winter comet]

i see stuff in the algebra-geometry-precalc sections

that i can't solve

[viscid thistle]

Just saw it in the book

[winter comet]

1 dimension is a line, 2 dimension is a flat screen, three dimensions is like real world 3d objects

did not explain that well but uhh 👍

💀

[viscid thistle]

Ahh I understand

[winter comet]

is it?

[viscid thistle]

1D is just a line?

[winter comet]

yes, and 0d is a point

[viscid thistle]

Like if we walked through 1D

We could look like a stick figure?

[winter comet]

no

we would look like a line

XD

stick figures are 2d

[viscid thistle]

Lol

Ohh

4D?

[winter comet]

controversial 🤣

[viscid thistle]

Ahh why?

[winter comet]

i guess it depends on context. sometimes people say its time, but honestly its just not defined. it's just a fourth aspect of a graph

kinda

i don't really know what i'm talking about too much so don't take my word for it but yea XD

i haven't taken linear algebra

[shadow summit]

If you are unable to solve something try looking at a the solution process, and if you identify something you don’t know/aren’t good at, look it up.

[viscid thistle]

Oh I know smth I don't understand

[winter comet]

it's really hard to make sure i've covered all my bases though

and once i think i've covered it

[winter comet]

i encounter some harder application of it

(not real world application)

[viscid thistle]

Lemme give the question

[winter comet]

that's a lot of trigonometry and differential trigonometry

[viscid thistle]

Like what's going on in 8b

Question

[shadow summit]

And that’s what mentioned earlier, it’s hard to apply applications (I encounter them most commonly in real world scenarios, but same reasoning applies to just more complex math problems.)

[shadow summit]

What are you finding difficult?

[winter comet]

they are finding the slopes of the tangent lines in order to find the equations of the tangent lines at the points (0,-1) and (pi,1)

that probably made no sense

[viscid thistle]

8B just don't understand what's happening in it

[winter comet]

you know what a tangent line is?

[viscid thistle]

No like i get that but the solution

[shadow summit]

Have you learnt about tangents yet?

[winter comet]

ok uhh

[viscid thistle]

I don't understand what they are doing in the solution

[viscid thistle]

Isn't it just a straight line touching the curve

Or smth

[winter comet]

they took the derivative of this equation:
f(x) = sinx - cosx

the derivative is:
f'(x) = cosx + sinx

[winter comet]

yeah pretty much

it only touches the curve at 1 point

[viscid thistle]

I forget tbh

Normal touches the tangent right?

[winter comet]

normal is perpendicular to the tangent line

[shadow summit]

It the a line that has the same rate of change as the function at a specific point.

[viscid thistle]

Does it have to touch the tangent or not nessacary?

[viscid thistle]

Ahh

[shadow summit]

So you take the derivative, then evaluate it at the specific point

And ofc solve for c in y=mx+c

[winter comet]

yes
if you find the tangent line at a specific point, the normal line will intersect the tangent line at the same point, and it will be perpendicular to the tangent line.

[viscid thistle]

What's that formula

[viscid thistle]

I don't understand what it is meant for

Is C a constant?

[winter comet]

no

well

[shadow summit]

That’s the equation for a straight line

[winter comet]

yes

[viscid thistle]

Curve?

[winter comet]

C is a constant mb

m is a constant as well

m is the derivative, in fact

[shadow summit]

So take the derivative, of f(x)=sin(x)-cos(x)

[viscid thistle]

M2 can be in both tangent and normal right?

Or just normal?

Nvm

Sorry yeah

Only normal

[shadow summit]

Slow down for a second

[viscid thistle]

Alr

[shadow summit]

Take the derivative of the function.

Do that now.

[winter comet]

he may not uhh

[shadow summit]

i believe in him

[winter comet]

ok 🤣

[viscid thistle]

Alr lemme get pen and paper

[shadow summit]

posting this as a little reminder

[viscid thistle]

What formula is that?

[winter comet]

thats the formula they gave you

[shadow summit]

thats the function you are trying to derive according to the question

[viscid thistle]

Mb.....

[winter comet]

🤣 👍

[shadow summit]

,,f(x)=\sin(x)-\cos(x)

[obsidian monolith]

TheLord26

[viscid thistle]

Do I also differentiation f(x)

Or doe that remain same

[shadow summit]

you are trying to differentiate f(x)

[winter comet]

well yes, it should be f'(x)

[shadow summit]

thats ALL i am asking you to do

im trying to take you step by steo

[viscid thistle]

Prime?

[winter comet]

yes

[shadow summit]

so just take the derivative for now

[winter comet]

that means derivative

[viscid thistle]

Alr

Lemme get calculator

[shadow summit]

just look at this diagram

[viscid thistle]

What's a gradian mode in the calculator?

[shadow summit]

dont worry about it, you are getting side tracked

[viscid thistle]

At (0,1) I got - 1

[shadow summit]

thats not what im asking

do you know what a derivative is?

[viscid thistle]

Yeah

Dy/dx?

[shadow summit]

yes

[viscid thistle]

Ohhh

Alr alr

I get it

[shadow summit]

do you know how to calculate the derivative of sin(x)?

how about the derivatie of -cos(x)?

[viscid thistle]

Its gonna be cos+sin?

[shadow summit]

yes

[winter comet]

i just realized

[viscid thistle]

1

[shadow summit]

now, plug in 0

to the derivative

[winter comet]

i did not just realize nvm

[viscid thistle]

Comes as 1 in (0,1)

[shadow summit]

good

now thats your gradient for the line tangent

you will now plug in 0 and f(0) for the x and y values of the tangent line

so you let x=0, find f(0) and make y=f(0) in the tangent line equation

(y=mx+c, which is now f(0)=1*0+c)

this is to find the c value

[viscid thistle]

Alright

I will go through it

What's the next step though

8b?

[shadow summit]

the next step would be finding the normal line

[viscid thistle]

Oh wait

I didn't find (pi, 1)

[shadow summit]

just focus on x=0

[viscid thistle]

Alr

[viscid thistle]

M2= - 1/M1?

[shadow summit]

what

[winter comet]

whats M2 and whats M1

[shadow summit]

yeah

[viscid thistle]

M1 is the gradient I think

No wait

Actually I have to go back a bit

[winter comet]

i dont even know what a gradient is...

[viscid thistle]

Cuz i forgot what they were

[shadow summit]

ok, we will both stay quiet for a minute as you type out/post photos of your working out so far

[viscid thistle]

So, i think I get it

M2 and m1 are variables

M2 is negative reciprocal

Not sure what that even means

[shadow summit]

okay, im going under the assumption that m_1 is the gradient of the tangent and m_2 is the gradient of the normal, m_2=-1/m_1

[winter comet]

does gradient mean slope?

[shadow summit]

yes

[winter comet]

🤦‍♂️

[willow bear]

you sure you didn't mean m_2 = -1/m_1?

we are talking about the tangent and normal at the same point right

[winter comet]

yeah i think he did

[shadow summit]

yes

[viscid thistle]

Finally

[willow bear]

"Yes, I am certain that I was not mistaken."

[viscid thistle]

Oh good

Finally

[winter comet]

?

[viscid thistle]

So basically

M1 is gradient at tangent I think

M2 is gradient at normal

M2 = - 1/m1

[shadow summit]

yes

[viscid thistle]

Gives you the gradient at normal

[winter comet]

um

[shadow summit]

and do you know how to make both of the lines?

[winter comet]

yes

[shadow summit]

(like finding the c values?)

[viscid thistle]

Y-y1=m(x-x1)

???

[viscid thistle]

Nope

[shadow summit]

uhh, you could just do y=mx+c

[viscid thistle]

Not at all

[viscid thistle]

Isn't that harder though?

[viscid thistle]

I find this a bit similar tbh

[shadow summit]

and because the tangent and normal both intersect the original function, you can just use the y and x values of the function.

[viscid thistle]

Low battery

[winter comet]

that works, yes

[viscid thistle]

Alr put it in the charger

[winter comet]

eh, depends. you can definitely do the point slope formula though

[winter comet]

bro faked us out 🤣

[viscid thistle]

Like my teacher and book teaches me one way and my friend was teaching me in another way

Though I do find the way my teacher did easier

[winter comet]

👍

[viscid thistle]

Can't you use this for everything or is there some cases where you just have to use y=mx+C?

[winter comet]

math is confusing if it is taught confusing, but once u truly understand it its not bad 👍

[shadow summit]

y=mx+c is the standard form, y-y1=m(x-x1) is the point-slope form, and you can simplify it down to the standard form

[winter comet]

i think it might be the opposite... but it doesnt matter too much, your way is fine

you probably should know both y = mx + c and y-y1 = m(x-x1)

[shadow summit]

,,y-y_{1}=m(x-x_{1}) \ y=mx-mx_{1}+y_{1} \ c=mx_{1}+y_{1}

[obsidian monolith]

TheLord26

[viscid thistle]

What is C though

Just a constant right?

[winter comet]

just a constant

yeah

[viscid thistle]

But that's what confused me

[shadow summit]

its the y intercept, so yes a constant

[winter comet]

in fact

its the y intercept yea

[viscid thistle]

I worked with C in intregration

But I was confused when there was c in differentiation

[winter comet]

oh because you add C when you integrate an indefinite integral?

[viscid thistle]

Ehh idk, am the one asking questions lol

Idk anything tbh

[winter comet]

I haven't done integration yet 💀

i just learned it once kinda idk

[viscid thistle]

Where does binomial expansion fall in?

[shadow summit]

for expanding (a+b)^n

[viscid thistle]

It's not difficult, just too annoying to do binomial expansion

[shadow summit]

yeah

[winter comet]

is binomial expansion used for calc 2?

[viscid thistle]

I got really low battery

[winter comet]

i thought you were charging 😭

[viscid thistle]

Idk my dad told me to not use phone while charging

Imma get back to y'all

1-2 hours???

[winter comet]

hm

strange

alr

[viscid thistle]

Imma do maths in that time

[winter comet]

good luck 👍

[viscid thistle]

Wait i need smth

Just explain the 8.b to me

I will check it out

Probably gonna go offline but still

Please just explain what going on

[shadow summit]

find derivative, remember derivative is rate of change/slope/grandient

use gradient to find tangent

and normal line

[late karma]

y=-9(|x^2-0.5|)+2 Does anyone know how to describe this transformation?

[viscid thistle]

Then what's the next time?

[viscid thistle]

Is transformation calculus?

I thought it was triangles and stuff

Like reflection, enlargement idk

[late karma]

idk

[chrome ether]

graph of x^2, translated down 0.5 units and then any part of it below the x-axis is reflected over the x-axis

then reflected over the X-axis again and stretched by a factor of 9, finally translated up by 2 units

[tender mist]

Transformation is just a sneaky word to describe a shift, stretch, or reflection of a graph

[willow skiff]

Also translations are transformations, moving the graph around

And rotations

But you need to understand matrices to rotate a general function (use the rotation matrix)

Hence it's not often taught at high school level

[tender mist]

That's what I meant by shift yeah

[willow skiff]

Ah right ofc

[sour oxide]

I can provide outline

1. find the derivative that is equal to slope m
2. find the equation of tangent line whose slope is exactly m
3. Find the equation of normal line whose slope is -1/m (being perpendicular to tangent line)

[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.

[languid plank]

@tender quest can you help me cheat on my test

[hallow tide]

@tender quest can you help me cheat on my test

[warped cipher]

cheating on quizzes/tests/exam isn't allowed

[stable gull]

the rules are a lie escape the mathtrix

[warped cipher]

bro can you help me with a test im literally failing rn

also why the hmmcat

[stable gull]

idk i wanted a cool emoji

i like cats 😄

show the test ong

[warped cipher]

I was jk lol

actually I need help with optimization but that's belongs in #calculus

[stable gull]

rip

ill be on that next year tho

[warped cipher]

I'm doing precalc and calculus at same time in this semester

[stable gull]

oh i could try that

[warped cipher]

it's actually stressful lol

[stable gull]

how do i apply to do that?

[warped cipher]

I'm doing calc before precalc

[stable gull]

????

[warped cipher]

it's a hs thing

[stable gull]

im in hs

[warped cipher]

look

ok

[stable gull]

calc before precalc is crazy tho

[warped cipher]

yea lol

I'm basically living in canada and my guidance gave me two math because I'm applying for a cs program after hs

[stable gull]

oh im in 9th in usa

[warped cipher]

precalc isn't available on this semester but rather it's on night school

[warped cipher]

idk about usa tbh

[stable gull]

its a lil diff

[warped cipher]

but probably better than canada ye

[stable gull]

cus its pre calc -> calc (at my school AB or BC) -> college

nah cus u cant multi class u have to pay for extra curriculars

[warped cipher]

I'm doing calculus and they don't teach things like integrals until uni

[stable gull]

cus at school im in normal alg and outside of school im precalc

[warped cipher]

ill show a list

[tender mist]

I just started learning integrals

[stable gull]

integrals a lil confusin tbh

outside of school math class for me started doing them but im still kinda clueless

[warped cipher]

https://app.prepanywhere.com/student/prep/textbooks/calculus-and-vectors-nelson

this is my textbook

for calc

[stable gull]

im savin that one

ty

[warped cipher]

yw

[tender mist]

They're not too bad yet, but I'm only just doing them for the first time officially. I have no idea how hard it'll get, just that it'll be hard

[warped cipher]

I also have the precalc textbook if you want

[stable gull]

im ok i get the book 1 unit at a time

i got textbook tho if i ask the teacher

[warped cipher]

honestly I did see the basic ones but it gets harder in early uni

[stable gull]

we hop units tho

cus we went from derivitives back to limits than to limits of peicwise functions than to integrals

:/

[warped cipher]

derivatives is so fun

never found it hard

but I've seen a lot people's questions in help channels and I was curious about them

e.g. the ones that has e

[tender mist]

Yeah e is a nice one

[warped cipher]

yeah

I want to learn it but they don't teach it here until like in uni lmao

I should probably start with some stuff I want to learn

[stable gull]

is there a science version of this server?

[warped cipher]

in #old-network

there's also a biocord if you want

but it's not linked there

[stable gull]

ty

[warped cipher]

np

[willow bear]

<@&268886789983436800> troll.

[languid plank]

Dude wtf is good with trigonometry

I’m on cosine sine and ya get of pi/6 and pi/3

And I’m so unbelievably lost

I mean dude doesn’t even try to ease into it from composite and inverse functions

Anyone can help?

[summer ruin]

if you have a question ask it

[languid plank]

My question is everything

I’m just gunna keep watching it until I can fathom what’s slightly going on then see if I can ask a question.

Bc rn I don’t even understand it enough to ask a question lmao

Khan academy I feel like they don’t even teach it and just assume you know and they do a practice problem and you have to follow along and use your own intuition to learn.

[worthy ocean]

s

[winter comet]

that looks like they are using it, not teaching it

they might be teaching it somewhere else?

[winter comet]

or rather, teaching you how to use it rather than teaching the concept itself

[tranquil inlet]

How do put tan(csc^-1 x) in terms of x

[honest aurora]

what's csc(x)

in terms of either sin cos or tan

[tranquil inlet]

1/sin

[honest aurora]

so

[tranquil inlet]

But like idk how to do the inverse

[honest aurora]

tan(1/sin(x))

[tranquil inlet]

Wouldn’t that be just for tan(csc x) and not inverse csc

[honest aurora]

true true

tan((1/sinx)-1)

[tranquil inlet]

then how would u write this in terms of x

[honest aurora]

hmm

lemme look up csc(x) properties

if there are any

wait

[tranquil inlet]

ok

[honest aurora]

is csc(x) cosec(x)

[tranquil inlet]

yea

[honest aurora]

and is cosec(x) 1/sec(x)

[tranquil inlet]

yes

[honest aurora]

whats sec(x)

[tranquil inlet]

1/ cos x

[honest aurora]

so cosec(x) = cos(x)

right?

[tranquil inlet]

oh wait thats not right

cosecant x = 1/ sin x mb

csc x = cosecant x

[honest aurora]

okayy

[tranquil inlet]

bro i plugged in mathway and i got

[honest aurora]

💀

[tranquil inlet]

rad((x-1)(x+1))/(x-1)(x+1)

i am confused

[honest aurora]

yea me 2

[tranquil inlet]

;(

[honest aurora]

lemme try finding it without mathway*

[tranquil inlet]

XD

ping me

[honest aurora]

💀

[tranquil inlet]

imma go try tosolve some more problems bye

[honest aurora]

yea bye lol

[light forge]

Help

the first one

im dying

[stray girder]

can you find 2 in the x column

i mean row

[light forge]

Crap i meant the second one

[stray girder]

can you find -2 in the f(x) column?

i mean row

[light forge]

Yes

aint it the furthest on the right?

Idk im trying to do homework but im tipsy so like-

[stray girder]

drink some water

and then tell me what you see around the -2 and whether any of that stuff seems relevant

[winter comet]

you need an equation to solve for x lol

yeah i really don't know what you mean by "in terms of x"

[winter comet]

f(2) means when x = 2, what is f(x)?

[light forge]

f(2)?

[viscid thistle]

hello

can someone help with this?

i cant figure out the way somehow

like f(x) looks like some e function but idk

[winter comet]

what does upsidedown A mean

[viscid thistle]

its for all

sign

[winter comet]

🤣

im really bad at terminology

[viscid thistle]

its ok

i just need answer

the solution is f'ing long

i want an alternative

coz i think there should be

viper bro found smth?

[winter comet]

nah i haven't really made too much progress

we don't know f(1),f(2),f(4), and f(5)

i'm interested to know the solution tho 💀

I also know that f(2)*f(1) = 1600

am i stupid

i am stupid

i might be able to make progress, gimme a bit of time

cuz we do know f(1) XD

wait

mb

no we dont

we know f(0)

so yea idk

[viscid thistle]

yeah

we know f(0)

and f(3)

but idk anything more

[winter comet]

i was also thinking we know f(6) but i don't think its helpful

lol

[winter comet]

we know 5f(3) = f(2) * f(1)

so f(2)*f(1) = 1600

[viscid thistle]

yeah

[winter comet]

not sure if thats useful tho

[viscid thistle]

lol

[winter comet]

💀

[viscid thistle]

we need individual sums

[winter comet]

yeah

[viscid thistle]

i thought 30 mins straight

then saw the solution

[winter comet]

if we were going up to a number bigger than 5 we'd be completely screwed

[winter comet]

💀

[viscid thistle]

but i found my brain fried

[winter comet]

you didn't understand the solution?

[viscid thistle]

nah

[winter comet]

dang

[viscid thistle]

it just fried my brain

[winter comet]

can you send a pic?

[winter comet]

🤣

[viscid thistle]

it actually has my email

and phone number

[winter comet]

oh

💀

[viscid thistle]

as watermark

so i am hesitating

[winter comet]

wiat what 💀💀

[viscid thistle]

wait let me see

[winter comet]

don't do it if you can't remove those lol

[viscid thistle]

wait let me pull some tricks

[winter comet]

the answer might involve not solving for each individual term but rather the entire thing

like maybe a converging sequence or something idk if its called that 💀

[viscid thistle]

nah it isnt working

[winter comet]

dang

alr

hmm

[split pelican]

What’s the problem

[winter comet]

^

[split pelican]

Oh helllll nah

[winter comet]

💀💀

[split pelican]

I ain’t trained for that sorry

[winter comet]

👍

i aint trained for it either

but i want to know

so uh

...

[viscid thistle]

trying new stuff is a part of being a mathematician

im more of a hustler than a mathematician

tho

[winter comet]

tru 🤣

by the way is this precalc?

[viscid thistle]

yeah

functions and stuff

[winter comet]

ah

[viscid thistle]

so thought precalc

there should be a calc channel tho?

[winter comet]

yeah

it may not be

but it MIGHT be a calc 2 thing

sequences and series

but might not

[viscid thistle]

nah this isnt sequence

[winter comet]

alr

[viscid thistle]

u know jee

?

[winter comet]

i havent taken calc 2 so yk...

xD

[viscid thistle]

heard of it?

[winter comet]

heard of it, don't know what it is

[viscid thistle]

india

joint entrance exam

[winter comet]

ah

[viscid thistle]

its the 1st part level sum

[winter comet]

this is a question from there?

[viscid thistle]

yeah

infact this is a qn of the easier part of jee

lol

[winter comet]

😭

[viscid thistle]

now guess the tough part

[winter comet]

😭 😭

i have no idea 😭

[viscid thistle]

lol

ok thanks for trying

[winter comet]

👍

if you/anyone gets the answer feel free to ping me or smthn lol 💀

[viscid thistle]

ok

i can dm and send the solution tho

if you are fine with it?

[winter comet]

sure

[chrome ether]

plug in $y=0,$ $x=1$ to extract $f(1)$

[obsidian monolith]

elrichardo1337

[chrome ether]

viper you're completely barking up the wrong tree here, it might be better to just

not

[winter comet]

yea....

[winter comet]

aight

now on a completely different topic

does anyone know how to solve this problem that i found?

💀 💀 💀

[chrome ether]

try this as the first step

the form of that FE makes me think it’s some sort of exponential

since $a^{x+y}=a^x\cdot a^y$

[obsidian monolith]

elrichardo1337

[willow bear]

i'd go for f(0) first myself

[chrome ether]

ah yea

[winter comet]

f(0) = 5

wait

i think it is but the way i got there is faulty

[winter comet]

how do you get f(0)?

[willow bear]

your functional equation is f(x) f(y) = 5 f(x+y)

what can you put for x and y so that f(0) appears somewhere

[winter comet]

0 for both, or -1 and 1 or stuff

but those arent useful

so 0 for both

actually

[willow bear]

well then do it, what do you get

[winter comet]

f(0) = 0 or 5

[willow bear]

you can narrow it down to one of these

[winter comet]

5, but why isn't it 0?

[viscid thistle]

This is kinda stupid but, what's a denominator?

[willow bear]

consider: $f : \bR \to (0, +\infty)$

[obsidian monolith]

Ann

[willow bear]

the bottom part of a fraction.

[winter comet]

the bottom of a fraction

[viscid thistle]

What's the one called above the fraction?

[winter comet]

oh they said that in the problem 💀 mb

[willow bear]

numerator

[viscid thistle]

Alright thank you

[winter comet]

ok so yeah f(0) = 5

f(3) = 320

is what we know so far

[willow bear]

find f(1)

by, again, plugging in some suitable values for x and y

now that you know f(0) you can use it

[winter comet]

5f(1) = f(1) * f(0)?

that doesnt get us anywhere nvm

uhh

hmm 💀

[viscid thistle]

A fraction cannot have a denominator of 0, can it have a numerator of 0?

[winter comet]

yes

[viscid thistle]

Alr

[winter comet]

and if the numerator is 0, the result will be 0 (as long as the denominator isn't 0)

[willow bear]

#prealg-and-algebra is more appropriate for questions of your caliber btw @viscid thistle

[viscid thistle]

Alr

[winter comet]

the only equation i can plug anything into is 5f(x+y) = f(x)*f(y)

[chrome ether]

what a completely vacuous statement

plug stuff in.

[winter comet]

yeah ok

5f(1) = f(0) * f(1)

[willow bear]

how's it vacuous

[winter comet]

5f(1) = 5f(1)

[willow bear]

anyway hang on a minute

[winter comet]

f(1) = literally anything...

we got nowhere 💀

[willow bear]

we need to use our knowledge of f(3) as well

[winter comet]

yeah

[willow bear]

f(x) f(y) = 5 f(x+y) implies f(x) f(y) f(z) = 5 f(x+y) f(z) = 25 f(x+y+z)

[winter comet]

um

how does 5f(x+y)f(z) = 25 f(x+y+z)

[chrome ether]

that’s just substitution, nothing particularly deep about it

[willow bear]

by applying the very same equation

[chrome ether]

you’re applying the identity given by that functional equation yea

[willow bear]

f(x+y)f(z) = 5f(x+y+z)

there is just an extra factor of 5 on both sides

[winter comet]

uhhh

[chrome ether]

this is literally just basic algebra

[winter comet]

🤔

[willow bear]

i am applying the same functional equation

only instead of x and y i have x+y and z respectively

do you understand this y/n

[winter comet]

no

my brain hasn't processed it 💀

[chrome ether]

what is there to process, it’s just a straightforward substitution

write it down if you have to

I find that often helps

[winter comet]

i am writing it down

what did you substitute f(z) with?

f(x)f(y) does not = f(x+y)

i think thats what ur trying to say it does, but im pretty sure it doesnt

[chrome ether]

you dropped the extra factor of 5

read carefully

[winter comet]

yeah but how did you get the five

what did you plug in for f(z)

[chrome ether]

they didn’t plug anything in for f(z)

they’re leaving f(z) the same and turning f(x+y) into 5f(x)f(y)

[willow bear]

you've got it a little backwards

im starting with the product of three values of f

[chrome ether]

oh lmao

[winter comet]

i understand everything except the 25f(x+y+z)

how did you get that

you can't just add z into the input function like that...

what am i missing lol

it looks like you did something like

[chrome ether]

who says we can't?

let a=x+y,b=z

f(a)f(b)=5f(a+b)=5f(x+y+z)

[winter comet]

wait

got it

i see

so like

f(x)f(y) = 5f(x+y)
letting f(x) = 5f(x+y) and f(y) = f(z)...
5f(x+y) times f(z) = 5 times 5f(x+y+z) = 25f(x+y+z)

😭

i can't think straight im tired

[willow skiff]

go sleep on it then

[winter comet]

25f(3) = f(3)f(0)f(0)
1600 = 320 times 5 times 5
got nowhere again._.

[winter comet]

yaa i think thats what im gonna do gn 💀

[willow bear]

25 f(3) = f(1) f(1) f(1).

oh oops, i'm late.

[viscid thistle]

wow

my qn made people think a lot

i think

[viscid thistle]

woooooww

@willow bear ur a genius believe me

[viscid thistle]

how did this slip my mind

a big round of applause

rest are easy to find

finally it will be a gp

and the solution is pretty straightforward

[viscid thistle]

this is the shortcut i was looking for

[silent oasis]

I want to learn calculus from the basics. From where do I begin?

[uncut mulch]

ensure you have the pre-req knowledge:
algebra, coodinate-geo, functions, trig, exponents/logs

[viscid thistle]

extra stress on "trig"

[willow skiff]

https://mathwithbaddrawings.com/2021/07/19/the-seven-deadly-sines/

https://matheducators.stackexchange.com/questions/926/whence-the-everything-is-linear-phenomenon-and-what-can-we-do-about-it

If you understand that sqrt(x + y) is not sqrt(x) + sqrt(y)

sin(x + y) is not sin(x) + sin(y)

ln(x + y) is not ln x + ln y and so on

You're pretty much there

[manic ledge]

Wait what? Doesn't arcsin(sin(x))=x?

[agile cloak]

can anyone give me a basic idea about calculus

[solid pilot]

No

Just like $\sqrt{x^2} \neq x$

[obsidian monolith]

Daddy_314

[solid pilot]

Actually Cauchy asked the same question

Which functions satisfy
$f(x+y) = f(x) + f(y)$

[obsidian monolith]

Daddy_314

[solid pilot]

Finding solutions f to this functional equation can be very easy if we suppose f has certain properties

But there are extremely strange monstrosities that can verify this

https://en.m.wikipedia.org/wiki/Cauchy's_functional_equation

[viscid thistle]

This really cracked me up wow

[viscid thistle]

I don't do this really smth happens to my gut that doesn't just let me do it

[static cliff]

I made a derivative tracer

https://www.desmos.com/calculator/aj5qqwmuoc

It has 2 different equations

[willow skiff]

No, only sin(arcsin x) = x

arcsin(sin x) is only true for x between -pi/2 and pi/2

[spark prawn]

do any of you know how to solve cubic to get the eqaution?

[willow bear]

bad wording on your part again

[spark prawn]

my bad sorry

[willow bear]

just to confirm: what you actually want to do is to find the equation of the orange curve, yes?

[spark prawn]

yep

[willow bear]

and you also specifically know it's a cubic equation

ok right...

!status

[tender quest]

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

[spark prawn]

ummm am I supposed to do something?

[willow bear]

you were supposed to answer the status query, which you did

ok

[spark prawn]

I see ok

[willow bear]

so let y = f(x) be the equation of this curve, which we don't know yet

immediate idea: if we shift this thing down by 10 units, we get a cubic with a single root at x=10 and a double root at x=30.

do you see what to do with that?

[spark prawn]

oh yeah

so you are taking it to the x -intercepts

[willow bear]

i don't know what you mean when you say "it" or "taking it"

[spark prawn]

and so you get like an eqaution I think y = a(x-10)^2(x-30)

[spark prawn]

oh like shifting the cubic downward to the x intercepts

[willow bear]

a(x-10)^2(x-30)
the square is on the wrong factor

[spark prawn]

so the cubic graph would have point such as (10,0) and (30,0)

[willow bear]

30 is the double root

anyway

f(x) - 10 = a(x-10)(x-30)^2

[spark prawn]

oh yeah my bad

[spark prawn]

why is it f(x) - 10?

[willow bear]

so let y = f(x) be the equation of this curve, which we don't know yet
immediate idea: if we shift this thing down by 10 units,

[spark prawn]

oh I see ok

so I have to use one of the point to get the a value

[willow bear]

yes

[spark prawn]

and the formula is f(x) = a(x-10)(x-30)^2+10

[willow bear]

yes

[spark prawn]

I got something like f(x) = 0.006(x-10)(x-30)^2+10 after substituting the point (40,30)

is it correct?

[willow bear]

,calc 0.006 * (40 - 10) * (40 - 30)^2 + 10

[obsidian monolith]

Result:

28

[willow bear]

can you tell me the exact value of a that you got

it can't have beeen 6/1000

[spark prawn]

20/3000

[willow bear]

or 1/150, for short.

[spark prawn]

yeah

[willow bear]

,calc (40 - 10) * (40 - 30)^2 * 1/150 + 10

[obsidian monolith]

Result:

30

[willow bear]

ok that checks out then

[spark prawn]

I added in desmos and I got pretty close

[willow bear]

why do you still put 0.006 ????

[spark prawn]

is it 30?

oh wait I am dumb yeah it works now because I needed to add 1/150 or 2/300

THANK YOU

wait

do you know how to do the horizontal shift?

like shifting cubic horizontally

[spark prawn]

and I really mean thank you because I have like a internal tommorow sooo THANK YOU SO MUCH

[static cliff]

I updated the derivative tracer

https://www.desmos.com/calculator/lrskreedkt

Now you change more stuff

[loud valve]

can someone explain how to do this

[chrome ether]

you know the roots and the y intercept

that uniquely determines the polynomial (assuming minimal degree)

[loud valve]

that just confused me even more

[winter comet]

do you know what the roots are?

[loud valve]

idk anything dawg

i was hoping someone could explain it

[winter comet]

lol

[winter comet]

i honestly don't actually understand how to do it either

but i can at least try to explain what he said ._.

[loud valve]

PLEASSESJE

AND IN DEPTHEYRFDK

theres like
20 quesigtoms

its been 3 hours

[winter comet]

x^2 + 3x + 2 = 0
do you know how to solve this for x?

[loud valve]

brain is saying no

i feel like i do

[winter comet]

ah

well you can factor that ^

so like

(x+1)(x+2) = 0

do you see how i did that?

[loud valve]

yea

[winter comet]

or like

yeah

so do you know for what values of x is this true?

u ok? XD

[loud valve]

would it be -1

[winter comet]

yes, but there is also another solution

[loud valve]

or -2 to get rid of the 2

[winter comet]

yes

-1 and -2 are called the roots

they are the values of x that are true when the y value is 0

y = x^2 + 3x + 2
-2 and -1 are the roots

when x = -2, y = 0. also, when x = -1, y = 0

right?

[loud valve]

yea

[winter comet]

alr

so in your problem

what x values make y = 0

like

when y = 0, what are the x values?

a.k.a the roots?

am i losing you lol

[loud valve]

a little bit

[winter comet]

alr

[loud valve]

would it be -3 and -4

[winter comet]

yes, but also 1

do you see why?

[loud valve]

ah yes

[winter comet]

yeah

and also the y intercept

is basically the opposite

so like

instead of "what is x when y = 0"

its

"what is y when x = 0"

[loud valve]

-3

[winter comet]

yeah

after that, I think i know the process, but i got it wrong so it may be better just for someone else to come here...

lol

[loud valve]

NOOOOOOOOOOOOOOO

[winter comet]

XD

i mean

[loud valve]

DONT BLUEBALL ME LIKE THATT

[winter comet]

LOL

[loud valve]

https://tenor.com/view/byuntear-baby-cry-crying-gif-25019897

[winter comet]

🤣

wait

i know how to do it

i just messed up on the algebra LOL

i got it now

[static cliff]

Okay

I think I know how to do this

You just have to compare the graph they showed to the parent graph

Since it changes direction 3 times

Its a cubic

So the parent graph is like the simplest version of that type of graph you can have

So it will be x^3

Now just like the factoring gave you x+2=0, and you got that x=-2

You can just flip the sign for the "roots" which is the part where what number for x makes y=0

Which he explained before

So x+2 is called the factor form

So now you need to write -3,-4, and 1 in the factor form

So that you can make the equation

So just like the example he showed before you think of it like thtis

You are looking at when x=-3 on the graph

So just add 3 on both sides to cancel it out

So the factored form for that would be x+3

So for the -4, it would be x+4

And for the 1, it would be x-1

So you factors are, x+3, x+4, and x-1

In the equation for them to work you would multiply them all together

So it is, (x+3)(x+4)(x-1)

But just like he showed you there is a y-intercept which is what number for y makes x=0 you have to count that also

So instead this time you will use y not x for your factor

So it would be y=-3

So for that it will be y+3=0 as your factor

Also, the equations are equal to y normally, but know they will be equal to y+3 because the equation the showed on the screen had a y-intercept as a different point instead of (0, 0)

S you would have, (x+3)(x+4)(x-1)=y+3

To make it easier to graph you would subtract the 3 onto the other side

So it is y=(x+3)(x+4)(x-1)-3

So with the picture I cannot really tell if there is any compress or stretch

But if there is no compress then that would be the equation for the graph

But if there is a compress or stretch then you would need to multiply by something in front of all of the parenthesis(factors) that are being multipled by eachother

I hope that helps

[loud valve]

this is what it does

[winter comet]

nah, thats not actually how you do it

i tried that too

initially

but then when x = 0, y would = -9

which is no longer the y intercept

what you actually have to do is start with the roots and MULTIPLY to satisfy the y intercept

so like

y = a(x+3)(x+4)(x-1)

right now, if x = 0, then y = -12a

it should be y = -3

thus, a = 1/4

the reason you multiply instead of add is because it makes the y intercept true without changing the x intercepts

so it would be

y = (x+3)(x+4)(x-1)/4

and while this could be correct, usually when writing an equation of the line they like it factored out

if that makes sense

[loud valve]

YES

OMG

TY

LUV U

[winter comet]

💀👍

[hybrid inlet]

Hey! Does anyone have any good resources for AP Precalculus (as opposed to general precalc)?

[static cliff]

Ohhhh

Yeah

Thats why I said there might be a compress and stretch value

That I don't know

[chrome ether]

their syllabus and sample questions are always a good place to start

finding a lot of AP style questions will obviously be difficult since this year is the first time they'll be doing that test

[lavish heath]

Can someone help me with this?

[chrome ether]

first find the paths from A to B

then the paths from B to C

[lavish heath]

And then just multiply, i guess

[chrome ether]

yeah

[pallid granite]

Hiii is basic calc also included in this chat?? Or just precalc?

[proven void]

worst case you get redirected to #calculus or #multivariable-calculus

[pallid granite]

Ohhh okay,, thanks for the info !!

[remote sable]

can we differentiate constants? would this become 3ax^2 + 30x - 39 ?

or do we leave b in so 3ax^2 + 30x - 39 + b

[sudden musk]

Do you know the rules of differentiation?

[remote sable]

i know that you multiply by the power and subtract 1 from it pretty much

any specific set of rules no just been using that one for now

[sudden musk]

alr

wait lemme send the rules of differentiation which may come in handy

[remote sable]

ok

[sudden musk]

Add one constant product rule

[remote sable]

what does it mean by equal to 0

[sudden musk]

d/dx(ax) = a * dx/dx

[sudden musk]

If you take the derivative of a constant, for example 2, then it is 0

[remote sable]

im not sure i understand

(ax) is representing y here right

[sudden musk]

Yes, you can define y = ax

[remote sable]

why is that equal to a * dx/dx (what even is dx/dx)

[sudden musk]

Because we take the constant out from the differentiation if it is attached to the variable

Have you not learnt these rules?

[remote sable]

no

there were definitely slides about them

[sudden musk]

You're answer is correct here

[remote sable]

but my teacher skipped a lot of slides

[sudden musk]

oh

Then I would suggest looking into YouTube or google for it

[remote sable]

alr

could i ask you back more questions in a little while i need to break my fast soon and prepare everything

[sudden musk]

Sure

[remote sable]

alr thanks

[white stump]

if its not making sense to you just based off of the rule, you can always think about the slope of y=a, where a is some constant. if a=2, then y=2, and y=2 is just a horizontal line with a slope of zero. so no matter what a you pick the slope will always be zero

also for the other "constant rule", if you have a constant "a" multiplying a function, then it's equal to "a" times the derivative of that function. once again, if you like to think about it more as the slope of a curve, then "a" can be seen as a "scaler" to the slope of the curve at any given point, and since the focus is just on the slope, which "a" is multiplying, then the derivative of a(f(x)) is just a(f'(x))

[viscid thistle]

They missed the rule used in integration or, is that just another derivation of the power rule?

What's the constant rule though? Never heard of it before.

[icy star]

the image literally says what the constant rule is

[winter comet]

the derivative of 8 is 0. c = constant, so the derivative of c = 0

it isn't a variable

if it were a variable, then you'd use the other rules

like x is a variable, c is a constant

[winter comet]

those are just the derivative rules, not the antiderivative rules.

[viscid thistle]

Yoo what? Antiderivative????

What are those?

[winter comet]

um

you know when you take the integral of something

you do something to the function

and add C/

[viscid thistle]

Yeah

[winter comet]

or you take that function and subtract the bounds

[viscid thistle]

No i know that

But what are they

[winter comet]

that function is the anti-derivative

[viscid thistle]

Are there many?

[winter comet]

you mean many rules?

[viscid thistle]

Yes

[winter comet]

idk

i don't know them really

[viscid thistle]

Ahh

[winter comet]

all i know is

you add one to the exponent and divide by the new exponent

basically do the opposite of what you would do with a derivative

[viscid thistle]

I see

So this applies to the product, quotient and chain rule aswell?

[winter comet]

i don'tk now

lol

[viscid thistle]

Alr i will check it out later then

[winter comet]

lmk if you find out XD

i have a very basic understanding of integrals

[white stump]

sort of

there are techniques that we use to do antiderivatives

not quite a formula

[winter comet]

if you find the function is sort of in a product-rule state then you can go backwards i guess right?

but that would probably almost never happen 💀

[white stump]

yes using integration by parts

oh sorry that would be a substituion

integration by parts is two function times each other

if you have a f'(g(x))g'(x) you can substitute u=g(x) and because you need dx in an integral you also need du so du=g'(x) so it gets replaced now you integrate f(u)du

[winter comet]

oh that's interesting

[ebon ridge]

I just took at a look at calculus for the first time, this is some crazy stuff

It seems very interesting though

[winter comet]

I think calculus isn't that hard to understand or remember, but it may be hard to learn depending on the way it is conveyed to someone.

like once you get it, its relatively easy

before that, its like wth is going on 💀

i mean different people have different experiences but i think this is just generally true

[chrome ether]

introductory calculus is not very deep and often taught in an extremely boring perfunctory way

(above all it’s just an algebra skill check, nothing that interesting is going on)

[winter comet]

hm

maybe im prolly just doing introductory calculus 💀

[winter comet]

unless that actually sounds like either precalc introducing calc or calc 1 entirely through maybe like half of calc 2 as i understand it 💀

actually wait

nah

i have no idea what you're talking about

lol

[chrome ether]

it is literally just algebra

derivatives?

algebra

integration?

algebra

[winter comet]

the math part is algebra yeah

but conceptually things are going on

lol

[chrome ether]

they’re not particularly deep concepts?

[willow bear]

well the concept of a derivative is there

and also that of an integral

[chrome ether]

you need real analysis to really solidify the foundations of those concepts

[willow bear]

wouldn't discount those still

[winter comet]

yeah

like

i think conceptually it can be hard to learn