precalculus

[scenic coral]

No

[cloud flower]

So

8

[chrome galleon]

oooooohhh

see

[ebon barn]

Get it?

[chrome galleon]

this makes so much more sense

[ebon barn]

Nice

[chrome galleon]

then whatever what being show

shown ngl*

[ebon barn]

Yeah

[chrome galleon]

math isnt my strong suit

lol

and im taking intro and precalc 1 at the same time

[ebon barn]

Intro to what?

Precalc

[ebon barn]

?

[scenic coral]

Context?

are yall actually in precalc im concerned

[chrome galleon]

im going in for cyber security but specifically i want to do system engineering

[ebon barn]

And you’re in college then?

[chrome galleon]

so my advisor told me there is a flip class where its both

[ebon barn]

Ah

[chrome galleon]

yeah just started

[cloud flower]

Yea but like over the summer ive forgotten everything so now im relearning the fundamentals

[ebon barn]

Yeah gl with that

Do you know the unit circle?

[chrome galleon]

me or legend?

[ebon barn]

You

[cloud flower]

And so im doing practice work on every kind of problem i could face

[ebon barn]

That’s smart

[chrome galleon]

like the one with pi symbols on it right?

[ebon barn]

Yep

[chrome galleon]

then yes

[ebon barn]

Good

That’ll carry you

[scenic coral]

???

[cloud flower]

So i just need help and allat

[chrome galleon]

180 degrees ia 1 pi

is*

[scenic coral]

ok

[ebon barn]

Correct

[chrome galleon]

i remember the funny things

[ebon barn]

He’s talking about the 2D real number unit circle

[chrome galleon]

the circle chart with the pi symbols to represent at certain degrees

[ebon barn]

Aka radians

Do you need calculus to graduate Apo11o

[scenic coral]

how do u know the unit circle but not fraction multiplication

[cloud flower]

Dont question it

[cloud flower]

Its required

For me atleast

[ebon barn]

Fr

[cloud flower]

Pre calc and calc or statistics is required for me

[scenic coral]

Oh that's a lotta req

I just need to pass alg 2

[cloud flower]

I already passed algebra 2

[chrome galleon]

ya know

[cloud flower]

But i forgot it

So now

[chrome galleon]

thats a good question

[cloud flower]

I need help with pre calc

So

[ebon barn]

Calc is extremely difficult if you are still shaky on your algebra basics by the end of precalc take stats

[chrome galleon]

oop

[ebon barn]

I can help you if you want me to explain concepts or help with problems

[cloud flower]

Y=sqrtX-4

Thats literally the first exercise question

[scenic coral]

can you provide more context?

are you doing substitution?

Your questions appear confusing

[cloud flower]

Im solving for the output

Thats the only context i was given

Take the formula and figure out the output

[scenic coral]

Do u have a specific input?

[cloud flower]

Idk broski thats all i was given

[scenic coral]

are you looking for range?

That question doesn't make sense

[cloud flower]

Looking for the output

I dont know the domain

I can probably figure it out if i did

I was given notes but they dont really help me

[ebon barn]

Output probably means range

[cloud flower]

Besides showing me the types of functions like mapping equtions graphs tables and machines

[ebon barn]

Considering it’s early precalc that’s usually what they focus on

[cloud flower]

Yea

[scenic coral]

Using the word output is confusing though

[cloud flower]

Okay yea then range

[ebon barn]

y>0

[cloud flower]

In the grand scheme of things this means range yea

[ebon barn]

Anything square root can’t be negative

[scenic coral]

=

[ebon barn]

Mb

[cloud flower]

So sqrt x-4 would be equal or greater than 0

[ebon barn]

If x-4 is under the square root, then yes

[cloud flower]

It is

[ebon barn]

Use parentheses so we know the exact statement

[cloud flower]

So is that my range

Greater or equal to 0

[ebon barn]

Yep

If an entire function is under a square root the range is y>=0

[cloud flower]

Thats good to know

Theres this other wacky one that seems to be troubling me

X=2y^2

[ebon barn]

Is x the input or output?

[viscid thistle]

that depends

[cloud flower]

Input

[ebon barn]

Ok

[cloud flower]

Output is 2y^2

[viscid thistle]

sqrt(x-4) has a different range

oh sorry

I get what you mean

[ebon barn]

Solve for y

And then we get a similar case as before

y>=0

[cloud flower]

So inclusive

[ebon barn]

Correct

[cloud flower]

Alright

That step by step process is wacky

How does it work

You turned ^2 to a sqrt?

[ebon barn]

I squared both sides which cancelled the y^2 into just y

[cloud flower]

Ooh

Thats kind of confusing

Could you do a more in depth process

Also what if a function isnt under a sqrt

How would the process go

[ebon barn]

There’s a lot of cases. Not much of a universal process besides analytic reasoning which is a skill you’ll pick up as you go

[cloud flower]

Lets go back to the original i asked

X-2

Or x-4 mb

[chrome galleon]

how would i go about to solving this step?

i thought i had it but i got it wrong

[cloud flower]

Idk man

[chrome galleon]

nvm i got it

it was 9/9

[cloud flower]

Oh w

[chrome galleon]

but now im stumped

hold up

[cloud flower]

Also im starting to wonder

Is 12-y literally >= 0 too

[chrome galleon]

hmmmmmm

[chrome galleon]

nvm

im just slow sometimes

i got it

[cloud flower]

Bro im strugglin

[red bolt]

with what?

[red bolt]

?

[cloud flower]

Pre calc functions

Basically im relearning the fundimentals of functions and all that

And i dont get any of it since i forgot it

But im starting to understand little by little

@red bolt

And im seeing if x=12-y is inclusive or not making it >=0

[scenic coral]

Isn't that just R

[cloud flower]

Real numbers is negative infinity, infinity is it not

= is anything that is inclusive

Either way its still a function

[red bolt]

sorry i was offline

[red bolt]

technically yes

[cloud flower]

Why technically

[red bolt]

to sound smarter

[cloud flower]

Dawg💀

Okay but like tell me what makes an equation a function

Nvm i remember now

[red bolt]

lol

[thorn creek]

equations are not functions

[red bolt]

ruh roh

[candid jetty]

Hey guys I’m back

Got a 55 on a 10 question quiz

So thanks for helping, I would’ve gotten a zero without you

[winged wave]

Hey guys I’m self studying pre cal. Does anyone know whether khan academy is good for that

[uncut mantle]

Id say its pretty good

[lapis bramble]

anyone know why it say's I used the wrong variable?

[lapis bramble]

I've done a lot of it and now school started and I whold say it's really helpful

[winged wave]

Ok Ty

[winged wave]

You don’t need the y= part

[lapis bramble]

oh shoot how did I not see that. Thanks

[winged wave]

Np

[foggy frigate]

So i know how to find doubling time but how am i supposed to with just this graph?

[thin elm]

😭

[foggy frigate]

Nah bruh they done did me dirty 😣

[halcyon heart]

puro mexico

[digital marsh]

what is the name of that formula again ?

[thorn creek]

!memes

[tender quest]

memes go in #chill

[viscid thistle]

🥲 i just used it

[keen arrow]

Can someone help me please

With precalc

[junior plover]

just send the question

[thorn creek]

or not

[bold osprey]

quadratic formula

[slim steppe]

Say that your head is the origin with your hands being a parabolic curve and your hands are above an imaginary line that is laying on your head. You could use the quadratic formula there to determine how far your hands are from your head

[thorn creek]

is it just me or do the guyt's arms in that image above form a parabola

[uncut mulch]

nah, its cosh

[foggy frigate]

Guys i dont get this, i don’t understand how im supposed to find it through the origin

Wait was that deleted ? Bro i dont need an answer i just need some sort of clue

Well dont tell me the answer , i just need some light help

[brave coyote]

What

[winged wave]

Well if you know what type of general equation a graph like this has, then try plugging in the points. Also think about it’s y intercept and the constant your are adding to your equation

[swift flax]

Hi! I have some questions about pre cal. Dm me!

[foggy frigate]

I FOUND IT!

Ahdlgodfmtmprph

Lets goooo

My work is never well organized 😭

The messier the most likely im finding it

Y= -8(1/2)^x+8 💪

[lament seal]

idk how to make the denominators the same

[viscid thistle]

$x^2-9 = x^2 - (3)^2 = (x+3)(x-3)$

[obsidian monolith]

dimpledoink

[grand girder]

What would u do next

Nvm

[rapid plinth]

Anyone wanna help me out w these last two boxes

Pretty please🥺

[shy sonnet]

I think the last two boxes are both 18 because you use the formula "i+n-1" where i = top number, n = bottom number when finding the number of terms in a series. (19+0-1=18).

[eternal swallow]

Convert x²-9 to (x+3) (x-3) and multiply the other fraction by (x-3). Then add the numerators and simplify as much as possible

Just realised you posted the message yesterday💀

[keen arrow]

can someone help me

with precalc

PLEASE

[willow bear]

if you want help you'll havae to post the problem(s) you want help with

[odd vortex]

does newtons method uses linear approximation?

how it all connected

where is everyone

[foggy frigate]

I typed 24 and 25 and it still marks it wrong

Is homework being picky or am i straight up wrong? This is supposed to be simple

[frigid cape]

Perhaps you meant 2024 and not 24?

[foggy frigate]

😦

Bruh thank you

[chilly tundra]

howdy Im doing running start going into precalc

[unborn thorn]

anyone tryna help me w a lowkey basic but making me feel stupid question for precalc

[unborn thorn]

nobody 😦

[scenic coral]

You can do it part by part

Pretty easy once you get started

[unborn thorn]

i did

[unborn thorn]

but i struggle at the x and y intersect part

can u show me what u got?

[scenic coral]

I just did the y intercept and the x intercept automatically occurred

¯_(ツ)_/¯

[unborn thorn]

what u get?

[scenic coral]

forgot 💀

I think it was like 6x(x-2)/[(x+2)(x-2)]- 4?

[unborn thorn]

oh shit

i did 2x on top

and got stuck

[scenic coral]

ah, yea u need to account for -4

xd

[unborn thorn]

alr

thx

have a g1

[grim maple]

can't cope up with calculus

[odd vortex]

help me

i dont understand what this means nd what to do can someone

explain

[zinc fulcrum]

use mvt: $$\frac{\sin(b)-\sin(a)}{b-a}=\sin'(c)$$ for some $c$

[obsidian monolith]

layla

[thorny cypress]

he did it in #calculus haha

he crossposted it here

[zinc fulcrum]

oh lol

[viscid thistle]

can someone pls explain how to find B

[wintry cobalt]

i need some help with these. ik there’s a trick or rule that im forgetting about

[viscid thistle]

Was I able to to answer this correctly?

[sleek cipher]

No, you didn't isolate the absolute value first.

[viscid thistle]

I think we're good now 👌💯

My textbook was showing me a different way - still got same answers tho.

[quartz oxide]

excuse me, what is an rF value?

[patent crow]

Hi #precalculus
(I’m merely guessing that this question is appropriate for here….)

I have a question about terminology:

Given two functions which are composed into each other, we know that this operation is not generally commutative. So we may distinguish between f o g and g o f. What do we call the function on the right, and what do we call the function in the left?

For context, other non commutative operations have names for their last and right sides. Minuend vs Subtrahend and Dividend vs Divisor, etc.

source on that image. https://kids.britannica.com/kids/assembly/view/200345#:~:text=In an addition equation%2C addends,multiplied to give a product.

[pine geyser]

Hi everyone, can someone please explain to me why these graphs intersect at three points?

[remote dune]

i'm no expert but i think it's the same values from intersection 1 to 3

[pine geyser]

Thanks for the reply, but I want to ask why it intersects in 3 points instead of 2

[pine geyser]

<@&268886789983436800>

[sleek cipher]

You are using the wrong rule here.

Essentially this means that if |u| is greater than or equal to any positive value, it is less than that negative value and greater than the positive value.

[sleek cipher]

I think the middle point is trying to denote the midpoint.

If that is the case

[pine geyser]

I found out why, thanks

[cerulean gyro]

would this be a jump or a hole

[scenic coral]

Does it look like a jump or a hole?

oop that sounds worse than I thought

the lines are not meeting meaning it's a jump

lines "jumping"

[cerulean gyro]

o ok

so it can be a jump if both endpoints are holes

[scenic coral]

what

[cerulean gyro]

like

cause normally i only see jumpslike

[scenic coral]

If the lines are not meeting it's a jump, i don't think thinking of the open/closed circles is a good idea

[cerulean gyro]

o ok

got it

thanks

[sleek cipher]

$x^3+5x^2+6x=0$

[obsidian monolith]

Arcturus ⬡

[sleek cipher]

can someone explain how to find the solution to this using the cubic formula?

[rugged crater]

does it say to use the cubic formula?

or can you use anything

because if you just take out x you can just factor

[sleek cipher]

I know, I'm using this as an example problem

Mostly because I tried to do it and ended up more confused

I failed to read and it resulted in over a page of work and a lot of research

[rugged crater]

oh ok

[scenic coral]

The ... cubic formula?!

[sleek cipher]

The depressed cubic formula

[scenic coral]

oh hell nah why

[sleek cipher]

I'm actually not writing it out for you

but essentially, I can simplify this question into

this is the cubic equation, the cubic formula rearranges the function to solve for x

$\bigg(x+\frac{5}{3}\bigg)^3+\frac{-7}{3}\bigg(x+\frac{5}{3}\bigg)-\frac{20}{27}$

[obsidian monolith]

Arcturus ⬡

[sleek cipher]

The depressed equation

That is the long form, give me a moment

$x=\sqrt[3]{\frac{-q}{2}+\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}-\sqrt[3]{\frac{-q}{2}-\sqrt{\frac{q^2}{4}+\frac{p^3}{27}}}$

[obsidian monolith]

Arcturus ⬡

[scenic coral]

I still don't understand why

[sleek cipher]

this is one of the two forms that the depressed cubic takes, where the function is t^3+pt+q

(x+5/3)^3 is t

[scenic coral]

Wait you can rewrite the generalized form into the depressed form?

yo that's sick

[sleek cipher]

all cubic's can be depressed, and it makes solving otherwise unsolvable cubic equations "easier"

I'm not sure I want to even witness the quartic formula yet

there is, importantly not a quintic or beyond

[scenic coral]

it's several times longer

[sleek cipher]

actually, there is not a finite quintic or beyond

[scenic coral]

truly a nightmare

[scenic coral]

luckily?

[sleek cipher]

I know, I meant like read it and figure out how it was derived

[scenic coral]

or maybe not

[sleek cipher]

that means that the formula for the quintic and beyond could be an infinitely long formula

[scenic coral]

Yea I'd be interest too, what organ did they have to trade to the devil for that formula?

[sleek cipher]

Leibniz's, Euler's, Pythagoras', and Newton's brains /s

[copper mango]

“I don’t understand what I have to do in this exercise. Can someone help me?”

[patent crow]

you have 2 functions, f and g, and they form lines in a 2D plane.

when you graph it out, you find the area they enclose

https://www.desmos.com/calculator/bbl7e0pajl

[autumn wadi]

@cinder valve not quite sure what you're trying to do

[cinder valve]

I'm not sure either

I will wait for the prof to free and ask sth

[autumn wadi]

f(x)=2-x-ln(x) and you've found the roots of this function. U then separated the function by it's roots and graphed 2-x=ln(x). You want to find where f(x) intersects that?

is that what u mean?

[cinder valve]

I found that, I needed to demonstrate there is a real root

For something that I have to do later

To aproximate the root using successive approximations, tangents and secants

[autumn wadi]

<@&268886789983436800>

[cinder valve]

Fun

We are nerds that does not interest us

[autumn wadi]

But... if you could solve for a real root, the root definitely exists?

[cinder valve]

I guess, it's not the point of the exercise

Maybe it's still only an approximate value

[pine light]

What is the definition of vectors? In my physics class, it is said to be a quantity to represent both magnitude and directions, while my math book defines vector essentially as a n-tuple and without mentioning to neither magnitude nor direction.

[summer ruin]

neither are technically correct

you would define a vector as any element of a vector space, while elements of the vector space satisfy some properties, in particular you can add vectors and multiply them by scalars

a vector doesn't have to be an n-tuple either, continuous functions are vectors too

[autumn wadi]

Just use newton method then

[scenic coral]

How do you define a vector space if the definition of a vector is dependent on it?

[summer ruin]

a vector space is a set and elements of that set satisfy what is known as axioms of vector space

any set that satisfies these will be a vector space

[scenic coral]

Oh that way of defining it is so weird i guess it's more general?

[summer ruin]

well it looks weird untill you meet more exotic (and useful) examples of vector spaces

in particular studying vector spaces whose elements are continuous functions is pretty important as far as applications in e. g. physics and differential equations go

and it's pretty natural that you can add functions and multiply them by scalars, there's the zero function and f + (-f) = 0 (the zero function)

[scenic coral]

wtf lmao

a continuous function is a vector now ._.

[summer ruin]

when your vectors are n-tuples, you can construct matrices and diagonalize them, such that the matrix has very simple diagonal form which is easy to work with in all applications

fourier transform does similar thing, but it diagonalizes some complicated function into a sum of simple sines and cosines

[foggy frigate]

Hey guys

The dashed line is me halving it to focus on the interval 0<theta< pi/2

Don’t need the answer just something to move me along **

Cus i am stumped now since i dont know how to find max range

[foggy frigate]

I attempted a few more and got the thing wrong but i got half the points

Since my pi/4 was correct but it was the amplitude v^2/g

That would be max range

[viscid marsh]

won't the maximum range be $\theta = 45$ because sin(2*45) = 1 ?

[obsidian monolith]

David

[junior plover]

<@&268886789983436800>

[foggy frigate]

IKR? Thats what i tried

But it marked it as wrong

Good to know i wasnt tripping thinking it was 1 too

[strong epoch]

Pls

I need help

My teacher had a mental breakdown trying to explain this she was just talking to herself the whole time and never ended up helping me

How do I do 3. 4.

These are the choices

[pine light]

I don't understand all of this yet but that made things way less confusing, thank you.

If only my teacher told me that the magnitude and direction definition was sugarcoating.

[chilly void]

Is there any easy way to evaluate this summation?

[willow bear]

conjugate shit and then it'll telescope

[chilly void]

Could you explain this in a more detailed way?

[vapid plaza]

multiply numerator and denominator by $\sqrt{i}-\sqrt{i+1}$

[obsidian monolith]

elon mask

[willow bear]

sqrt(i+1)-sqrt(i) slightly better

[vapid plaza]

just trivialities

but yeah you should get something which obviously telescopes, and the problem is pretty much done

[prisma radish]

Then they're the right one probably

🤓

[strong epoch]

Ty for nothing

[chilly void]

Thanks for your help : )

[chilly void]

Thank you for helping

[viscid marsh]

how lol

[vivid iron]

doesn't n have to be greater than 30 for the central limit theorem to apply?

It doesn't say that the parent distribution is normal either

[hushed sphinx]

That's more a question for #probability-statistics.

I'm no expert, but (i) "30" is at best a rough rule of thumb, not a hard cutoff. (ii) the point of the central limit theorem is that it applies no matter whether the individual experiments are normal distributed, so long as they're independent and identically distributed.

[vivid iron]

Ok sorry ive added it to my channel list

I'm still.in high school

And the stats was in uni section

[obsidian monolith]

qathh

[thorn kestrel]

Hi, what is a_n as n approaches infinity?

[hushed sphinx]

Here's a hadwavy way to approach that:

• Obviously the limit will be somewhere between a1 and a2.
• But it will also be somewhere between a2 and a3.
• And since everything is linear it will be the same place, relatively speaking, between a1 and a2 as between a2 and a3.
• So there must be some constant k between 0 and 1 such that the limit = a1 + k(a2-a1) = a2 + k(a3-a2).
• Since you know a1, a2, and a3, you can solve for k.

[copper mango]

Someone can help me, please

[noble vessel]

A function is bijective iff it is injective and surjective

[viscid thistle]

u all are rlly smart

[copper mango]

How do I show if it is injective and subjective?

[hushed sphinx]

suRjective.

[noble vessel]

Injective -- if f(x) = f(y) implies x = y for all x,y \in Dom(f)
For surjective you need to specify the codomain first

[autumn wadi]

@digital mirage

[digital mirage]

ohhhhh thank u so much broo

[digital mirage]

how to get at that circled step from the last one

[hushed sphinx]

First, it appears, you have to invent an alpha out of thin air ...

[digital mirage]

hwp they get to that underoot 169/4 thinG

[coarse marsh]

did you read the link i sent you?

[digital mirage]

and how that underoot entered the game ?

[hushed sphinx]

169/4 = (13/2)².

[digital mirage]

ya , i know this bruhh . but how to get that full step ?

hello ?

plzz help me out

[digital mirage]

ya i overlooked it sorry , i m looking , may it help

[wise spoke]

So I had a question regarding performing row operations on matrices.
How to correctly identify what row should we perform on first? Or does it not matter since we're just converting it to row echelon form?
For example:

We're supposed to convert this into the row echelon form and then use that to get a new system of equations to solve the equation for a unique solution.
I performed the row operation shown in the picture. The book on the otherhand performed different set of row operation and got a different answer, but since we're both converting the bottom triangle to 0s, shouldn't we have the same answer?

[summer ruin]

if the answers look different it doesn't mean they are different, especially in linear algebra

[wise spoke]

Oh

hmm

alright

[hushed sphinx]

The reduced row echelon form ought to be unique, though -- but the calculaton here doesn't quite go all the way to RREF.

[wise spoke]

Hmm

This is how the book did it

[hushed sphinx]

,rccw

[hushed sphinx]

Hmm, that doesn't go to RREF either -- but the solution it gets is definitely different from yours.

[wise spoke]

Yeah, that's what I was concerned about.

[hushed sphinx]

Have you checked whether your solution actually solves the original equations?

[wise spoke]

yeah

they do

oh

nvm

i copied the question wrong

i get the same answer too

but the matrix looks different

[hushed sphinx]

Oh, your original matrix is different from the book's. You have a different sign on the 5.

[wise spoke]

Yeah lol, copied the matrix wrong

also one question @hushed sphinx

if you're finding an inverse of a matrix using row method

then no matter the order of operation

you'll arive at the same answer right?

[hushed sphinx]

Yes, you should. A matrix can only have one inverse.

[wise spoke]

Okay, thanks

[thorn creek]

matrices are so boring that way

[thorn kestrel]

thats pretty smart, thank you

[digital mirage]

here domain of x in 16 - x^2 will be -4 to + 4 but how to find sinx domain along with it ,

[noble vessel]

When's sin(x) \geq 0 in the interval [-4,4] ?

Take the intersection that's it

[digital mirage]

geq 0 means ?

like sinx domain is all real numbers so now what to do , how to combine these both . intersection means , common things in both set , so then domain will be - 4 to + 4?

[digital mirage]

,

[noble vessel]

Greater than or equal to

[digital mirage]

\ what this sign means here , i m not introduced with these short cuts

[noble vessel]

Ahh sorry just ignore that
It simply means greater than or equal to

[digital mirage]

ohk

so u mean points where sinx is >= 0 in theinterval [-4 , 4] take those point and and then take intersection ?

[noble vessel]

Yep intersection with [-4,4] (domain of f+g is dom(f) intersection dom(g))

[digital mirage]

but how to know sin value from -4 to +4 ?

like sin deals with angle

these are numbers

[noble vessel]

Visualize the Unit circle

or the sin graph

[digital mirage]

sin graph has things in pi form (domain ) how to knwo about -4 and +4

[noble vessel]

hmm the intersection step is kind of done when we restrict the solutions of sin(x) \geq 0 to [-4,4], so the solution set of this inequality is the domain of the original function

[noble vessel]

pi < 4 , -4 < -pi

[digital mirage]

oh yeeees , hmm now i got it , sorry that was dumb Q

all these could also be domain , i guess ?

cuz they all giving 0 to 1 value

so now what is domain of sinx here lmaooo

@noble vessel ,

oh yes they cant be

cuz we have limit of - 4 to +4

[noble vessel]

2π > 4 , -2π < -4 < -π

[digital mirage]

so 0 to pi is the domain here ?

[noble vessel]

so [-4,-π] ∪ [0,π]

[noble vessel]

include the negative values of x as well

[digital mirage]

but then range of sin x will not be from 0 to 1

[noble vessel]

sin(x) is greater than or equal to 0 for x in [-4,-π]

[digital mirage]

ignore that 1st line x belongs to .....

[noble vessel]

.

[noble vessel]

I was saying you need to include [-4,pi] as well

[digital mirage]

ohhhh lmaoo i didnt saw that bruhhhh

[noble vessel]

ahh no that is between [-4,4]

[noble vessel]

.

[digital mirage]

so [-4,-π] ∪ [0,π] this is the final ans ?

but pi < 4 so 4 is excluded here , it is bcz we took intersection so now these so [-4,-π] ∪ [0,π] are doamin of both fx +gx after intersection ?

ok ty very much

one more thing to ask ...

[shell nova]

[-4,4] *

[digital mirage]

but if we took 4 in domain , it will be exceed pi and then sin will give -ve value

which is not possible in underoot

[digital mirage]

no.of solution of this equation ?

[scenic coral]

Probably 1

[heavy rapids]

is x a natural number or

[digital mirage]

this info is not given

[heavy rapids]

honestly just use mod 2

[dim dove]

Only 1 solution

1.5599

[jaunty crow]

Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.)
f(x) =3/x^2

[viscid marsh]

wow dr stone irl

[broken lagoon]

anyone able to help me with compostite functions?

[scenic coral]

🤔

[jaunty crow]

i got the ans

[wise spoke]

Can someone explain how J came to be about?
Shouldn't the leading diagonals in J be 1, 0, 1?

how is -1, 1, & 2?

both my S and M values are correct but can't figure out J

[wise spoke]

nvm

got it

[digital mirage]

??

[thorn kestrel]

Hi i've got a question, what's the symbol for like "equivalent" in math? I want to write that
f(x) = 5 - x is equivalent to a_n = 5 - n (the question is about arithmetic progression, but it's written in the form of a function)
but im not sure what symbol to use

and im not sure if this is the right channel so sorry about that

[hushed sphinx]

Just use words. Do you have such an intricate argument in mind that having a symbolic notation would make it clearer what your line of thought is?

[viscid marsh]

ur username

[tardy aurora]

can anyone help me with this, im takin a quiz rn and i forgot how to do this stuff

[hushed sphinx]

If you're taking a quiz, you're almost certainly not supposed to receive external help during it.

[tardy aurora]

Hmm what if I’m not taking a quiz

[solar olive]

we would help u

but

[tardy aurora]

ok i submitted it what was the answer tho

[noble vessel]

B I and III

[tardy aurora]

damn

[noble vessel]

What did you mark?

[tardy aurora]

C

wait

no D

[noble vessel]

hmm quite close

[tardy aurora]

i thought it was 2 and 3 but wasnt sure about 1 tbh so i just picked the one with 2 and 3

[noble vessel]

hmm x-intercept is when the graph crosses the x-axis
As you can see f(x) is positive in the interval (-inf,-3) and negative in the interval (-3,1) thus value of f(x) is zero at x=-3

[tardy aurora]

thank you, I'll make sure to study the stuff before my test I suppose

[dapper estuary]

I think the answer is no.1 but the video says no.2. Pls explain if you know why

[summer ruin]

it is 1

[thorn kestrel]

take the case of x = 1 and check the answer for both 1 and 2, then compare them to the graph

[crisp bane]

Is it possible to solve a trinomial using logarithms

I tried this

[scenic coral]

tf

[digital mirage]

is it possible to find its limit without using sandwhich theorem ....

[fallen sequoia]

How would one graph cos$(2\pi x) + i$sin($2\pi x)$?

[obsidian monolith]

okeyokay

[fallen sequoia]

in the complex plane that is

we have $0 \mapsto 1$, $\frac{1}{2} \mapsto -1$, but $\frac{1}{8} \mapsto \frac{\sqrt{2}}{2} + i\frac{\sqrt{2}}{2}$, so how would you map that

[obsidian monolith]

okeyokay

[scenic coral]

you need 3 dimensions ?

[abstract portal]

no
doesn't work

given $\log_9(x) = \log_{12}(y) = \log_{16}(x+y)$, how to find $\frac{x}{y}?$

[obsidian monolith]

baba tū est

[broken lagoon]

my brain is shit could anyone help me learn some things about 1.compostiton of function

[viscid thistle]

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/function-composition

[amber comet]

can anyone help me differentiate the problem below?

[junior plover]

oh you want to differentiate?

[amber comet]

yeah

[junior plover]

you didnt mention that earlier

back to calculus you go

[amber comet]

😤

[bright tusk]

im rlly struggling w precalc im homeschooled but i do classes online i got sent to recovery like 5 times cuz idk what to do 😭

[viscid thistle]

lemma try.

@drowsy beacon hold on I am still looking for solution so do not worry answer when find out the answer.

these are very useful for me

[drowsy beacon]

bro is dedicated

[lusty scaffold]

Hey quick question dudes does the formula for arithmetic series sum start at n=0 or n=1

actually i think it n=1 cause you counting amount of terms

talkign to myself here basically but there's one for n=0,n=1 or any value you choose but just one i was thinking of was for n=1, bad question i guess lol

[scenic coral]

Plug in some numbers and see

[digital mirage]

a sequence (Sn) is said to be bounded if and only if (|Sn| <= k ) where k is a positive real number . so my Q is if this is the case so this means those sequence which have their highest and lowest value between -k and k are said to be bounded . like -k<Sn<k is bounded but -k<Sn< m is not bounded .... ? and if this is the case then why defination of bounded sequence says that Sn is bounded if m< Sn< n exist .....

what are actually bounded sequence

[scenic coral]

Why would -k < Sn < m be unbounded

[hot holly]

The sequence starts at n=1 for arithmetic sequence, and each term is a + (n-1)d

Btw I was talking about iundied’s question

[granite apex]

In mathematics, an inequality like this is typically used to describe a range of values for a variable (in this case, Sn). Whether or not it is unbounded depends on the values of k and m and the specific context in which it is used.

Bounded Range:

If there are specific values for k and m such that -k < Sn < m, and these values create a finite range for Sn, then the range is bounded. For example, if k = -5 and m = 10, then the range of Sn would be -5 < Sn < 10, which is a bounded interval between -5 and 10.

Unbounded Range:

If there are no specific values for k and m that limit the range of Sn, then the range can be unbounded. This means that Sn can take on values that are not restricted by any specific upper or lower limit. For example, if k = -∞ (negative infinity) and m = ∞ (positive infinity), then the range of Sn would be -∞ < Sn < ∞, which is an unbounded range because Sn can take on any real value.

In summary, whether -k < Sn < m is unbounded or not depends on the values chosen for k and m. If specific values are provided that bound the range of Sn, then it's bounded. If no specific values are given, and the range is not restricted, then it's unbounded.

[digital mirage]

my q is why this theorem exist if we have general understanding that Bounded Range:

If there are specific values for k and m such that -k < Sn < m, and these values create a finite range for Sn, then the range is bounded. For example, if k = -5 and m = 10, then the range of Sn would be -5 < Sn < 10, which is a bounded interval between -5 and 10.

[digital mirage]

why we need this theorem which focusing on special case of -k to + k

[static mesa]

Who ever needs help with trigonometry ping me

[onyx drum]

Probably this theorem will be used in some proofs for limits, which have absolute value in their definition

[digital mirage]

ohk

[marble scaffold]

@cinder veldt

[foggy frigate]

Guys how can i better my algebra skills

Like is there a website for that? My skills are starting to become better as I learn more calculus but I want to be able to ace calc because of my first failed test. If the concepts remain as easy as they are now then its just the algebra i need

[viscid marsh]

you got the first one

do the same for the second

[warped cipher]

that didn't make sense

but if you're looking for a website use khan academy

[golden frost]

Can anyone remind me how I would solve this problem

[summer ruin]

trig identities

[golden frost]

idk how to do those

[summer ruin]

first of all what identities can you recall

[golden frost]

well I have them infront of me . I just dont know how to use em. (Reciprocal Identities, Quotient Identities , Cofunction Identites)

[summer ruin]

what can you say about tangent

[golden frost]

opp/adj

[summer ruin]

in terms of sine and cosine

[golden frost]

uh, idk

[summer ruin]

$\tan (x) = \frac{\sin (x)}{\cos (x)}$

[obsidian monolith]

Transparent Elemental

[golden frost]

ah ok

[foggy frigate]

Sorry, main point, want to strengthen my algebra skills for calculus.

[foggy frigate]

Okay thanks

[native fulcrum]

Can someone please help me with this question

[digital mirage]

difference b/w limit point and limit of sequence

plzzz tell me in simplest way possible , i cant understand the difference

[onyx drum]

limit has all the seq members closer to it after some n; accumulation point has infinitely many, but not necessarily all

[onyx drum]

limit point and limit for seq are the same

[digital mirage]

really ? like almost same or exactly same ?

[onyx drum]

my bad, just replace the accumulation point with the limit point in the answer above and forget about limit point and limit being the same

[digital mirage]

i m asking about limit point vs limit of a sequence

[digital mirage]

@onyx drum

[onyx drum]

limit of a seq has all the seq members closer to it after some n; limit point has infinitely many, but not necessarily all

[swift oxide]

Hello, can someone help me factorize this : mx^2 -(2m-1)x + m -1 without using delta.Thanks

[viscid thistle]

limit as x—> inf

and -inf

[fiery heath]

Does anyone have any conversion sheets i can memorize?

[minor pollen]

Conversion sheets?

[willow bear]

wdym by conversion sheets?

like unit conversions?

[obsidian monolith]

Progameyen

[obsidian monolith]

Progameyen

[onyx roost]

Is it ok if I ask help for assignment

[viscid thistle]

hi sorry with respect to a calc question is 1+cosx = 2cos^2x

if so how

[hushed sphinx]

That is true only when x is a multiple of 120°.

On the other hand 2cos²(x) = 1 - cos(2x) for all x; that looks somewhat like your equation :-)

[digital mirage]

how 3 point is true (2-e , 2+e ) belongs to set {1, 2, 3 }

[hushed sphinx]

The point 2+e/2 (where e is some small positive real) is an element of (2-e,2+e) but is not an element of N.

[digital mirage]

sorry i was asking for point number 3 ,

how point number 3 is correct

[hushed sphinx]

Same, though. No matter which positive number you choose for e, the set (2-e,2+e) will always contain a number (many numbers, in fact) that is no one of 1, 2, or 3.

[digital mirage]

@hushed sphinx so this set contains only 1, 2 , 3 , and there is no numbers in between ? so { } means this ? like if instead we used [ ] or ( ) that means infinite numbers are there b/w 1, 2,3 like 1.2 , 1.3 etc

this is what ur saying right ?

[hushed sphinx]

The notation {1,2,3} means a set whose only elements are the exact numbers 1 and 2 and 3.

[digital mirage]

ohhk thanku u so much

[hushed sphinx]

The notations (a,b) and [a,b] are quite different from that.

[digital mirage]

hmm these notions means there are infinite numbers b/w a and b

[hushed sphinx]

If a<b, there is always an infinity of numbers between a and b. The question is whether those numbers are elements of the set we're talking about. The interval notations (a,b) and [a,b] are ways too say they are, but list notation {a,b,c} doesn't say any numbers other than the ones explicitly written down are elements of the set.

[delicate belfry]

Can I simplify this more. And how if I so.

[hushed sphinx]

You could write y²(8y³-2)(5-5y³) where y = e^-200t -- but whether that constitutes a simplification is up for debate.
Or perhaps even -40y^8 + 50y^5 - 10y^2.

[delicate belfry]

Ok, I see thank you

[dense mango]

Guys I need help with deriving this function, I know the correct answer to it but I'm trying to do it myself

With respect to x of course, R is a constant

[nova moat]

*for sufficiently big T

[severe pond]

How can you always factorise f(x) - f(a) by x-a?

[near flume]

I've already formally proved this by setting x = log_b(c) and y = log_b(a), but is there any nice intuition for it?

[frank vigil]

@viscid thistle

[viscid thistle]

u scared me again

look u need this

[frank vigil]

i don’t take pre calc

[warped cipher]

what's the function?

you always need plug f(x) given into the function and solve

[warped cipher]

log

[severe pond]

No it’s like a simplifying technique for when you calculate the derivative at a given point

[junior plover]

its not a simplifying technique unless you know what f(x) is

[severe pond]

For ex, f(x) = x+1/x^2+x+1 and a is -2

[junior plover]

so many pings at the same time ahh

[viscid thistle]

My friend has a "degree" from harvard university and he sent me this.

Anyone to solve it ?

[hushed sphinx]

I don't see how any of those can be said to be "PREcalculus".

[viscid thistle]

Oh sorry my bad!

I need desmos on my computer rn lol

[viscid thistle]

I’m stumped ngl

[onyx drum]

(fog)(x) = f(g(x)), won't be able to find (fog)(x) if g(x) is undefined

[sleek dome]

idk why but i like integral more than diffrential

[true bear]

Is E considered a Square matrix?

C and G are, since they got the same number of rows and columns

[thorn creek]

a 1x1 matrix is square

[true bear]

and what is a scalar matrix?

[thorn creek]

something akin to a horse bicycle?

[true bear]

huh

[thorn creek]

that's not a term i'm used to seeing

[true bear]

aight np

[thorn creek]

it looks like some people use it to refer to a matriux that is equal to kI where k is a real number and I is the identity matrix

[thorn creek]

this is not a term normally used by actual mathematicians

scalars are not matrices

[true bear]

aight

[thorn creek]

i think the idae is that it's a matrix that "acts like" scalar multiplication

[true bear]

I see

[thorn creek]

since it's a scalar multiple of the identity matrix, which is both a left and right identity for the vector spaces you'll encounter at this level of your studies

[true bear]

yeah i have scalar multiplication in my chapter

okay then, thanks

[thorn creek]

so you'll need to learn that definition even if you'll never encounter it after the class you're currently taking lol

[true bear]

gotcha lol

[hushed sphinx]

Well ... the ring of n×n matrices is an unital associative algebra over the scalar ring/field, and it's pretty common when talking about unital algebras to identify the underlying ring with its image in the algebra ... especially when that image is injective.

[viscid thistle]

I'm testing my understanding of multiplying complex numbers by explaining it in my own words

Is it correct to say that multiplying z by another complex number w results in a phase shift?

I'm having trouble concisely describing the result.

The multiplication creates a new complex number, m.
m = z*w
arg(m) = arg(z) + arg(w)
|m| = |z||w|

[pine geyser]

Can anybody explain to me why I got the answer wrong? The correct answer to this question is -1.2

I guess I have done everything right, but the answer is wrong

[candid idol]

the last step is wrong

actually idk

[raven lily]

My professor gave me this great tip about the unit circle that I've forgotten but I did write something down to remember it. Sadly, I don't think it was enough.. Does anyone have an idea of what I meant by this?

"For the unit cirlce, think about the xa nd y. Is it big x and small y or small x and big y"

[elfin hollow]

are you talking about x and y axis or what ?

[raven lily]

honestly I can't tell

I think this might be something for just tan

Cause it doesn't make sense for sin or cos

[elfin hollow]

ohh yes that is unit circle is tan (theta) = y/x

this is the definition of unit circle

[raven lily]

yeah

idk

that's my only guess

[elfin hollow]

okay but this is the definition

[raven lily]

right

which I don't think was what he was trying to show

oh well

I'll just try to email him

[snow steeple]

why is the derivative of a vector of constant magnitude orthogonal to that vector

[pine geyser]

You mean x=1?

[summer ruin]

$\frac{d}{dt}(c) = 0 = \frac{d}{dt}\left((x(t),x(t)\right) = (\dot{x}(t),x(t)) + (x(t),\dot{x}(t)) = \\ = 2\left(x(t),\dot{x}(t)\right) = 0$

[obsidian monolith]

Transparent Elemental

[candid idol]

try that

and if it doesn't work then idk lol

[onyx lotus]

anyone have a video link how to solve this? i cant find something similar

[summer ruin]

you need to show two complex numbers are equal

when are two complex numbers are equal?

[ornate depot]

How does ^3sqrt(x) even works?

[hushed sphinx]

Are you sure you're in the right place with that?

[viral mesa]

[viscid thistle]

yes'

[north anchor]

hey can i get tips on factoring x^8 + 8?

i feel like there's something i could do with roots of unity but i can't get it down

[vapid plaza]

you can find the complex roots of x^8 + 8, and pair them up to get a factorization over R

if that is what you want

[north anchor]

it is but i need to find the complex roots first lol

how would i go about that?

[hushed sphinx]

They won't be particularly nice anyway, since 8 is not a perfect eighth power. (Being a perfect third power doesn't really help us, alas).

[north anchor]

they won't be nice but how would i find them?

[hushed sphinx]

They are the eighth roots of -8, so take the eighth root of the modulus and divide its argument (± multiples of 2pi) by 8.

[north anchor]

eighth root of the modulus as in take the roots of 8 and make one negative?

i know this might be a stupid question. but i was never formally taught roots of unity so i'm a bit lost

i understand the idea behind taking the root of the modulus and the argument but idk the mechanics

[hushed sphinx]

No, just $\sqrt[8]{8}\cdot e^{k\pi i/8}$ for odd $k$.
This is not really roots of unity, just De Moivre.

[obsidian monolith]

Troposphere

[north anchor]

ah okay, thanks!

yeah i'm even less familiar with de moivre

just double checking: so $(x-\sqrt[8]{8}\cdot e^{\pi i/8})$ would be a factor?

[obsidian monolith]

peachscribbles

[hushed sphinx]

Yes, if you're okay with complex coefficients in your factors.

Otherwise you'd multiply out $(x-\sqrt[8]{8}\cdot e^{\pi i/8})(x-\sqrt[8]{8}\cdot e^{-\pi i/8})$ to get a real quadratic factor instead.

[obsidian monolith]

Troposphere

[north anchor]

makes sense, thanks!

would that be a fourth root? or are there others

[hushed sphinx]

There are 8 different roots.

[north anchor]

based on the different values of k?

[hushed sphinx]

Yes.

[pine geyser]

Ok thank you anyways

[pine geyser]

I found what I had done wrong, the part where I convert "4x^2-3x-1" to "(x-1)(x+1/4)" should be multiplied by 4, that's why the answer is four times the correct answer lol

[orchid wasp]

why does -ln(1/2) = ln(2)

im confused

[summer ruin]

1/2 = 2^{-1}

[obsidian monolith]

Bob.

[boreal escarp]

@orchid wasp

Here

[orchid wasp]

thank you

[digital mirage]

why they give this info taht f(x) = 0 when x= 4 . what is the need of this info here ?

second Q is , when they are saying f(x) = |x-4|/x-4 when xis not equal to 4 then how they are taking this |x-4|/x-4at x=4 to find the limit ?

[candid idol]

k

[sage lichen]

I have ap calculus I need help can anyone help me?

[warped cipher]

#❓how-to-get-help

[little arch]

Guess i screwed myself over

[dim thunder]

i need help with pre calc

[wind flint]

Dawg

Use the answer channels

They specifically designed for that 😭

[dim thunder]

how do i use it?

[pine geyser]

Do you know what is the answer for (f-g)(x)? If you know please reply and write it here

So we can go on with your question

[sage lichen]

@pine geyser can u help me?

[pine geyser]

yes whats your question

[sage lichen]

its a pre-calc question

[pine geyser]

ok np

[sage lichen]

so to find the answer for the first one, do i just solve the equation?

then for the second one do i substitute 5 for t?

[pine geyser]

i guess by "intially" they mean that the month is 0 right? P(0)= your answer

[sage lichen]

yh.

[pine geyser]

it is 5 years and the function "P" is based on month, so we should convert year to month which means 5 * 12(12 months per year) and we will write P(60)

[sage lichen]

and how do i solve the last one

[pine geyser]

lemme think for a sec

[sage lichen]

kk

[pine geyser]

does this function even have a limit? Im not 100 percent sure what it means by the end of the population

it goes to infinity and it doesnt approach anything as far as i know

[sage lichen]

I dont think it has a limit the question didn't state so.

[pine geyser]

idk maybe

[sage lichen]

so how do i put that in a answer?

[pine geyser]

oh no im so sorry, i havent studied the limits of infinity

[sage lichen]

I dont think its the limit of infinity then because we didn't study that too.

[pine geyser]

hmm

[pine geyser]

one of the ways you can find the limit of the function is using derivative

https://en.wikipedia.org/wiki/L'Hôpital's_rule

this is somthing i havent learnt yet

[digital mirage]

why they give this info taht f(x) = 0 when x= 4 . what is the need of this info here ?

second Q is , when they are saying f(x) = |x-4|/x-4 when xis not equal to 4 then how they are taking this |x-4|/x-4at x=4 to find the limit ?

[summer ruin]

in the neighborhood of x = 4 f(x) is given by |x-4|/(x-4)

[edgy edge]

How would I be able to solve this?

[split prairie]

can somebody help me

[jagged stump]

guys i got a cool and fun question

if you knew that f(x) = 4x^n-1
n is a true positive number
and if u knew that f'''(x) = a
also "a" is a true positive number
find out how much is a-2n

got some tricks in it

its fun to solve ngl i had so much fun solving it

[thorn creek]

what's a "true positive number"

[jagged stump]

derive it normally, 4(cos2x)(2)+1/x ln10 +1

[jagged stump]

like

normal number

not 0.2 or smth

[thorn creek]

you mean an integer

[jagged stump]

its either 123457 to infinity

[jagged stump]

idk my main language is arabic

its a positive number, a one whole number

not 0.smth

[thorn creek]

integer

[jagged stump]

i d k

solve the question

[thorn creek]

yes, i am telling you, that's an integer

[jagged stump]

good to know ye

[thorn creek]

it's not that interesting, for a moment i thought it would require number theoretical techniques, but then i noticed the constraint

[jagged stump]

it is kinda interesting

its fun

nothing too serious

[thorn creek]

also kinda above the level of this channel

this is precalc, people in here aren't expected to know differentiation

[jagged stump]

i did not find any other channel

[thorn creek]

id:customize

[jagged stump]

dude literally asked for help

[jagged stump]

here

[thorn creek]

sadly, lots of people ask questions in the wrong place

[jagged stump]

no problem

solve it dude

just solve it

i want u to have fun

you

[thorn creek]

i don't think iut would be fun for me

[jagged stump]

ok then how much is it

[sinful dome]

is it 18?

[jagged stump]

no

almost 18

u got close

i think you did everything correctly, review your answer and check for any mistakes in the numbers

[honest meteor]

Always enjoy maths

I always enjoy it

[sinful dome]

well gettin 16 now

ion even know what im doing

[edgy edge]

I already solved it

Aight, it turned out to -8sin2x+1/x+1

[jagged stump]

ye its 16

[jagged stump]

u derived it again?

[sinful dome]

well you can't really tell if the (n-1) is in the exponent or if its (4^n) - 1

gettin 18 the other way

[jagged stump]

the trick is simple

[sinful dome]

yeah for it to be positive integer x^(n-4) has to be 1

taking n to be 4 we get 16

[jagged stump]

isnt the third derivative 4(n-1)(n-2)(n-3) x^n-4

and thats equals to a

depending on that, a is multiplied by x^n-4 but where is it?

meaning its multiplied by 1

so x^n-4 should be x^0

n=4

[jagged stump]

yeah

[thorn kestrel]

hi, is it possible to turn any sequence's recurring formula into an explicit formula via some method?

[obsidian monolith]

qathh

qathh

[thorn kestrel]

specifically this

[summer ruin]

you can just google how to solve recurrence relations

[thorn kestrel]

didnt know they were called that

[jagged vine]

can somebody please walk me through this I have a chapter test next week and don't understand how to get it from a graph

[onyx lotus]

can someone explain why this is wrong

i mean how did they get 7/9 instead of 17/9

[hushed geode]

Can you share how u got to the conclusion of 17

[scenic coral]

17^2 is 289 bro what u on

[snow quail]

who wants to help me with integration

like study with me

writing a really important test in 2 days

[coarse jacinth]

What topics get covered in UK A-levels?

I don't know where to start advanced stuff

[pine geyser]

For the first two blanks, where do you think the graph intercepted with the x?

[unique path]

Can anyone solve this integral?

Need some help ASAP

[viral juniper]

pretty sure you can just use u-substitution to calculate that

[jagged vine]

figured it out ty thp

[viral juniper]

solved it, is the answer meant to be really ugly tho?

cause i got a really ugly answer

[viral juniper]

https://www.youtube.com/watch?v=ngnH0ZSyPfk my reference video, you prolly can use this to calculate out a solution

but it basically uses u-substitution to split the integral into two components, one with an ln integreal and one of a tan^-1 integral

hopefully this helps!

[willow bear]

@knotty shard do you still need help w/ this

[pine geyser]

ok np

[unique path]

Yeah

It is ugly

[unique path]

Can you share the solving steps please

[viral juniper]

Sure, not immediately tho

Ill share soon tho

[willow bear]

ok

how familiar are you with limits in general

well ok then

as x goes to infinity, what happens to 9-x^2?

@knotty shard wait why did you just delete all your messages???

[willow bear]

you asked why $\lim_{x \to +\infty} \pm \frac{1}{9-x^2} = 0$ ...

[obsidian monolith]

Ann

[willow bear]

why do you deny that you asked it though...?

[modern valve]

Alumi please stop trolling and denying that you asked a question

[willow bear]

you are either trolling or just very strange

the question is perfectly legitimate and in no way a "taint to the channel"...

sin(1) isn't minuscule, is it?

it's around 0.57 or something.

,calc sin(1)

[obsidian monolith]

Result:

0.8414709848079

[willow bear]

oh, i must have been thinking of cos(1).

sin(1 radian) is about that much.

it is the default in calculus

you need to stop obsessing over which questions are "great" and which are "taints"

good job doing EXACTLY what i told you not to.

ffs

my reasoning for what?

you can view it as a criticism towards your attitude/behavior.

anyway if you really want an explanation of my reasoning: such dichotomies help nobody and only waste time and mental effort.

jesus fuck you're overthinking it

[glass rampart]

lol

[glacial tiger]

How come the limit as x approaches 0 of sinx/x = 1? I know that if I do L'hopital rule ill get 1 but is there a way to get 1 without doing that?

[uncut mulch]

sandwich

aka squeeze

[urban vigil]

exactly

[glacial tiger]

what exactly is that?

[uncut mulch]

sandwich/squeeze theorem

do a search on it then
another on
limit sin(x)/x squeeze theorem

[rapid plinth]

How tf did she work this inequality I can’t get it at all

Do u flip the sign when u take reciprocals?

[sinful halo]

you only flip when multipling the inequality by -1

she didnt flip the sign she just multiplied .007 and took out the n+1^3 nothing special

[sleek oxide]

Wait does that rule apply to divison as well? I forgot

[sinful halo]

wdym?

[sleek oxide]

The sign flip

Like if I divided -2 from the left side of (-2x<4)

I feel like I just answered my own questions..

[sinful halo]

idt so because your also doing the same to 4 and not necessarily multiplying by -1 like if it was x<4 then -x>-4 but for this example it would still be x<-2

[rapid plinth]

multiplied by what?

[sleek oxide]

Yeah it's for both

Just checked

[sinful halo]

by the n+1^3 then she multiplied by n+1^3

thus removing it from the demoniator and multipling to the one on the other side

[sinful halo]

so it would be x>-2?

[sleek oxide]

Is it because division is still scaling, but by a value less than |1|?

Yup

I wonder if we can verify this geometrically

[ionic tapir]

Hi, could anyone please help with this. When will solving f(x)=x give all the intersection points between f and f^-1? I've heard that it's when f is strictly increasing but I'm not too sure. Thanks!

[hallow geyser]

How would one find the equation of a parabola if the vertex (5, 0.47) and the x intercepts are 0 and 10

[warped cipher]

yes

if a graph only goes up or down solving f(x) = x shows where the line meets its flip side

[warped cipher]

you need to use the given vertex in the formula as y = a(x - h)² + k then use an x-intercept where y is 0 to find the value of a

[thorn creek]

"flip side"?

[warped cipher]

flip side can be also known as inverse no?

[thorn creek]

f(x) = x does not necessarily have the same roots as f(x) = f^(-1)(x)

also a function can be neither increasing nor decreasing and still have an inverse

such functions are often pathologically weird, but they do exist

for example the graph of inverse of f(x)=1/x intercepts the graph of f itself at every point

since f(x) = 1/x is its own inverse

and if you limit the domian to the positive reals, this function is monotonically decreasing over its domain

or consider f(x) = x/2 for rational x, -x/2 for irrational x. this function is invertible but not monotonic. however, f(x) = x occurs when x=0 which sht eonly point at which the function and its inverse coincide

hm, what about f(x) = 1+x+floor(x)? this function is increasing and is invertible (although its inverse has a weird domain)

eh, no the inverse never coincides with the funciton

[cinder ivy]

#book-recommendations message

[frigid trout]

finding f^(-1) = (x-5)/(x-6) question

Not sure if this work is correct

[compact juniper]

ok i know this is dumb but what’s the invers of 1/2? is it 2 or -2?

[candid schooner]

It's 1/ 1/2 = 2

[compact juniper]

ah ok thanks!

[thorn creek]

depends on which invers eyou want

[mint glacier]

cancel the negatives?