help-0

[pliant barn]

Both examples do not satisfy the hypothesis of the theorem you mentioned.
First does not converges uniformly
Second is not compact interval

[warped pine]

8x²-24xy+18y² , help.

[pliant barn]

lol guys there are other channels

[jagged imp]

Uh is this a question? Not sure what you mean by second is not compact interval, you could choose any compact interval and f_n's integral over that interval as n goes to infinity would still be the same as f's. If you don't have any specific questions im out

[pliant barn]

Not a question, just a conclusion of our discussion.
You are correct when you state that on any compact interval the integral of fn as n goes to infty would be the same as f.
But it does not work on non compact: $$ \int_0^\infty f_n = 1 \neq 0 = \int_0^\infty 0 = \int_0^\infty f_n$$

[jagged imp]

oh. yes that is correct.

[pliant barn]

Thank you so much for helping me see through this and sorry if any confusion was caused!

Channel free I guess 🙂

[ocean seal]

Mattan Hoory

[jagged imp]

yeah just non-compact

[pliant barn]

Should have used open interval instead of non compact maybe

because we were talking about reals

so

damn using words to describe math is problematic huh

[jagged imp]

I mean non-compact describes better what you're trying to say there imo

since the property of [0,inf) you're interested in there is

well, that its non-compact

any open interval is non-compact anyway, its not a big issue

[pliant barn]

I see

[warped pine]

#help-1 died so ill ask again here, whats the factor of 8x²-24xy+18y²?

[prisma cape]

first divide the whole thing by two first

2*(4x^2-12xy+9y^2)

then use the identity (a-b)^2=a^2-2ab+b^2

such that you can see its equal to 2*(2x-3y)^2

[warped pine]

Is there any other way without dividing it by 2?

[prisma cape]

im not saying to divide two

im just saying two is a factor of the polynomial

cuz its clearer to see the identity if i divide it

[warped pine]

i see, but can there be a solution to it withouth doing /2? because i want an answer with (-)²

[prisma cape]

hmm

so 2*(2x-3y)^2 is not ok?

[warped pine]

with the 2 infront i believe so

[prisma cape]

it must be (a-b)^2?

ok

the only way i can think of is (sqrt(8)x-sqrt(18)y)^2

but idk

[warped pine]

I'll try to use that too, thanks for the advice!

[prisma cape]

np : )

$d/dx x^2+9$

[ocean seal]

Pig 2 Man

[prisma cape]

:/ this bot is hard to use

[surreal meadow]

$\dv{x}(x^2+9)$

[ocean seal]

maximo

marc

[prisma cape]

$/dv{x}(4x^3+8x^2-10)$

[ocean seal]

Pig 2 Man

[surreal meadow]

\ not /

[prisma cape]

lmao

$\dv{x}(4x^3+8x^2-10)$

[ocean seal]

Pig 2 Man

[surreal meadow]

you can edit it and the bot will change it

i don't know number theory

[prisma cape]

oh ok

[somber osprey]

uh

[rapid olive]

i have figured it out

lol

really wasnt thinkinh there

[alpine sable]

$2+5

how would you solve ah = d^2 - 3hR for h?

[alpine sable]

I have tried like every way but nothing works

[ocean seal]

marc

marc

marc

[alpine sable]

Thank you!!

[rapid olive]

Hey, im really struggling with these questions

can someone please give me a hand?

[alpine sable]

? 🥺

[prisma cape]

if you want to throw something to the other side by addition or subtraction the sign changes

[dire whale]

you probably forgot to put a sign somewhere. every time you move something to the other side of the equal sign, you have to change the sign. constant terms are just those that dont have an x.

[main zephyr]

i am stuck, can anyone help me with question 2

[kindred warren]

it has it underneath

[prisma cape]

ye

easy

just use cos^-1(2/3)

[main zephyr]

i cant use the pytho theorm thingy

[prisma cape]

find theta

wait

theres no need

cos is just adjacent/hyp right

[main zephyr]

ye

[prisma cape]

as adj is 12 hyp shall be 18

done

[kindred warren]

then minus 10

because

[prisma cape]

oh yeah

[main zephyr]

wait

[prisma cape]

forgot

[main zephyr]

eh

[kindred warren]

we finding LP

[prisma cape]

minus 10

[main zephyr]

oh

[prisma cape]

hes right

the answer is 8

[main zephyr]

OH

OHHH

i understand now

thanks

[prisma cape]

great

: D

[main zephyr]

how do u know which is a which is h and which is o in a trapezium?

i just realised that might confuse everyone so im gonna rephrase

which is the hypotenuse, adjacent and o

at question 3

like on a triangle its obvious which is which

but at question 3, tan 0 is pointing at the edge of the trapezium

[prisma cape]

tan is supposed to be an operation

so if its referring to an angle it doesnt have to work on a triangle

[main zephyr]

hm

can u check my answer for question 3

i calculated 12

[prisma cape]

but in this case you move bc to point d and create a triangle abc

[main zephyr]

ye

[prisma cape]

i got the answer 25 tho

[main zephyr]

i just realised i can do that

[main zephyr]

eh

[prisma cape]

cuz you forgot to add 13 in bc

lol

[main zephyr]

OH

bruh

ty btw

[prisma cape]

np

[alpine sable]

can anyone help me with this

[alpine sable]

<@&286206848099549185>

please help

[burnt wharf]

Has anyone did it I sent it yesterday

[lapis valley]

what is this notation

also how do i explain doing a translation of a certain dataset

mathematically

[buoyant leaf]

depends on context

usually brackets are related to sets in some way, but it may be piecewise function notation or something different entirely

[lapis valley]

Oh ok

I just see it a lot so was wondering

[lapis valley]

Can i ask another question?

How can I mathematically explain translating a set of points.

[buoyant leaf]

$g(A) = {f(x) | x \in A}$

[ocean seal]

Fawful

[lapis valley]

So suppose I have this dataset and I want to flip it over the x axis and then for the x values I want to add a constant on them

How would i do that in that notation

i want to change both x and y

f(x) is y right

[alpine sable]

How is this symbol called?

[glass lichen]

theta

[vale wigeon]

theta (the ugly kind)

[stable grotto]

we know that when you multiply both sides of an equation by x you might get extra solution and at the end you should check the answers. But is there any general rule according which you can guess will there be extra solution or not without putting the answers in original equation and this way checking them ?

[granite raptor]

can someone help me with this question

[vale wigeon]

are you familiar with how polynomial division works?

[granite raptor]

yes i am

[vale wigeon]

so you should know that since the dividend is already smaller in degree than the divisor, the quotient will just be zero.

[granite raptor]

oh

so the answer is a?

[vale wigeon]

no

you are asked about the remainder.

[granite raptor]

cuz i cant divide any further cuz the degree is lw

[granite raptor]

ohh

so c

[vale wigeon]

yes

[granite raptor]

more then two as 7 > 2

[granite raptor]

got it

thnks man.

[alpine sable]

Hello

does anyone have any idea how to do this?

i haven't studied variance very well but it's not like i will understand anything from slides without practice xd

im usually bad at definitions and math language

[steep briar]

E(X) is simply the average of X, which has a simple answer. Var(X) = E[X²] - E[X]², uses your previous answer for E[X], so now you just have to find out E[X²]. Literally square all the X's and find the average of that. For Y, it's the same process but I believe it only has 2 elements, instead of 3, due to overlapping elements, just add their respective probabilities and you should be good).

[eternal arrow]

Could y’all help me with this question?

[small bear]

There is a formula for finding the k-th term of a binomial expansion. Do you know it or have you written it down before?

[eternal arrow]

im not really familiar with this type of question

[small bear]

That's alright, so what we have here is a binomial 2x+y raised to some power, in general we can write the binomial as (a+b)^n

When we have (a+b)^n, we can find the k+1 term with the following formula:

[eternal arrow]

Mhm

[ocean seal]

peaceGiant

[small bear]

^this is when the binomial is given as (a+b)^n

Can you perhaps see how that can relate to your problem?

[eternal arrow]

ummm

Im conf

[small bear]

What about?

[eternal arrow]

Il be bqck later

Gotta get to class

[small bear]

Uh, sure

[eternal arrow]

wait i still got time

Can you tell me what I have to plug in?

[small bear]

In that formula, you want the third term which is 3 = k+1 (you can easily find k), you have a=2x and b=p. You want that formula to give you 60x^4

After plugging all of that in, you need to solve for p

[eternal arrow]

so the formula would be?

Im a little conf tbh

Slept only 3 hours lol

[small bear]

I wrote the formula here

[eternal arrow]

???

uhh

[small bear]

Look at the message which I replied

#help-0 message

[eternal arrow]

can you plug it into me??

😅

[small bear]

Alright, I'll give a nudge in the right direction, let's start by plugging in k first (which is 2)

[ocean seal]

peaceGiant

[small bear]

Now, what were a and b

This channel is occupied, you can go to another one

[eternal arrow]

Wait il be back in like 30min

Im in a eng lesson at

Atm

[small bear]

Perhaps ask your question when you are at home, that way you can concentrate on the answers given (or when you don't have classes)

[mossy geyser]

how would you do this analytically

max is at x = 6

[placid pollen]

hey i've got a good idea. if this channel's occupied, why don't you take this channel out on a date, buy it some nice clothes once in a while

[vague coral]

xd

[alpine sable]

may someone help me finish it

[small bear]

Sorry this channel is on a date - I mean occupied, since you already posted in Q1 you might want to get an answer there

[alpine sable]

alright, sorry

[small bear]

If it somewhat helps, try the substitution 3 log_6 (x) = a which is x = 6^(a/3)

Maybe that way it is easier to solve in terms of a

[ocean seal]

marc

[lapis valley]

anyone uses gnuplo

gnuplot*

how to make a grid for the key like this

was working before now its like this

and i forgot

[fierce thistle]

anyone can help me with sets 7th grade

I'm having a hard time understanding it

[lapis valley]

send the question maybe?

[signal bone]

I have a question with this problem can anyone help me?

[ocean seal]

marc

[signal bone]

yes young modulus= stress/strainm

[ocean seal]

marc

marc

marc

[signal bone]

so my set up was 17.6*10^9= (200/100mm^2) / change is length(x) /0.1

but solving algebraically its confusing to me

i need to solve for change in length but how do u do that

[ocean seal]

marc

marc

[signal bone]

yes

okay so i need to do 200pa/ (delta L/0.1m)

first off i want to ask

because E=stress/strain

[ocean seal]

marc

[signal bone]

okay let me think for a sec

okay so, youngs modulus E was given in the question but is that same thing as e for strain formula?

if not i can't solve for delta L

[ocean seal]

marc

marc

[signal bone]

right..

so then how can i solve for delta L if i don't know strain e

yes

[ocean seal]

marc

[signal bone]

yea

its really stupid question but

how did u convert 100mm^2 to 0.1m^2

okayt

100/1000

got it

yes its clear

[ocean seal]

marc

marc

marc

[signal bone]

so that theta is stress =F/A this i get it

whats that theta= E *e

sigma okay

so they share same symbol?

stress=hooks

sigma=F/a sigma= E*e

okay

delta L= e*L(initial)

okay so

delta L= [(F/a)/E] * Lo

?

[short peak]

what would this be?

😢

[signal bone]

hmm..

i get 0.000113636

i think i did something wrong

answer whould be 1.14*10^-2mm

so for F/A for area it's 0.1*10^-4m^2 right?

yes 17.6E9

ohh ok

let me try it

[(200/0.1)/17.6E9]*0.1

now i get way off

1.1e-8

answ is 1.14e-2 mm

what did i wrong?

ok so i got 1.14 e -8 this time

idk how the answer is is e-2

lol

hmm okay

maybe its system error

i will ask professor for the unit

thank you for your help

i got the logic

yes

[mellow kiln]

I'm curious why do 4⁸ and vice versa not equal to each other

4⁸ and 8⁴

[ocean seal]

marc

[mellow kiln]

Yes

[ocean seal]

marc

[mellow kiln]

2•2•2 and 3•3

[ocean seal]

marc

[mellow kiln]

Ohh the one with the bigger power have more number to multiply

I got it thanks

What? Why

[ocean seal]

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

[north zenith]

hello how can i solve something like this:

a+b=x
b+c=y
a+c=z```
a,b,c are unknown and i want to find them

I did and i didn't understand it much that's why I wanted an explanation 😅

[mellow kiln]

So even tho they just swap place it doesn't mean that they are equaled to each other

[alpine sable]

HELLO ! ! can someone please explian to me how can i find out which function is EVEN or ODD

[north zenith]

ok i will look at the video

thx

[mellow kiln]

Thanks

[alpine sable]

x E f (x) => -x E f(x)

[merry pendant]

<@&286206848099549185> a=2, b=3, c=4 find the cos@

👀

what i use here

[ancient creek]

im pretty sure that you have to use law of cosines

[rugged thistle]

DOES ANYONE KNOWS HOW TO USE AUTO CAD?

[merry pendant]

but how i find the cos

👀

the switching side method?

[ancient creek]

this is the law of cosines, isolate cos@ to get the answer ig

[torn crescent]

Does anyone know the applications of the parent function y=x^2

[merry pendant]

i know but the problem is

the cos

[merry pendant]

so switch side with the c^2?

[merry isle]

hi

[merry pendant]

that been isolated?

[ancient creek]

square both the sides, then subtract a^2 and b^2 from both the sides and then divide both sides by -2ab.... that should give you the answer....

[merry isle]

I need help, how are fractions solved? I don't remember xd

[merry pendant]

square root both sides or square both sides

[north zenith]

@zinc cosmos i solved it! thx again!

[ancient creek]

square

[merry pendant]

ok

[merry pendant]

a^2 and b^2 in the one you sent or in my question?

the teacher told us to use a^2=b^2+c^2-2bccosÂ

[ancient creek]

after squaring both sides, it should look something like this: $c^{2}=a^{2}+b^{2}-2ab\cos\left(@\right)$

[ocean seal]

Hashing Power

[ancient creek]

i mean... those are just different variable names right?

[ancient creek]

follow this

[merry pendant]

using the c as a in my question?

but

THATS THE PROBLEM

so i do like

cos@=3^2+4^2-234/2^2

?

@ancient creek

@tropic sail head to other channel

[tropic sail]

did i interupt?

[merry pendant]

yes

[tropic sail]

3mins apart?

[merry pendant]

my answer isnt solved yet

so

please go to other channel

@ancient creek something like:
cos@=3^2+4^2-2•3•4/2^2

?

[ancient creek]

umm something like this: $\cos\left(a\right)=\frac{\left(c^{2}-a^{2}-b^{2}\right)}{-2ab}$

[ocean seal]

Hashing Power

[merry pendant]

oooo

[tropic sail]

is your question solved yet?

[merry pendant]

no

[tropic sail]

what do you need to find?

[merry pendant]

@ancient creek isnt it supposed to be -2bc?

for me

oh ok

thanks

i solved it

[ancient creek]

oh.. ok np

[tropic sail]

What does the colon mean in this context?

[worthy dock]

Please

Help me

the Question is

A Hotel charges 10% sales tax on the price of the food taken. Mr Saxena and his family had food for $685. Find the total money he had to pay?

please help

How to solve this problem

Help please

anyone?

[alpine sable]

are you doing your english problem or math problem... I see no numbers there

[worthy dock]

Maths

I's about percentage and Applications Word Problems

[worthy dock]

Read it carefully there are

[elfin talon]

This is an algebraic mess, the only way that I know of to interpret a colon in math is ratios or probability btw

But idk what a probability ration would be doing in a summation

[tropic sail]

this is vectorising mulrivariable functions of chain rule

[alpine sable]

in a polynomial functions

if no factor is a multiple of any other factor

can the polynomial be written as a product?

(except +-1)

[elfin talon]

Alr the only chain rule is in differentiation I’ll take a look at this as well later

[queen snow]

I think it's to denote a mapping

[queen snow]

How is it an English problem? It's literally mathematics

[sullen mantle]

does someone have gaokao question sheet?

[queen snow]

Considering the person making the "joke" doesn't know what the quadratic equation is, I'm not sure they were being humourous

Thanks for your insightful input though!

[lean tartan]

I'm trying to form a basis using Lagrange polynomials up to degree 2 in 2 dimensions. I know I need 10 functions, and i assumed they would be $P^2(K_j) = \text{span}\big{1, x-x_c, y-y_c, z-z_c, (x-x_c)(y-y_c), (x-x_c)(z-z_c), (y-y_c)(z-z_c),\frac{3}{2}\left(x-x_c \right)^2-\frac{1}{2},\frac{3}{2}\left(y-y_c \right)^2-\frac{1}{2},\frac{3}{2}\left(z-z_c \right)^2-\frac{1}{2}\big}$.

[ocean seal]

Gabagool

[tropic sail]

whats that?

[lean tartan]

Here, $x_c$, etc are a centroid of a cell. Is the product $(x-x_c)(y-y_c) $ orthogonal?

[ocean seal]

Gabagool

[lean tartan]

I didnt think it would be, because the moment of inertia $I_{xy} = \iint_{\Omega_k} (x-x_c)(y-y_c)$ isn't always zero. What second order function combination of $x$ and $y$ would be orthogonal?

[ocean seal]

Gabagool

[tropic sail]

https://www.youtube.com/watch?v=dxZ8a-oIu7U&t=1324s it comes from this lecture

[alpine sable]

would anyone be able to help me with some algebra 2 in a private chat?

[elfin talon]

Ok Dm me

[dense blaze]

if we have 2 points that have the minimum value of f, do we call them both absolute minimum or do we say there's no absolute minimum?

[rigid kiln]

Can someone give me a hand in visualising this? I think I kinda get it, but I don't really know how I'd illustrate it

[flint kettle]

How do I calculate the eigenvectors of a 3x3 matrix if I have the eigenvalues

[wary stream]

$$A - \lambda I = 0$$

[ocean seal]

dldh06

[wary stream]

Find the null space

@flint kettle

[flint kettle]

Sure but I struggle to derive the values of x y and z from the equations

I have an example that I’m trying to do from a website

[wary stream]

Post it in #help-7｜zen1thxyz since that channel is free

[buoyant leaf]

the absolute minimum is an element of the range of f, not the domain - but that singular absolute minimum can occur in multiple places

[ocean seal]

Fawful

[novel lintel]

hey guys, I wonder how we got to the double sums

is it becaue if we substitute k in 2^k + 1 by k = 0 we get the previous j = 1 + 1 = 2 ? Similarly at the upper side we have 2^(k+1) so substituting k = i - 1 we get 2^i ?

[novel lintel]

@alpine sable sum all the number of books and divide by the amount of students

[twin crest]

how to know when to use sin v, cos v, and tan v, and how to know what side is a b and c

[wary stream]

Do you know SOH CAH TOA?

[twin crest]

nope

[wary stream]

That's a good place to start then

[opaque trellis]

prove sin(2x)=cos(x)*sin(x)*2 help pls

[wary stream]

https://www.khanacademy.org/math/geometry-home/right-triangles-topic/intro-to-the-trig-ratios-geo/v/basic-trigonometry

[twin crest]

ok ill check it

[slim topaz]

Question 18 i need help

[thorn vortex]

You know that $\tan(k \cdot \pi + \alpha) = \tan( \alpha)$

[ocean seal]

Pealover

[alpine sable]

i need help with some maths questions

[glass lichen]

For k in Z

[maiden knoll]

hey can someone please help explain this to me, ive watched a million videos and am really stumped

[onyx flower]

looks like a trig function translated up 2

[ancient creek]

well one thing to notice is that at -90 degrees the graph shoots up while at 90 degrees the graph shoots down...

we know that sin(x) as x approaches 90 degrees will get closer and closer to 1, while cos(x) as x approaches 90 degrees, gets closer and closer to 0.

thus this graph matches the behavior of -sin(x) / cos(x), because the numerator gets closer and closer to 1 while the denominator becomes smaller and smaller, which causes the whole expression to shoot up to infinity as x approaches -90 degrees.

note that -sin(x)/cos(x) = -tan(x)

also notice that at 0, the tan(x) function equals 0, but here it equals 2... so we have to shift it up by 2

Therefore, we get final equation as -tan(x) + 2

[nocturne igloo]

Can anyobody help me out with this equation?

[cyan basalt]

3.14*6?

[stray estuary]

$6\pi$

[ocean seal]

blanket

[sick frigate]

Didnt expect someone will put letters on number

God why!!!!!

Spare my life

[kindred wadi]

Can anyone help with interpreting secant method? <@&286206848099549185>

How would i use the secant method for finding an approximation to $\sqrt{7}$ with an accuracy of 10e−7? With my function being $exp(x)-sin(x)$ , im not sure what to put as $x_0 $ and $x_1$ and the tolerance?

[ocean seal]

EmilB

[alpine sable]

you’re joking right? price + (price/10)

i know you use l'hopital if you get a limit equals 0/0 but if i got something like 3/0, would i just say the limit doesnt exist or is there another step im supposed to take? i forgot

@jagged raptor michale help

[jagged raptor]

@alpine sable michale help

[alpine sable]

mf

[jagged raptor]

if its infinite it doesnt exist

[alpine sable]

oh would i still write infinity

bc 1/0 equals infinity

that makes sense actually LOL

thank you mf

[jagged raptor]

i mean it kinda depends

[alpine sable]

my prof likes infinity i think

[jagged raptor]

if both one sided limits tend towards infinity then you can write that

but if one goes to +inf and the other to -inf its dne no matter what

[alpine sable]

the limits are chiral

[jagged raptor]

HAHAHA

[alpine sable]

anyways thats not an issue i realized that e^0 does not equal 0

but thank you

hwat

[nimble cave]

hi is this free i

[alpine sable]

no please venmo me

for legal reasons this is a joke do not ban me

[nimble cave]

lmao ok

[charred heron]

how do i do (b)

[alpine sable]

use this: "when c is a real number, cc ≥ 0"

[charred heron]

whats cc

[glass cedar]

Guys I have a test coming up , in the test how can I tell if the question requires me to complete the square or quadratic formular ect

[alpine sable]

cc = c^2

[alpine sable]

@charred heron
you can apply this mathematical fact to the question you're asking about

[charred heron]

but there is no c

in the question

[jade birch]

Unless it's specified to do it a certain way, you can do it however you want. If it's specified that you must complete the square, then complete the square. If still unsure, then ask the prof

[alpine sable]

you can regard this c as any real number

that's the meaning of "when c is a real number, "

so I could choose 'd', for example, instead of 'c'.

[jade birch]

1/f(x), is lowest when f(x) is highest
1/f(x), is highest when f(x) is lowest

[alpine sable]

yeah

and to know the minimum of f(x), we can use the theorem: "for any real number r, rr ≥ 0"

[random pelican]

whats the angle

of the car

[rigid kiln]

it looks like 45 but it doesn't say

[kindred hull]

get ur protractor out bro

[rigid kiln]

^^^

[random pelican]

?

whats that

[kindred hull]

a thing u use to measure angles

[small bear]

From part (a) you obtain that f(x) >= 9, divide both sides with 9 f(x) (since f(x) is positive the inequality doesn't change) and thus you get 1/9 >= 1/f(x) and trivially 1/f(x) > 0 (is positive)

[random pelican]

oh

ok

ty

[charred heron]

i understand that the max value would be 1/9

bc the max value of f(x) is 9 and since y and f(x) are interchangeable i can say y = 9 but that gives me 1 value for y, i dont understand how there's a range

the answer of 1/f(x) would just be 1/9 but i dont understand how theres a range

[rigid kiln]

can someone explain what I've gotten wrong here? this feels right to me; except for 2.), where i feel like the answer is just "may or may not diverge"

[jade birch]

What do you mean by range? There is no range, only 1 exact value of f(x) gives you a maximum for 1/f(x).

[charred heron]

yeah but in the answer given to us it says

this is supposed to be the answer

where does the 0 come from

[alpine sable]

even a toddler could figure out that

[alpine sable]

hum... that's not enough

im 13 and found it effortless

you should consider the definition of maximum

[jade birch]

You can write that after you find the minimum

[small bear]

f(x) is always positive, the fraction involving f(x) will also be positive, but never zero, thus >0

[charred heron]

yeah but why is it always positive

[jade birch]

The minimum value is when f(x) is maximum, the maximum of f(x) is positive infinity, so the minimum of 1/f(x) is 0

[small bear]

Look at part (a)

[jade birch]

Because it is an upwards facing parabola

[alpine sable]

i just made a project in scratch to find the factorial of numbers lmao

[jade birch]

The range for y values is [9,+infty) i believe

[alpine sable]

literally just a counting down number multiplying the input

[charred heron]

i don't understand this

[jade birch]

Ok

Let's look at f(x)

You know that f(x) can take only certain values

[alpine sable]

simply showing an evaluation (here, " 1/f(x) ≤ 1/9") cannot prove that 1/9 is the maximum.

[small bear]

Elaborate

[jade birch]

Those values are called the range

[charred heron]

are those values the roots of x

[jade birch]

No no

[alpine sable]

a hilarious thing with the coding site scratch is that you can code to find the factorial of any number in half the code it takes to make a item bobble up and down when u hover over it

[jade birch]

Those values are from the vertex to infinity, if it's facing upwards
And from -infty to the vertex if it's facing downwards

[alpine sable]

and thats without using custom math functions

just variables

[jade birch]

Take a look at this one

just a sec

@alpine sable can you move?

[alpine sable]

k

[jade birch]

ty

,w graph x^2-4

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[jade birch]

This one is facing upwards, so you can see that y cannot go below a certain point

[charred heron]

yes

[jade birch]

That point is called the vertex

[charred heron]

so the turning point in this case?

[jade birch]

So the range will ve [-4,+infty)

[charred heron]

where the parabola is facing up this would be the turning point?

[jade birch]

yeah

[charred heron]

okay

[jade birch]

The minimum of the parabola f(x) =x^2-4 is - 4, right?

[charred heron]

yes

[jade birch]

the maximum is +infty?

[charred heron]

yes

[jade birch]

And if you flip it

,w graph - x^2-4

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[jade birch]

minimum is?

[charred heron]

-infinity

[jade birch]

exactly

[native knot]

this channel free?

[charred heron]

nop

[jade birch]

No

Let's move to ur question niw

What is the minimum of f(x)?

[charred heron]

according to my graph, 9

[jade birch]

, w graph x^2+6x+18

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[charred heron]

yes 9

[jade birch]

Yep

And the maximum of f(x)?

[charred heron]

infinity

+infinity

[jade birch]

Yes

Bow what is the maximum of 1/f(x)?

[charred heron]

1/+infinity?

[jade birch]

You need to use the minimum for f(x) here

Nah

[charred heron]

oh

[jade birch]

1/3 is bigger than 1/1000

[native temple]

active?

[charred heron]

ohh okay

yeah

[jade birch]

That's why we use the minimum for f(x) to find the max of 1/f(x)

[charred heron]

okay

[jade birch]

So the maximum will be 1/9 right?

[charred heron]

yes

[jade birch]

And now the minimum?

1/(the maximum of f(x))

[alpine sable]

sorry, but as far as I know, there is no maximum in the set {y | y = x^2 - 4}, according to the definition of maximum. (but don't mind for now. I don't want to bother you.)

[charred heron]

1/+infinity then

[jade birch]

yep

and when you divide some constant by a huge number you get a number super close to 0

[charred heron]

yeah

[jade birch]

so we can say the minimum of 1/f(x) is 0,but not axtually 0

[charred heron]

sure yea

[jade birch]

Now we have a minimum and a maximum

[charred heron]

its infinitely small which is close enough to 0 right

[jade birch]

That means we have a range right?

[charred heron]

yes

[jade birch]

And that range of values is...?

[charred heron]

0 and 1/9

[jade birch]

ehh

[charred heron]

0 < 1/f(x) <= 1/9

since its not actually 0

[jade birch]

Yep

[charred heron]

sure

thank you

[small bear]

0 would technically be an infimum

[jade birch]

For now I don't think it hurts to use maximum and minimum

They'll learn the other more correct terms later on

[jade birch]

Yes

[alpine sable]

ok, i understand. thanks

[jade birch]

np

[onyx flower]

can someone explain how to do this limit

for -8

-00

for infinity i just did the trick with 3/(2+4

but for negative im not sure how

nvm i see it

3x^3/(2x^3-4x^3)

easy stuff

[strange blade]

any ideas?

[keen sand]

why f1 / f6 results in 100?

[warped grotto]

How would you find the derivative of e^((x)^2)

[glass lichen]

Chain rule.

[warped grotto]

But would would you differentiate first

[glass lichen]

You'd apply chain rule...

Review chain rule if you don't know it

[glass lichen]

Cause it says F1/F6=100

[wild olive]

anyone know how to simplify square roots on a graphing calculator?

i have a ti-84 plus c-et python edition graphing calculator

[glass lichen]

You don't need a calc to do that.

[wild olive]

doesn't answer my question

[keen sand]

how did he find this result if he doesn't have any number? '-'

[native temple]

Hey

Is radian measure splitting the circle

into arc length

measuring it

by how many radians fit into the circle when an arc of length x is subtended to form an angle?

[earnest rover]

2pi radians

is how many radiuses cover the circle

[native temple]

okay

Uhh what is radian measure

as seem here

By open stax text book is confusing

[jade birch]

Radian is the same everywhere

[earnest rover]

yea

[native temple]

what is radian measure explain what my textbook is saying please….

[jade birch]

Let me read it a couple of times

What a way to complicate a simple concept

Take the radius of the circle and wrap it around the circle, the angle formed at the center is exactly 1 radian

2 radians are two wrapings of the radius around the circle

pi radians equal to 180° degrees

etc. etc.

If you wrap the radius 2pi times around tbe circle, you get it's perimeter

L=2r pi

Which is why the circle has 2pi radians

2pi radians =360 degrees

@native temple

[tropic sail]

This server isnt supposed to give you the answer for hw and tests

#❓how-to-get-help

Rule 6

[torn crescent]

Yo

can someone help me with a problem

Pre calculus

[tropic sail]

Post problem

[torn crescent]

Okay

[torn crescent]

?

[placid zinc]

@native temple

Radians are good because they use circle properties to describe angle.

[odd eagle]

Use quadratic formula

[keen wigeon]

Say $f:X\to Y$ is open then is it true that if $B \subset X $ is closed and $x\notin B$ then $f(x) \notin$ closer of B

[ocean seal]

bchaotic

Say $f:X\to Y$ is open then is it true that if $B \subset X $ is closed and $x\notin B$  then $f(x) \notin$ closer of B

[keen wigeon]

I feel I am forgetting something very simple

[sly mantle]

@tropic sail ty for citing rules but academic dishonesty is bannable, pls ping mods for future reference

[ivory gulch]

ok could i get some help with this quesiton

well aside from the fact that it's -119 and not 119, is this right?

[shell vault]

find the nineth term, r is 2/3 and the first term is 3

[oak jewel]

can you translate?

[glass lichen]

they did...

[oak jewel]

is it a geometric row and R=2/3?

i feel like there is more to it

[glass lichen]

geometric progression

but yes.. it's just a geometric progression

[glass lichen]

what have you tried?

[shell vault]

i just figured it out

[crude hamlet]

sorry, if this channel is free, could someone please explain to me what skew lines are ?

[oak jewel]

lines that wont intersect but are not parallel

[crude hamlet]

ooh okay thnajs

thanks*

[scenic ether]

any death grips fans

[oak jewel]

wrong server m8

[ivory gulch]

ok i've gotten very far into this question but i don't understand the last step

[oak jewel]

<@&268886789983436800>

[oak jewel]

yeah let me have a quick look

[scenic ether]

bro stfu 💀

[tall wing]

please behave

[ivory gulch]

so so far i've done this. rewrote the equation as:

$\lim _{t\to 0}\left(\frac{f\left(2+t\right)}{t}\right)\lim _{t\to 0}\left(\frac{\left(g\left(1+t\right)-g\left(1\right)\right)}{t}\right)$

[scenic ether]

you probably remind the teacher about homework

[ocean seal]

ski

[tall wing]

@scenic ether memes go in chill

[scenic ether]

are you good at geometry transformations

[ivory gulch]

which means the second portion there is just g'(1)

[tall wing]

read #❓how-to-get-help and follow the rules

[glass lichen]

channel is clearly in use

[sly mantle]

b&

[tall wing]

ty

[ivory gulch]

in the first portion, i just subtract 0 from the top because f(2) = 0. so i rewrite it as

$\lim _{t\to 0}\left(\frac{f\left(2+t\right)-f\left(2\right)}{t}\right)$

[ocean seal]

ski

[ivory gulch]

which is clearly just f'(2)

so now i have f'(2) * g'(1)

[woven sparrow]

is there a question channel open at the moment

[ivory gulch]

since i don't have any info about f'(2), i look at something that can give me a value of 2

in this case, g(1) = 2.

so now i have f'(g(1)) * g'(1)

and now here's where im not super confident

[oak jewel]

you will get 0/0

f(2)=0

t lim 0

so have you heard of L'h?

[ivory gulch]

cant use it

[oak jewel]

why not?

[ivory gulch]

will get docked points

teacher hasn't taught it yet

[oak jewel]

rip

[ivory gulch]

so need to pretend like i don't know it

[oak jewel]

ok

lol i do the same all the time XD

[ivory gulch]

so

where do i go from herre

f'(g(1)) * g'(1)

[oak jewel]

so... you could do the engineer approach and say 0/0 = 1 QED or i will have a look again

[ivory gulch]

well i have the answer key

the answer is 3

its not a test btw

obviously

[oak jewel]

hah i dont care

[ivory gulch]

i'm watching the video lecture and prof goes
"f'(g(1)) * g'(1). and that looks exactly like the rule for the derivative of a composition of functions. In other words this is the chain rule. so this is the derivative, of
(f o g) (1) so that means this is h'(1). and h'(1), in fact, is 3."

i just don't get how f'(g(1)) * g'(1) = h'(1)

bc g'(1) = h'(1) so how does the f'(g(1)) just disappear

[oak jewel]

so what operations and theorems can you use?

[ivory gulch]

chain rule, product rule, quotient rule, power rule, uhh rules of limits

[oak jewel]

ok

[ivory gulch]

thank you

for the repost

got interrupted by a death grips fan

[placid zinc]

It's worth saying that
If h(x) = f(g(x))
Then h'(x) = f'(g(x)) g'(x)

As that's the chain rule

[ivory gulch]

ohhhhhhhhhh

ok

makes sense

just reverse chain rule

thank you

i get it

how ab this one? i don't mean to hog the chat

if anyone else has a question feel free to ask

[oak jewel]

channel is busy

yes and delete your previous messages

[ivory gulch]

me?

[oak jewel]

no lol someone else came in

yeah so i tried unsuccessfully to solve your other thing, but this one i can do 😅

so pi/2+ is more than pi/2

which means than tan(x) is -

and the absolute value is always positive ofc...

[ivory gulch]

yeah i can replace with parenthesis

[alpine nacelle]

are you supposed to not use asymptotic expansion ?

[oak jewel]

So divide tan(x) into sinx/cosx

and split the limit in two parts

so you have essentially lim...sin(x) * lim... |x-pi/2|/cosx

[ivory gulch]

considering i have no idea what that is, ima go with no

[oak jewel]

x-pi/2 will go to 0

cos(pi/2)=0

[ivory gulch]

yeah bc i get 0 on numerator

so final answer is 0?

[alpine nacelle]

no

[oak jewel]

so i would use L'H there as well

nah its not 0

[ivory gulch]

wish i could

[oak jewel]

but you can solve for it without L'H

[ivory gulch]

ok so what do i do now ill show u where im al

[oak jewel]

,rotate

[ivory gulch]

lol

[oak jewel]

thats perfect

and replace that sinx with 1

and cross it out

and dont forget your ||

[ivory gulch]

ok

[oak jewel]

your teacher will hang you

[ivory gulch]

where do the || go

[alpine sable]

. In how many ways can you roll either a sum
of 4 or a sum of 11 with a pair of dice?

not sure how to do this

[ivory gulch]

#❓how-to-get-help

[oak jewel]

??

[ivory gulch]

oh just around those lol ok

[alpine nacelle]

you can remove it since x > pi/2

[ivory gulch]

yeah i didnt think they were really relevant

ok so now what

lets go just got active role

[oak jewel]

nice

[ivory gulch]

🆒

lol

[oak jewel]

ok, so let me find the proof for that thing again....

erh... this is pointless, if you havent learned L'h there is no way you have learned this lol

[ivory gulch]

ok lol

[oak jewel]

you could do sec(x)

yeah lets try that...

[alpine nacelle]

you can make a sub, y = x-pi/2
then lim y->0+ y/cos(y+pi/2) = lim y->0+ -y/sin(y)

and you know the limit x/sin(x) as x goes to 0

it's 1

so lim y->0+ -y/sin(y) is -1

[trim remnant]

How do you add complex numbers again?

[ivory gulch]

#❓how-to-get-help

[oak jewel]

channel is very in use

[ivory gulch]

could you dumb this down for me a bit

[alpine nacelle]

nah because there is a problem

[ivory gulch]

alr

[oak jewel]

you still use L'H for that

how do you prove its -1?

[alpine nacelle]

you can use asymptotic expansion, again

or any other proof depending on what equivalent definitions of sin you accept

[ivory gulch]

ill send u the vid of my prof doing it if youd like with timestamps

bc idk what she's doing

[oak jewel]

its getting late here

but sure lets do it

[ivory gulch]

if you have to go feel free bro

get some rest if you need

[alpine nacelle]

you can't split the sin and say it's 1, because it changes convergence order

[alpine sable]

Triangle XYZ has its vertices at the following coordinates:

X(2, 1) Y(4,-1) Z(1,-3)

Give the coordinates of the image triangle X'Y'Z' after a 90° counterclockwise rotation about the origin.

[oak jewel]

i would be furious if i got dunked points because i used stuff we "had not learned yet"

[alpine sable]

Help

[oak jewel]

channel in use read rules

[ivory gulch]

starting at 45:47

[ivory gulch]

#❓how-to-get-help

[ivory gulch]

yeah. its pretty annoying

[civic root]

how old are u guys?

if i could ask

[alpine nacelle]

she uses that lim x-> 0 sin(x)/x = 1 too

sorry pinged wrong message

anyway

[civic root]

wha are ytall ages?

[alpine nacelle]

you have to know this limit

[civic root]

im curious

pzl

[alpine nacelle]

that's what your teacher uses

[ivory gulch]

damn

[oak jewel]

aah so what she does is that she says cos(x)=sin(x-2/pi)

and you can use trig identities to get that into another format

didnt even think of doing that, i guess its the 2 am syndrome

[ivory gulch]

ok so knowing that, how do i get to the answer that way

[alpine nacelle]

it's a sub that the teacher doesn't fully write out cause it's obvious
lim x-> pi/2+ sin(x-pi/2)/(x-pi/2) = lim x->0+ sin(x)/x

[shy prairie]

but im not sure what to do after that to try and find k

[ivory gulch]

#❓how-to-get-help

[shy prairie]

oh mb

[oak jewel]

delete and read rules

[alpine nacelle]

it's a sub that the teacher doesn't fully write out cause it's obvious
lim x-> pi/2+ sin(x-pi/2)/(x-pi/2) = lim x->0+ sin(x)/x

(I rewrite because of the damn kids who can't even read one rule)

[ivory gulch]

ok im a little confused on what u said

can u like lay it out in the format the bot uses or whatever

so i can see what you're saying

[alpine nacelle]

yeah I'll do it wait a sec

[ivory gulch]

np

[oak jewel]

can you get that video back?

[ivory gulch]

yeah

ill dm

[oak jewel]

also, its not totally correct to write cosx as sin(x-pi/2) but ok..

[alpine nacelle]

you have to flip sign

sin(x-pi/2) = -sin(x+pi/2)

that's why it's -1 in the end

[oak jewel]

lmfao

[alpine nacelle]

$\lim_{x \to pi/2^+} (x-pi/2)\frac{sin(x)}{cos(x)} = \lim_{x \to pi/2^+} (x-pi/2)\frac{sin(x)}{sin(x+pi/2)} \newline = \lim_{x \to pi/2^+} -sin(x)\frac{x-pi/2}{sin(x-pi/2)} = \lim_{x \to 0^+} -sin(x+pi/2)\frac{x}{sin(x)}$

[ocean seal]

Mélo

[oak jewel]

she just says that goes to 1, how do you prove that? by using L'H

[alpine nacelle]

I insist, but there is a lot of proofs besides l'H

[ivory gulch]

yeah she doesn't prove it. just tells us it all the time

[oak jewel]

yeah there probably are, but her example doesnt mean shit when she does it like that

[alpine nacelle]

I mean, when you know it's 1 you can put a 1 lol

[oak jewel]

i know the answer is -1 so its -1 qed

[ivory gulch]

$\lim{x \to pi/2^+} (x-pi/2)*\frac{sin(x)}{cos(x)} = \lim{x \to pi/2^+} (x-pi/2)\frac{sin(x)}{sin(x+pi/2)} $

[alpine nacelle]

and there is the -1

[ivory gulch]

this part i dont get

[ocean seal]

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

[ivory gulch]

oops

[alpine nacelle]

cos(x) = sin(x+pi/2)

[ivory gulch]

am i just supposed to know that

[alpine nacelle]

you can use the unit circle to check why it's true quickly

but yeah you should know it

[oak jewel]

its very standard trig identities, just remember those

[ivory gulch]

how do i check on unit circle

okay cool

[alpine nacelle]

you take an angle x, you rotate, you check that what was the cos becomes the sin

like, cos(pi/6) = sin(pi/6 + pi/2), you can quickly check

[ivory gulch]

when you swap the sin(x) and the (x-pi/2) why did the sin become negative

[alpine nacelle]

because sin(x+pi/2) = -sin(x-pi/2)

look at the denominator

I made this change at the same time

(you add pi to the angle)

[oak jewel]

i hate what im about to say

but maybe you should just blindly follow her example

as she clearly does not want you expanding your knowledge

and solve it using l'h as you would do later in calculus

for your own learning

im off now though

[ivory gulch]

how are these = what

im confused

im not very familiar w the unit circle btw. having a lesson w a dude from this server on satuday but yeah

just started to understand it today. long story short covid kicked me out of school for the last half of pre calc so i never learned it

[alpine nacelle]

sin(x+pi/2) = sin((x-pi/2)+pi)

= -sin(x-pi/2)

[ivory gulch]

yep idk

ill just hope this one isnt on the tes

cant do much else

in the meantime, could you show me how to solve it using l'h?

just so i can at least get some points

[alpine nacelle]

l'H just gives lim x->0 sin(x)/x = 1

[ivory gulch]

oh

damn

[alpine nacelle]

that's what you use from here

to conclude

[ivory gulch]

ig this is the part im not understanding

but like i said

not much i can do until i fully understand the unit circle

[alpine nacelle]

pi/2 = -pi/2 + pi

[ivory gulch]

oh wait i didnt see the change inside thesin

ig that makes sense

[alpine nacelle]

side note: don't listen when people say you need l'H for everything, really, just lim x->0 sin(x)/x = 1

[ivory gulch]

okay lol

good to know

[alpine nacelle]

once you're in undergrad you'll know how to show it without l'H anyway

[ivory gulch]

so i get how you swapped sinx with the (x-pi/2)

but why

like did you have to do that

switch the sin i mean

[alpine nacelle]

which switch ?

[ivory gulch]

ok here

so

,rotate

[ivory gulch]

here's where im at

[alpine nacelle]

yeah, now you use sin(x+pi/2) = - sin(x-pi/2)

and then it's a substitution

[ivory gulch]

oh ok and u did that to make the bottom not 0?

make the denominator

i mean

[alpine nacelle]

no to have y/sin(y)

I want the same thing in the num and in the sin

so I can use lim x->0 sin(x)/x = 1

[ivory gulch]

,rotate

[ivory gulch]

so i can just sub in pi/2 from here?

[alpine nacelle]

you make the sub y = x-pi/2

it will become lim y->0+ -sin(y+pi/2) * y/sin(y)

[ivory gulch]

wait y/sin(y) also = 1?

i thought it was sin(y)/y =1

[alpine nacelle]

if lim f/g is 1, lim g/f is 1 too

x ~ sin(x) when x->0

[ivory gulch]

so then i just get down to -sin(x)

now i sub in pi/2?

[alpine nacelle]

you can calc lim y->0+ -sin(y+pi/2) * y/sin(y) directly now

y/sin(y) becomes 1

-sin(y+pi/2) is -1

-1*1 = -1

[ivory gulch]

wait wait wait

[alpine nacelle]

https://cdn.discordapp.com/attachments/490557019623915520/890741604170752020/249632691564183553.png

(either you name it x or y it doesn't matter)

[ivory gulch]

,rotate

[ivory gulch]

meant to have sin(x) there

[alpine nacelle]

???

[ivory gulch]

but u get the idea

[alpine sable]

can someone hop in vc w me i wanna screenshare my screen im so confused on how this is the answer (grade 12 math)

[ivory gulch]

#❓how-to-get-help

[alpine nacelle]

https://cdn.discordapp.com/attachments/490557019623915520/890741604170752020/249632691564183553.png

look at what I wrote

and look at your last step

[ivory gulch]

oic

[alpine nacelle]

you failed the sub

[ivory gulch]

yeah i see what you did

but i dont get how

how did the sin(x+pi/2) get there