help-19

[mystic saffron]

can i see the question?

[pastel orbit]

there doesn't always need to be any holes in the graph though

[restive night]

huh?

[mystic saffron]

whats the question?

[restive night]

I'm confused about how to get the range of a rational function

[mystic saffron]

i can help u out w that

[restive night]

What does this mean

[mystic saffron]

get on a vc

cant type it out

[restive night]

Alright?

[pastel orbit]

in general, if the numerator and denominators share linear factors, then there will be a hole where said factor equals 0

[mystic saffron]

just perform elementary operation on the domain

okay which vc are we getting on\

[restive night]

we gotta add right

or like we can vc directly?

[mystic saffron]

okay listen, x/4+1/4 right

you understoodf this?

[restive night]

yeah

[mystic saffron]

now x belongs to R-{3}

cool?

[restive night]

ok wait nvm

x/4 + 1/4?

where is that

oh

[restive night]

I have no idea what's linear factors also...

[mystic saffron]

whatever you didnt understand here lmk

this

[mystic saffron]

this is the function

[restive night]

yeah I understood it now

[mystic saffron]

you sure? feel free to ask anything

[restive night]

no I meant

[restive night]

This

[mystic saffron]

im just performing elementary operations on the given domain

hop on a vc

imma explain it

create one pleas

[restive night]

how

[mystic saffron]

okay imma dm call u

[restive night]

ok

[mystic saffron]

hop on

[odd edge]

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[fierce pebble]

can anyone help me understand POTENTIAL DIFFERENCE?

[hoary marsh]

In what context?

[fierce pebble]

the definition and why there is a need of potential difference for elecetrons to flow

[hoary marsh]

So circuits

Basically, potential difference (p.d.) is the difference between voltage/current passing through a component as work is done

[fierce pebble]

cant understand

[topaz ibex]

Why askin bout physics in a math discord tho

[fierce pebble]

explain me like i am layman

[hoary marsh]

Circuits isn't physics

[fierce pebble]

i get fast replies here

[topaz ibex]

Bet

[hoary marsh]

I'll answer in like an hour later ig

[topaz ibex]

Kay let me answer for u

[hoary marsh]

Do you know what a resistor is?

@fierce pebble

[fierce pebble]

yes

[hoary marsh]

When charge(s) passes by a resistor

Work is done

[fierce pebble]

yes

[hoary marsh]

Which makes a difference in the input charge and the output charge

Let's use nodes for an easier understanding

If you have node A and node B

For instance

Node A might have 10V input

And node B might have 4V output

Because energy was used

[fierce pebble]

ohh

yeah i got it

thanks

[hoary marsh]

Np

[topaz ibex]

Ok so why circult is not physic

[hoary marsh]

Just because you have circuits in AP Physics 1, it isn't physics

[topaz ibex]

Idk

I believe the foundation of circult still physics tho

Its true that

[hoary marsh]

Well in that case, you can also state that physics is math too

[topaz ibex]

Damn

Alright

Understand

[hoary marsh]

Discrete math proof techniques coming in handy 😍

[pale atlas]

Math ≠ calculation
Calculation are used in physics

[topaz ibex]

Shes joking

Xd

Ig

[pale atlas]

That's ok, but you were right circuits are part of physics. And we use calculation in phy, chem and other things

That doesn't make them math to be precise

[topaz ibex]

In my pov

Circult like a foundation of many other fields

Like computer e

Or electrical e

And its a part of physic tho

[hoary marsh]

I guess I would say circuits in a "part" of physics

[hoary marsh]

e?

[topaz ibex]

Like a "bridge" ?

Engineering

[hoary marsh]

Oh yes

[topaz ibex]

Im freshman computer science btw

Any tips?

Seem like you studying it tho

Shit this help channel turn into discussion

[hoary marsh]

Computer Engineering != Computer Science

[topaz ibex]

My bad

[hoary marsh]

But you're welcomed to talk about it in some other channel

[topaz ibex]

So engineering is like

[hoary marsh]

Just ping me

[topaz ibex]

Learnin about hardware?

And science is about software?

[hoary marsh]

Not exactly

[topaz ibex]

Alright

[odd edge]

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[mystic saffron]

Hi sorry, I had another question in help3 that I'd like to learn more about. Basically I'm wondering, if I get a question like "how would you model workplace bullying?", I want to be able to have muscle memory about mathematical structures such that I know which is appropriate for the situation. I don't necessarily want to be able to compute anything in my head, just be able to estimate things. Is rapidly answering a question usually something that takes a lot of time thinking? Or is there a kind of simple decision tree for modeling?

[low locust]

modeling stuff is very hard

what do you even mean with modeling workplacs bullying

[mystic saffron]

So one way to model it is by modeling the cognitive states of the inhabitants of the workplace as 3 booleans: "Is agitated", "isrelaxed" and "is aggressive" and then having weights between those variables that represent their association. Then have something like an ABM of the workplace with a "space" where agents interact, kind of like the SIMS. However, I'm asking a simpler question, which is "is there a book/resource that teaches the basic tips and tricks for modeling a situation if you have 15 minutes to answer an interview question"

[low locust]

you could try asking in the book channel

[mystic saffron]

Thanks!

[odd edge]

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[ivory sleet]

hello, im trying to understand what it means for a morphism in category theory to be a "structure preserving map"

for the category Vect_R, objects are vector spaces and morphisms are linear maps, and the "structure" of this category is given by the axioms of vector space.
so for a morphism m; x, y in some element of ob(Vect_R); k1, k2 in R:
m(k1*x + k2*y) = k1*m(x) + k2*m(y)

if we had m(x) = 0 if |x| < 5 else x then going by the linear map example, this wouldnt be a morphism for Vect_R right?

does this notion generalise to other categories? that is, if the result of applying the morphism then applying an operation defined on objects in that category isnt the same as the other way around, then the morphism is invalid?

[low locust]

well you dont necessarily always have an operation

for example the morphisms in the category of topological spaces are the continuous maps

but those play "nicely" with the structure of the space, namely the topology

"close" points get sent to "close" points, so in that sense the "structure" is preserved

[ivory sleet]

hmmm, im getting the impression then there isnt really any general way to define "structure preserving map"? like is it just a case of "for a given category, look at the axioms used to construct the objects, applying the morphism to every object should result in an object which abides by those same axioms"

[fresh ocean]

In category theory its very difficult have structure for object because it dont work it elements of this object

But if your "structure" is category with information about underlying sets it can be done by Concrete category

[ivory sleet]

i dont rlly understand what u mean by this

[fresh ocean]

Category theory only says information about relations between morphisms and object but nothing about elements

[ivory sleet]

ah ok i get you, so the meaning of "structure preserving map" depends entirely on the category in question

so you cant really "define" it generally at all beyond the vague notion of that it has to preserve the structure

[fresh ocean]

But you can be more precise if you work with set with additional structure It is Concrete category.

Concrete Category is Given category and functor from Given category to category of sets

[ivory sleet]

ok i think i understand enough for now

well to unblock me anyway

thanks jotigo and denascite

.close

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[molten totem]

Hi

[molten totem]

I have one more question regarding this srry

[mystic saffron]

this isnt related to math

[molten totem]

So all the questions are already solved thanks again @fervent summit you are the best but the final question I’m having trouble with

[molten totem]

I figured after I asked the first time but I was receiving some solid help

That I’m grateful for

@fervent summit last question can u help me oh great one

https://tenor.com/view/kittew-gif-23901607

[odd edge]

@molten totem Has your question been resolved?

[molten totem]

<@&286206848099549185>

[vital sinew]

this is not related to math

(there is dish spelt backwards at the top row on the left)

but cmon, dont ping helpers for this

[odd edge]

@molten totem Has your question been resolved?

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@molten totem Has your question been resolved?

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[green sage]

Hello! 👋
How do I solve this for $z_1$?

$\frac{3}{2 z_1^{2/3}} z_2^{-2/3} = 12 z_1^{-1/3} z_2^{1/3}$

I know the solution would be $z_1 = 8 z_2$

[clever fjord]

890s

[odd edge]

@honest geyser Has your question been resolved?

[dry lintel]

sorry

anyway

if you multiply both sides by z_1^(1/3) then you get z_1^(3/3) on the left and z_1^0 on the right

you can do the same for z_2

@honest geyser

x^a * x^b = x^(a + b)

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[stable rose]

how do i find the surface area?

[odd edge]

@stable rose Has your question been resolved?

[pastel adder]

So we are forming a hexagon with equal side lengths on the base.

This is the first trick i believe the question is asking.

Solve from here but i will spoiler the rest of the solution if you need to come back for more.

||The radius is equal to its length, for a regular hexagon.

Therefore we can create an imaginary right triangle, with side lengths 4, and 3.5

sqaure root of (4^2 + 3.5^2) is therefore the length of one of these triangles that forms the surface area.

Since every triangle is made up of these lengths, with a base of 3.5, we therefore have 6 isocles triangles, with base 3.5 and height undetermined.

We can break these triangles up into 12 right triangles, with base 3.5/2 and height =

(sqaure root of (4^2 + 3.5^2) )^2 - (3.5/2)^2

therefore the surface area = 1/2 * 12 * 3.5/2* ((sqaure root of (4^2 + 3.5^2) )^2 - (3.5/2)^2)

However, i think surface area also includes the base of the hexagon on the bottom. Not sure, you'd probably know better. So we also have to add that hexagon's area.||

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[stable rose]

thx

[stable rose]

.close

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[young sedge]

this good so far?

[orchid torrent]

,w \frac{2x+arctan y}{1-\frac{x}{1+y^2}}=\frac{-(1+y^2) (2x+arctan y)}{-1+x-y^2}

[clever fjord]

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[orchid torrent]

yeah

[young sedge]

um

i got 1+y^2-x

[brittle beacon]

The negative takes account of that

[young sedge]

not sure how you mean

(1+y^2)(1)-(x)/(1+y^2)

[orchid torrent]

$1+y^2-x=-(-1+x-y^2)$

[clever fjord]

Civil Service Pigeon

[young sedge]

you pulled out a negative?

[young sedge]

was that negative there before we isolated y'

[orchid torrent]

nvm

[young sedge]

im so confused

[orchid torrent]

$\frac{2x+\arctan y}{1-\frac{x}{1+y^2}}=\frac{(1+y^2)(2x+\arctan y)}{1+y^2-x}=-\frac{(1+y^2)(2x+\arctan y)}{-1+x-y^2}$

[clever fjord]

Civil Service Pigeon

[young sedge]

so we pulled out a negative for no reason

from the denom

is what it looks like to me

[orchid torrent]

you do you ig

[young sedge]

im just extremely confused

oh

i did y'(1+y^2 - x)

and then isolated y'

i wanted to solve the fraction before i moved it to the denom so it would be easier

[orchid torrent]

yeah that's the same thing

[young sedge]

it is which is why i was confused

im like why would you make that distinction in the first place 😭

i plugged in the x and y values

is this correct so far

[orchid torrent]

why is it -8pi/4

[young sedge]

huh

its just -pi/2 mb

[orchid torrent]

alright yeah it's good then

[young sedge]

ok how do i get the arctan of 1

[orchid torrent]

tan(...)=1

find ...

[young sedge]

so pi/4

[orchid torrent]

yeah

[young sedge]

i got -pi/8

as my slope

(-pi+pi/2)/(2+pi/4)

[orchid torrent]

,w tangent to x^2 + x arctan y = y-1 at (-pi/4, 1)

[clever fjord]

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[young sedge]

is this right tho

so far

[orchid torrent]

,w \frac{-2pi}{8+pi}-\frac{-pi/2}{2+(pi/4)}

[clever fjord]

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[orchid torrent]

yes

[young sedge]

so my slope is -2pi/(8+pi)

[orchid torrent]

yes

@young sedge how's it going?

I might head off soon

[young sedge]

ugh

[orchid torrent]

yeah your intercept is off by a mile 😭

[young sedge]

oh was it a sign issue

[orchid torrent]

the denominator is completely off

[young sedge]

you said yes 😭

[orchid torrent]

the slope is fine...

not the intercept

[young sedge]

m= (-2pi/8+pi)
x1=-pi/4
y1=1

[orchid torrent]

are you trying to use point slope form or smt

[young sedge]

yes

is that not what im supposed to do?????

[orchid torrent]

$y-1=-\frac{2\pi}{8+\pi} \left(x+\frac{\pi}{4} \right)$

[clever fjord]

Civil Service Pigeon

[orchid torrent]

idk how you got from this to that

send your work if you want me to check it

[young sedge]

hold on its all over the place i gotta organize it

@orchid torrent

[orchid torrent]

this is fine tbh

not sure how you got from that to this

[young sedge]

think i just did a sign issue

[orchid torrent]

you changed the entire denominator 😭

[young sedge]

brain issue then

okay it was right

ill let you go now

thanks for all the help

[orchid torrent]

[young sedge]

.close

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[past briar]

How would I find (a) f * g and (b) g * f and find the domain of the function and composite function of f(x) = 3/(x^2-1), g(x) = x + 1

[odd edge]

@past briar Has your question been resolved?

[runic swift]

,rccw

[past briar]

?

[runic swift]

you want to find the domain?

[past briar]

Yes

Is my (a) and (b) correct?

[runic swift]

yeah

[past briar]

K

How would I write out the domain

[runic swift]

which function

[past briar]

for both the function of g and f and for fg and gf

[runic swift]

well what do you think the domain of f should be

[past briar]

all real numbers x such that x <= 5?

[runic swift]

no

look at the bottom of your fraction

are there any values that makes the function undefined

[past briar]

oh wait that was a different question my bad

[past briar]

x squared?

[runic swift]

values

numbers

can you divide by 0?

[past briar]

no

[runic swift]

so can x² - 1 be 0?

[past briar]

no

[runic swift]

so we know we should avoid numbers that make that equal to 0

what numbers are they

[past briar]

1?

[runic swift]

just 1?

[past briar]

all real numbers?

[runic swift]

no

-1 and 1

[past briar]

ah

[runic swift]

because (-1)² - 1 is also 0

[past briar]

understood

[runic swift]

so whats the domain for f

[past briar]

all real numbers expect x = 1 and x = -1? {-infinity, -1}U{-1,1}U{1,infinity}

[runic swift]

yes

[past briar]

really?

[runic swift]

yes

[past briar]

Is it the interval or the part about real numbers expect 1 and -1

[runic swift]

both could work

[past briar]

ok

So for the g function would it be all real numbers since x is adding by 1 or would it be something else because of the adding of 1

[runic swift]

yes

all real numbers will work

[past briar]

ok so domain of g is {-infinity, +infinity}

Why wouldn't the 1 change anything in this function? Would you mind explaining that part to me?

[runic swift]

the 1 in x+1?

[past briar]

yes

is it since that x can be any number and that adding one to it doesn't skip over a number?

[runic swift]

yes

well idk what you mean by skip over a number

but theres no value of x that will make g undefined

[past briar]

so would the domain still be all real numbers if x isn't being added by 1 but by for example 3?

[runic swift]

yes

[past briar]

is that the same explantation is that no value of x would make it undefined?

[runic swift]

yes

[past briar]

ok

for f*g how would the domain work for that

the denominator is x squared + 2x

[runic swift]

actually can f(g) even exist

[past briar]

idk man I had got 3/(((x+1)^2) -1)

[runic swift]

i dont think f(g) exists

because the range of g is all real numbers but domain of f is all real numbers except -1 and 1

and you need the range of g to be a subset of the domain of f

[past briar]

does g(f) exist?

[runic swift]

yeah it does

[past briar]

would the domain be similar to as function f?

[runic swift]

for?

[past briar]

of g(f)

[runic swift]

yeah

[past briar]

would it be all real numbers expect 0 and 2?

[runic swift]

why 0 and 2

[past briar]

honestly I had based it off the domain of f

now realizing the +1 is on the outside

does the one on the outside do anything to the domain?

[runic swift]

no

[past briar]

so would the domain be the same as the f function?

[runic swift]

yeah

[past briar]

so to conclude this f and g(f) domain is all numbers expect x = 1 and x = -1/[-infinity, -1]U{-1,1}U{1,infinity}. the domain of g is all real numbers or {-infinity,+infinity}

[runic swift]

yes

[past briar]

and no domain for f(g)

[runic swift]

i mean it doesnt exist so

[past briar]

well i do apperciate the help provided

and all the hassle provided

.close

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[hard marsh]

How can I solve it?

[fluid tundra]

use 45-45-90 and 30-60-90 special triangle ratios

you can set up a single equation in terms of the variable x

[leaden karma]

(To make it clearer, you may find it useful to label the side adjacent to the x and 10m sides as y)

[hard marsh]

srry how should i make the equation??

[pastel adder]

for triangles of two 45 degree angles, the triangle lengths must be equal, other than the hypotenuse.

Therefore x + 10 is the bottom side length.

The bottom left of the triangle is 90 degrees because 180-45-45 = 90, but this fact can be used for the larger triangle.

We can use the same principle to find the total degree of the top left angle.

Now it is simply a law of sines, sin 30 / x = sin of top angle / (x+10)

Multiply across, distribute and subtract and divide for your answer.

[hard marsh]

AIGHT THX SO MUCHH

.close

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[vale anvil]

Need help with my practice test the real test is Friday and I’m kinda nervous since I don’t know much of the topic

[vale anvil]

I need help understanding all of these topics mostly domain and range and etc

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185> anyone?

[hardy pilot]

yes

[vale anvil]

thank you

I was starting to lose hope

[hardy pilot]

which topic do u want me to help u in?

[vale anvil]

I need help understanding domain and range and how to solve the problems

[hardy pilot]

which one

[vale anvil]

The whole worksheet basically but if possible maybe like the first couple problems

I wanna be able to confidently solve the worksheet

[hardy pilot]

ok , so u select one of them then i'll help u in that

[vale anvil]

Number 1

Like how do I know if it’s all real numbers or what is the domain and range

[hardy pilot]

ok

[ancient rampart]

its real numbers unless mentioned otherwise

so always solve for discriminant of sqrt greater than or equal to zero if evaluating domain of function

for range there are multiple ways...

depends on the type of experssion tbh

[vale anvil]

I’m still confused

you need to explain it step by step or show me visually

[ancient rampart]

im not sure u can really have somoene tutor u like that here try khan academy functions introduction or something

[vale anvil]

Ok

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[balmy sparrow]

How do you notate / read when a variable is over an equals sign or an approximate sign?

Pardon the random context (and photo of a screen instead of pasting it in directly) - it's related to my work, so I can't share actual files or information. I'm working solely on writing an alternative text description / notation of figures and formulas.

For example, "log begin fraction S subscript T end over S subscript 0 end [blackboard bold P approximates?] N left bracket M T comma sigma squared T close bracket"

[pearl cargo]

It seems like that's the symbol they're using for "has probability distribution"

[balmy sparrow]

Does it seem correct to integrate that by saying, "log begin fraction S subscript T end over S subscript 0 end has probability distribution with N left bracket M T comma sigma squared T close bracket" ?

[cursive field]

this server has latex

so

[balmy sparrow]

(would it be "with" or "to"?)

[cursive field]

you dont need to write it like that

[clever fjord]

ren

[balmy sparrow]

I specifically am looking for it written like this

I'm generating text notation, not formulas

Since we don't alway know the context of the client's formulas or figures, we try to take the literal approach to notating how symbols appear. But it's tricky in this case. We could say "Blackboard bold P over tilde" if we wanted to be real literal, I guess...

We can trust that end-users likely understand the context a whole lot better, hence we just need to correctly write what a seeing user can see. A seeing user doesn't see a function, they interpret a function.

As someone who is better at math than me, would you visualize this correctly if you closed your eyes and only read/heard the "Blackboard bold P over tilde" or "has probability distribution with" ?

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[patent shard]

how do you integrate this?

[quasi sparrow]

those are two separate integrals

[patent shard]

do i integrate the numerator using substitution?

[tacit wasp]

That's one possible way, yes

[patent shard]

what’s the other way?

[fossil hawk]

Integration by parts

[uneven osprey]

Am I dumb or that m/m actually gave a m in the end?

[fossil hawk]

Huh?

[uneven osprey]

0.574 m

that's supposed to be m^{n}/m^{n}

[fossil hawk]

Ohh wait yes the dimensions are incorrect

[patent shard]

alright thanks guys

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[finite oxide]

how do i find limits for this

[fossil hawk]

Limits for what?

[odd edge]

@finite oxide Has your question been resolved?

[finite oxide]

the area under the shaded region

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[fierce fable]

Can anyone help me figure out c)

[odd edge]

@fierce fable Has your question been resolved?

[mental lotus]

From (b) you know the slope of the tangent to be 1

now just put the point P in equation of line: y=mx+c, where m = 1

[fierce fable]

so -1 = 1 (2) - c?

since we have P (2, -1) and m = 1 what is c

[mental lotus]

Yes. Solveing this gets you the c

[fierce fable]

ah ok

[fierce fable]

so I suppose something like this could work?

[mental lotus]

yes, but you messed up the signs in last step

-1-2 = 2-2 **-**c

gets you -3 = -c OR c= 3

[fierce fable]

so its both, or c cant be negative so it becomes c = 3 is what youre saying

[mental lotus]

wdym?

I am simply dividing by the common factor -1 on both sides

[fierce fable]

so c = 3 is the final answer

[mental lotus]

yes

dont you already know that since you have it on your question screenshot?

[fierce fable]

yeah I had an answer sheet and just put it there and said Id come back to it later

I didnt know how to get it though

[mental lotus]

Although, as a sidenote you should know the figure drawn in red is wrong for the curve 1/(1-x)

[fierce fable]

so our final answer is y = 1 (x) -3?

[fierce fable]

oh

I just assumed since our first point given was (2, -1)

how would it be done correctly

actually never mind yeah I just drew it because I wanted to I didnt even know any other point in hindsight it doesnt make sense 😭

[mental lotus]

the nature of the curve is correct but you can easily see, the function is undefined at x = 1

[fierce fable]

yeah lol

[mental lotus]

so the asymptote should be at x = 1 and not at x=0 as you drew in the figure

[fierce fable]

makes sense

ill prob think it through next time

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[narrow patio]

How do you actually compute this? I thought it was evaluate it at the upper bound and subtract the same calculation for the lower bound but that doesn't work out

[royal herald]

show your work

[narrow patio]

this isn't mine. I am trying to understand the example

[royal herald]

ok so for the first evaluation, itd be

$(\frac {3(21)^2}{4} - 21(21)) - (\frac {3 (14)^2}{4} - 21(14))$

[narrow patio]

and then do the same thing for the other one and add them together? because thats what I tried and I couldn't get their answer

[royal herald]

ok yea thats what i wanted you to show me

can you show me your work

[narrow patio]

one second and I can its on paper

ok so the thing I scratched out was right not hte 36.75

-110.25 is what that comes out to

but I'm still wrong in some form or fashion

[royal herald]

where did -441/4 come from

[narrow patio]

I don't know. Thank you for your help. I'm going to start over and come back to it with a clearer head.

[royal herald]

ok

[narrow patio]

.close

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[twin osprey]

For reference, this is the problem as provided:

[uneven juniper]

Help

[twin osprey]

I posted a question, but it doesn't look like the channel was moved to "Occupied". Did I do something wrong?

[wide drift]

Oh shit

Is the server broken

<@&268886789983436800>

[viscid flint]

yes i think so

i'm seeing a lot of errors in our logs

[pulsar elbow]

cringe server fr

[viscid flint]

that's me i serve cringe

they seem to be 500 errors so discord's fault. probably.

[torpid cosmos]

is "for every" the same as "for all" the same as $\forall$?
in other words is $\text{for every } e \in E$ the same as $\forall_e \in E$?

[clever fjord]

PolloTundra | Aidan

PolloTundra | Aidan

[glacial pollen]

o

[dusky ermine]

i honestly have no clue how to do this

i know that f(2) is 11 but thats about it

[low tinsel]

its 0/0

so

[dusky ermine]

how do you get the 0 in the denominator

[low tinsel]

h tends to 0

[dusky ermine]

i mean numerator

[low tinsel]

so its 0

[dusky ermine]

sorry

[low tinsel]

oh

you said f(2) is 11

h is 0

so its just f(2)

is this the whole exercise?

[dusky ermine]

no this is the only question like this

out of 37 questions

[low tinsel]

ok ok

give me a minute

[dusky ermine]

ok thanks

[stark wolf]

can someone help me with this one problem I’ve been stuck on it all day 😀

[low tinsel]

make a different thread

[dusky ermine]

yeah the bots are broken rn

[low tinsel]

oh nvm mb

[stark wolf]

oh when will they be back up

[dusky ermine]

i got no clue

[low tinsel]

i dont know how to factorize the top and bottom

gotta use the lateral limits

[dusky ermine]

yeah i got no clue either to be honest

[glacial pollen]

bru

.reopen

[dusky ermine]

broken still

i emailed my teacher about this problem but still hasnt responded

i also emailed him about this cause idk what to do for this either

[low tinsel]

you gotta let the inside of the lim be another function

i can do that

[dusky ermine]

yeah this is like our third lesson on limits cause the year just started so im still learning alot

[low tinsel]

nice

what grade of you in

[dusky ermine]

11th

oh shit i think the bot is back up

[low tinsel]

aight

give me some time im in a game

[stark wolf]

How do u get the bot to help

[odd edge]

@twin osprey Has your question been resolved?

[dusky ermine]

it doesnt help it just creates channels and stuff

[cinder prism]

can you please explain how i go from the first equation to the one i syellow

i know we square root everything

making it sqrt (cdeltat_(vdeltat)=cdelatau

[low tinsel]

@dusky ermine im doing it rn

[dusky ermine]

ty

[cinder prism]

OH MY BAD

SORRY

[dusky ermine]

lol youre good

this channel is still broken cause the channel was never closed

.close

nope

[low tinsel]

whoever made this exercise is a mathnerd

[low tinsel]

this

idk i give up

[dusky ermine]

lol its good

thanks for trying

[low tinsel]

yw

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[tropic escarp]

so when im doing my first integration which variables do i use from the x+y+z=2, im supposed to be integrating in terms of x first and then z second so do i use x's and z's and remove the y's, or do i use all three variables?

[tropic escarp]

is my upper bound going to be 2-z or 2-z-y?

[odd edge]

@tropic escarp Has your question been resolved?

[tropic escarp]

<@&286206848099549185>

[odd edge]

@tropic escarp Has your question been resolved?

[odd edge]

@tropic escarp Has your question been resolved?

[tropic escarp]

.close

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[lapis schooner]

36 - 36(½)⁶ ÷ 1 - ½

[lapis schooner]

help-

[robust wyvern]

just start in order

which one goes first?

[odd edge]

@lapis schooner Has your question been resolved?

[lapis schooner]

i- idk

36 -36(½)⁶
——————
1 - ½

[robust wyvern]

u would start with parentheses and brackets

then exponents and roots

then multiplication and division

then addition and subtraction

just apply that to your expression

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[robust wyvern]

Find the cartesian equation of this straight line

You only need two coordinates

[full elk]

what is a?

[austere blade]

the "y" coordante of a point with x = 0

[full elk]

so what number is a?

[austere blade]

thats what you need to find out

[full elk]

can u find it out?

[austere blade]

the sugestion that donia made is good

[robust wyvern]

tyty

[full elk]

so what is a?

is it 1?

[austere blade]

show your work

[full elk]

my working is that the gradient for the first two coordinates is -1

and the gradient has to be the same for the one with 0 and the second coordinate

so 5,-4 and 0,a have a gradient of -1

[austere blade]

but by that logic "a" would be 0 right ?

[full elk]

if it is 0 then there won't be a gradient of -1

there has to be a gradient of -1 for the two coordinates

because they are on a straight line

[austere blade]

gradient is - 1

[full elk]

yes

[austere blade]

so y = -x + b

right ?

[full elk]

a has to be one because the difference ill show a graph

[austere blade]

it is

1

i didnt understood your reasoning so i will show mine

since the gradient is - 1

we have y = -x + b

since (-2,3) belongs to the line

we get

3 = 2 + b

<=> b = 1

so we get that y = -x + 1

a also belongs to the line

[full elk]

like this

[austere blade]

0,a

so a = -(0) + 1

= 1

yes you are right a = 1

[full elk]

alr thanks

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[stark kettle]

found this on wikipedia, but how would i prove this?
$\eta(s)=(1-2^{1-s})\zeta(s)$

[clever fjord]

pixel

[stark kettle]

i tried just expanding all the series, but i get
$\eta(s)=\sum_{n=1}^{\infty}\tfrac{1-2^{1-s}}{n^s}$

[clever fjord]

pixel

[mental lotus]

2^(1-s) = 2/2^s

so, you can split the sum as 1/n^s - 2/(2n)^s

so in the end you just turn every even term into -1/n^s

which is the eta function

(I am assuming its the riemann zeta and dirichlet eta fns)

[stark kettle]

yes

okay thanks

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[fair notch]

how should i approach this one?

[fair notch]

i thought about common factor but im not sure how to deal with it when i have an equation

[pale atlas]

Look at the 2nd denominator on left side , then look at denominator on right side

You will be able to see common terms that might get

[fair notch]

i thought of that, but then i didnt really know what to do with the first term on the left

[pale atlas]

Its ok you know how to solve left side ? Like cross multiplication and all?

a/b -c/d
ad-bc/bd?

[fair notch]

i think i do, but dont i need to do the same in the other side of the equation?

[pale atlas]

Not yet

Let that be

Just solve the left side first

[fair notch]

alright, ill update in a minute, thank you

[pale atlas]

Sure

Don't multiply the denominator @fair notch , keep them as ()() terms , only solve the numerator of left side

[fair notch]

eh i think i got very lost

[stoic torrent]

@fair notch just looking at denominators

[pale atlas]

@fair notch

[stoic torrent]

Can you find link between the first and the second one, between the first and third one

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[oak python]

Why for B) you multiply the surface area by volume?

[oak python]

isnt the volume just 2x^2h?

[pale atlas]

That's what they have done right? h * 2x * x

That's 2x²h

[oak python]

yea but later they multiply by the SA

why do they do that

[pale atlas]

Whereee

[oak python]

OH

lmfao my bad

[pale atlas]

[oak python]

dawg 💀

.close

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[oak python]

Sorry ive been doing math for so long

that im tripping atp

[pale atlas]

No worries

Good luck

[oak python]

ty

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[brittle notch]

How do u use epsilon delta

For solving 3rd question

Any one of a b or c

I'll try the rest

[mystic saffron]

I am back

So, what we want to do is

Suppose we have any delta>0

We want to find an x such that 0<|x-1|<delta but |f(x)-1/2|>=1/2

Does that make sense?

[odd edge]

@brittle notch Has your question been resolved?

[brittle notch]

Yes

Back

[mystic saffron]

Can you think of how to find such an x?

[brittle notch]

Exactly that's the problem

I cant

Ok so first

Remove the mod

-d<x-1<d

And same for f(x)

@mystic saffron ?

[mystic saffron]

So 1-d<x<1+d

Can you tell me of some x satisfying these conditions?

[brittle notch]

Yes

Wait

What

x between that range

Satisfies the condition?

So something like

Divide by 2 or 3 or something

1-d/2 or 1-d/3?

Something like that?

[mystic saffron]

Yes, that is very good

[brittle notch]

Mhm

[mystic saffron]

Can you tell me what f(1-d/2) is?

[brittle notch]

Ok so

Wait

The problem here is

Which x do I choose

d/2 d/3 d/100

Whatever

Which one do u choose

[brittle notch]

1-d/2

[mystic saffron]

Why?

[brittle notch]

Wdym why?

f(x) is x when x<1

Hmm?

[mystic saffron]

Right

[brittle notch]

Yes

[mystic saffron]

So what is |f(x)-1/2|?

[brittle notch]

...

[brittle notch]

1/2-d/2

[mystic saffron]

Wait we want to ask what |f(x)-2| is actually

[brittle notch]

Yes ok ig

It's -1?

When x tends to 1

Wait idk

[mystic saffron]

I mean when x=1-d/2

[brittle notch]

Mhm yea

Just put 1-d/2 in f(x)

We get some relation again

We remove mod

Then what

[mystic saffron]

You get |-1-d/2| = 1+d/2

[brittle notch]

Yes

[odd edge]

Channel closed

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[brittle notch]

What

.reopen

[odd edge]

✅

[brittle notch]

@mystic saffron

[mystic saffron]

Is that < 1/2?

[brittle notch]

Ues

Yes*

[mystic saffron]

1+d/2 is < 1/2?

[brittle notch]

Yes?

Cuz f(x)-2<1/2

According to question

??

[mystic saffron]

We picked d to be >0

We wanted to find a counterexample to the claim in the question

[brittle notch]

Uh?

Didn't get you

[mystic saffron]

The question asked

To show that no d>0 satisfies that condition for all x

So to show that

We wanted to find an x such that 0 < |x-1| < d and |f(x)-2| >= 1/2

[brittle notch]

Yes

We chose x to be 1-d/2

And put it in second equation

[mystic saffron]

We also put it in the first one, and that worked

[brittle notch]

Yes

[mystic saffron]

So what happens when you put 1-d/2 in the second inequality?

[brittle notch]

This??

[mystic saffron]

No idea where you get that from

Can you just compute |f(1-d/2)-2| ?

[brittle notch]

Wdym

....

[brittle notch]

1+d/2

[mystic saffron]

Yes

[brittle notch]

Yes

And in the question

Is it not mentioned that

The thing is <1/2

[mystic saffron]

We want to prove the claim in the question is false

[brittle notch]

Ohh ok

Now what?

[mystic saffron]

This isn't < 1/2

Despite x satisfying 0 < |x-1| < d

So d does not satisfy the condition in the question for all x

[brittle notch]

What y

[mystic saffron]

d>0

so d/2>0

[brittle notch]

Oh yeaa

Yes

[mystic saffron]

so 1+d/2 > 1 > 1/2

[brittle notch]

Got it

[mystic saffron]

And since our delta was arbitrary

Our proof works for any delta

[brittle notch]

Okeyy

[mystic saffron]

So we shown no delta>0 satisfies that condition for all x

[brittle notch]

Yes

So that thing is wrong

Ok so

Y only d/2

Why not something like

5d/6

[mystic saffron]

That would work too

[brittle notch]

Ohh nice

Ok lemme try b part

Wait we just solved b also

We show that it doesn't work for one epsilon then it means it's not equal to 2 right

[mystic saffron]

Yes, if the limit was 2 then for every epsilon there'd be a delta satisfying that condition

[brittle notch]

Yes

So

What to do from here

For the c part

@mystic saffron

[mystic saffron]

Why did you write this?

[brittle notch]

f(x)-1

That thing

f(x)-L<epsilon

Definition right

[mystic saffron]

You don't know if it implies that

[brittle notch]

Wdym?

[mystic saffron]

Let's restart from the beginning

You want to show that the limit as x->1 of f(x) is not 1

Can you tell me what it means for that limit to not be 1?

[brittle notch]

I didn't get it

😅

[mystic saffron]

What did you not get?

[brittle notch]

Basically everything

[mystic saffron]

The question is asking you to show

this

[brittle notch]

Yes

[mystic saffron]

Do you know what it means for that limit to not be 1?

[brittle notch]

Nop

[mystic saffron]

Well, before trying to do a question we should know what the things in it mean

So you don't know what a limit is?

[brittle notch]

Yes I do

[mystic saffron]

Then tell me what it means for $\lim_{x\to 1} f(x) = 1$

[clever fjord]

Bequi

[brittle notch]

I don't understand reeee

[mystic saffron]

What do you not understand?

[brittle notch]

No like

Wdym mean

[brittle notch]

This

[mystic saffron]

You told me you know what a limit is

[brittle notch]

Yes

No like

[mystic saffron]

What is a limit then?

Can you define it?

[brittle notch]

Limit is is like

Yes

It's like

U approach a certain value of x

And try to determine

The value of function there

Even if function doesn't exist

[mystic saffron]

That is not a definition

In math everything has a rigorous definition

[brittle notch]

Uhh

Lemme think

U mean the epsilon delta defition?

[mystic saffron]

Yes

[brittle notch]

Ahh I c

So

This thing

[mystic saffron]

Not quite

[brittle notch]

I'm basically lazy to write the whole thing down

But yes I know the definitions

[mystic saffron]

Also it should be 0 < |x-c| < delta

you forgot the 0 <

[brittle notch]

Yes

Ah fine

[mystic saffron]

Anyway, we want to show that this limit is not equal to 1

That means we need to negate the definition of limit

Do you know how to negate statements?

[brittle notch]

Yes

[brittle notch]

No

I'm basically new to this stuff

Like the epsilon delta thing

[mystic saffron]

The definition of limit says that for all epsilon>0 : something

[brittle notch]

Yes

[mystic saffron]

To negate something of that form

It becomes there exists epsilon>0 : not(something)

Does that make sense?

[brittle notch]

Uh no

[mystic saffron]

Let's take a better look at basic logic then

$\forall x : \phi(x)$

[clever fjord]

Bequi

[mystic saffron]

This means that every x satisfies phi(x)

For example, if phi(x) says x>0, this statement is saying that every x is greater than 0

Does this make sense?

[brittle notch]

Yes

I get it

[mystic saffron]

So if this is false

Then not every x is greater than 0

That is, there is a x that is not greater than 0

[mystic saffron]

The negation of a statement of this form is of the form $\exists x : \neg\phi(x)$

[clever fjord]

Bequi

[brittle notch]

Yes I get it

[mystic saffron]

Similarly, can you see what the negation of $\exists x : \phi(x)$ would be?

[clever fjord]

Bequi

[brittle notch]

It isn't loading

Nop

I didn't understand

[stoic torrent]

Try to guess something

Itll be easier to understand what you dont get

[brittle notch]

What

Hello?

[mystic saffron]

Sorry, I'm not really sure how to help you, you are missing a lot of basic logic background

[brittle notch]

Uhh

I'm trying to understand

That's the problem I'm not able to

Suggest something to learn from or something like that

[mystic saffron]

Maybe ask in #book-recommendations

[brittle notch]

Or I'm not understanding ur sentences well 😅😅

[mystic saffron]

That is also a possibility

[brittle notch]

Yes

[odd edge]

@brittle notch Has your question been resolved?

[brittle notch]

.close

[odd edge]

Channel closed

Closed by @brittle notch

Use .reopen if this was a mistake.

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• Be polite and have a nice day!

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[quartz adder]

Guys can u tell me a youtube channel for maths that will be useful for a class 9 student

[small lichen]

organic chem tutor

[quartz adder]

Thank u

[vernal yacht]

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

@quartz adder Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[faint charm]

does anyone know what these 3 mean

[woven plaza]

I'm not sure how to interpret angle brackets here, but this is telling you some details about a function. Specifically its domain and range

The top, I would read as "f is a function which maps numbers from the range a to b (inclusively) into the real numbers"

[static totem]

the angles make me think of pairs

it's the [] that i don't get

i guess it's both intervals?

[faint charm]

hmmmm

[woven plaza]

I think the <> are meant to be ().

[] is how you specify an interval including the ends. () is how you express an interval excluding the ends.