help-19

[quasi falcon]

We plug (whatever is the other root) and a

yep

[versed siren]

we live in a society

https://tenor.com/view/gfl-gfl2-suomi-gif-5927541470036042616

.close

[odd edge]

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[versed siren]

@short terrace @quasi falcon thank you for oyur help

[quasi falcon]

again, theres probably an easier geometric method, but im not a greek philosopher to know what that would be

[odd edge]

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[karmic arrow]

!status

[odd edge]

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

[drowsy river]

1

[safe vapor]

Even if you answer (1), tell us everything you know about the problem. Do you know what an intersection and union is? Lacking that, do you at least know what M and V represent?

[drowsy river]

literally nothing

not even what the variables represent

[safe vapor]

You don't know what M = {-1, 2, 5} means?

[drowsy river]

no

is it a function

[wooden python]

no, it's a set

[safe vapor]

Do you know what a set is?

[drowsy river]

no

use too I forgot

[safe vapor]

read the first page then get back to us
https://www.math.uh.edu/~dlabate/settheory_Ashlock.pdf

[drowsy river]

aaalright

[drowsy river]

alright

got a general idea

[safe vapor]

So now, can you define a set in your own words?

[drowsy river]

a group of numbers defined as one?

[safe vapor]

any group of things

{apple, banana, orange} is a set

{1, 2, 3, 8} is a set

[drowsy river]

ah

alright

[safe vapor]

They just contain "things"

So M contains -1, 2, and 5

[drowsy river]

gotcha

can we talk about the notation?

[wooden python]

(M contains -1, 2 and 5, and no other things)

[drowsy river]

would the variables be called sets?

[drowsy river]

gotcha

cool pfp btw

[wooden python]

no, the things that go into a set are called its elements.

thank you

[drowsy river]

I mean the letters

In this case M abd V

and*

[safe vapor]

The things in a set are "elements", the M is just a "set"

[wooden python]

M and N? yeah. these are the names of those sets

[drowsy river]

alright alright

so what do the U’s mean

[safe vapor]

So the set called "M" has elements -1, 2, 5.

[drowsy river]

and V has -1, 1, 3 and 7

[safe vapor]

Read definition 2.5 and 2.7 now.

[drowsy river]

on it

[safe vapor]

(example 2.3 & 2.4 are useful here too)

[drowsy river]

2.5 was confusing

in one the middle was shaded

but in the other everything was shaded

so in the first is it only similarities and the second is everything?

[safe vapor]

Did you read definition 2.5?

[drowsy river]

in this case -1

[drowsy river]

lemme look

ok ok I see

I defined it correctly

upside down u is the collection of sets

so what they both have

and normal u is what they don’t have

[safe vapor]

yep

no

[drowsy river]

is that right or do I got it flip flopped

[safe vapor]

upside down u, the intersection is correct

[drowsy river]

what about normal u

whats the case with that one

[lean ivy]

Thats union

[safe vapor]

the intersection of two sets, $A \cap B$ is the set of all elements in both A and B

[clever fjord]

Stitches

[lean ivy]

A set including elements of both the sets

[drowsy river]

okay

so {-1}?

[safe vapor]

yes

since -1 is in both sets

[lean ivy]

Intersection yes

[drowsy river]

do I just say { -1 upside down u -1 }?

[safe vapor]

hence it is in the intersection

[lean ivy]

No

[drowsy river]

Oh

how do I use the notation when it’s the same number

[safe vapor]

no, you just say $M \cap V = {-1}$

[clever fjord]

Stitches

[drowsy river]

ohhh

[lean ivy]

A upside down u B={-1}

[safe vapor]

with curly brackets {-1}

[lean ivy]

Yes

[safe vapor]

the intersection of two sets is a set itself, so you need the curly brackets

[drowsy river]

okay and what does upside down u do again

[lean ivy]

The common elements

[drowsy river]

can you do this please

but for other

I meant upside

sorry impulse

Like U

not inverse

[lean ivy]

Union

[drowsy river]

yeah

I should probably say that

[lean ivy]

Set including elements of both the sets

[safe vapor]

read def 2.7 and try to understand it yourself

[drowsy river]

I thought that was an intersection

[lean ivy]

Intersection is only the common elements

[safe vapor]

then get back to us

[late dust]

\{-1\}

[drowsy river]

common doesnt equal same elements?

[lean ivy]

It does

[drowsy river]

im lost

[lean ivy]

Eh maybe I am complicating things

[safe vapor]

youre getting caught up in terminology, read 2.7 and you can come up with terminology you're comfortable with

[drowsy river]

alright

[drowsy river]

okay so

Is it like functions?

where you don’t have to reiterate it it’s the same number

{ -1, 2, 3, 5, 7}

for the union

[safe vapor]

yes exactly

[drowsy river]

okay

how do I properly notate that

U is union inverse is intersection

[safe vapor]

$M \cup V = {-1, 1, 2, 3, 5, 7}$

[drowsy river]

oh I literally just list the numbers

thats pretty simple now that I know

[late dust]

You missed one

[safe vapor]

yeah, just dont forget the curly bracket

[drowsy river]

whuch

only one I missed is the other -1

do I need to write it twice?

[clever fjord]

Stitches

[safe vapor]

you missed a positive 1

[drowsy river]

oh wait

my bad im tired

you’re right

[safe vapor]

So, in one sentence each, with no math words, explain what the intersection and union of two sets are.

[drowsy river]

The intersection of two sets is when the sets have matching numbers. The union of two sets is when you compile all the numbers present in both sets

[safe vapor]

exactly

[drowsy river]

yay!!

can we do some example problems

btw normal U is compiled and upside down is similar right

[safe vapor]

Wdym compiled and similar

[drowsy river]

all the numbers present in both sets for normal U and just the same in both sets for upside down

[safe vapor]

yep

[drowsy river]

what happens when theres nothing in common for upside down

[safe vapor]

{}

def 2.1

[drowsy river]

ok

ah 0 marked through

[safe vapor]

A set can have nothing in it. It's called the empty set (2.1). If there is nothing in common for the intersection, $U \cap V = {}$ simply

[drowsy river]

got it

[clever fjord]

Stitches

[safe vapor]

(or the O marked through symbol, same thing)

Basically both mean that "this set is empty"

[drowsy river]

gotcha gotcha

do they have to be in alphabetical order

when it’s letters

[safe vapor]

Like what?

[drowsy river]

let’s say

M = {a,b,j,z}
V = {i,a,y}

for normal u do I have to write it as

{a…

or can I do {z…

[wooden python]

order doesn't matter

[drowsy river]

aleks is dumb then

[safe vapor]

I mean... there isn't a strict rule. It's typically nice to have some sort of order but both are acceptable.

[drowsy river]

marked me for not putting in in alphabetical

[wooden python]

it's conventional to put the elements of a set in order if an obvious ordering exists

[drowsy river]

thanks for the real world clarification though

[wooden python]

but you can list the elements in any order you want and it'll still be the same set

[drowsy river]

gotcha

do you think I’ll ever have to write the U symbols myself

or will it always be formatted like M u Z etc

[safe vapor]

like on a computer?

[drowsy river]

yeah

or paper

[safe vapor]

Paper sure, computer probably not?

How would you write $\cap$ on a computer

[clever fjord]

Stitches

[drowsy river]

well like a website like this

[karmic arrow]

They could make it a drop down list

[drowsy river]

😂

good point

[wooden python]

if they expect you to write fancy symbols they will provide you with the means to do so

[drowsy river]

do you guys have any good way to remember the difference

[karmic arrow]

U -> [U]nion

[wooden python]

i$\cap$tersection

[clever fjord]

Ann

[drowsy river]

oh wow never thought of that

[drowsy river]

this is the one where it’s just what they have in common right

[karmic arrow]

Yes

[drowsy river]

ah Ikay

math is so fun when it clicks

is there any hard examples

[karmic arrow]

Of what?

[drowsy river]

this

[karmic arrow]

Of Union and Intersection?

[drowsy river]

yeah

[karmic arrow]

I mean, not really, no. Mostly in like infinite sets or in cases of large sets the questions could feel daunting but like, it's a super simple concept

[safe vapor]

Not in the standard form you're used to (ie. here's M, here's V, find the intersection). The proofs can get tricky because they're abstract (can't rely on any literal elements). You can find some in the document's latter pages.

Like a relatively simple one would be show $|A \cup B| = |A| + |B| - |A \cap B|$

[clever fjord]

Stitches

[drowsy river]

ooof

[safe vapor]

Where |A| is the number of elements in set A. Ie. if A = {1, 5, 6}, |A| = 3

[drowsy river]

Maybe thats later on

[safe vapor]

yeah

[drowsy river]

is this kinda like how log has its own rules

multiply = add

vice versa

[safe vapor]

kinda? the rules are less obvious though

[shell haven]

Oh is this the reason for that one probability rule thingy

[safe vapor]

yeah it holds for cardinalities, combinations, etc

pretty cool

even vector spaces

[karmic arrow]

P(A or B) = P(A) + P(B) - P(A and B), yes.

[shell haven]

Cool

[drowsy river]

yeah dont know what that is yet

but I didn’t know this and now I have an understanding so

I don’t know it yet

could someone tell me my mistake here

[safe vapor]

either use {} or the O with the line through it, not both

teh O with the line through it already means "an empty set". so no need for curly brackets here

[drowsy river]

oh shit

okay thanks

I basically double crossed out

[safe vapor]

not really double cross, more like saying "the empty set set"

[drowsy river]

ah ok

thats all for now

thank you everyone who helped

.close

[odd edge]

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[fickle girder]

can someone give me a brief overview of converting heaviside functions to piecewise functions, just want to understand

[devout hedge]

the Heaviside step function?

[fickle girder]

yes

[devout hedge]

what convention are you using for H(0)?

alternatively, what is your definition of the Heaviside step function?

[fickle girder]

this is the convention that we use (engineering)

[devout hedge]

I see. this itself is piecewise.

[fickle girder]

yeah we are just given examples like this with our definition and told to convert to piecewise

ok

i think it is clicking in my head now

[devout hedge]

hm, this is more of converting transformations of Heaviside functions to a piecewise function.

[fickle girder]

i see that now, we are just taught its an on-off switch and its the most simple piecewise function

but its starting to make more sense to me now

[pallid epoch]

I'd suggest expanding each of the step functions

And then looking at the different sections you're left with

Combining anything that overlaps

[fickle girder]

okay i get it now, thank u both

[devout hedge]

if you're done, please remember to close the channel, OP.

[fickle girder]

.close

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[tranquil basin]

There is a geometric sequence of length 3 and if you add 24 to the 2nd term and subtract 24 from the 3rd term you get an arithmetic sequence. The sum of all 3 terms is 168

[wooden python]

thats a nice fact about a sequence of numbers

what are you asked to do with that?

[tranquil basin]

i am asked to find the sequence

here is my previous work but i sidnt reallly get anywhere

[wooden python]

ok so i was gonna ask whether 168 was the sum of the AP or that of the GP but those two total to the same amount anyway.

[tranquil basin]

yes

[wooden python]

you've already found that $a_1 + d = 56$ and you know that $a_1 + d = a_2 + 24$ as per your write-out of the terms in both sequences.

[clever fjord]

Ann

[wooden python]

so you can find the 2nd term in the GP. as in you straight up know its value.

[tranquil basin]

right

80

i will rewrite it in clearer terms

no 56 my bad

[wooden python]

wrong both times, it's 32.

the middle term of the AP is 56 and this is 24 higher than the middle term of the GP

[tranquil basin]

i meant 56 in the arithmetic

[wooden python]

yes that is true then

[tranquil basin]

ok

[wooden python]

work out the entire GP though

you know that its other two terms are (in your notation) 32/k and 32*k

[tranquil basin]

yes

but i dont know what k is

[wooden python]

good thing you can find out what it is

you still know the sum of the GP is 168

[tranquil basin]

you are right i took a different approach but i think that the results will be teh same

[odd edge]

@tranquil basin Has your question been resolved?

[tranquil basin]

ok thanks ann i wopuldve never seen that myself

.close

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[viral robin]

heres what i tried

AB_C_D_E_

nevermind i mis clicked my calculator

.close

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[viral robin]

.reopen

[odd edge]

✅

[viral robin]

nevermind i didnt

heres what i tried

AB_C_D_E_
5P2 * 4! * 2!

5 slots for F and G

and AB, C, D, E is 4 factorial * 2! for AB

wait never mind i did misclick my calculator

.close

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[proven harbor]

Lmao

[atomic hornet]

what

[vernal yacht]

.unsolved

[odd edge]

✅

[viral robin]

bro this C and P stuff looks so similar sorry

[atomic hornet]

@viral robin Alright, so no hurries

we'll wait until you get the answer

We don't bite lol

[viral robin]

bro i got it guys seriously

i misclicked

[proven harbor]

Nice

[viral robin]

thanks everyone

[atomic hornet]

I see

[vernal yacht]

.solved

[odd edge]

Channel closed

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[proven harbor]

Why did you open?

[warped urchin]

blud is thanking everyone for doing absolutely nothing

[viral robin]

sorry guys and thanks to everybody

[proven harbor]

Eat 5 stars

[tranquil basin]

youre welcome radium

[vernal yacht]

I was waiting for them to post the answer. The were too rushy to clopen the channel

Rushy*

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[fleet lake]

help me with 13

[narrow crypt]

[ \sin^2\left( \frac{x}{2}\right) = \frac{1-\cos x}{2}] might be useful?

[clever fjord]

k

[fleet lake]

i thought that but it will increase variables i guessed

[waxen talon]

wdym increase the variables?

[fleet lake]

cos😅

[strange aspen]

Maybe check the range
sin(x)sin^2(x/2)=-1
sin^2(x/2) can only be positive
sin(x) should be -1

[fleet lake]

yeah

yep

[void yew]

maybe divide both sides by 13, then take alpha= arccos(12/13), and simplify LHS into sin(alpha+x)

[stoic cloud]

I’m pretty sure this has no real solutions.

[fleet lake]

i got same

but doubted it

[strange aspen]

Well it doesn’t have Real solution

[stoic cloud]

Don’t doubt yourself! If you got that answer, you should say so to those trying to help! You might be able to get your answer faster that way.

[fleet lake]

ohk ill take care next time

the thing id i always doubt my solution in ranges and domains

who knows if i forget to include some imp stuffs

does it have a solution @stoic cloud ?

[strange aspen]

Nah

[stoic cloud]

I don’t believe it has a real solution but it probably does in the complex plane.

[void yew]

Yeah it has no solutions in real numbers

[stoic cloud]

Although I don’t have proof of it other than using a calculator.

[fleet lake]

pls no

[void yew]

If you simplify LHS into ||sin(x +alpha)||

Then you know its max is 1

[fleet lake]

wait man

[fleet lake]

i mean solution of this problem

[void yew]

Yeah I mean that too

Divide both sides by 13

Then you can simplify into sin(x+alpha)

And RHS will be >1

[fleet lake]

i mean the prblm of doubting myself

[stoic cloud]

There are solutions in the complex plane. However, they are EXTREMELY repulsive.

[void yew]

Oh

[stoic cloud]

no closed forms exist, and they’re multivalued

so I would just say NSE

[fleet lake]

man
help me with 17 too pls

[stoic cloud]

Okie dokie

let’s see

[fleet lake]

i g no solution

[stoic cloud]

uh it’s hard to see

do you know latex?

or can you zoom in on it?

[fleet lake]

2^(sec^2x) + 2^(cosec^2x)= cos^2 x.sin^2 2y

[waxen talon]

Find the number of solutions as ordered pair $(x, y)$ such that 2^{\sec^2x} + 2^{\mathrm^2y} = 2\cos^2x(1 - \cos^22y)$ in the range of $0$ to $2\pi$

[stoic cloud]

\csc is not a defined function

you will hvae to use \mathrm

[clever fjord]

1 divided by 0 equals Infinity
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[waxen talon]

yeah i used 😭

[fleet lake]

well rn im pretty sure for it has no solution

.close

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[wooden python]

$\max_{\bd{x} : \nrm{\bd{x}} = 1} \nrm{\bd{Ax}}$ would be the maximum value of $\nrm{\bd{Ax}}$ taken over all $\bd{x}$ such that $\nrm{\bd{x}} = 1$.

[clever fjord]

Ann

[wooden python]

argmax refers to specifically the x that makes this maximum happen.

[lyric marlin]

in this case yes

🗿

well

no

it's going to be a set of vectors

it might as well be treated as one (even if formally it probably wouldn't be)

[wooden python]

heres the difference between max and argmax illustrated

you may also see argmin. its relationship to min is the same.

because funny

yes

[1,4] \cup {4.20} rather.

[clever fjord]

mq

[wooden python]

$[1,4] \cup {4.2}$

[clever fjord]

Ann

[lyric marlin]

no, you've written down a set with exactly two elements

4.20 and the set [1,4]

[errant dew]

We want a set only with numbers

[lyric marlin]

wdym

of what

the incorrect set

?

nothing particularly concise

like, short of {x in R : 1 <=x <= 4 or x=4.20}

I can't think of anything else

[odd edge]

@thin dagger Has your question been resolved?

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[ornate bolt]

hello guys i need some help with this physics exercice

[ornate bolt]

here i tried to add R/2 with R/2 because there is eventually the same current in both of them. They get divided in the first place then they reunite again

the problem is if i try to calclate V1 using this method it gives me a wrong answer compared to the normal method

can anyone clarify this pls?

[summer wave]

what answer did you get, and how did you get it

[errant dew]

(Show working)

[ornate bolt]

okay

omg i just found the mistake

[errant dew]

!done?

[odd edge]

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

[ornate bolt]

i converted it to the norton model then calculated I in V1. then multipliyed it by R instead of 2r

thanks anyways

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[molten vigil]

hello, i need some help real quick, it seems easy but idk why i cant think of how to do it, but how do i find the limit of x-3ln(x) in +inf??

[molten vigil]

im just missing an easy thing ig but i've been on it for 5 minutes and it's a bit annoying to see something that easy but not finding the solution

[short terrace]

My first thought is raising e to this power

[molten vigil]

why that??

[short terrace]

Just seeing ln

[molten vigil]

oh yeah but even if it was the solution i cant really just put as an exponent

there's no equality

[short terrace]

e^(x-3ln(x)) = (e^x)/e^(3ln(x)) = e^x/x³

And then you can probably use the power series of e^x?

[short terrace]

You can take ln afterwards again

[molten vigil]

im not sure i can just summon the exponential function just like that

it seems a bit too useful lmao

[short terrace]

You can yes

[molten vigil]

still it's not equal to the original function

[short terrace]

Yes which is why you take ln after you're done

[molten vigil]

so what's your final result???

[short terrace]

I'm not gonna solve it for you lmao

I've given you a direction

!noans

[odd edge]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[molten vigil]

i havent seen this method so if there's a trick i dont know it

[short terrace]

There genuinely isn't a trick

To find the limit of f(x)

[molten vigil]

and by graphing the function with ln i still dont have the same curve

[short terrace]

You instead find the limit of ln(e^f(x))

[molten vigil]

in green my function in purple yours

[short terrace]

Why are you graphing the function with ln

Show me the equations you're graphing

[molten vigil]

or i've messed up

[molten vigil]

maybe that

[short terrace]

Show the equations

[molten vigil]

oooh no right okay i see how it works now

sorry for being a bit annoying to you

[short terrace]

Lmao as long as you got it

[molten vigil]

anyway thanks

i wouldnt have thought of that tbh so thanks

.close

[odd edge]

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[short terrace]

It's smth you get used to after doing it a lot of times

No worries, feel free to ask again if you have more questions!

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[fair moon]

How does the leading coefficient in a function determine limits?

[errant dew]

The power also matters like x^7 and x^8 will be different

(Note: this is for when x tends to positive and negative infinity)

[fair moon]

Oh. So how does that affect it too?

[errant dew]

The even odd ness of it

Like x^1=x how does that behave for x tending to infinity and - infinity

[fair moon]

Ohhhh.

[errant dew]

Key thing about limits is you’re trying to say what the value would be near a number but not at it, for infinity it’s a bit different instead you’re letting x get bigger and bigger “closer to infinity”

[errant dew]

Compare that to x^2

[fair moon]

Then it would be positive to infinity?

All odd powers behave the same?

[errant dew]

Yes

[fair moon]

Same with even?

[errant dew]

Yes

The difference with even is that -infty goes to infinity

But odd goes to -infinity

Also if the coefficient is negative then everything i said is flipped

Except the bit about evens and odds being the same as each other

Like x^2 goes to infinity both ways -x^2 goes to -infinity both ways

If it’s like 2x^2 nothing changes

Try graphing the function x^n in Desmos or Geogebra

[fair moon]

So if my limits are as x to infinity f(x) -infinity, and x to -infinity, then f(x) to infinity, then I have to have a negative coefficient with an odd exponent?

[errant dew]

lol autocorrect

Can you post problem again

Just to make sure

[fair moon]

Hm.

[errant dew]

If they match both ways it’s even power and if they don’t it’s odd power then you work out sign based off which is positive and negative

[errant dew]

Which of these has a dominating term like that

[fair moon]

B.

[errant dew]

Yes I think it’s that one try graphing it

[fair moon]

But how do I determine right end vs. left end behavior?

[errant dew]

For next question?

[fair moon]

No, same one.

[errant dew]

Oh so with the answer get the question?

[fair moon]

What?

The negative sign affects which end? Right or left?

Or is it something else?

[errant dew]

I’m confused what you’re asking

I can share a graph with your answer to the question to see that it’s correct

[fair moon]

So left and right ends of the graph have different behaviors. If I were to be asked if the left side went negative or positive infinity, how would I find that?

[fair moon]

I checked the key, it is.

[errant dew]

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

[fair moon]

Yes.

[errant dew]

So regardless of the power, for x tending to infinity it will have the same sign as the coefficient

[fair moon]

Uhhh.

Ohhhh.

So positive coefficient is positive infinity, same goes for negative?

[errant dew]

Yes

If you think about it x^n for positive x will be positive because you are multiplying positive stuff together

Then the coefficient is the only thing that matters

[fair moon]

So a positive coefficient, both are positive, if it’s negative and the exponent is odd, both are negative, if it’s a negative coefficient and exponent is even, only right side is negative?

[errant dew]

No

[fair moon]

Ok.

[errant dew]

Even exponent they are same odd exponent they are different

[fair moon]

Ohhhh.

[errant dew]

the x tending positive infinity is infinity but the sign of that infinity depends on the sign of coefficient (they are the same)

[fair moon]

So best thing to do is look at the exponent first to see if the behaviors are the same?

[errant dew]

I think the coefficient is more important as that tells you the limit for when x tends to positive infinity

Then use powers to find the negative infinity case (same or different*)

[fair moon]

Ok.

So,
Positive coefficient and even exponent, both to positive infinity
Negative coefficient and even exponent, both to negative infinity

How do you know which side is negative and which is positive though when odd exponent?

[errant dew]

The coefficient of the term is the positive infinity case

So if it’s like 17 then the positive infinity case is positive

[fair moon]

Ok.

Negative 17, it’s negative?

[errant dew]

Regardless of exponent

[fair moon]

Ohhh, ok. Thank you!

[errant dew]

!done?

[odd edge]

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[fair moon]

Yes.

.close

[odd edge]

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[fair moon]

Thank you!

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[floral badger]

is this south of east or north of west?

cause chatgpt keeps telling me south of east but i thouhgt it was north of west

why is it south of east?

[woeful briar]

you want to create an equilabrium

so its supposed to be in the opposite direction of the total force

[errant dew]

Firstly you need to work out what the total force is

[floral badger]

ohhh ok that makes sense. tysm

[zinc glacier]

also stop trying to use chatgpt as an authority on physics, it will be right sometimes, but it can also be incredibly wrong

[floral badger]

yah thats why i came here to double check

[devout hedge]

click the X next to the embed when hovering over your message.

[floral badger]

are u in oxford or something?

Dang nice

.close

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[acoustic marsh]

I can't tell if pearson just hates me or not. I've been going at these questions for who knows how long but it just won't click and the explanations aren't helping me. can someone explain this to me?

[manic grail]

hey

are you stuck on 1 ?

or which

so discontinuity

in graph

looks as if there is a gap in drawing the function

[acoustic marsh]

Hey 🥹 there are more parts after this but I thought I understood discontinuity and got it wrong, this is my last try so I came here

[manic grail]

so think of it if we have to raise the pen at some point to continue drawing then its not continious

if its continious we can draw it out in one go

[acoustic marsh]

oh no it doesnt matter if the there is a hollow dot, only if the line jumps

so*

[late dust]

It'd be better if you showed what you tried and why you think it's right or wrong

[manic grail]

short of

ok so where do you see the first point where there is a gap in the graph

[acoustic marsh]

1 because it cuts off? or 2 because of the jump

[late dust]

Go through the checklist

[manic grail]

yes on x=2

[errant dew]

Where do you think the discontinuities are

[manic grail]

it has a gap

[late dust]

At x=1, is f defined?

[acoustic marsh]

um no?

wait

[manic grail]

is the orange line denoting a asymptotic line ?

[acoustic marsh]

im assuming

so no yea?

[late dust]

Yes it is

[manic grail]

probably is

[late dust]

Correct, so that's a discontinuity

[manic grail]

if not then there is no point in talking about continiouty there

[acoustic marsh]

oooh

[late dust]

Next point, again go through the checklist

[manic grail]

ok so check one by one

and tell us what you think of each

[acoustic marsh]

next would be 3 because it violated #1 yea?

[manic grail]

no no

like the 3 rules

that might be violated

[acoustic marsh]

yesh

it violated rule 1?

[manic grail]

go from 1 to 3 and tell me which are violated and which not

[acoustic marsh]

cuz no solid dot?

[manic grail]

yeas it does

[late dust]

Correct, but there's another point

[late dust]

You said it here, why skip it now?

[acoustic marsh]

OOH

ok so 1, 2, 3 are discontinuities?

[manic grail]

yes but why is 2

[late dust]

Yes, do you know why 2 is?

[acoustic marsh]

because #3 isnt satisfied?

[late dust]

No

[acoustic marsh]

WAIIT

CUZ

#@

#2

cuz asympote

asymtope

[late dust]

?

[manic grail]

we are talking about at x=2

[late dust]

There's no asymptote at x=2

[acoustic marsh]

wait im smart

OMG

[acoustic marsh]

i cant read a graph sorry xd

because #2 isnt satisfied

the lim isnt the same of both sides

[manic grail]

also asymptote doesnt mean the limit exist

[late dust]

Exactly

[acoustic marsh]

oooh ok ok

[manic grail]

its only giving you info that one of the side limits is infinite

[manic grail]

ok so these are all

[late dust]

So you have 1,2,3; any more points?

[acoustic marsh]

5?

[manic grail]

what would it violate?

[acoustic marsh]

#2

[manic grail]

you might be confusing it with derivative

why would the limit not exist

[late dust]

Careful about this

[acoustic marsh]

OOOH I COMPLETELY FORGOT ABOUT THAT

[manic grail]

even if it wasnt that is a point of continuity btw

[late dust]

No it's not

[manic grail]

how is it not

[late dust]

f is not defined there

[manic grail]

oh 5

i was looking at 4

[manic grail]

yea well not discontinuity either

we cant talk about continuity there

[late dust]

We can; it is a discontinuity, just not in the interval (0,5)

[manic grail]

how can we

its out of the domain

[late dust]

.

[manic grail]

can you talk about continuity at x=7?

its not defined there either

[late dust]

Yes

[acoustic marsh]

oh cuz its not a [0,5] interval?

[manic grail]

it makes no sense to talk about discontinuity at a point that is at x=7

[late dust]

Continuity implies that the function is defined; the function is not defined at 7, so it's obviously not continuous there either

[manic grail]

it makes no sense to talk about continuity there at the first place

[late dust]

Yes, in your problem you are not counting 0 and 5

[acoustic marsh]

oh so its just because there is no line that actually touces x=5?

OOOH

THATS SO SMARRT

ok so my discontinuities are 1,2,3

[manic grail]

@late dust talking about continuity for example for lnx in negative numbers is meaningless

[acoustic marsh]

now its asking for what violates the 1st condition, that would be 2 and 3?

[late dust]

I have news for you: https://en.wikipedia.org/wiki/Complex_logarithm

[manic grail]

in the reals

obviously im talking about the real numbers

a condition of continuity is the limit

[late dust]

Still applies: not defined, not continuous

[manic grail]

the limit expects that the function is defind around the poitn

either on (x,a) or (a,x)

or both

you cant talk about continuity on places where the limit isnt even properly defined

[late dust]

I'm not gonna argue with you; a function f is continuous at c if the limit x->c of f(x) equals f(c); if f(c) is not defined, there is no equality, and so no continuity

[manic grail]

there is no meaning to talk about continuity

its like examing limit x->-oo lnx

[late dust]

[acoustic marsh]

i did it 🗣️

[manic grail]

i dont think we talk about discontinuity at x=a where a have interval gap with the domain on both sides

[acoustic marsh]

its asking for the 2nd condition now, that'd be 1, 2 yea?

[manic grail]

yes

[acoustic marsh]

yea it was right 🥹

ok this is the tricky one i was stuck on

it satisfies the first 2 but violates the third

none of them do, no?

[manic grail]

yea i dont see any

youd need both lines to go into a empty dot

and there to be a full dot upper or lower than the other one

like this

[acoustic marsh]

OOOH I SEEE

thank you i fineally understand

🥹

[manic grail]

here the limit exists

the limit doesnt care about what happens at x=a

[acoustic marsh]

oooh

okkk

thanks you so so so so much

🥹

.close

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[wise rain]

hi i have test review and i dont know how to do this complicated improperly

[errant dew]

Do you get a calculator?

[wise rain]

i already have a calculator

[errant dew]

You could just put the numbers in, but you should try to simplify first, like $\frac{1}{\frac{1}{x}}=x$

[clever fjord]

BBMaths

[wise rain]

i have another math question

i also dont know how to do fento Liters to tablespoons

[errant dew]

Do you know how many L in a tablespoon?

[odd edge]

@wise rain Has your question been resolved?

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[crystal radish]

It looks like C might be the center of the circle here

am I wrong to assume that?

and if I am right, how do I know for sure?

[short terrace]

Hmm yes it should be the center

You already have CD = CB

You need to show they're equal to CA

Use congruent triangles

[vernal yacht]

[short terrace]

Hullo Sky

[vernal yacht]

I have another idea tho

[vernal yacht]

Wsp

[short terrace]

Just another day not being green

[vernal yacht]

Today is the day 🔥🔥

[short terrace]

Actually you don't even need those lmao

Just connect A and C and tell me what happens

[crystal radish]

what do you mean by that?

congruent triangles make sense to me because it splits the 120 into 60 & 60

[short terrace]

Join A and C using a line

Yes

It's also just a property of rhombuses

[crystal radish]

oh yeah diagonals are equal

[short terrace]

I thought maybe you could invoke it without proving

[crystal radish]

right?

[short terrace]

Not that one

[crystal radish]

wait no

[short terrace]

Diagonals are angle bisectors

[crystal radish]

ahhh

that makes sense

[short terrace]

The proof uses congruent triangles

But if it's mentioned as a property

You can just use it directly

Check what your book says

[crystal radish]

dont have a book, this is a competition problem

[short terrace]

Ah in that case prove it ig

[crystal radish]

but anyway, moving on from this part, i also got the question wrong 😭

from here i set r=1

so area of circle is pi

then i found area of rhombus by doing 1/2 * base * height of the two triangles

height is sqrt(2)

base is1

so area is sqrt(2)

is then ido sqrt(2)/pi

for ~0.45 but thats wrong

correct is 0.2757

[short terrace]

That sounds wrong

The area of a rhombus is just base * height

Your base is 1

And your height is sin 60

Which is sqrt(3)/2 right

,calc sqrt(3)/2pi

[clever fjord]

Result:

0.2756644477109

[short terrace]

Yup

[crystal radish]

oh ok

so i just found area wrong

[short terrace]

Yeah

[crystal radish]

im going to write this formula down

actually ill prob just write all area formulas

[short terrace]

Essentially a rhombus is two congruent triangles

A triangle is 1/2* base * height

So a rhombus is base * height

This is true of a parallelogram as well

[crystal radish]

yeah that makes sense

now i realize i just assumed height of each triangle was

sqrt(2)

but its actually sqrt(3)/2

now that i do pythagorean

so i was on the right track anyway

[short terrace]

Yup

Also another fun fact

Area of a parallelogram is ab sin θ

So you can just use that directly

[crystal radish]

what is the value of a & b?

[short terrace]

a and b are the side lengths

[crystal radish]

so for a rhombus you can just do

2a

sin theta

[short terrace]

...no

[crystal radish]

arent sides equal?

[short terrace]

a.a is not 2a

[crystal radish]

oh 💀

a^2

mb

[short terrace]

Yes

[crystal radish]

alright thank you so much

this is all very useful

.close

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[rich eagle]

if $a(a^{24}-1)$ is divisible by p for all interger a (p is a prime number) then $a^{24}-1$ is divisible by $a^{p} - 1$ (basically 24 is divisible by p)

[clever fjord]

shio6695

[rich eagle]

it's related to fermat little theorem but im not sure how to prove it

if $a(a^{24}-1)$ is divisible by p for all interger a (p is a prime number) then $a^{24}-1$ is divisible by $a^{p-1} - 1$ (basically 24 is divisible by p-1)

[clever fjord]

shio6695

[rich eagle]

fixed it a little

[twin vigil]

you problem is not clear on reading it

!original

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@rich eagle Has your question been resolved?

[rich eagle]

well the original problem is find all n where $a^25-a$ is divisible by n

well the original problem is find all n where $a^{25}-a$ is divisible by n

[clever fjord]

shio6695

[rich eagle]

(for all interger a), i just need to find the possible prime factors of n though

[waxen talon]

it's kinda obvious that $n$ could be $1$, $a$, $a^{24} - 1$ and $a^{25} - a$

[clever fjord]

1 divided by 0 equals Infinity

[waxen talon]

ofc negate all that and you got 8 results

[rich eagle]

well no i got it to be 32

you can just test it and see that n can be 2;3;5;7;13

but also things like 6 because n = 2*3

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[rich eagle]

so we have n = 2^(a1) x 3^(a2) * 5^ (a3) * 7^(a4) * 13^(a5)

[vernal yacht]

.unsolved

[odd edge]

✅

[rich eagle]

a1,a2,a3,a4,a5 cannot be 2 or larger since for example if a1 is 2 or larger you can just pick 2 and it won't work

so a1,a2,a3,a4,a5 can be 0;1 and so there's 32 number n

[rich eagle]

i still have to prove that 2;3;5;7;13 are the only prime numbers n can be though, which mean i have to solve this which idk how to

[odd edge]

@rich eagle Has your question been resolved?

[orchid torrent]

You know that the largest $n$ is bounded above by $\gcd(3^{25}-3, 2^{25}-2)$

[clever fjord]

Civil Service Pigeon

[orchid torrent]

,w gcd(3^25 - 3, 2^25 - 2)

[clever fjord]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[orchid torrent]

,w prime factor 2730

[clever fjord]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[orchid torrent]

oh

well there you go lol

yeah ||fermat's theorem|| kills it

[rich eagle]

can ya explain this

[orchid torrent]

If an n works for all a, then it must work for a=2

that should be intuitive

and similarly it must work for a=3

aka it must work for both of those

[rich eagle]

hmm alright

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[stoic sparrow]

can some1 help idk if my answer is correct

[forest sky]

what made you decide those limits DNE?

[faint knot]

whats making you say its DNE for both of them

[stoic sparrow]

since the left side and right side isnt equal

[fluid bluff]

second one is totally 5

[forest sky]

what are the left and right limits you are getting?

[fluid bluff]

because both sides are equal

and i think first one is 3

both sides also equal

[stoic sparrow]

can u point out to me where that line is like the approaching stuff

[fluid bluff]

wdym

you can figure out its a quadratic

[stoic sparrow]

waitt what

[fluid bluff]

x=>5

is a quadratic

[stoic sparrow]

wait so x

wait

[fluid bluff]

yea?

[errant dew]

!noans

[odd edge]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[stoic sparrow]

what if x=>1?

[fluid bluff]

then its a root and quadratic intersection

try calculating the limits from both sides and you get that they are equal

[stoic sparrow]

wouldnt it be x=>1- = 1+3=4 then x=>1+=1? then since its not equal its DNE or is my x=>1+ side is wrong?

[errant dew]

I’m a bit confused what you both mean by =>

[stoic sparrow]

its like approaches to

[errant dew]

Do you mean $\ge$ >= or $\rightarrow$ ->?

[clever fjord]

BBMaths

[stoic sparrow]

yesyes

2nd one

[errant dew]

Also asking you here

[fluid bluff]

yea

=> is $\ge$

[clever fjord]

Roy

[stoic sparrow]

ohhh

[fluid bluff]

this is correct

[tacit wasp]

Shouldn't't it be >= ?

[fluid bluff]

limit to 1 is DNE

[fluid bluff]

some ppl write it like that

[tacit wasp]

But that's wrong

Because that would mean implication

[stoic sparrow]

im sorryy

[fluid bluff]

no it has both meanings

[tacit wasp]

Mmhh

[fluid bluff]

so ye your answer for limit to 1 is correct

[stoic sparrow]

im so dumbbb u were right on the 1 and 2 which is the answer is 3 and the 2nd one is 5

[fluid bluff]

no you're not

i just learned it earlier so i know these kind of questions

[stoic sparrow]

ohhh

[fluid bluff]

if you practice a bit you will master it cause you already did the limit to 1 right

[stoic sparrow]

thank you so muchh and may i ask if its like thisss

[fluid bluff]

4 is incorrect

look at it closely

[stoic sparrow]

is it also 1?

[tacit wasp]

Indeed

[stoic sparrow]

so its the same thing in number 5?

[stoic sparrow]

yes

but on number 5 the point is at 7,5 rightt

[tacit wasp]

Nope, there's an empty dot at x = 7, meaning it's undefined there

[tacit wasp]

Huh?

[stoic sparrow]

ohh so if its unshaded then its automatically undefined?

[stoic sparrow]

the coordination of the f(7)

ohh okayyy thakn you so much guysss

how do i close

[tacit wasp]

Unless there's a shaded dot as well, like in question number 4 (at x=1))

[fluid bluff]

.close

[stoic sparrow]

yesss

.close

[odd edge]

Channel closed

Closed by @stoic sparrow

Use .reopen if this was a mistake.

[stoic sparrow]

thank u guys

[fluid bluff]

np

[errant dew]

I’ve never seen => before, you should try to use what’s more common so less confusion

[tacit wasp]

Use >= for ≥
Use -> for →

@stoic sparrow

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[chrome prawn]

hi there, I was just wondering how to do question ii.
the answers are simply: 5/2 * 5/2 = 25/4.
the answers to i. is c >= 25/8 btw

[fleet tapir]

Find the area as a function of c and take the limit as c->0

[chrome prawn]

i tried that wasn;t too successful, the answers' explanation is this: dyk why??

[errant dew]

Answers being unclear as always

Do you know the area as a function of c?

[fleet tapir]

Show your attempt

[chrome prawn]

area should be somethinggg along the lines of 15/4 = 2(ln(4))/c ?

unless i am wrong

15/4-2ln(4)/c soz

[fleet tapir]

Well this says that the area will be infinite

Show your working

[chrome prawn]

my original working for the previous question was wrong

ill try again

ok area function is very complex, something like this

and this is a tech free exam

so i think its more conceptual rather than area of a function hence the bare bones explanation

[manic lava]

Hi

[chrome prawn]

I just did g(x) = x solve

[fleet tapir]

Ah okay the 3 is outside the square root

[chrome prawn]

but this exam is tech free so i dont think it calls for an area functgin

[fleet tapir]

when c goes to 0 your area function just becomes -2-x from -2 to 1/2. So the integral you actually need to compute is $$2\cdot\int_{-2}^{\frac{1}{2}}-x-2\mathrm{d}x=\frac{25}{4}$$ alternatively, this is just 2x the area of a triangle with base 5/2 and height 5/4. I.e the area is $2\cdot\frac{5}{2}}\frac{5}{4}=\frac{25}{4}

[clever fjord]

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

[chrome prawn]

uh huh is this a hard question or am i just not thinking hard enough LMAO

[fleet tapir]

Did you not understand this?

[chrome prawn]

i did understand it but for a calc free exam i dont know if i would've gotten that

on my own

[fleet tapir]

That's why you prepare for it

[chrome prawn]

I hate math

Alr thanks you were a great help

.close

[odd edge]

Channel closed

Closed by @chrome prawn

Use .reopen if this was a mistake.

[fleet tapir]

We didn't need any calculator here

[fleet tapir]

Just plug in c=0 everywhere in this integral and the integral you need to do is much simpler

[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>.
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• 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.

[brittle plinth]

Given that A and B are subsets of M. Prove that these following statements are equivalent:

[wooden python]

a six-way equivalence huh

[brittle plinth]

now I haven't started yet but what is confusing me is the way they present the proof of the equivalence of f) and a)

[wooden python]

are you sure that's actually what they're doing? proving f=>a and also proving a=>f?

[brittle plinth]

They only proved f -> a it seems

which is the part that confused me

because I think you also have to prove a -> f

[wooden python]

can i see the whole proof

i dont speak viet but i should be able to figure out the notation

[brittle plinth]

it's in Vietnamese so I'll translate

[wooden python]

show the original too

or, post the original first, then translate afterwards

google lens tends to screw up math notation badly

[brittle plinth]

alrighty

Wait nvm

they said the rest is "left for readers"

[wooden python]

show anyway

i wanna know exactly how much and what is left for the reader

[signal yacht]

knowing math books, presumably all of it