help-13

[hexed vortex]

both A and B are subset of X?

[floral arrow]

Yes that's how I read it

Wouldn't make much sense if A wasn't a subset of X anyway

[hexed vortex]

oh ok thank you guys for help

.close

[cedar kiln]

Channel closed

Closed by @hexed vortex

Use .reopen if this was a mistake.

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.

[fringe night]

uh.. a,b,c > or = 0 ; 0 < or = a < or = 8 and a+b+c =9 prove 2a-2ab+abc < or = 18

[fringe night]

@uncut veldt

yays

bro

😭

[cedar kiln]

@fringe night Has your question been resolved?

[dreamy void]

Let a be fixed, try to derive a quadratic equation in terms of b

[cedar kiln]

Channel closed

Closed by @fringe night

Use .reopen if this was a mistake.

[fringe night]

i cant use calculus

[cedar kiln]

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.

[dreamy void]

try group theory then

[dreamy void]

.close

[cedar kiln]

Channel closed

Closed by @dreamy void

Use .reopen if this was a mistake.

[cedar kiln]

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.

[round lava]

what I have thought of:

so there could be four cases:

1. both A and B are knights
2. A is a knight but B is a knave
3. A is a knave but B is a knight
4. both A and B are knaves

since B says nothing, we take two possibilities:

1. A is a knave
2. A is a knight

if A is a knave, it means that negation of whatever A said should be true

that means, A' = both of us are knights

but since A is a knave, that's a contradiction

so now, possibility 2, A is a knight

[round lava]

this validates (?) what A says

but what can we conclude about B here, since it says nothing?

also, is there a better way to solve this, which is less prone to error-making?

if someone decides to reply, please ping me

[floral arrow]

Hah you're doing logic puzzles now?

[floral arrow]

Yes, given A is a knight, one of them is a knave, so B is a knave

[floral arrow]

Yes, using propositional logic

[round lava]

this comes under pre-requisites of a topic in discrete mathematics, which is one of the courses I am taking in uni xD

[round lava]

right

in such kind of questions, is there always a single answer?

[round lava]

truth table and all?

[floral arrow]

If it's a proper puzzle, of course it should have a single answer

[floral arrow]

No truth table needed

[unreal vortex]

a cant be false as if a is false a' also requires to be false and this is a contradiction

so a should be true then a is a knight

now b is null so i cant say anything about b

[round lava]

that is exactly what I said

[round lava]

what if it was something like:

A: one of us could be a knave

[unreal vortex]

so b is knave

[floral arrow]

Then A would be a knight and we couldn't conclude about B

[round lava]

how did you conclude that?

[unreal vortex]

that what i can conclude

if a is a knight and a said one of us is knave so b is knave

[round lava]

no?

it says A said one could be a knave, is not necessarily one

[unreal vortex]

here its written atleast on of us is knave

[round lava]

oh, I thought you were talking about the other case

got you

well, thank you both!

[floral arrow]

For the original:

• let P: "A is a knight"
• let Q: "B is a knight"
• A says "-P or -Q"
• P implies (-P or -Q)
• -P => (P and Q)
• so P is true
• so -Q is true

[round lava]

how are we getting P implies (-P or -Q)?

[floral arrow]

If A is a knight then what they say is true

[round lava]

right, makes sense. is this propositional logic? also, why did we negate P?

[floral arrow]

Negating P leads to a contradiction

[round lava]

what's the need though

[floral arrow]

Well you need to know the truth value of P to continue... There's a term for the process but I can't search right now

Hm I made a mistake actually

[round lava]

where?

[round lava]

then why don't we just work with P and not -P? if that makes sense

[floral arrow]

Nevermind, I didn't

[hexed vortex]

I tried but I cant read cursive 😭

[round lava]

I got the solution

[floral arrow]

P => (-P or -Q) because knights tell the truth
-P => -(-P or -Q) because knaves lie, and if A isn't a knight, they're a knave

In general though, the first expression doesn't imply the second

First gives -Q as a conclusion, and using that with the second gives P as a conclusion

[round lava]

then how can we use it to prove something, like you did?

[floral arrow]

In the context of the question, these two expressions come from different assumptions

[round lava]

I don't think I follow you properly

I gotta learn more about propositional logic first

[floral arrow]

The question explicitly says that knights tell the truth and knaves lie

[round lava]

right

[floral arrow]

Additionally there's the assumption that A and B are both either knights or knaves

[round lava]

question

[round lava]

why? aren't we just negating the whole equation?

[floral arrow]

No, "if P then Q" does not mean "if not P then not Q"

[round lava]

what if it is bi-conditional? it then follows that, right?

[floral arrow]

Wdym

[round lava]

okay, first if we talk about "implies"

say there's two statements

well, it is given that "if it rains, the kids get happy". so,

P: it rains
Q: the kids get happy

now, if it is given that the kids get happy, it does not necessarily mean that it is raining

meaning, if -Q does not mean -P (always)

but if it does not rain, does that not mean that the kids will be unhappy?

meaning, -P then -Q?

[floral arrow]

No, you mean Q doesn't imply P

[round lava]

no?

if the kids aren't happy

[floral arrow]

No, give them candy or something and they'll be happy

[round lava]

meaning -Q

[round lava]

that is what I meant here:

[round lava]

.

[floral arrow]

This is what you said though

[round lava]

yeah

[round lava]

then why is it incorrect

like it is given kids are unhappy

so -Q, right?

[floral arrow]

No?

if it is given that the kids get happy

[round lava]

isn't Q: the kids get happy

so if the kids are unhappy

isn't that -Q

[floral arrow]

Yes... I'm not sure what to tell you here, read what you wrote again

[round lava]

ah

right

sorry

well

[floral arrow]

[round lava]

if it was given

[floral arrow]

Look up contrapositive

[round lava]

I will later, got a class in five minutes

well, thank you

I think I got a gist of it

.close

[cedar kiln]

Channel closed

Closed by @round lava

Use .reopen if this was a mistake.

[cedar kiln]

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.

[wet grotto]

Can someone please explain this recurrence formula and how to use it? Like how did they get a value for S4

[tropic oxide]

this one?

or ig this one more generally?

the first one i screenshotted looks wrong; i think the +20 should've been a +5...

@wet grotto

[wet grotto]

Why? Isnt it 4xe according to the second one?

so 4 x5 ?

Also yeah for the blue one i dont get how they got a value for s4

And an explanation for the more general one would be nice too

[tropic oxide]

oh yeah wait nevermind that one's correct

yeah ok the 20 is 5*S_0

And an explanation for the more general one would be nice too
this one is actually easy

gimme a min to write it down

@wet grotto here you go

using almost the exact same method you can actually prove the more general recurrence, i.e. $$aS_{n+4} + bS_{n+3} + cS_{n+2} + dS_{n+1} + eS_n = 0$$ for any integer $n$

[wraith dagger]

Ann

[frail citrus]

this is indeed the part of newton's theorem, aint it?

[tropic oxide]

"the part"?

[frail citrus]

not literally

it is the result of newton's theorem

[tropic oxide]

oh yeah i guess it is

phrased here for 4th degree polynomials

[wet grotto]

Ahhhh I see tysm

[frail citrus]

yes

it is inside my syllabus too, so i had a general idea of it

[wet grotto]

.close

[cedar kiln]

Channel closed

Closed by @wet grotto

Use .reopen if this was a mistake.

[cedar kiln]

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.

[empty barn]

i have a task that says the number of permutations of set A (n+1 elements) is greater than those of set B (n elements) by 600

[slender atlas]

you can just divide both sides by n!
actually wait.

[empty barn]

oh?

damn bruh

wait but what would that do

id just have (n-1)!=600/n

[slender atlas]

never mind, I apologize for jumping the gun.

[stiff brook]

we need n*n! = 600, that is correct

now the best u can do is guess values!

[empty barn]

so apart from guessing the n, idk what to do

lmao

[chrome elk]

It won't take a lot of guesses

[empty barn]

wait but theres really no proper solution?

[chrome elk]

6! Is already 720

Factorial grows stupidly fast

[empty barn]

aight so then it'd be n=5

[chrome elk]

Yes

Didn't want to say that

[empty barn]

but is that really what i have to do??

[chrome elk]

Yes

[empty barn]

welp im not a fan of guessing games but if theres no other solution then ig i have no choice lmao

thanks for your help

[chrome elk]

Well the other option is to find a nice closed form of the gamma function

[empty barn]

and whats that?

[chrome elk]

I'm playing, it's a generalization of the factorial lol

[empty barn]

ah well this is pre-uni math lmao

[chrome elk]

Yeah so all you have is guessing

[empty barn]

aight

ill close this then unless peter hurries up and sends the msg

[spiral orbit]

sec

while you can call it guessing, it is more casework, where you show that for example taking n>=6 will yield very big numbers, and it remains to just check n=1,2,3,4,5

[empty barn]

oh okay i see

thank you

.close

[cedar kiln]

Channel closed

Closed by @empty barn

Use .reopen if this was a mistake.

[upbeat seal]

Guys

[idle tusk]

#❓how-to-get-help

[wicked mantle]

Hello, claim your own channel

[upbeat seal]

?

[wicked mantle]

Type a message in https://discord.com/channels/268882317391429632/903430333888884736

[cedar kiln]

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.

[timid plover]

number of values of z(real or complex) simultaneously satisfying the system of equations
$1 + z + z^2 + z^3 + \ldots + z^{17} = 0$ and $1 + z + z^2 + z^3 + \ldots + z^{13} = 0$

[wraith dagger]

Sypse

[timid plover]

I dont really know how to go abt this

[last apex]

Notice any such z satisfying one of these equations is a root of unity of order 18/14

[timid plover]

yes, but is 1 a solution of this equation?

[last apex]

no

not all roots of unity work

[timid plover]

I see

[last apex]

note that gcd(18,14)=2

so if you have a root of unity of order 18 and of order 14 it must be a root of unity of order 2 or equivalently 1, -1

[tropic oxide]

that 18/14 is doing a lot of heavy lifting

i think you mean "order 18 or 14 resp"?

[last apex]

yeah yeah ofc

[timid plover]

why?

[last apex]

z^18 = 1, z^14=1

can you show z^2 =1?

[timid plover]

oh ok

got it

[timid plover]

so the roots of z^2 are the only ones which are gonna be common in both and only one of them satisfies the equation.

right?

[last apex]

yeah only -1

[timid plover]

alr thanks

.close

[cedar kiln]

Channel closed

Closed by @timid plover

Use .reopen if this was a mistake.

[cedar kiln]

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.

[round geode]

I'm stuck here ngl

[round geode]

yeah nvm that should be it

korrek?

[cedar kiln]

@round geode Has your question been resolved?

Channel closed

Closed by @round geode

Use .reopen if this was a mistake.

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.

[tender ore]

hello so i have a question about probability. So in a class there are 22 students and 1 gets picked as the class president one as the vice president and one as the accountant. Now the question is what are the odds that i get to be an accounant and what are the odds that i get chosen for any of the 3 roles

[tender ore]

now i belive i worked it out i just don't know who to ask

now for me to get chosen as the accountant specifically wouldnt that be just 1/22

because there are 21X20 possibilities where i am an accountant and then there are 22x21x20 possible combinations

[floral arrow]

Yeah that seems correct if there are no other constraints

[tender ore]

so the 21 and the 20 cancel out

ok thanks

[floral arrow]

I mean it's simpler than that: if anyone of the 22 students is equally likely to get picked, then each has a 1/22 chance; including you

[tender ore]

you're right

but what got me questioning that is what if we arent picking the accountant first

for example the president gets picked first

now there are only 21 people left

[flat mica]

that's not how elections work

unless the election is by lottery

[tender ore]

the election is by who brings the fattest envelope

[flat mica]

what's in the envelope, i dont understand

[floral arrow]

Doesn't matter, you have 1/22 chance to be picked as president, and then 21/22 * 1/21 = 1/22 chance to be picked as accountant

[tender ore]

but all the students are equally broke so its by lottery

[tender ore]

bribes

[tender ore]

that makes sense thanks

and now to be picked at all its just 1 - 21/22x20/21x19/20 right

[floral arrow]

Seems right yeah

If 3 people are picked out of 22, you have 3/22 chance to be picked

[tender ore]

oh is it really that simple

i severly overthought this thank you

[floral arrow]

This particular problem is that simple, yes

If you split a group of 22 into a group of 3 and a group of 19, then every element of the original group has a 3/22 chance to be in the group of 3 and a 19/22 chance to be in the group of 19

If you're just starting to learn probability, things are going to get more complicated of course

[tender ore]

yeah we are gonna be learning about probability in the next couple of months and these are the problems our teacher gave as examples so i tried to solve them on my own

i guess finding more elegant solutions like yourse takes a lot of practice

thanks for the clear axplanation

[floral arrow]

An understanding of combinatorics helps, but that's probably for future you

[tender ore]

Combinatorics is an area of maths that really interests me

I've just learned the very basics of inclusion exclusion yesterday and i think its really interesting

how do i close this chanel

[tropic oxide]

.close

[tender ore]

thanks

.close

[cedar kiln]

Channel closed

Closed by @tender ore

Use .reopen if this was a mistake.

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.

[agile vessel]

yo

[agile vessel]

how is cos(180 - (A+B)) = -cos(A+B)

[oblique flare]

do it in the unit circle or use the angle difference identity it's up to you

[agile vessel]

how do i do it in the unit circle

[oblique flare]

cos(180-x) = cos(180)cos(-x)+sin(180)sin(-x) =>
(-1)cos(x) = -cos(x)

[oblique flare]

draw an angle t for example locate it's location on the x y plane do the same for 180-t
the y's would be equal while the x values are additive inverses

[agile vessel]

u mean cos(180)cos(x) - sin(180)sin(x)?

[oblique flare]

$\cos(A\pm B)=\cos(A)\cos(B)\mp \sin(A)\sin(B)$

[wraith dagger]

qimmah

[oblique flare]

@agile vessel

[agile vessel]

yh

[oblique flare]

But either way sin(180) is 0

Got lucky with that lol

[agile vessel]

lets say I have the value of cosA, cosB, sinA, sinB

why can't i just expand it to

cos(180 - (A+B)) = cos(180 - (cosAcosB + sinAsinB))

nvm

[oblique flare]

like it'll work yes but let's be honest look how fucking long that would be

[oblique flare]

lol

[agile vessel]

nah it wont work

it will expand to cos(180)cos(A+B) + sin(180)sin(A+B) which is also -cos(A+B)

i was just being dum

[oblique flare]

I may have misread that so badly I need to sleep

https://cdn.discordapp.com/attachments/1225236265449029731/1373334293388202014/3dgifmaker97902.gif

[agile vessel]

.close

[cedar kiln]

Channel closed

Closed by @agile vessel

Use .reopen if this was a mistake.

[cedar kiln]

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.

[cedar kiln]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[brittle umbra]

Like I’m trying to do a competition exercise and i need to find all i>=1 that have sequence set to 0 (no direct answer, more like how to do it)

[oblique flare]

,rccw

[brittle umbra]

last two a=0 was 3 and 12

i can send full question but it is in polish

[brittle umbra]

like dont give me full formula

[fierce zenith]

You can send it anyways

[cedar kiln]

@brittle umbra Has your question been resolved?

[brittle umbra]

I closed my pc and I don’t have it on my phone

I can send tomorrow

[fierce zenith]

alr

[brittle umbra]

Maybe you have some idea?

[oblique flare]

not really, and please do not ping specific helpers because it can be bothersome to some people

[dire geode]

you can also try https://mathematics.isodn.org/

[brittle umbra]

Sorry

[brittle umbra]

Thank you 🙏

[oblique flare]

like I'm cool with it but others might not

[cedar kiln]

@brittle umbra Has your question been resolved?

[cedar kiln]

@brittle umbra Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[cedar kiln]

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.

[quiet ledge]

why is that not rref form? what did i do wrong?

[fossil dawn]

the last row has a pivot and it isn't 1, i believe

plus, the elements above it are not zeroed

[quiet ledge]

so is the last column supposed to be 0,0,1

[fossil dawn]

since it has a pivot, yes

[quiet ledge]

ohh ok thanks

.close

[cedar kiln]

Channel closed

Closed by @quiet ledge

Use .reopen if this was a mistake.

[cedar kiln]

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.

[vernal shell]

can someone tell me why C is wrong

[split ice]

well, x is always -2 and z is always 5, so is it possible to get to (0,0,0) on this line?

[vernal shell]

no

i am confused

[split ice]

then this line won't pass through the origin, which is required in this problem

[vernal shell]

how do i do this

[split ice]

can you show your work for (c), and maybe we can go from there?

[vernal shell]

yeah

hang on

okay it isnt loading

but it wouldnt help, i basically just wrote x+at and then made it into <>

so my answer is my work

[split ice]

hmm thats probably not the best way to do this

[vernal shell]

is this not just x+at, y+bt and z+ct

??

since a and c are 0 wouldnt my answer be correct

ohnvm

i see it says thru the origin

so what would i do

i set each to 0?

[loud gyro]

this is the general equation of a line that passes thru a point (x,y,z) along the direction <a,b,c> right?

[vernal shell]

yeah

[loud gyro]

and you know what the point is supposed to be

[vernal shell]

yes

[loud gyro]

(0,0,0)

[vernal shell]

0,0,0,

okay

yes

[loud gyro]

so thats it

[vernal shell]

oh

so then its just at, bt, ct?

[loud gyro]

well, a and c are 0s

so yea

[vernal shell]

oh gotcha

thanks

.close

[cedar kiln]

Channel closed

Closed by @vernal shell

Use .reopen if this was a mistake.

[cedar kiln]

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.

[errant heart]

Hey guys

[errant heart]

Just want someone to confirm if my answers are correct, because I'm gonna submit this tomorrow

[chrome elk]

Shoot

[chrome elk]

,rccw

Wrong image bot

[errant heart]

Are my answers correct

??

Even the parentheses and brackets??

[chrome elk]

Man I do not wanna calculate

Have you verified using a calculator

[near flower]

we literally helped you solve these a few days ago

[errant heart]

Yeah, just want to confirm for the last time

[chrome elk]

The domains look correct on the second image

[pastel vault]

thx for the warning

but yeah if it's just confirming you should still repost your work

[errant heart]

I already sent it

[near flower]

no worries

[errant heart]

I fixed the range on the d) question

Is it correct that the zero is a bracket??

[near flower]

range of f is [0,+∞) correct

come again, ambiguous cause you're not given the whole graph

[cedar kiln]

@errant heart Has your question been resolved?

[errant heart]

Aight, I'll send the graph

Sorry for the late reply, I'm doing some other task

Here is the graph

[cedar kiln]

@errant heart Has your question been resolved?

Channel closed

Closed by @errant heart

Use .reopen if this was a mistake.

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.

[last apex]

!status

[cedar kiln]

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

[stoic crystal]

1

[last apex]

Try going through the definitions

[stoic crystal]

what definition

[twilit escarp]

Multivar functions limit i suppose

You have to prove it ?

[stoic crystal]

yes

[stoic crystal]

can you send it

[dusk finch]

does your book not have a definition?

[stoic crystal]

we have classes but I dont think there is a reader we can use for this class

[last apex]

well it sthe same definition as in calc 1

[stoic crystal]

you mean the epsi delta, thingy?

[last apex]

just multiariable

yes epsilon delta

[stoic crystal]

can u send

[last apex]

just google man

its the same thing as in calc 1

[stoic crystal]

oof looks complicated, how to prove it?

[last apex]

just show this holds for the sum of the functions

this should be easy

[stoic crystal]

according to who?

[twilit escarp]

Seems logic enough to have the euclidian distance

In your case S = T = \bR

[stoic crystal]

[stoic crystal]

wdym

[twilit escarp]

For the use of the definition applied to your problem

[stoic crystal]

I dont think I follow how to use epsi delta here

[last apex]

yeah this is the limit definitioon

when you move to multivaribale its just a different notion of distance

[stoic crystal]

this is my second week of uni

a little bit of handholding would be appreciated

[native heath]

godly $\implies$

[wraith dagger]

Percy

[native heath]

$\Rightarrow$ ig

[wraith dagger]

Percy

[native heath]

nope

[last apex]

multivariable calc on 2nd week?

[stoic crystal]

yes!

[last apex]

start by taking some epsilon

you want to show |f(x,y) + g(x,y) - L1 - L2| < epsilon where (x,y) is "close enough" to (x0,y0)

where by close enough I mean where |(x,y) - (x0,y0)| < delta for some delta

so your mission is to understand how to build this delta

[stoic crystal]

wtf is going on with this definition

[stoic crystal]

any tips?

[last apex]

triangle inequality

tip for the future, it is your best friend

[stoic crystal]

you mean |a+b| <= |a| + |b|?

[last apex]

yeah

and its less then or equal

[stoic crystal]

edited

[stoic crystal]

i dont think I follow, care to elaborate?

[last apex]

it is very usefull in a lot of questions regarding limits, derivative, integrals etc

any way using it here you can see that |f(x,y) + g(x,y) - L1 - L2| <= |f(x,y) - L1| + |g(x,y)-L2|

which means if you can bound from above both summands on the right side then you get a bound on the left side also

[stoic crystal]

can we slow down?

[last apex]

what did you not understand?

[stoic crystal]

the epsi delta def I dont understand

[last apex]

do you know the definition in non multivariable calculus?

its the same thing

[stoic crystal]

how does this epsi delta work?

the fuck is this egyptian symbols saying dude?

i understand the forall and there exists

the universal quantifiers and existencial quantifiers

[last apex]

yes

[stoic crystal]

i understand the distance between 2 points formula

but the rest is just, wow

[last apex]

ok.... intuitivly what this means is that if you get close enough to x0 then f(x) gets close enough to L

epsilon is how close you want f(x) to get to L

delta is how close you get to x0

[stoic crystal]

why |f - L| < epsi

[last apex]

this is the defnition

[stoic crystal]

[last apex]

man I really think you should go back to calc1. no to be rude but you should not be doing multivaribale calculus when you don't understand calculus 1 concepts

[stoic crystal]

as I said, this is my second week of uni

no idea why you have to be rude

[last apex]

yeah I have nothing against you...

https://www.youtube.com/watch?v=kfF40MiS7zA&pp=ygUZY2FsY3VsdXMgbGltaXQgZGVmaW5pdGlvbg%3D%3D

https://www.youtube.com/watch?v=YNstP0ESndU&pp=ygUZY2FsY3VsdXMgbGltaXQgZGVmaW5pdGlvbg%3D%3D&themeRefresh=1

some videos explaining limits

maybe this will explain better

when you understand the single variable case it will be easy to jump to multivariable

at least in the case of limits

[stoic crystal]

[last apex]

I need to go. gl

[stoic crystal]

I mean we could just assume this definition is true

[wraith dagger]

Renato

[last apex]

Take some epsilon, and consider eps/2

You get two deltas from what you wrote in the picture

[stoic crystal]

eps/2?

[last apex]

Epsilon/2

[stoic crystal]

yea but what.?

[last apex]

Use the definitions in the picture on eps/2

[stoic crystal]

where's is this epsilon/2 coming from?

[last apex]

You are very close

[last apex]

You will see in a second

What I did is I chose some constant a and used it instead of epsilon/2 and got that I want 2a <= epsilon

[stoic crystal]

when do i use the distance formula

[stoic crystal]

you are saying L1 + L2 = 2a < epsilon?

[last apex]

No

[stoic crystal]

ah

i think i follow

[stoic crystal]

the problem is i have two different epsilons, and why take delta = max(delta1, delta2)?

oh you mean i do that twice?

where epsilon 0 is the epsilon of each limit = l1, l2

[last apex]

epsilon0 in the definition of the limit of f+g

remember what we are trying to show

every eps0 has a delta

[stoic crystal]

right, i forgot triangle inequality

what i find interesting is you used delta1, delta2, but only one epsilon, could it mean epsilon = epsilon1 + epsilon 2?

no

epsilon0 = episilon1 + epsilon2

[cedar kiln]

@stoic crystal Has your question been resolved?

[paper edge]

The amount of times I've seen ε/2 show up in these is absurdly high

[stoic crystal]

is my proof convincing you?

[paper edge]

Seems reasonable enough, don't take my word for it, though

Epsilon-delta is the bane of my existence

[stoic crystal]

same here

i can send the proof my classmate did

[dreamy void]

I think the only down side is, you are taking the max instead of min. But taking the max wouldn't guarantee that proofs holds for both δ1 and δ2 always.

[stoic crystal]

why?

[dreamy void]

because you want both conditions to work

[stoic crystal]

right

my proof sucks though even if i change max to min

[dreamy void]

You have sqrt(...)<δ1 and sqrt(...)<δ2, and if you took the greater bound, then there might be values within the greater bound that are not within the smaller bound.

Your proof is going into the right direction

Indeed, for arbitrary ε1,ε2>0 we have always a δ1,δ2>0.

Maybe the wording is unfortunately, because of saying choose

You apply the triangle inequality and then argue that for any δ1 and δ2, we can bound |f-F| and |g-G| as we want, since they converge by assumption.

So you can bound it by ε1=ε2=ε/2

So rather, you can say after the two lines, that therefore, for some δ1>0 we have |f-F|<ε/2 and for some δ2>0 we have |g-G|<ε/2 as well.

(The two lines are not necessary to write down for the proof actually, but to keep that in mind. You would instead straight away start to bound them with ε/2)

[cedar kiln]

@stoic crystal Has your question been resolved?

[stoic crystal]

okay

[stoic crystal]

that's one way of seeing it yeah

my issue is that i am saying what i need to proof at the start of the proof and that looks wrong idk

aswell as what you mentioned

let me try to fix it with this suggestions

[cedar kiln]

@stoic crystal Has your question been resolved?

[stoic crystal]

I am at another class, let me write the proof in the break

[cedar kiln]

@stoic crystal Has your question been resolved?

[stoic crystal]

wait, if epsilon/2 = epsilon1 = epsilon2, then, what?

let delta = min{delta1, delta2}

@dreamy void

I think I get it

let h(x,y) = f(x,y) + g(x,y)

let L3 = L1 + L2

let epsilon/2 = epsilon1 = epsilon2

then

lim (x,y)->(a,b) f(x,y) <=> |f(x,y) - L1| < epsilon1

lim (x,y)->(a,b) f(x,y) <=> |f(x,y) - L1| < epsilon/2

lim (x,y)->(a,b) g(x,y) <=> |g(x,y) - L2| < epsilon2

lim (x,y)->(a,b) g(x,y) <=> |g(x,y) - L2| < epsilon/2

and then, we use triangle inequality

let epsilon > 0, there exists a delta = min{delta1, delta2}

delta > 0 such that

0 < √(x-a)^2 + (y-b)^2 < min{delta1, delta2} = delta

then we get

and use the triangle inequality

|f(x,y) + g(x,y) - (L1 + L2)| = |(f(x,y) - L1) + (g(x,y) - L2)| <= |f(x,y) - L1| + |g(x,y) - L2|

and since we know |f(x,y) - L1| < epsilon/2

and we know |g(x,y) - L2| < epsilon/2

we get that

|(f(x,y) - L1) + (g(x,y) - L2)| <= |f(x,y) - L1| + |g(x,y) - L2| < epsilon/2 + epsilon/2 < epsilon

the trick is that if

|A| < x/2
|B| < x/2
then by triangle inequality
|A+B| <= |A| + |B|
and thus |A+B| < x/2 + x/2 = x
and so we get that |A+B| < x

anyways, I think thats the ideA

.solved

[cedar kiln]

Channel closed

Closed by @stoic crystal

Use .reopen if this was a mistake.

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.

[eager flower]

guys i need someone to help me so basically i have a problem which is. in a standard deck of cards game so 52 cards per deck, we draw 5 cards at a time. what is the probability that in these 5 cards we get 2 pairs of cards for example two kings, two spades and another spare card?

[floral arrow]

You might find this interesting: https://en.wikipedia.org/wiki/Poker_probability

[cedar kiln]

@eager flower Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[zenith lintel]

Dont understand how to get the point of intersection here, when I make a system of equations i always get infinite solutions when I need a single value for s and t

[stiff brook]

can we see your work

[zenith lintel]

ok sorry nvm i jusr got it right

i messe up the systems somehow

[stiff brook]

awesome!

[zenith lintel]

ty

.close

[cedar kiln]

Channel closed

Closed by @zenith lintel

Use .reopen if this was a mistake.

[cedar kiln]

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.

[viscid star]

Hello, I am trying to finish this problem and for some reason struggle with shell method. Can someone walk me through this? Used a calculator to try to find the process but nothing. Thank you

[cedar kiln]

@viscid star Has your question been resolved?

[viscid star]

help pls

[lone dune]

!status

[cedar kiln]

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

[lone dune]

are you completely lost or do you have a general idea of what you should do

[viscid star]

2

[viscid star]

.

im having trouble finding the radius and width

[cedar kiln]

@viscid star Has your question been resolved?

[viscid star]

man i just had to put anything down and submit

[cedar kiln]

@viscid star Has your question been resolved?

[lime bloom]

try visualizing one of the cylindrical shells generated when the region is rotated; it could help you assign variables to their proper place within the formula

[cedar kiln]

@viscid star Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[upbeat smelt]

Hopefully I'm allowed to ask for this but I don't need help I straight up need to be taught how to do these sorts of problems because this is supposed to be review but I took a weird pathway to take this course and I've never learned this before

[pastel vault]

okay for question 1, you should substitute n = 2 into the relation

so $t_2 = -2t_{2 - 1} + 1$ right?

[wraith dagger]

south

[upbeat smelt]

The normal prerequisite is taking the 3U but I took the 3M and then a 4C to get to 4U

right

am i ever supposed to find t

[pastel vault]

no

[upbeat smelt]

what is this called

[pastel vault]

so $t_5$ means the 5th term

[upbeat smelt]

like what is this type of equation called

[wraith dagger]

south

[pastel vault]

recurrence relations

[upbeat smelt]

oh

okay

yeah never learned that

[pastel vault]

yeah it is in the discrete maths part of 3U

[upbeat smelt]

so how do i get a number

[pastel vault]

well, you know that t(1) = 3

[pastel vault]

and now look here

[upbeat smelt]

i still don't know what to do

[pastel vault]

well 2 - 1 = 1

[upbeat smelt]

right

[pastel vault]

so you have $t_2 = -2t_1 + 1$

[wraith dagger]

south

[upbeat smelt]

so should my answer be negative

none of the multiple choice ones are

[pastel vault]

no, that's t(2)

the answer wants t(5)

[upbeat smelt]

right

okay

[pastel vault]

so you'd have to keep applying this equation

the equation actually means (next term) = -2 * (last term) + 1

[upbeat smelt]

so -5 is term 2?

[pastel vault]

yeah

[upbeat smelt]

OKAY I'M GETTING SOMEWHERE

[pastel vault]

keep going!

[upbeat smelt]

TYSM

i'll lyk what i get i don't think there's an answer key posted

[pastel vault]

question 2 is actually really important

so notice that if you do:
2 - 6
-2 - 2
-6 - (-2)

basically, if you do (next term) - (first term), the answer is always -4

so because all of these differences are the same, we have a common difference

we have a linear function t(n) = an + b

because of the common difference, we have a = -4

[cold stirrup]

what 2+3

[pastel vault]

don't troll pls

[cold stirrup]

... sorry i was joking

[upbeat smelt]

i got 43

for the first q

[spiral fog]

That seems good

[upbeat smelt]

question 2 and south's explanation confusing me

[spiral fog]

The second question. Due to this being a multiple answer question unfortunatly can be solved just by checking every answer

[upbeat smelt]

i see how what he said is true i just don't know how to turn that into the multiple choice answers

what does the 10 have to do with anything

[spiral fog]

Well normally when you have

$$a_n = bn + c$$
This gives a sequence
$$c , c + b , c + 2b , c + 3b , \dots $$

[wraith dagger]

casework

[spiral fog]

Assuming we start from $a_0$ but i see thats not the case there

[wraith dagger]

casework

[spiral fog]

If you have a sequence
6 , 2 , -2 , ...
What would be the number before 6

Trying to apply the same "rules" what makes sense to be in that spot
x , 6 , 2 , -2 , ...

[upbeat smelt]

8

no

10

i see

[spiral fog]

Yes

So 10 is basically the 0-th number in the sequence

I mean that doesnt help you solve the question but i hope it gives you the answer of what is the 10 doing there

I meam you can just play with every answer plugging in $n = 1 , 2 , 3 , 4$ and seeing what you get. Ill give you an example. For $$a_n = -4n - 10$$
You have a sequence (starting from $a_1$ this time)
$$-14 , -18 , -22 , - 26 , \dots $$

[wraith dagger]

casework

[spiral fog]

So as you can see. The $-4n$ is basically making every next element for $4$ less than the previous one. And then the $-10$ is just some shift

[wraith dagger]

casework

[upbeat smelt]

I'm sorry I'm lost

I need to get ready for school anyway so I'll have to ask my teacher, maybe I can get in early to do that

Thank you for the help so far I'm like halfway there I think

.close

[cedar kiln]

Channel closed

Closed by @upbeat smelt

Use .reopen if this was a mistake.

[topaz coral]

can anyone solve this?

[cedar kiln]

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.

[frail citrus]

try putting x=tanp, then go for by-parts prolly

[frail citrus]

.close

[cedar kiln]

Channel closed

Closed by @frail citrus

Use .reopen if this was a mistake.

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.

[tepid fractal]

Help me out gang

[digital bane]

what have you tried

[tepid fractal]

wait i need to go to the toilet brb

[wicked mantle]

[long swan]

Tmi

[tepid fractal]

apparently

ive tried

dividing both side by 2 and then solve for x

which did nopt work

ive also tried square root both side

and i didnt know how to do it further

and then i gave up

[digital bane]

show your steps thus far

[long swan]

Are you familiar with rules of logarithms

[tepid fractal]

yeh

[digital bane]

including your unsuccessful attempts

i have a feeling we can go from your second attempt

[tepid fractal]

then idk how

[tepid fractal]

wait

[digital bane]

ok probably not the right way to go about it

[flint cape]

those aren't how logs work

[digital bane]

and yeah that isn't how logs work

[frail citrus]

its easy. take ||the 2 on the lhs to the|| power of 3x+2, and then go on and simplify

[digital bane]

but from 2 log (3x + 2)

[spiral fog]

That line is wrong

[digital bane]

nvm i'll let you guys do it then

[tepid fractal]

WAIT

[tepid fractal]

UR RIGHT

thanks

idk why did i overcomplicate it 😔😔

[flint cape]

There we go

[frail citrus]

i told the same thing.

[digital bane]

there we go.

[feral sapphire]

oh i thought its absolute value of 2

[digital bane]

well done

[tepid fractal]

u were late, i didnt say u were wrong 😓😅

thanks

.close

[cedar kiln]

Channel closed

Closed by @tepid fractal

Use .reopen if this was a mistake.

[frail citrus]

[cedar kiln]

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.

[indigo shore]

can someone explain set theory to me?
please?

[neat dune]

Uhhhhh

That's a very broad question

maybe try #study-discussion or #book-recommendations

Unless you have a more specific question in mind

If your request really is as broad as say, "can somebody explain to me all the set theory I need to know for an intro to proofs course" then I'm afraid I don't think anybody here has the time for that. That would be more up to the task of a teacher or a personal tutor.

Or self-study

[cedar kiln]

@indigo shore Has your question been resolved?

[neat dune]

Ok what do you want?

Sorry that came across as harsh

But it's just unrealistic to expect somebody to answer such a broad question in this server. You need a more specific question than this.

!da2a

[cedar kiln]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[neat dune]

The server doesn't do paid tutoring either

So nobody can take an offer to tutor you on set theory for payment, and nobody would spend hours doing it for free :/.

If you had a problem set on set theory to complete

That'd be something you could ask about!

[cedar kiln]

@indigo shore Has your question been resolved?

[cedar kiln]

@indigo shore Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[ivory jay]

help

[ivory jay]

i'm having some trouble determining the critical points and the maximums/minimums of this function. although i think that the critical point is x=3, how do i know whether it is a minimum or a maximum?

[worldly chasm]

There is a third option

[ivory jay]

oh?

[worldly chasm]

yup, a critical point doesn't have to be a maximum or a minimum

[ivory jay]

but see, i've been doing this kind of stufff before

and according to the program, in this case, x=1 is a minimum

so im sort of wondering wherre this logic is coming from

[worldly chasm]

x=1 is not a minimum in the above graph

it's not even a critical point. It's a point of inflection though

[ivory jay]

it was deemed as correct previously

although it doesnt make sense in my opinion

[dawn junco]

the graph is of f**'** omni

[worldly chasm]

oh

[ivory jay]

whioch is why im wondering wtf is going on

[worldly chasm]

yeah I just realized 🤦

[worldly chasm]

It's because it's a graph of f', not f, like I had assumed

[worldly chasm]

similarly this seems to be f' not f

[ivory jay]

OH

right

so if it's f' then when its a negative on the right and a positive on the left it should be a maximum

right

and then whether the function increases or decreases just depends on whether it is positive or negative, right??

so (-inf, 3) would increase, whilst (3, inf) would decrease??

[worldly chasm]

yup, you got it

[ivory jay]

riiight

thank you so much

i'm a dumbass, holy shit

hope you guys have a good one !! <3

[worldly chasm]

Not a dumbass, just learning

besides, I made the exact same mistake

[cedar kiln]

@ivory jay Has your question been resolved?

Channel closed

Closed by @ivory jay

Use .reopen if this was a mistake.

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.

[neon hinge]

so this if from precise definition of limit

[neon hinge]

and im wondering why my prof choose |x-1| < eps/3 not <= eps/3

i mean based on the yellow line (3rd from the buttom) |x^2-1| is already less than 3|x-1| so even if |x-1| equal epsilon |x^2-1| is still less than epsilon, no?

[dusk finch]

what's the context?

[neon hinge]

heres teaching how to solve this question using the definition of limit

[dusk finch]

oh i see what you mean now

[neon hinge]

the |f(x) - L| < eps -----> 0 < |x-a| < delta thingy

[dusk finch]

you are right that you could chose <= eps / 3

but you can choose it to be < eps / 3, and it makes more sense with the delta

because if you recall the definition, it has |x - c| < delta, not <= delta

[neon hinge]

ohh

[dusk finch]

but it really doesnt matter that much

it's certainly not a thing to be concerned about

[neon hinge]

alr

btw another question

why wont he just ans:
delta = eps/3

why is there a need for 1

i meant the delta = min{ 1,esp/3 }

since we dont need to best answer we just need an answer that fulfilled the condition (|f(x) - L| < eps -----> 0 < |x-a| < delta) , no?

[dusk finch]

How did he conclude |x+1||x-1| < 3|x-1|?

[neon hinge]

he restrict delta to < 1

[dusk finch]

exactly

without that restriction, |x+1||x-1| < 3|x-1| would be false.

so we really need that restriction

[neon hinge]

ohh

[dusk finch]

and we need to reflect that restriction in our choice of delta

[neon hinge]

so like the 1 is the base of the whole thing that way we need to include it otherwise that esp/3 wont work

smth like that?

[dusk finch]

Yeah

[neon hinge]

ohhh alr thx a lot

appreciate it

.close

[cedar kiln]

Channel closed

Closed by @neon hinge

Use .reopen if this was a mistake.

[neon hinge]

but wait hold up

he restrict delta to < 1

how come he said that delta = 1 at the end

[cedar kiln]

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.

[hexed vortex]

I'm not understanding reflection of a pentagon

[chrome elk]

How much do you understand/don't understand

[floral arrow]

(those are reflections + rotations)

[chrome elk]

(technically they're also reflections through different mirrors)

[floral arrow]

(oh, true)

[chrome elk]

(wait nvm the diagrams actually have both, my bad)

Either way where's the helpee

[hexed vortex]

Sorry I was talking to someone, so these are reflections plus rotations? or what do you mean by different mirrors

[chrome elk]

The first

[floral arrow]

Pictured are reflections along the axis that crosses the "1", combined with rotations

[chrome elk]

The second was me being blind

Also this is a very weird way to write D_10, I don't think I've ever seen this notation before

[hexed vortex]

ye im confused lol

so they do a rotation but shouldnt rotation have like 5 numbers in it

[chrome elk]

I mean D_10 is a subgroup of S_5 but this is just weird notation

[chrome elk]

How familiar are you with dihedral groups

[hexed vortex]

I think im pretty familiar with it, I know the identity is R_0, and how rotations and reflections work with a square but when we get to the pentagon im confused on how these are reflections

like with a square you have to diagonal lines and 2 other lines

and the coordinates essential swap places over that line to the one directly across from it

[chrome elk]

Good

[chrome elk]

As for how these are reflections

[hexed vortex]

@chrome elk Can I think of it instead of rotating it, I just change the line from going through 1 to isntead going through 2

and then apply a flip in the same way they did for 1

[chrome elk]

That's essentially what a dihedral group is no?

It's generated by reflection and rotation

So yes you can think of it that way

[hexed vortex]

wait so reflections are dependent on rotation?

so R_0 correlates to F1

[chrome elk]

You can rotate the "mirror" to get new reflections essentially

[hexed vortex]

R_30 or something correlates to F2

[chrome elk]

I have no idea what these notations are lol

[hexed vortex]

oh sorry its like 0 and 30 degree rotation

F1 is just some reflection or flip and F2 is another

I was thinking of these reflections

as chaning the axis of reflection

but I think I get what you mean by rotation

were rotating the axis of reflection?

and then reflecting it?

to get a new reflection?

[chrome elk]

Okay let's start very basic

You have a pentagon

You rotate it 72° in one direction

You still have the same pentagon, just the vertices are in different places

Now you have a pentagon

You pick a vertex and drop a perpendicular on the side opposite to it

And you reflect using this line as a mirror

By combining these two simple operations

You get every possible symmetry of a pentagon

[hexed vortex]

Oh ok I see now

That makes sense

thank you

.close

[cedar kiln]

Channel closed

Closed by @hexed vortex

Use .reopen if this was a mistake.

[cedar kiln]

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.

[stray crypt]

any hint how to deal with it

ive tried to multiply by the conjugate and also do lhoptials rule (since it went inf/inf) but it just went uglier

plz just hint no full answer

[cobalt iron]

take x common inside the root

[native heath]

x^2*

[cobalt iron]

ans =0?

[native heath]

2.5

[cobalt iron]

itshouldbe 0

[stray crypt]

i also got 0

[cobalt iron]

yes it is 0

[native heath]

oh i did x-3 mb

[stray crypt]

@cobalt iron @native heath actually i get inf * 0

[cobalt iron]

same

its indeterminant?

[native heath]

yall

its outside the domain

[stray crypt]

wym

[native heath]

functioned defined on [0,3]

nvm.

I MISREAD IT TWICE

kill me

wait yall

😭

so i didnt misread it afterall

so no its 2.5

[stray crypt]

its not defined here

[native heath]

,w limit as x to inf (x-\sqrt{(x-2)(x-3)})

[wraith dagger]

Results provided by WolframAlpha

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

Requested by percykel

[native heath]

yep

[stray crypt]

its defined for x>=3 or x<=2

i think

[stray crypt]

wish i could do this on a test

ez mode

[stray crypt]

its all good lmao

[stray crypt]

how can i reach this ans

only hint tho

[native heath]

generalise binomial maybe?

that looks like suffering

or you can look at series expansion at x=inf

a bit less suffering

[cobalt iron]

rationalise the numretor

[stray crypt]

you mean multiply by conjugate

[cobalt iron]

yes

[stray crypt]

ive tried

worked for you?

[cobalt iron]

multiply divide x+root((2-x)(3-x))

[cobalt iron]

yes

[stray crypt]

so y it didnt work for me at the beginning

[cobalt iron]

maybe did it wrong way

in numerator it will be 5x-6?

[stray crypt]

and then take the common inside the root? in the denominator?

[stray crypt]

yes

[cobalt iron]

yes

[stray crypt]

bruh this goes wild

[native heath]

its not

@stray crypt id do this

[cobalt iron]

it will be 5/2

[native heath]

you might think its kinda out of left field tho

but i like it

its pretty

[stray crypt]

what you mean

[cobalt iron]

u get the ans?

[stray crypt]

still trying

[native heath]

use newton's generalised binomial theorem

[cobalt iron]

damn

[cobalt iron]

its not like this

[stray crypt]

finally got it

[native heath]

it feels less irritating than magically multiplying by the conjugate and it works

[stray crypt]

bruh this wild

[native heath]

its not

try

you literally end up with just $x-(x-\frac52)$

[stray crypt]

@native heath @cobalt iron

[wraith dagger]

Percy

[native heath]

my eyes

[stray crypt]

looks good but i havent learned of it

[native heath]

yes you have

[stray crypt]

lmao i did it fast

[native heath]

zyada na karo

[cobalt iron]

hey u are indian?

[native heath]

no, my eyes because holy shit treating like infty like a number is wild

[native heath]

its literally just the binomial theorem expression

[stray crypt]

i can do it more elegant its just a sketch

[stray crypt]

ok but we dont take it in calculus 1 rn

if you would have written it in the test tho it could be cool