help-26

[chilly walrus]

r is 7

[arctic rock]

wait how

won't we end up doing

10-r+r?

[restive inlet]

binomial theorem gives you terms in the expansion based on the value of r

you want to use the r value where that results in x having a power of 7,
which in this case will be 7

[arctic rock]

okay but what if we're finding x^16 or sumn

[restive inlet]

well there won't be an x^16 here

[arctic rock]

oH so its only possible if its for eg (x^2)^r

[restive inlet]

no.

[arctic rock]

HUH

(1-x^2)^10

we can do it here no?

cus then (10 c r) (1)^10-r x (-x^2)^r

[restive inlet]

what you have depends on your expression

(1-x^2)^10
does have an x^16 term

[arctic rock]

SWEET

tysm

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[normal coral]

Hi

[normal coral]

Here's this q 11

Shouldn't it be practically wrong

It could be rewritten as

nf(n) - 1 = a(x-1)(x-2)(x-3)(x-4)(x-5)

a can be easily given as -1/5!

But is there any way to find f(0)?

Obv except taking it as a 5 degree polynomial with 5 variables and using f(n) = 1/n for the variable substitution

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@normal coral Has your question been resolved?

[normal coral]

<@&286206848099549185>

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[proper vessel]

Find the limes

[topaz sinew]

@proper vessel Has your question been resolved?

[pastel salmon]

Krysicki :))) mam rację ?

to się w pamięci robi, o które pytasz ?

[proper vessel]

Tak tak tylko nie jestem pewien czy zrobiłem błąd czy jest błąd w odpowiedzi a bez tego nie zasnę hah

2.40

[pastel salmon]

4/7 , z tego co widać by to wylizcyc uzywasz sprzezenia do mianownika

[pastel salmon]

$\frac{1}{a-b}=\frac{a+b}{a^{2}-b^{2}}$

[thorny flame]

Joanna Angel

[pastel salmon]

wtedy na dole zostaje ci 7n, a na górze suma z ktorej wyciagasz n przed nawias skracasz i koniec

wtedy na gorze w wliczinku 2 + 2 w granicy

a na dole 7

[proper vessel]

Jejku dzięki wielkie, tak zrobiłem tylko wkradł się mały l
Bład plus na górze stał się minusem

[pastel salmon]

ok 🙂

ja te zadania robilm z moimi uczniami i studentami setki razy z tego zbioru

ale lubę ten zbior

[proper vessel]

Przyznam póki co pierwsze zadania z niego robię, ale w porównaniu do niektórych ksiazek akademickich naprawdę wydaje mi się przystępnie napisany

Chociaż będę się wypowiadać jak dojdę do czegoś trudniejszego może

[pastel salmon]

dokladnie, znam anegdote, 40 lat temu Kysicki pojechal do ameryki lacinskiej

i na lotnisku, uslyszeli jego nazwisko i pytaja czy to ten od zbioru zadan :))

alob nawet i wczesinej niz 40 lat temu

haha

[proper vessel]

Wow aż tak popularna ksiazka?

Ale to naprawde musi już znaczyć o jakosci

Tymbardziej że jest nieodłącznie od 40 lat

[pastel salmon]

wiesz, wtedy to bylsimny komuinsci haha, i oni wtedy jezdzli na kube albo nikaragua haha

wlasnie

całe pokolenia matemtykow sie wychowala na tym zbiorze

[proper vessel]

Ale faktycznie wypożyczyłem trochę tego materiału z biblioteki i są w tych książkach historyczne kartki i no Krysicki zebrał najwięcej autografów

[pastel salmon]

🙂 czyli przekonujesz sie na wlasnej "wiedzy" 🙂

tam sa dwa tomy, zcesc 1 i 2, jak zrobisz 3/4 z tego to wymiatasz na studiach o ktorym wpsominales

[proper vessel]

Mam nadzieję bo po rozmowie z absolwentami mogę stwierdzić że egzamin z rachunku różniczkowego ponoć jest najcięższy

[pastel salmon]

tak, taki egzamin zastepuej egzaimnb wstepny na uzcelnie, obecnie

[proper vessel]

Z tego co wiem ma bardzo nietypowa formę gdzie można napisać go na 90% i nie zdać

[pastel salmon]

tego to nie wiem jak jest na agh , to zalezy tez od wydzialu

[proper vessel]

Właśnie słyszałem o tym, że teraz tak się weryfikuje i poniekąd rozumiem ale przyznam że 1 rok to napewno sporo nowych bodźców i można z naprawdę wielu czynników mieć trudnosci

[pastel salmon]

mój starszy mentor, obecine kolega po fahcu Górniak, razem z Inlgotem słynymn swego czasu na PWR, wymyslili regulamin ze nawet jak si emial 100% to nadal sie nie zaliczalo hahahah

maskra

[proper vessel]

Chyba nie wszędzie, ale na tym wydziale jest eg,amino modułowy i pp trzeba zaliczyć każde zadanie na 50%

[pastel salmon]

polecam wideo na youtube od Górniaka

objerzy jsboie

dam ci link na dm

[proper vessel]

24 odcinek za mną

[pastel salmon]

ah super

haha

aporpo poczytaj legendy w inteneecie o Pietraszko, niestety zmarl niedawno, a on byl legenda we wrocławiu na PWR

hahaha

matemtyk

zadawal masakryzcne kolokwia z analziy

[proper vessel]

Wpisałem i wyskoczyła pasta na wykopie

[pastel salmon]

haha

[proper vessel]

Musiał naprawde niejednemu studentowi dać w kość, bo chyba całkiem popularna

[pastel salmon]

haha

dokładnie

[proper vessel]

To jest coś w stylu matematyka dyskretna zabiera przeciwnikowi 7 pkt etcs

[pastel salmon]

ale juz go ine ma niestety , mam niexla kolkecje jego zadan w razie zcego

[proper vessel]

Jak przejdę przez Krysickiego i uznam ze potrzebuje silniejszych wrazen To się odezwę hah

[pastel salmon]

dobrze:) Powodzenia! 🙂

[proper vessel]

Dzięki :)

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[ivory needle]

hello! im looking for help with this proof. i've attached my work and an example of how the proof should look from my class slides

[ivory needle]

my work is the image on the left (For question 2a)

im looking for some x such that for all a>1, M>0, a^x > M

im thinking along the lines of some kind of large negative exponent to make the left side of the inequality a very small fraction, but im not sure if that is correct

<@&286206848099549185> just following up on this!

[jade fulcrum]

?

[ivory needle]

hi! i just havent heard from anyone regarding this question yet

[jade fulcrum]

which 1

[ivory needle]

this one

i just gave a brief explanation of where im at under it

[jade fulcrum]

relations and functions question?

[ivory needle]

its a logic proof i guess

[jade fulcrum]

m not gud with proofs, mayb sm1 else could help

[ivory needle]

no worries, do you know if i should ping helpers again or would that be annoying lol

[jade fulcrum]

sm1 will help, just wait like 5 mins ig

[ivory needle]

kk thanks anyway!

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[ivory needle]

.reopen

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✅

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@ivory needle Has your question been resolved?

[mighty hound]

HELP PLS

draw the parallelogram ABCD in the figure; O is the intersection point of its diagonals. The point K is outside the plane of the parallelogram. KA=KC and KB=KD. Prove that KO is perpendicular to (ABCD).

[ivory needle]

sorry im still waiting for someone lol

theres some open channels tho

<@&286206848099549185> hi sorry im still waiting for help if anyone is able

[late marlin]

what was the ques?

[ivory needle]

this one

i gave some points of where im at right under it for some context

[late marlin]

I didnt get what you want help with in actual

[ivory needle]

im looking for some x such that for all a>1, M>0, a^x > M

i just cant figure out what x would have to be since a, M have the range of all real numbers

[late marlin]

oh wait lemme give it a try

[ivory needle]

thank you!

im thinking it has to equal something with a and/or M

[late marlin]

aint x should belong to (0,1)

if proving a>1, M>0, a^x < M

[ivory needle]

x can be any real number as well

sorry idk if i understand what you said

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[dire tinsel]

I got dummy question lol

[dire tinsel]

We have a 20 sided dice where every side is assigned to a number, let's say we throw it 3 times, how many results can you get from throwing the dice (assuming that{1,2,3} is the same result at {3,2,1}

My ans is 20³ / 3!

Is it correct

[abstract wadi]

Your reasoning is that you choose 1 number from the 20 in each turn, then divide by 3! Because of the repetition (1,2,3) ; (1,3,2); (2,1,3)...?

[dire tinsel]

Yes

[abstract wadi]

This is incorrect, because while that 3! Does work when all three numbers are different. Because then you'd have counted them differently, bit of (1,1,1) is counted only once, and dividing that by 3! Is wrong.

[dire tinsel]

Oh crap ur right

[abstract wadi]

Might wanna count them separately.

3 different numbers, 2 different numbers and only 1 number.

Like that.

[dire tinsel]

Ah like make cases for each similar number

[abstract wadi]

yeah

[dire tinsel]

Is there a faster way lol

Seems like a bit of work for me lol

[abstract wadi]

Not one I can think of just by looking at it immediately.

But as you already know the issue in what you got, maybe you can fix that by adding something?

Because what you've gotten is probably less than the actual answer?

[dire tinsel]

Hmmm can also work but how can I approach that

[abstract wadi]

Meh, that sounds more work than what I originally stated.

[dire tinsel]

Yeah lol

Guess I will stick with ur first solution

Thanks man combinatorics has been fairly mysterious to me lll

.end

[abstract wadi]

.close

Ah come on mate.

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[restive kernel]

hi! so, im learning tautologies. so there's a theorem, if A is a propositional formula, which is tautology, and it got letters A1, A2, ..., An; B is obtained by substituting A1, A2, ..., An instead of letters A1, A2, ..., An, so B is tautology too. what does every thing in this theorem mean? like, i got that any letter in the form is proposition, which means, in A as tautology, A1 is tautology too. but how we are getting B by substituting forms with indexes instead of letters with indexes?

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[restive kernel]

<@&286206848099549185>

ayo...

[restive kernel]

this is stressful

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@restive kernel Has your question been resolved?

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[graceful leaf]

Pls

[graceful leaf]

I know how to do this whole worksheet that has 20 questions except this problem

[worthy storm]

what is the question?

[graceful leaf]

wait why the negatives look like that

wait i retake pic

Nvm same

Ok

I take picture of what i have so far

sometjing like this? or bad

[worthy storm]

^

what are you asked to do

[graceful leaf]

Oh

simply and express answer with positve exponent only

[worthy storm]

ah ok

[worthy storm]

so far ok

[graceful leaf]

ok nice

So do i do anything to the 8 and 1/2

like = 4?

[worthy storm]

sure

[graceful leaf]

Oh ok

[worthy storm]

and then you need to deal with m^-2

since negative exponents are not allowed

[graceful leaf]

oh

Then make it

in denominator?

[worthy storm]

yep

[graceful leaf]

Ok perfect

thnxs

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[tight rivet]

What do I do

[torpid sparrow]

The instruction says in terms of sine

[hollow drum]

It does say in only terms of sine

[torpid sparrow]

But your wrote tan for some reason

[tight rivet]

Oh I didn’t see

But I still don’t understand it

How did they get -sinx from cot or cos

[torpid sparrow]

No

[hollow drum]

Do you know your reciprocal identities?

As that's what you are applying

[torpid sparrow]

The are doing from the left side

They get the -sin(x) from -sin(x)

[tight rivet]

Oh

[tight rivet]

Like cot from tan?

So it should be 1/sin(x)?

[torpid sparrow]

That’s what csc(x) is

[granite hull]

1/sin(x) - sin(x)

Left to right.

[tight rivet]

??

1/sin -sin =1/sin - sin^2/sin

[granite hull]

-sin^2(x)

The exponent goes before the variable.

[tight rivet]

Bruh it’s still wrong

[granite hull]

holdon.

[hollow drum]

What happened to the 1?

You have 1/sin - sin^2/sin

$\frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}$

[thorny flame]

CaptainNova22

[granite hull]

You have to multi. both sides by sinx/sinx

You should get sinx-sin^2x/sinx

[tight rivet]

Ok I added the 1

What about the last one

.

[granite hull]

You confused me.

Its a pythagorean identity.

[tight rivet]

I wrote the reciprocal identity

[tight rivet]

I wrote reciprocal and it says it was correct

[granite hull]

I got confused again. I thought it meant something else.

Yeah, thats a reciprocal identity.

Then you rewrite 1-sin^2x to cos^2x

Break up the cos^2x into cosx * cosx

[tight rivet]

Yeah I got those

[granite hull]

OK.

Good?

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[mighty zodiac]

The answer is k=1, which is one of the answers I got, but why isn't k=-39 an answer as well?

[vapid sonnet]

Why you put -24-k-15=0

They are coffecient of different variables

[mighty zodiac]

Oh crap yeah

Lmfao

Alright thanks alot hahaha

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[frozen totem]

Need a explaination why this improper integral diverges.

[north panther]

the graph diverges

[frozen totem]

Would it be possible to solve this without a graphing calculator?

Im not too sure how to start with this

[frozen totem]

Would you plug in your limits

[north panther]

yes

I dont' think the C matters as it is a definite integral

so you would do (-1/(0)+1) - (-1/(-1)+1)

do you have the answers for this probelm

[frozen totem]

Yes

[north panther]

is it undefined or infinty?

[frozen totem]

it only says its diverging but not the reason why

Would it be infinity presumably?

[north panther]

yes

[north panther]

if you look at the graph

[frozen totem]

okay then tysm!

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[topaz sinew]

Please don't occupy multiple help channels.

[whole igloo]

^

pick one channel and close the other @proud seal

[proud seal]

I could not find another

Im noob

How do i close it

[agile harness]

.close

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[proud seal]

Thanks

I accidentally clicked another channel

[grave bough]

when calculating area under graph with integral under two functions intersectinfg, and f(x) is greater than g(x), do you do f - g or g - f?

[noble laurel]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[proud seal]

Question: How do I calculate the integral? It looks quite complicated.

[agile harness]

u have to use reopen

[proud seal]

Ok

.reopen

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✅

[proud seal]

Thanks

[noble laurel]

Is this a test/exam?

[proud seal]

Mid term prep

I do have the answer, but I do not know how this prof simplify and solve for volume

Does anyone know how to evalute this?

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@proud seal Has your question been resolved?

[snow nimbus]

Cavalierie?

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[obsidian bone]

.open

[royal glacier]

!status

[topaz sinew]

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

@obsidian bone Has your question been resolved?

[obsidian bone]

!status step 2

[topaz sinew]

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

[obsidian bone]

i have completed part a

i need help with part b

i have tried and opened like 4 help channels n not got any help till now

[obsidian bone]

<@&286206848099549185>

[jade fulcrum]

man still not solved

i saw this question like 14 hours ago

sadly i dont know how to prove things

[obsidian bone]

yup

[eternal kayak]

do you know trigonometry?

Or concept of similar triangles?

take angleMAD as theta, then angleDAK is 90-theta and so angleKAB is theta, AM/AD = AB/AK, AM.AK=AB.AD= Area of each rectangle

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[plucky yoke]

.close

[slender sonnet]

In a aretmatic sequence a1+a2+a3 equals 15 .if we minus 1 from the first 2 numbers and add 1 to the third one the new numbesf make geometric sequence need to find the arethmatic sequences sum of first 10 numbers

[topaz sinew]

@slender sonnet Has your question been resolved?

[restive inlet]

!status

[topaz sinew]

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

[slender sonnet]

Idk where to start

[restive inlet]

start by expressing a_2 and a_3 in terms of a_1

[slender sonnet]

A_1 equals a_3-a_2 ??

[restive inlet]

no

do you know the definition / proerties of an arithemetic sequence?

[slender sonnet]

I think i do

[restive inlet]

apply that here

[slender sonnet]

Wich one?

An??

[restive inlet]

apply the given definitions to get an expression for a_2, (using a_1 as your first term)

(also introduce a variable to represent your common difference)

[slender sonnet]

a1+d right?

[restive inlet]

yes

and what about a_3

[slender sonnet]

Same but 2d

[restive inlet]

why didn't you write the actual expression...

[slender sonnet]

a1+2d

[restive inlet]

anyway, your first three terms are
a_1
a_1 + d
a_1 + 2d
now write the equation saying the sum of those is 15

[slender sonnet]

Ok now what?

[restive inlet]

afterwards:

we minus 1 from the first 2 numbers and add 1 to the third one
what are the new numbers

[slender sonnet]

Sry gtg now got class if you tell me what the next steps are it would help a lot thanks

A1-1

A2-1

[restive inlet]

using

a_1
a_1 + d
a_1 + 2d

[slender sonnet]

And a3+1

[restive inlet]

i shouldnt' see a_2 or a_3 anymore

only a_1 and d

[slender sonnet]

Ok got that

What next

[slender sonnet]

.

[restive inlet]

the new numbesf make geometric sequence

apply the defintion / property of geometric sequences

that'll give you another equation

you'll now have a system of two equations with two variables
a_1 and d

solve that to determinet their values

then arithmetic series formula to find the desired sum

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[deft wing]

I'm preparing for an exam by doing old tasks, and I've come across the following.

Prove by induction, that the following is true for every n ∈ N
(My professor defines N as not including zero)

[deft wing]

now, When I start with n = 1,
I get the following

(0-1) + (2-1) = 0 obviously, 0 != 1^2

am I doing something wrong here, or is the formula itself bogus?

[mint crescent]

Yeah the sum should start from 1, not 0

[deft wing]

Thanks, that's what I thought but wasn't sure about.

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[gritty matrix]

can somebody check my work ty

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[neon iron]

i cant simplify

[neon iron]

no. 5

[craggy haven]

what's your goal?

[neon iron]

cos⁴x is the answer

(from the book)

i just

dont know how to simplify

[craggy haven]

the book says #5 is equal to cos⁴x?

[neon iron]

uh huh

[craggy haven]

what is the question

it says #3 is 0 and it very much is not

[neon iron]

no. 5 from here is the question

[craggy haven]

that's an equation

not a question

[neon iron]

wait what

[craggy haven]

what is it asking you to do with this equation

[neon iron]

OH

SHIT

find the derivative

im sorry

[craggy haven]

well now we are getting somewhere

that explains where the x ran off to from 3/8 x...

[neon iron]

yeah mb

i thought i caught the question from the photo

[craggy haven]

you missed an application of the chain rule in your derivative

[neon iron]

oh hol on

[neon iron]

aaahhhhh

OH

ok waitt

still answering btw

ok i need more help 😭

was i right factoring cos²x?

but then what do you do with the 3sin?

[versed cairn]

maybe use sin^2x = 1 - cos^2x so everything u have becomes cos function

and then open brackets and check if anything simplifies

[neon iron]

alright tyty ill try it

[neon iron]

OMG THANK YOU 😭

I FINALLY DID IT

[neon iron]

dang i didnt knew you could do this

ty again

[versed cairn]

there are 3 main trignometry identify which u can use to solve

sin^2 + cos^2 = 1
1 + tan^2 = sec^2
1 + cot^2 = cosec^2

[neon iron]

man my trigonometry sucks

[neon iron]

i see i see thank you

[versed cairn]

np

[neon iron]

again thank you guys

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[flat dagger]

is there a flaw in this? i have to show that the function is injective, but i have come to the conclusion that it is not

[hollow shard]

the last line looks wrong

f'(x) < 0 monotone strictly decreasing

imagine a always dropping curve

[flat dagger]

oh so criteria is that it only must be strictly increasing or decreasing

and so in this case decreasing

[hollow shard]

idk any criterias

[flat dagger]

i mean for a function to be one to one

deriv can be below 0?

should my last line be 'f'(x) < 0, which is strictly decreasing and therefore the function is injective ''

[hollow shard]

i mean on (-infty, 0) its injective

[flat dagger]

is injectivity and one to one not the same?

[hollow shard]

yeah

[flat dagger]

yeah

okay thank you

[hollow shard]

no

[flat dagger]

oh

[hollow shard]

actually idk

just forget i said 1 to 1

[flat dagger]

haha alright

thank you

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[glad sierra]

is there any pattern for perfect squares ?

[glad sierra]

like how they are distributed ?

[obsidian solstice]

The distances between consecutive perfect squares form an arithmetic progression

0 1 4 9 16
The distances are 1, 3, 5, 7,...

[glad sierra]

why is this happening?

how do we prove it?

[obsidian solstice]

I'll give you a hint: how would you write the distance between two numbers?

[glad sierra]

n^2 - (n-1)^2

[obsidian solstice]

Yes

Use that

[glad sierra]

d=2n-1

[haughty mural]

we can use some python 🙂

here we plot all the perfect squares up to 1000
the value of the square is on the y axis
the x axis just orders them
so the difference between the squares is the difference between the y values of these points
notice that this looks like x^2

[glad sierra]

how do i procced from here?

[obsidian solstice]

Well, that depends on how you define what an arithmetic progression is

You can prove for example that the distance between 2n-1 and 2(n+1)-1 is constant

[topaz sinew]

@glad sierra Has your question been resolved?

[glad sierra]

distance between 2n-1 and 2(n+1)-1 ?

aren't they same number?

[obsidian solstice]

No

[glad sierra]

2(n+1)-1 = 2n+2-1= 2n+1

mb

[glad sierra]

so this distance is always 2

[obsidian solstice]

Yes

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[hoary wraith]

Good Evening!
I am trying to solve c) from the exercise but I only manage to get one equation for the SLE.
Any advice how I can calculate the second?

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@hoary wraith Has your question been resolved?

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@hoary wraith Has your question been resolved?

[hoary wraith]

<@&286206848099549185>

[fervent horizon]

Can anyone help me with this plssss

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[tawdry hedge]

Hey y’all for the tables I need to find out if the tables are Quadratic function or a Linear or a exponential function.And for the next question I need to write down in the boxes which function that goes into (I mean the first 3 functions you see) And for the last one it already tells you what to do (I just wanna say that this is just a review I’m supposed to do for a test).

[topaz sinew]

@tawdry hedge Has your question been resolved?

[tawdry hedge]

<@&286206848099549185>

[trim inlet]

Ye

[tawdry hedge]

any help on this?

[rigid ivy]

To know if it's a linear function, the rise over run of any two points must remain constant.

For example, here, the rise over run is always -3/5

For quadratic and exponential, it may be easier if you can graph the points

A quadratic function will usually start decreasing, then eventually turn around and start increasing (or the other way around)

An exponential will just grow faster and faster

[tawdry hedge]

Ok thank you so much since that answered half of my question. I don’t really quite understand the last 2 problems

[rigid ivy]

I just realized this is a test. We can't help you with tests. It's considered cheating

[tawdry hedge]

It’s not a test it’s just a review

We are taking a test about it next week

[rigid ivy]

The last two questions are asking a lot of things

I'm confused by the graph and the function though. Are they supposed to match or no?

[tawdry hedge]

I’m aware of that since we usually get reviews about something that’s exactly like the ones on the test but just different numbers

[tawdry hedge]

I’m pretty sure they should match

Since it says match it with the property according to the function

[rigid ivy]

Is there like a list of graphs/functions to choose from or how does it work?

[tawdry hedge]

I made like a small example, your Just supposed to check it off

[rigid ivy]

Ohh I see. One for the graph function and one for the written function

gotcha

Well let's break it down one-by-one

Are either of them quadratic functions?

[tawdry hedge]

Wouldn’t the written one be a quadratic function?

While the graph would be a exponential

[topaz sinew]

@tawdry hedge Has your question been resolved?

[tawdry hedge]

Almost I just need help with these ones now

<@&286206848099549185>

[lucid quiver]

Sorry that is a tiny bit difficult to see in the picture I just ask you to take it 1 last time, is that possible, to make sure it is clear, because it's hard to see those answers.

can you do that or is it not possible?

[tawdry hedge]

It’s easier to see from here

Just Zoom in a Little

[topaz sinew]

@tawdry hedge Has your question been resolved?

[tawdry hedge]

Well y’all I solved the other one so I just need help with this one

<@&286206848099549185>

[tawdry dagger]

well 3 has to be g, since f and h dont have asymptotes

4 is also g, since it has the biggest value at x = 2

2 is f since it has by far the smallest value at x = 7

idk about 1 though

f and h grow at the same speed

but g grows faster

so the answers are
g
f
g
g

@tawdry hedge

( I think )

[tawdry hedge]

OK THANK YOU 🙏🙏

[tawdry dagger]

is it correct

[tawdry hedge]

Yeah it is thank youuu

I Need Help with one more question though sorry y’all 😭

Ik the first 2 but not the rest

@everyone

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@tawdry hedge Has your question been resolved?

[tawdry hedge]

.close

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[wary prairie]

need to find the oblique asymptote

[jade meadow]

i think what you have is right, though i dont know where the x in the denominator came from

oh wait i get ur question now

💀

[wary prairie]

my problem is i know that this limit is 0

so b is also 0, right?

[jade meadow]

what is b?

[wary prairie]

a = f(x)/x, b = f(x) - ax

[jade meadow]

also consider the fact that there is an x-2 in the denominator of the power

[wary prairie]

to calculate the oblique asymptote

[jade meadow]

lim of a as x approaches inf would be 0

[wary prairie]

right

[jade meadow]

wait but isnt f(x)-ax just always 0

because a= f(x)/x

[wary prairie]

I think so

[jade meadow]

ng;l i never used these methods when finding asymptotes

but

remember that x-2 cant be 0

[wary prairie]

but then, the oblique asymptote should be y=0?

[jade meadow]

y=e^-3 as you said for normal asymptote

[wary prairie]

I don't understand

[jade meadow]

because as x approaches inf, f(x) approaches e^-3

[wary prairie]

right

but should the oblique asymptote be y=0, as y = ax+b, where a = 0 and b = 0.

[jade meadow]

ohhh that's what you meant

also

i dont think theres oblique asymptotes

for this equation

i only see vertical and horizontal asymptotes

[wary prairie]

in this example, when oblique asymptote is y=0, I think it's an exception, where it's a horizontal asymptote, no?

[jade meadow]

the asymptotes i found were x=2 and y=e^-3 for f(x) = e^(-3x/(x-2))

[wary prairie]

right

[jade meadow]

for e^(-3x/(x-2))/x it would be x=0 and y=0

[jade meadow]

right

[wary prairie]

That's my question

[jade meadow]

but i dont think theres any other asynmptotes here

[wary prairie]

as the oblique asymptote is y=0, shouldn't it be counted as additional horizontal asymptote?

[jade meadow]

additional?

[wary prairie]

I calculated the oblique asymptote and it came out to be y=0

[jade meadow]

wait what's the functin

[wary prairie]

but I know that e^-3 is already a horizontal asymptote

you have it at the thop

[jade meadow]

the expression with e^(-3x/(x-2))?

[wary prairie]

exp(-3x/x-2)

[jade meadow]

how did u do this

[wary prairie]

what

we did it above

[jade meadow]

over x?

that doesnt work here

[wary prairie]

i don't understand

[wary prairie]

we calculated the oblique asymptote here

[jade meadow]

i just dont get where you got a 0

[wary prairie]

here

[jade meadow]

when a=0 it's a horizontal asymptote

not oblique

[wary prairie]

that's what i mean

so the horizontal asymptote is y=0

right?

[jade meadow]

e^-3, as you calculated here

[wary prairie]

it's an exception when the oblique asymptote is the horizontal asymptote

[jade meadow]

oh ok

[wary prairie]

what

how

but we calculated that it's y=0

I know I already calculated y=e^-3

as an horizontal asymptote

but we got another one

calculating the oblique one

[jade meadow]

why do you think b=0 as well?

[wary prairie]

oh yeah Im dumb

holy

I forgot it is f(x) - ax

not f(x)/x - ax

[jade meadow]

😭

[wary prairie]

so b = e^-3, and the 'oblique' asymptote is y = 0 * x + e^-3

and everything is right

i hate it

haha

[jade meadow]

yeah lol

[wary prairie]

I got so confused

well

[jade meadow]

happens

[wary prairie]

thank you for going through this with me

[jade meadow]

np

[wary prairie]

i see you play chess aswell

are you good?

[jade meadow]

nah not really i used to play during covid but nowadays im just playing otb with my friends for fun

[wary prairie]

oh okay, that's cool

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[inland oak]

hey I was just wondering how did they get the equations and points from the original question?

so far we've only done double integral as well?

[lucid quiver]

Original question? Sorry what do you mean there?

[inland oak]

i mean given the original question, how did we derive the points and equations in the second image which came from the textbook solution page

i get what enclosed by the coordinate planes mean now, but they then transform it into 2d which is just weird

[lucid quiver]

Oh sorry what was the first image?

[inland oak]

i get how we got the points now

and since we transformed it into the 2d plane, did they just get rid of the Z variable? so 2x+y+z=4 then just became 2x+y=4 which is y=4-2x

[lucid quiver]

Well no, I don't think they copied the formula from the first page, i believe that z was used, to determine something different. This is not what I was expecting honestly, this looks more higher level than what I anticipated to be honest with you. No they did not get rid of the z variable they wouldn't do something like that.

That at least I know

[inland oak]

well they transformed it to the 2d plane, so they didnt remove it but just made it 0 for all intents and purposes

bad wording on my part

I understand the question now much better after examining it though, I was just unsure since this was the first time I encountered the Z variable while solving for doulbe integrals

[lucid quiver]

From what I am seeing yes, but to be honest with you, everyone including myself has strengths and weaknesses in different levels of maths, but this one looks out of my reach. From what your saying though, the z would be a zero in this regards yes. because it would be a crossover. Are you sure, you don't want to extra help from someone who is an expert at this field, just to make sure your right?

since it is 2d it wouldn't show so it would be a zero yes

[inland oak]

oh just realized that the first image is meaningless 😅 it was asking for the volume of the given solid

[inland oak]

Yes, I think I understand it now. I recreated the inmage and the double integral without looking at the solution. I do appreciate your help through this, it took me a second to think it through

[lucid quiver]

Wait did I really help you through this, for real? I appreciate you are so positive to see me as a helper, but I am curious how positive are you that you know the answer is true?

This will determine if you really, are ready and prepared, but if you aren't as sure, you might need extra assistance you get what I mean that's why I asked.

[inland oak]

explaining my thoughts was able to help me understand it as I was writing what I was thinking and seeing why it is as it is. so I appreciate you helping by listening

[lucid quiver]

Getting tht extra practice to perfect yourself, that's what math is all about

[inland oak]

absolutely, I love it

[lucid quiver]

Wow I am glad, that this helped you, sometimes a lot of people overcomplicate, and overthink the problem and this happens only in math, and I have done that to where many of mistakes were in fact minor ones, like forgetting a negative number or not putting a subtraction sign in the right variable, but sometimes it can change an entire equation, so yes one has to be careful, and think through the problem and know what it's asking. Don't just jump into it so quick.

Eitherway I am not perfect either, but I do try to help those in fields where I am familiar with, but in certain levels like these, it is different, but do you know the command to ask for a helper here just in general?

[inland oak]

yea I do

which fields are you familair with btw? I see the pre-university role you have and am always interested when someone has that and is wanting to help others. specially in university math😅

[lucid quiver]

I am more familiar with geometry, more, I liked shapes more, but algebra for me can get at times, confusing with all of those numbers, but eitherway a little secret I am trying to master it myself, seeing all of these problems people do, and than seeing how the helpers explain it, is slowly making me learn everything, and that's what it's about.

[inland oak]

yea I get what you mean, personally I love algebra and is really my fav part of math which can get annoying when I also have to study geometry or trig or anything else 😅 Calculus is by far my favourite class even though im barely scraping by

[lucid quiver]

Oh wow, your taking calculus, that's amazing I wish you the best of luck right there that is not the easiest course in the world, so I can tell you are intelligent, please I really hope you can do well, there are always people ready to help you here, even if they aren't perfect, they really do try to help out. I took precalc I wasn't able to get to calc in high school but I would take it in the future in college.

Yeah everyone has his stregths and weaknesses I guess.

[inland oak]

yea, I took precalc in high school and have been doing all the calculus courses my university offers. i wouldnt rush calc though, take your time with it and study it througohly

[lucid quiver]

Yeah I am sure, I would love to think thorughly on it, and get tutoring for that, because that was a subject that apparently many people in my school struggled with, so them telling me this, was what made me bypass it, but I will definitely look and consider this absolutely for sure.

[inland oak]

Yea I wish you the best for that man, math is best learned at your own pace so I'd say even pick up a textbook or watch professor leonard and his series on calculus over the summer. I personally love leonard as he always explains everything in very simple terms though his videos can get long

I dont wanna clog this channel up any longer though, Good luck man on your studies!

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[sour egret]

Hello,
Where do I put the 2? It doesn’t have an x so I don’t think I should put it underneath 5x ….

[sour egret]

Hold up

The 2 SHOULD have an x right

Bc 3x times 2 would just be 6x

Not 6x^2

I got this all wrong

Omg

So many mistakes

Sorry 🫣

Okay I got it now

Thx

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[fleet fossil]

can someone helep me on how to do these type of question

[neon iron]

You need to learn the trigonometric identities

[fleet fossil]

can you do the 1st question as an example for me pls

[neon iron]

do you know the sine rule

[fleet fossil]

i know a little bit but i just do best with an example answer that shows all the work so i can figure the step out

i dont really get it honestly

[neon iron]

You can refer to this and fill in the corresponding numbers

we cant answer them for u unfortunately

You can probs use a calculator at this level

The Length a is opposite to Angle A
so you put a/sinA

[neon iron]

You try that for Side 10 in your question

[fleet fossil]

ok tyty

.close

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[fresh lance]

Hello

[fresh lance]

can I get help with this problem

[vernal vale]

what did you try?

[fresh lance]

ok I substituted x^2 +3 for U

This was my attempt

it was incorrect

[vernal vale]

the substitution seems good

i mean the choice of u

doesnt look like you did it right, though

whats du?

[fresh lance]

dx = du/2x

[vernal vale]

i dont think this is the most helpful way to write it

how about $x \dd x = \frac{\dd u}{2}$

[thorny flame]

jan Niku

[fresh lance]

yeah

that is what I got

[vernal vale]

okay

[fresh lance]

after I canceled the x with du/2x

x times du/2x = du/2

[vernal vale]

then you should get $\int \frac{\dd u}{2} u^4$?

[thorny flame]

jan Niku

[fresh lance]

I moved the half to the side

1/2u^4 du

it's the same

[vernal vale]

okay

and you integrate?

to get what

[fresh lance]

ohhhh

wait are you supposed to bring the value in for U at the end?

[vernal vale]

bring the value?

[fresh lance]

I integrated to 1/10u^5

[vernal vale]

okay

and undo the substitution

[fresh lance]

Ohhhh so just put in x^2 + 3

[vernal vale]

yea

[fresh lance]

(1/10(x^2+3))^5?

So weird

[vernal vale]

,w Integrate[x(x^2+3)^4]

[thorny flame]

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Requested by janniku

[vernal vale]

[fresh lance]

Yesssssiirr let me check it rq

Thank you very much amigo

U r goated

Could I get your help on one more

[vernal vale]

i can try

[vernal vale]

hmm well whatd you try?

[fresh lance]

hmmmm well I tried subbing the cos(t)

with U

is that correct

[slender edge]

why u sub

what function, if you take the derivative of it, will give you cosine?

[fresh lance]

It's review on substitution and basic integration I just assumed it tbh

sin

sine

[slender edge]

so the antiderivative is just 2sin(t) yes

then evaluate with ftc

w the given bounds

[fresh lance]

do i have to change the bounds in this case?

I forget when I have to do that

[slender edge]

not if you dont change the variable youre integrating with respect to

[fresh lance]

ok

so I got

2sin(2pi) - 2sin(pi)

0?

I am using my mind to remember the unit circle

I believe I am correct

yessir

I am

W gura pfp

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[outer portal]

how did you get y = alpha

no no

you wrote down three equations

and then three more after a =>

keep the steps consistent

to stay consistent, the first three equations should be purely from reading the matrix
x - 3y = 0
z = 0
0 = 0

then its only after the => that you write down the next three equations, which should be sorted x-y-z:
x = 3alpha
y = alpha
z = 0

take a moment to fix your work like this and youll see where you made the mistake after this

staying consistent lets you make this oversight and have it be a useful shortcut instead of a mistake

you still made the mistake and asked the question, thats more than "no" difference

you can take the suggestion or use an alternative way

np

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[unkempt niche]

can someone

tell me

why (iii) is wrong

my reason is that rate increases is that as dh/dt is negative
so h decreases over time
and as h is being subtracted from 12
with more time
h will be smaller
so denominator will be greater and greater than numerator
so the value will become smaller and smaller
but as there is a negative sign
it is actually increasing
like in -8/(12-9) when h decreases it becomes for eg -8/(12-4) which is greater than -8/(12-9)
so it increases
like numerically as there is a negative sign ase value increases
but like magnitude of the value decreases
SO
mathematically which is numerically
so with more time
the rate should increase
WHY IS IT WRONG

or is the examiner wrong

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[outer portal]

Im still in the middle of working through all the details, but the reason could just be that you said "the rate will increase" when you mean "the rate will decrease to be more negative than before"

[unkempt niche]

um no the value will decrease to be more negative than before

the rate will increase to be less negative then before

which is basically it will be more positive

so it will increase

[outer portal]

oh right I was thinking of something else

I ought to not say this until Im through

[unkempt niche]

its fine

[outer portal]

did you make sure that they read "this rate will increase" as "this rate will decrease less"

[unkempt niche]

thats the examiners job not mine : )

[outer portal]

and the examiner still marked your answer wrong, you dont think to ask?

[unkempt niche]

i did

they just said

that

as the rate becomes slower

its decrease

but literally

numerically

its increase

[outer portal]

no bud

thats exactly the reason

all of this work and the end result was "they read increase/decrease differently than you did"

cmon man

they didnt even do -1, they did -2

that means no credit, the examiner did not think you earned any points

you already have an opinion on whether your answer was right or not which you can convince the examiner to fix

but the question's been answered - its not that either of you are wrong, its that neither of you had the correct idea of what the other person wrote as an answer

[unkempt niche]

ahhhhhhhh

.close

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[past lintel]

help I'm quite struggling about functions 😭

[bitter hemlock]

https://archive.org/details/the-cartoon-guide-to-calculus-by-gonick-larry-gonick-larry-z-lib.org/page/11/mode/2up
Check out Chapter 0 (called Meet the Functions) of Larry Gonick's "Cartoon Guide to Calculus," (free pdf you can view in browser at link) it does a good job presenting a fun intuitive understanding of how functions work. Ik you're not in calculus class but just check out that chapter at least : )

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[bitter hemlock]

@past lintel you will be more likely to get help by asking a more specific question than "im confused about functions" and pasting your whole homework assignment

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[elfin raven]

how do you find integral of (2x+1)/(3x+1)^1/2

[elfin raven]

^dx

[woeful stone]

You can use integral calculator. They will the full step by step working out. If you have specfic question then that is another story.

[elfin raven]

i've used the calculator before, and i got the answer eventually, but I want to see how others would approach it

[fair thorn]

can u write the question again, more clearly?

possibly in latex/desmos notation

actually use desmos and copy the resulting ensemble of symbols here

[woeful stone]

So I would use a u-substition.

[fair thorn]

hm

yea he's right u-subs seem to be the way to go

no clue to be honest

lemme try to work it out

[elfin raven]

I tried using u-sub but i got lost

[cursive patrol]

no that's it this integral is just u-substitution

you want to consider something to make the square root a bit more simple to deal with

[fair thorn]

hmmm

i mean takign it directly doesn't seem to work

[elfin raven]

any suggestions?

[fair thorn]

nope nvm

3x + 2 works as u

just simplify the top bit to be smth like 2u - 1

i checked using an integral calculator

[elfin raven]

let me try working it out with 3x+2

i've been using u-sub with the ^1/2 included

can you show me your working @fair thorn ?

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[elfin raven]

<@&286206848099549185>

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[elfin raven]

I don't get this answer, can you elaborate pls

[near whale]

Which part of that answer do you not understand?

[elfin raven]

what would be the result of that integral?

[near whale]

Well the t on the denominator would cancel with the t next to the dt

I think you can do the rest from there

[elfin raven]

.close

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[topaz sinew]

Please don't occupy multiple help channels.

[muted cobalt]

HELO

HELP

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[neon iron]

Closing this. You already have a channel occupied

.close

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[frozen shore]

Isn’t this graphed wrong? I found it in the exercises of my calculus textbook.

[frozen shore]

How it graphed the point at (2,3)

[ruby mural]

Ig only the blue dot is the problem

[frozen shore]

Ah, okay. Thankyou.

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[golden iron]

i have to find an angle

[golden iron]

this is regular pentagon and regular decagon

[cursive patrol]

fascinating problem

[golden iron]

the answer is 36 btw but need proof

[cursive thorn]

If the answer is 36, then the intersection of the 2 lines has to lie on a corner

You can use some circle theorems on the circumcircle of the decagon for that

[golden iron]

I'm trying to prove that the point is lying on the circles but I can't

[cursive thorn]

What is known about the sizes of the two actually?

[golden iron]

nothing

[cursive thorn]

Yeah, I was just playing around on geogebra

[regal forge]

@cursive thorn Jack?

[cursive thorn]

?

[regal forge]

?

[cursive thorn]

The point of intersection of the lines seems to be the point of intersection between the two n-gons reflected in the line joining their centers

(and the decagon can be a pentagon without changing the problem I think)

[golden iron]

yeah

[cursive thorn]

that's equivalent to it lying on the circumcircles though

[golden iron]

yeah

[cursive thorn]

Maybe you can prove it if the two circumcircles have the same size, and then argue that scaling one doesn't change the point of intersection of the lines

[golden iron]

I'll try

[cursive thorn]

second part might not be that easy though

If nothing else works, then complex bash maybe (with 0 being the point of intersection between the decagon and pentagon)

I have to go now, maybe I'll have time later if you don't solve it

[golden iron]

ok

thanks

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[flint narwhal]

guys

[flint narwhal]

i need help

with division de polinomios ruffini

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[civic nymph]

how do you convert hz to radians?

[civic nymph]

i looked it up online and it seems to be 2pi/second?

i'm a bit confused based on the results i'm getting