help-39

[midnight reef]

not sure what to do next

[plush bramble]

I guess you deal with empty X separately. If you even consider the empty set compact

[pearl pond]

@midnight reef Has your question been resolved?

[pearl pond]

@midnight reef Has your question been resolved?

[midnight reef]

@merry carbon could you help me here please 🙏

[merry carbon]

Do you know e.g. that a set is compact if any sequence in the set has a subsequence that converges to a limit that lives in the set?

[midnight reef]

I have a theorem which states that a set if compact if every sequence of points in that set, has a subsequence converging to some point of the set

[merry carbon]

Yep, basically what I said

[midnight reef]

Let $x, y \in X$, since $X$ is compact, there exists $x_n \to x$ and $y_n \to y$

[jolly parrot]

Halex

[midnight reef]

($x_n + y_n) \to x + y$

[jolly parrot]

Halex

[merry carbon]

Well, I mean, that isn't a false statement, whether it's helpful though

[midnight reef]

yeah

[midnight reef]

how do I define a sequence converging to points in S?

[pearl pond]

@midnight reef Has your question been resolved?

[wide bough]

<@&286206848099549185>

Can u help solving 2nd question

<@&286206848099549185>

[pearl pond]

@midnight reef Has your question been resolved?

[deep marten]

i'm not sure but can't you say that X contains it boundary points cause it's closed which make S contains all its boundary points so it closed as well

[pearl pond]

@midnight reef Has your question been resolved?

[midnight haven]

Is the answer for the second one 5?

[wide bough]

What.? How did u get a number as an answer ?

[midnight haven]

The second one is asking for the value of x

[wide bough]

They asked to prove equations with no rational

Oh its the 3rd one I guess then

[midnight haven]

Yeah

3rd in the book

[wide bough]

Yeah its right

Used the bpt right?

[midnight haven]

I used Thales's theorem

An extension of it

For the "second" one you need to use the properties of similar triangles or something

[midnight haven]

Yes

They're both the same

[midnight haven]

@wide bough For the proof question, triangle ABC is similar to ABD. So AB/AC = AD/AB. Cross multiply and you have your answer

[pearl pond]

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.

[tulip oak]

How would i simplify the following expression: (k+1)! -1+(k+1)((k+1)!)

[pseudo oxide]

you mean

$(k+1)! + (k+1)\cdot(k+1)! - 1$

[jolly parrot]

ren

[tulip oak]

yeah

mf

oh

yeah that looks right

now that you put it that way it looks a lot easier to do

[pseudo oxide]

you try doing it yourself

i'll explain if you get stuck

[tulip oak]

oh i got it thanks so much

that little reording helped

.close

[pearl pond]

Channel closed

Closed by @tulip oak

Use .reopen if this was a mistake.

[pearl pond]

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.

[echo needle]

hi

[echo needle]

this

[pseudo oxide]

add the two eqs: you get 1.5x + 1.5y = 0 -> x = -y

[echo needle]

both these can work with that?

@pseudo oxide

[glossy compass]

Try multiplying the top one by -2, then add the two equations together

[pearl pond]

@echo needle Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[oak patrol]

find all primes p and q such that pq | 5^p + 5^q. What I got: if p=q => p^2 |25^p=> p=5=q; now p≠q p=2: 2q | 25+5^q => 2q | 5(5+5^(q-1)) => 2q | 5(5+1) => q = 3 or 5; p=3: 3q | 5^3 + 5^q => For it to be divided by 3, 3 and q must have different parity => q = 2 ; p=5: 5q | 5(5^4 + 5^(q-1) => q | 625 +1 => (626 = 3132) q = 2 or 313. Now p ≠ 5 and q ≠ 5. 5^p+5^q = 0 mod p => 5+5^q=0 mod p=> 5^(q-1) = -1 mod p Symmetrical for mod q 5^(p-1) = -1 mod q. 5^(p-1) = 1 mod p => 5^(q-p) = -1 mod p; symmetrical for mod q: 5^(p-q) = -1 mod q => 1/5^(q-p) = -1 mod q => -1 = 5^(q-p) mod q (that is same mod p) . maybe we can use orders here.

[pearl pond]

@oak patrol Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[median nexus]

hello

[median nexus]

Our assignment was to look for a Fibonacci Sequence around us and we should explain how it is considered a Fibonacci Sequence. I can’t seem to find an object that would best fit a Fibonacci Sequence but while I was watching videos related to fibonacci, it tells that it is everywhere..

Does that mean I could use any object?

But I don’t know how I’ll explain it

<@&286206848099549185>

[craggy tendon]

Probably not

judt search for fibonacci patterns in nature or something

[median nexus]

i dont have the ones I see on the internet

😵‍💫😵‍💫😵‍💫

[midnight haven]

flower?

sea shells

[median nexus]

i dont

[midnight haven]

damn

[median nexus]

well i have a flower but its a dead one so basically none

[midnight haven]

just pluck one from outside?'

[median nexus]

we dont have flowers outside that would resemble the ones you see on the internet

i need help 😭

[midnight haven]

damn

do you have a rat with you?

[median nexus]

bro WHAT

HAHAHAHAHAHAHHAAH

[median nexus]

hey

i have a correction tape

[midnight haven]

...

[median nexus]

would this work?

[midnight haven]

that'd do the job

yup

i mean like youll have to explain why

[median nexus]

how could I explain that its a Fibonacci Sequence?

[midnight haven]

loll

[median nexus]

what’s the answer

[midnight haven]

is it a written thing

or should you explain it verbally

[median nexus]

nope i dont think so

[median nexus]

yes

[midnight haven]

Ooo

then uhm

okay

just say it represents that because of the golden ratio or smth

phi = 1+root5/2

smth like that

[median nexus]

how will I justify that it represents the golden ratio

[midnight haven]

uhm

uhm

[median nexus]

we havent formally discussed FIBONACCI SEQUENCE

this is like an introduction assignment or wtv

[midnight haven]

Oh

i see

a set of steadily increasing numbers where each number is equal to the sum of the preceding two numbers. The golden ratio of 1.618 is derived from the Fibonacci sequence. Many things in nature have dimensional properties that adhere to the golden ratio of 1.618.

[median nexus]

so I could say that this object represents the golden ratio?

as simple as that?

[midnight haven]

you can see it almost everywhere ......in the architecture and things like that

[midnight haven]

i guess?

[median nexus]

ok thanks!

.close

[pearl pond]

Channel closed

Closed by @median nexus

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.

[weak plaza]

a

[pearl pond]

Please don't occupy multiple help channels.

[weak plaza]

is it possible to solve for n using a ti84 plus?

[craggy tendon]

yes

[old marsh]

u can use table function if u want

[weak plaza]

how?

[old marsh]

but i recommend simplifying

before u even try that

[cyan lily]

isolate n

[weak plaza]

like this?

[craggy tendon]

yws

[cyan lily]

sure, keep going

[weak plaza]

then i can just use log

[craggy tendon]

without using decimals

yws

[weak plaza]

is it just the ti84 plus that doesn’t allow you to do it directly

or do all calculators require u to simplify the equation

[old marsh]

some calculators can solve directly like this

wait is ti84 the graphing one

[cyan lily]

some calculators will do it for you, in fact ti84 might have an ability to do it?

[weak plaza]

yeah

[cyan lily]

im not sure

[old marsh]

i think maybe it can do this

just search online

[cyan lily]

anyways you can also just graph and trace it

for approx

[weak plaza]

i have this

[weak plaza]

yup i did but all the tutorials are about single line equations (no fractions)

[old marsh]

that shouldnt matter

if it does, just make it 0.5

[weak plaza]

yes i mean i’m not able to input the original equation as it is

[cyan lily]

why not? just use parenthesis if you can't use frac

[weak plaza]

yeah i guess so 😭 just gets confusing for me

but thank you

[pearl pond]

@weak plaza Has your question been resolved?

Channel closed

Closed by @weak plaza

Use .reopen if this was a mistake.

[pearl pond]

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.

[rich idol]

Can someone please help me?

[rough forge]

You could calculate the volume of the cylinder and the volume of a cube and divide by that.

[rich idol]

Ohh

Ok, Thanks.

[rough forge]

How many triangles can you count in total?

[rich idol]

In the hexagon?

[rough forge]

yes

[rich idol]

6

[rough forge]

and additionally to the drawing

[rich idol]

12?

[rough forge]

yes

Now all those 12 triangles are similar and make a total of 140 cm² area

[rich idol]

So will it be 140 divided by 12?

[rough forge]

divide now the area by the 12 triangles and you will get the area for one

[rich idol]

Kk thanks

You're a lifesaver

[rough forge]

and then 3 of them are shaded, you know what to do.

[rich idol]

Ya

Do you mind helping me with one more question please?

[rough forge]

I can try.

[frosty creek]

I thought it said the area of the hexagon, not the entire drawing was 140 cm²

[rich idol]

Oh wait

Ur right

💀

[rough forge]

Oh you're right.

So then it's 140/6

[rich idol]

Oh

Ok

[rough forge]

3 is correct

[rich idol]

So it would be 70 cm² right?

Because 140/6= 23.333..
23.33x3= 70

[rough forge]

yes

[rich idol]

Yay

[rough forge]

It's basically half the hexagon

3 of 6

[rich idol]

Got it

I have checkpoint exams tomorrow I'm so scared

[rough forge]

Just make sure you read correctly (unlike me)

[rich idol]

I'll try 😅

[rough forge]

For b) Percentage Increase = [ (Final Value - Starting Value) / [Starting Value] ] × 100

FV = (3x)² and SV = x²

[rich idol]

What's FV and SV

[rough forge]

Final Value and Starting Value

[rich idol]

Oh ok

Tho I'm kind of confused honestly

[rough forge]

About?

[rich idol]

a part

Or the whole question rather..

It's asking us to find the value of k without giving us x

[rough forge]

We don't need a specific x

[rich idol]

Oh

[rough forge]

k is determined by the percentage value

What ever number you take for x, the factor k will remain the same

x -> 3x we incready by 200 % the length
For example
x = 1 then increasing 1 by 200 % returns 3 * 1 = 3
x = 2 then increasing 2 by 200 % return 3 * 2 = 6

[rich idol]

Ohh

I think I get it

[rough forge]

And that works with every number

[rich idol]

Ok

Ur a great teacher btw

[rough forge]

Thanks I guess

[rich idol]

Do u teach in schools?

[rough forge]

No

[rich idol]

Oh

[rough forge]

I am an unprofessional math student

[rich idol]

Oh ok

To be honest

I'm trying to be interested in maths as a subject

So I get good marks

Because to be good in the area, you obviously have to be interested.

But it's soo hard every math class I almost sleep off

[rough forge]

I disagree, but I understand your POV.

[rich idol]

Yeah I guess

Everyone has different interests

[rough forge]

Interest can be a huge advantage to be successful, but it's not necessarily an indicator for success.

I wouldn't force it.

[rich idol]

I suppose so

[rough forge]

I also sleep in some math lectures

Maybe you just have a bad teacher.

[rich idol]

Phew I'm not the only one

[rich idol]

Hmm..Idk she's mid

[rough forge]

I think math in its own, if taught intuitively, then it raises a natural interest in all of us I think

[rich idol]

Yeah

When my father teaches me maths (He's an electrical engineer)

It's much more interesting

[rough forge]

I can tell.

[rich idol]

Than what my teacher teaches.
She tries to formulate everything

Like my teacher tries to memorize the whole syllabus
Meanwhile my dad is strictly against it, he keeps telling me to understand it conceptually which is understandable
Unfortunately, he's very busy. I don't get to study often with him

[rough forge]

Listen to your dad.

You are in school, right?

[rich idol]

Yeah, I try. It's hard tho 😭

[rich idol]

Yes

[rough forge]

If you really wanna do it, I would self study at home, the topics.

There are great resources, as YouTube videos, that may give you an intuition on a variety of topics.

[rich idol]

Hmm..Yeah.

I watched videos for other things

[rough forge]

Also, you need to really dedicate and invest time

[rich idol]

But this whole angely thingy is rlly hard

[rich idol]

I'm a time waster

[rough forge]

You really need to try to figure things

on your own terms

and that takes time

[rich idol]

I guess

[rough forge]

It's like

[rich idol]

I spend all my time on playing sports

[rough forge]

You're absorbing all the information, and then it's like a puzzle, and it's up to you to solve that puzzle and bring all the pieces together.

[rich idol]

I never thought about it like that

[rough forge]

And when you brought them together, that's when you get the Aha

[rich idol]

😮

[rough forge]

This is great and also necessary

You need to balance your life out, otherwise you will get a burnout and crash mentally.

[rich idol]

Ya I suppose 😅

It was great talking to you, I'm going to continue study now.

[rough forge]

Everyone of us has an innate curiosity

listen to it

and ask questions

when they show up

[rich idol]

K

I ask my dad so many questions in the evening

I'm honestly more of a chemistry person

Okay I'm going offline now

Bbye thanks for your help again!

[rough forge]

Have a great day/night!

[pearl pond]

@rich idol Has your question been resolved?

Channel closed

Closed by @rich idol

Use .reopen if this was a mistake.

[pearl pond]

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.

[pliant shuttle]

how do i answer this question. i tried using algebra but it gave me a large fraction as an answer

[oak quiver]

can you send a zoomed in pic?

[pliant shuttle]

sorry whatsapp compressed it

[oak quiver]

i dont need to see the space given below it

0.70484848.. right?

subtract 0.001 from it

what do you get?

@pliant shuttle

[pearl pond]

@pliant shuttle Has your question been resolved?

[pliant shuttle]

oh you just subtract it hahaha i thought it was more complicated than that

soz

[pearl pond]

Channel closed

Closed by @pliant shuttle

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.

[bright flare]

Can someone please help me estimate the area under a graph using a lower sum with two rectangles of equal width?

[midnight haven]

yes ?

[bright flare]

Perfect, so I got the answers before but I forgot to take the notes and I'm stuck figuring this out again

I know that the second and fourth questions are just finding the lower and upper bounds, but its the 1st and 3rd that are confusing me

[midnight haven]

why dont u just do like the 3rd for the first, but with 2 rectangles only ?

[bright flare]

like x=0 and x=1?

[midnight haven]

wdym ?*

[bright flare]

idk you told me 😭

[midnight haven]

hm for b)

[bright flare]

cause the bounds are [0,4]

[midnight haven]

you did 4 rectangles from 0 to 4 right ?

[0,1]

[bright flare]

No

[midnight haven]

[1,2]

ah ?

[bright flare]

for B I added the result of x=0 to x=3 cause that's the lower bound

for D I added the result of x=1 to x=4 for the upper bound

f(0) + f(1) + f(2) + f(3) is the lower bound of 108

[midnight haven]

what is " the result of x=0" ?

f(0) ?

[bright flare]

f(1) + f(2) + f(3) + f(4) is the upper

x=0 is just 0

[midnight haven]

so what is this ?

[bright flare]

the function is y=3x^3, so 3(0)^3 would be 0

[midnight haven]

so this was for b) ?

[bright flare]

yep

[midnight haven]

ok i see what u did

i think

so for d) u did f(1) + f(2) + f(3) + f(4)

[bright flare]

yep

[midnight haven]

so why cant u do the same proccess for b ?

[bright flare]

because f(0) + f(1) = 3

and the final answer for b is 48

I'm thinking the key is hidden behind the note of "two rectangles of equal width"

because four rectangles for b and d are just the lower and upper bounds

but even if I were to multiply f(0) and f(1) by two each, the answer is 6

because the f(0) just eats itself out

Oh shit my bad

I meant I'm having trouble with parts A and C

[midnight haven]

by doing this u added the values of f but it was the good result because it is also the value of rectangle with a lenght of f(1) , f(2) ... , and a widht of 1 so u didnt multiply by 1

[bright flare]

not B and D, those are the upper and lower bounds

[midnight haven]

for rectangle of widht 2u have to do f(1) / 2 and etc..

u see ?

wep

i meant f(1) * 2

not /

[bright flare]

the answer is still 6

[midnight haven]

for b ?

[bright flare]

no for a

I need help with a and c

the ones that say "two rectangles of equal width"

a and c are the ones with awkward answers

B and D are the easy lower and upper bounds

[midnight haven]

uh isnt a) 48 here ?

[bright flare]

yeah I need help with A and C

A is 48 and C is 432 but I dont know why

[midnight haven]

ok

imma make a draw

2 sec

@bright flare

[bright flare]

ok

[midnight haven]

a) is green

do u see why ?

[bright flare]

OH, those are two rectangles of equal length

[midnight haven]

yes

but try to calculate their area

[bright flare]

(f(0) + f(2)) * 2 = 48

OHHHH

AND (f(2) + f(4)) * 2 IS 432

[midnight haven]

ye here yoo

[bright flare]

Ohhhh I get it

[midnight haven]

before u were right because u were calculating the area of rectagnle of withd 1

[bright flare]

the function goes across [0,4]

[midnight haven]

so f(1) *1 = f(1)

[bright flare]

delta x for four rectangles is (4-0)/4

which is 1

but for two rectangles

delta x is (4-0)/2

which means you multiply it by 2

Perfect, thank you!

[midnight haven]

u know the formula for the area ?

[bright flare]

?

[midnight haven]

cuz u say weird way to just say lenght * width

[bright flare]

triangle x

same thing tho no?

[midnight haven]

what ??

[bright flare]

🔺 X

[midnight haven]

ah delta x

[bright flare]

ye

[midnight haven]

yes same but i just wasnt sure u understood what u were doing

but ok then

[bright flare]

at this point I dont recognize the names but I do recognize the symbols

I should probably fix that

[pearl pond]

@bright flare Has your question been resolved?

Channel closed

Closed by @bright flare

Use .reopen if this was a mistake.

[pearl pond]

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.

[golden star]

Am I misunderstanding something, or does everything past $\lim_{x->\infty} (1 + \frac{1}{\frac{x - 1}{2}})^\frac{x-1}{2}$ seem unnecessary?

[jolly parrot]

kernel

[golden star]

Because... this all eventually evaluates to e anyway, right?

The second factor on the left-hand side evaluates to 1, and the first factor evaluates to e^2, but you'd apply sqrt to both sides

[golden star]

I'm wondering because this is what our professor showed us how to do today, and everything past this (the reply) seems like it's redundant because we already have a way to a solution

[pearl pond]

@golden star Has your question been resolved?

[rough forge]

why would you apply sqrt?

The limit is e²

but I agree kinda, the solution is kinda meh at least for me it was to follow

[golden star]

There is a mistake I believe, she forgot to write the *2 from the x = (x-1)/2 proof, because it's meant to be x = 2 * ( (x-1) / 2)

[golden star]

From what I understand, you are allowed to apply an nth-root operation to both sides, and in this case sqrt seems like it'd apply, no? Because then the limit would result in e

[rough forge]

It's a limit, not an equation

I would have done it a bit different but I will try to explain

[golden star]

Okay, I think I understand what you're saying

[rough forge]

sorry for the re-edits

i am trying to show it obvious

[golden star]

No worries, this is actually really helpful; our professor likes skipping a lot of these steps and just assumes we know everything she's doing

[rough forge]

it's not even skipping

her proof is all over the place

[golden star]

Though I'd like to ask what sort of operations you are permitted to do within limits?

IIRC you're allowed to yoink constants under lim(f(x)) -> f(lim(x)); i.e. lim(2a) -> 2 * lim(a)

[rough forge]

this is applicable if we know the limit exists

she did a mistake

[golden star]

What happens if it's not known? And how can we tell?

[rough forge]

I will show

multiplying by 2 is equivalent to dividing by 1/2

but she divides by 2

[jolly parrot]

bacc (unhelpful)

[rough forge]

silly me i confused n with x lmao

but I wouldn't have done it like this

[golden star]

well if she divided by 2, wouldn't the numerator cancel out?

[rough forge]

you didnt understand

[golden star]

And then there'd be 1/2 + 1/(x-1)

[jolly parrot]

bacc (unhelpful)

[rough forge]

the factor 2 must be written as division by 1/2 if she wanna get it down

this is so fucking complicated what she did (and she did even a mistake)

[golden star]

it's not (1/(x-1)) / (1/2) it's (1/1) / ( (x-1) / 2)

the notation seems weird yeah

[jolly parrot]

bacc (unhelpful)

bacc (unhelpful)

[rough forge]

essentially 2/(x-1) which you could have done from the beginning

[golden star]

,, \frac{2}{x-1} = \frac{\frac{1}{1}}{\frac{x-1}{2}}

This is the notation she was going for

[jolly parrot]

kernel

[rough forge]

well she messed up lol

looked like (1/(x-1))/2

anyway

[rough forge]

until step 4isoki

but then unnecessary

just do u = x-1

[jolly parrot]

bacc (unhelpful)

[rough forge]

could also do

1/u = 2/(x-1)

[golden star]

sorry, do you mind explaining how its equivalent? because the exponent is x initially, not (x-1)/2

[rough forge]

where

[rough forge]

this is a general formula for e^x

[golden star]

ah

[rough forge]

nothing to do with your variables of the task

[golden star]

okay yeah then I got everything

thank you so much for your help

[rough forge]

no problem kernel

[golden star]

.close

[pearl pond]

Channel closed

Closed by @golden star

Use .reopen if this was a mistake.

[pearl pond]

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.

[midnight haven]

where can i get study material for the 2024 shsat

[midnight haven]

<@&286206848099549185>

!da2a

[pearl pond]

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/

[midnight haven]

was just

checkiing

this

yep

[pearl pond]

@midnight haven Has your question been resolved?

[plush bramble]

Not a math question. Check somewhere else

[midnight haven]

.close

[pearl pond]

Channel closed

Closed by @onyx kite

Use .reopen if this was a mistake.

[pearl pond]

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.

[hard locust]

Having some issue figuring out where to go from here

[pearl pond]

@hard locust Has your question been resolved?

[hard locust]

<@&286206848099549185>

[pearl pond]

@hard locust Has your question been resolved?

[pearl pond]

@hard locust Has your question been resolved?

[hard locust]

<@&286206848099549185>

[hard locust]

<@&286206848099549185>

[hard locust]

where did the e^y come from?

oh, its the inverse

[deft merlin]

yes, it's inverse since you need to have x=x(y)

[hard locust]

this is the cylindrical shell method right? shouldnt there be a 2pi?

[deft merlin]

It's volume by the definition. So it's finding volume using cross-sectional area

[hard locust]

oh

[deft merlin]

You have a circle in the cross-section. Its radius is x = e^y

In your example cross-section is perpendicular to y-axis, so you need integral of A(y)dy

Does it make any sense?

[hard locust]

yes

[hard locust]

how did you get negative infinity in the bounds?

i could see it going positive but i dont get why its negative?

[deft merlin]

Your region is bounded by x=0, y=0 and the curve , right?

[hard locust]

yea

[deft merlin]

Look at my picture. It means y is from (-inf, 0]

or if you prefer inequality y <= 0

Does it make any sense?

[hard locust]

the bound just looks like from 1 to -1?

[deft merlin]

It's boundaries of x. How about y ?

[hard locust]

The infinte is coming from the the curve I presume but its going to the right?

I think i get it now, were following the curve along the y-axis which is curently pointing downwards

[deft merlin]

Your variable of integration is not x, but y. That's why you need to look at values of y to find boundaries

[deft merlin]

Exactly, it's from the bottom (that is negative infinity) up to 0.

[hard locust]

yea, i get it now, thx

[deft merlin]

Np.

@hard locust Do you have any other questions about this exercise?

[hard locust]

where did pi come from?

[deft merlin]

Area of a circle = pi times Radius^2

[hard locust]

oh yeah, havent done cross sectional area in a minute

[deft merlin]

@hard locust do you have any other questions about this problem?

[hard locust]

one more, shouldnt the answer just be pi? somce 0/2 = 0?

[deft merlin]

No, the answer should not be just pi, because e^0 =1, so (pi times (e^0))/2 = pi/2, so my answer is correct

[hard locust]

also wouldnt it be e^-inf(y)?

nvm, sry im tired

[deft merlin]

Look at my picture
e^(-inf) = 0 because when y appoaches -inf, e^y approaches 0

[hard locust]

y = -inf

[deft merlin]

Do you remember graph of exponential function?

[hard locust]

no, ill look use desmos real quick

oh , yeah

[deft merlin]

I see. -inf is so-called left-end behavior on the graph. Do you see in desmos, that x-axis is horizontal asymptote for the graph of exponential?

[hard locust]

yea

[deft merlin]

@hard locust Do you have any other questions about this exercise?

[hard locust]

dont think so, thx

.close

[pearl pond]

Channel closed

Closed by @hard locust

Use .reopen if this was a mistake.

[pearl pond]

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.

[north barn]

I have difficulties to find the limits of this integral. Idk how to calculate those the rest is clear for me

[north barn]

.close

[pearl pond]

Channel closed

Closed by @north barn

Use .reopen if this was a mistake.

[pearl pond]

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.

[unborn marsh]

Five playing cards are randomly selected from a standard deck of 52 cards. These five cards are shuffled, and then the top 3 cards are placed in a row on a table. How many different arrangements of three of the 52 cards are possible?

[nimble osprey]

it seems like 52 times 51 times 50

what do you think ?

[unkempt yacht]

nosols?

[nimble osprey]

it was a sort of guess

more than a sol

[unborn marsh]

Why

[nimble osprey]

I think you can get rid of the part about the five cards

[unborn marsh]

Bro your answer matches the answer script

But i cant understand why still

Damn i suck so hard at statistics

[unkempt yacht]

technically the "picking 5 cards" stuff is kinda redundant

this has the exact same effect as shuffling and pick 3 cards

[nimble osprey]

it is probability.. I suck at statistic too

[unborn marsh]

What? thats permutation innit

Anyway yay prob solved

[unborn marsh]

Im so mad at the question makers smh

How do i close this channel

[unkempt yacht]

.close

[pearl pond]

Channel closed

Closed by @unkempt yacht

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.

[shut dawn]

Is this legitimate?

[compact ridge]

yes

[shut dawn]

It's not ambiguous at all right?

[compact ridge]

no, in fact we use that notation for integration

after we integrate you want to plug in numbers into a function, so we can write $x^2 - 2x |_2^5$ for example

[jolly parrot]

south's secret twin brother

[compact ridge]

for $(5^2 - 2 \cdot 5) - (2^2 - 2 \cdot 2)$

[jolly parrot]

south's secret twin brother

ren

[compact ridge]

yeah [] is better tbh

[shut dawn]

Do you think I can use that notation for my IGCSE exam 😭😭

[compact ridge]

probably just write $x = 1 \implies y = 3$

[jolly parrot]

south's secret twin brother

[shut dawn]

How about

y at x=1 equals 3

I don't like using words but

Would this work

[pearl pond]

@shut dawn Has your question been resolved?

[pearl pond]

@shut dawn Has your question been resolved?

[winter wind]

Yeah definitely

You can just write:

at x = 1, y = 3

[winter wind]

Or id prefer this as well

x = 1 => y = 3

=> means "implies" so you can write that

[pearl pond]

@shut dawn Has your question been resolved?

[pearl pond]

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.

[upper gate]

Can somebody explain this etap for me please?

[next dove]

it is just quadratic formula

[upper gate]

yes but I can’t see the “a”,”b” and “c”

Feeling stupid

Srry

[severe adder]

just compare with ax^2+bx+c=0

you end up with a = 1, b = -2i, c = -1+9i

[upper gate]

oh yes

thanks 😅

[severe adder]

!done

[pearl pond]

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

@upper gate Has your question been resolved?

Channel closed

Closed by @upper gate

Use .reopen if this was a mistake.

[pearl pond]

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.

[dusk zealot]

Hey Can some one help me with this? I solved and have all the info for it i just need help understanding better please!

[dusk zealot]

full page

[pearl pond]

@dusk zealot Has your question been resolved?

[pearl pond]

@dusk zealot Has your question been resolved?

[flint gyro]

4/612/9+(-3/8)(-12/9

[pearl pond]

@dusk zealot Has your question been resolved?

[dusk zealot]

what?

I just need help on the graph really

[dusk zealot]

<@&286206848099549185> can some one please help me out here im a lil lost atm and my teachers wont get back

I just need to solve for the graph

I think i got the maht i just gotta get some help or see what they mean

[pearl pond]

@dusk zealot Has your question been resolved?

[pearl pond]

@dusk zealot Has your question been resolved?

[dusk zealot]

No

[pearl pond]

@dusk zealot Has your question been resolved?

[calm wing]

is this all the quetion is asking you to draw?

like just that line

[dusk zealot]

yea

i just wanna make sure im putting it in the right area

im slow af

i mean i can do the math

i just gota feeling im doing it wrong

[pearl pond]

@dusk zealot Has your question been resolved?

[pearl pond]

@dusk zealot Has your question been resolved?

[dusk zealot]

wtv dagw no one gonna help me

[foggy carbon]

but that's not an asymptote because the population is decreasing slightly after that

that would just be a maximum

[calm wing]

i noticed that too but that's the only thing i can imagine they can mean by that

[foggy carbon]

yes, the question sucks

[coarse harbor]

It might be this line

[dusk zealot]

yea i already solved it but ty!

idk how toclose thjistho

thought i did]

[coarse harbor]

.close

[dusk zealot]

.close

[pearl pond]

Channel closed

Closed by @dusk zealot

Use .reopen if this was a mistake.

[pearl pond]

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.

[real spindle]

I’m stuck here for some reason

[real spindle]

I’m told to use half angle formula

Just need to simplify

[pearl pond]

@real spindle Has your question been resolved?

[pearl pond]

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.

[midnight haven]

I am doing 2nd degree log equations, however I do not know how to factor my problem after setting my problem equal to 0. I have an answer sheet here, but I don’t know how to get this answer.

[midnight haven]

I was taught to make multiply a by c (12 x 14) and set it over b (29) and find two numbers that multiply to equal the sum of AC and add to equal the sum of B. However, I have no idea what is going on here.

[uneven smelt]

they factorised it

[midnight haven]

I’m aware, but my method of factoring doesn’t result in the answer listed. I’m confused immensely as the method I’ve been taught doesn’t work

So I am doing something wrong, but I don’t know what or how to do it correctly

I just need someone to dumb it down for me haha

[nimble osprey]

https://tenor.com/view/how-tell-me-how-spiderman-goblin-gif-8129067

[uneven smelt]

what is your factoring method

hi snow

[nimble osprey]

hi snow

[midnight haven]

This

They called it X factoring but no matter how I do it, it doesn’t work.

I can do the part afterwards and all the rest of it, but this is one part that is just messing everything up for me

[uneven smelt]

oh.. u can but thats hard in this situation

[midnight haven]

I’m sure I’m glossing over something simple

[uneven smelt]

theres the algebraic way which is to use the quadratic formula

[midnight haven]

If you have another method I’d be happy to take a shot at it

[midnight haven]

Alright lemme try that

[uneven smelt]

the factorisation way is like guessing

[versed mica]

why do you spell it like that?

[uneven smelt]

and this is a simplification of the quadratic formula

[uneven smelt]

spell wot

[versed mica]

factorisation

you mean factorization

[uneven smelt]

s>z

[uneven smelt]

by adding both solution together u get b/a

sorry no c. i misread it

[midnight haven]

You’re awesome

It worked thank you so much

[uneven smelt]

i am 😊

[rustic gate]

thonk

[midnight haven]

How do I close this

[rustic gate]

if you're gonna use the quadratic formula

[midnight haven]

I’m new to asking for help haha

[rustic gate]

there's no point to factorising at all

you're just done by that point

29 is 8 + 21 though

[midnight haven]

It got me what I needed so I am grateful

[rustic gate]

8 * 21 = 12 * 14

[midnight haven]

Oh I’m dumb

.close

[pearl pond]

Channel closed

Closed by @devout elk

Use .reopen if this was a mistake.

[pearl pond]

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.

[lunar cliff]

I need help with eighth grade transformations like dilations, reflections, rotations, and translations

[leaden wadi]

Just ask your question. No need to ask for help.

[lunar cliff]

this is the paper question

[regal herald]

how are a and b related to 2.1 and 1.4

[lunar cliff]

idk

oh wait they’re corresponding

[regal herald]

which means

[lunar cliff]

umm

they are similar 🙂‍↕️

[regal herald]

hmm, try think about what the lesson title is

[lunar cliff]

they’re side lengths

and there is some division because of quotient

<@&286206848099549185>

[thorn geyser]

a/1.4=b/2.1

[torn needle]

if i'm not wrong 2.1/1.4 because they would be multiplied by the same value to grow them so fractions stays the same

[lunar cliff]

oh

I got 1.5

so do I multiply 2.1x1.5 to get the a

[torn needle]

if they're similar then ratio should stays the same

[torn needle]

you don't need the value of a

the question is the value of a/b which would be 1.5 or 2.1/1.4

[lunar cliff]

oh

ohhhh okay thank you

[torn needle]

np

[pearl pond]

@lunar cliff Has your question been resolved?

Channel closed

Closed by @lunar cliff

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 sparrow]

Im lost with #4

[zenith sparrow]

i keep getting 40 but the answer is 2/25

[vital hull]

try drawing a picture pictures help

[zenith sparrow]

okay wait i try tht

[zenith sparrow]

im still lost

[vital hull]

let me see what you did

[zenith sparrow]

idk what picture to draw ☹️

[vital hull]

it says that

when r = 100 cm and h = 3/2 cm, dr/dt = 4 cm/ min i think

[zenith sparrow]

i know that

i wrote that on the paper

but i tried to finf dh/dt but im doing it wron and idk how to do it right

[vital hull]

let me get a piece of paper really quick

i’m gonna try writing it down

[zenith sparrow]

oh i jus realize the 3 is in the line of the cylinder 😭 sorry

[zenith sparrow]

okay

[pearl pond]

@zenith sparrow Has your question been resolved?

[vital hull]

would the equation not be 2000pi = pi(2(100)(4)(3/2)+(4^2)dh/dt)?

[zenith sparrow]

but isnt it suppose to be 100^2?

[vital hull]

no

[zenith sparrow]

but the radius is 100 😭

[vital hull]

oh wait

one sec

[vital hull]

yeah

ur right

i got 2/25

[zenith sparrow]

Howd u get 2/25

Im so lost

[vital hull]

took dV/dt = pi(2r(dr/dt)h + r^2(dh/dt))

plugged everything in

then isolated dh/dt

[vital hull]

when you solve everything you should get 2/25

[zenith sparrow]

I PLUGGED IT IN LIKE THAT

I DID THE MATH WRONG 😭 we're not allowed to use calculator so I messed up badly

[vital hull]

oh at least you got it though

[zenith sparrow]

thank u and sorry 😭

.close

[pearl pond]

Channel closed

Closed by @zenith sparrow

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.

[scenic basin]

Is there a channel here for computability theory related questions? Which channel would be best for that?

[scenic basin]

Ah nevermind I see a meta discussion I will ask there first .close

.close

[pearl pond]

Channel closed

Closed by @scenic basin

Use .reopen if this was a mistake.

[pearl pond]

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.

[stoic imp]

let $f : (0,+\infty) \to \mathbb{R}$ defined by $f(x) = \begin{cases} \frac{3x^2 \ln x - 3x + 3}{x - 1} &\textbf{if} x \ne 1 \ 0 &\textbf{if} x = 1 \end{cases}$ find if it exists f'(1)

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

,, \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \ \lim_{h \to 0} \frac{f(1+h) - f(1)}{h}

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

,, \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \ \lim_{h \to 0} \frac{f(1+h) - f(1)}{h} \ \lim_{h \to 0} \frac{\frac{3(1+h)^2 \ln (1+h) -3(1+h) + 3}{(1+h)-1} - 0}{h} \ \lim_{h \to 0} \frac{3(1+h)^2 \ln (1+h) -3(1+h) + 3}{h(1+h)-h}

[sonic geyser]

you need to find $\lim_{h \nearrow 1}\frac{3x^2 \ln x - 3x + 3}{x - 1}$ and $\lim_{h \searrow 1}\frac{3x^2 \ln x - 3x + 3}{x - 1}$

[jolly parrot]

Awesam

[sonic geyser]

and see if they're equal

[stoic imp]

but we need to use the definition of derivative at a point

[stoic imp]

also this limit is respect to h and the rational function is wrt x, there is a mistake

[stoic imp]

that sounds like the definition of continuity and not about differentiability I think

[sonic geyser]

oh right then you take the derivative first and then you check the limit from both sides

I misread

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

problem is if we use derivative like that we assume the derivative exists I think? like we prolly need to use the derivative as a limit

also is a piecewise function yeah we need to check both sides but I am stuck trying to do that

I thought the variable with respect to my limit should be x to 1 but is h to 0

we prolly need to use lhopital as well

[summer imp]

There are two equivalent definitions of the derivative.

$$f'(a) = \lim_{h\to 0} \frac{f(a+h) - f(h)}{h}$$
or
$$f'(a) = \lim_{x\to a} \frac{f(x) - f(a)}{x-a}$$
Whether you choose one or the other doesn't change a thing

[jolly parrot]

Azyrashacorki

[stoic imp]

ok

do I need to check both sides or no

[summer imp]

No

[stoic imp]

otherwise we can apply lhopital because we have a 0/0 indeterminate form

problem is how to differentiate that numerator and that denominator

[summer imp]

You can probably rewrite stuff first

[stoic imp]

wdym

[summer imp]

The definition of the derivative will always yield 0/0

Before you use lHR, simplify things

[stoic imp]

LHR?

ahh lhopital rules

[summer imp]

l'HR

[stoic imp]

how to simplify

,w expand (1+x)^2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

,, \lim_{h \to 0} \frac{3(h^2 + 2h + 1) \ln (1+h) -3-3h + 3 }{h + h^2 - h}

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

,, \lim_{h \to 0} \frac{3(h^2 + 2h +1 ) \ln (1+h) -3h }{h^2 } \ \lim_{h \to 0} \frac{(3h^2 + 6h +3 ) \ln (1+h) -3h }{h^2 } \ \lim_{h \to 0} \frac{(3h^2) \ln(1+h) + (6h)\ln(1+h) +3 \ln(1+h) -3h }{h^2 }

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

I dont think simplifying anymore will do any good

I think I over simplified @summer imp in a non productive way

let me fix that

$\lim_{h \to 0} \frac{(3h^2 + 6h +3 ) \ln (1+h) -3h }{h^2 }$

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

we can use product rule and chain rule

for the numerator

[summer imp]

Yeah that's fine. You can l'HR now

[stoic imp]

,align \frac{d}{dh} \left[ (3h^2 + 6h + 3) \ln(1+h) \right] &= (6h+6) \ln(1+h) + \frac{(3h^2 + 6h + 3) }{1+h} \ \frac{d}{dh} \left[h^2\right] &= 2h \ \frac{d}{dh} \left[3h\right] &= 3

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

$\lim_{h \to 0} \frac{(3h^2 + 6h +3 ) \ln (1+h) -3h }{h^2 } \ \lim_{h \to 0} \frac{(6+h) \ln(1+h) + \frac{3h^2 + 6h + 3}{1+h} -3 }{2h }$

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

,, \frac{d}{dh} \left[(6+h) \ln(1+h)\right] = \ln(1+h) + \frac{(6+h)}{1+h} \ \frac{d}{dh} \left[ \frac{3h^2 + 6h + 3}{1+h}\right] = \frac{d}{dh} \left[\frac{f}{g}\right] = \frac{f'g - g'f}{g^2} \ \frac{d}{dh} \left[ \frac{3h^2 + 6h + 3}{1+h}\right] = \frac{(6h +6)(1+h) - (3h^2 + 6h + 3)}{(1+h)^2}

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

$\lim_{h \to 0} \frac{3(h+1 )^2 \ln (1+h) -3h }{h^2 } \ \lim_{h \to 0} \frac{(6+h) \ln(1+h) + \frac{3(h+1 )^2 }{1+h} -3 }{2h} \ \lim_{h \to 0} \frac{\ln(1+h) + \frac{6+h}{1+h} + \frac{(6h+6)(1+h) - 3(h+1 )^2}{(1+h)^2} }{2}$

[summer imp]

You're drastically overcomplicating this. 3h^2 + 6h + 3 = 3(h+1)^2

[stoic imp]

oh my

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

everything I did should still be valid though

but this allows me to simplify

$\lim_{h \to 0} \frac{3(h+1 )^2 \ln (1+h) -3h }{h^2 } \ \lim_{h \to 0} \frac{(6+h) \ln(1+h) + \frac{3(h+1 )^2 }{1+h} -3 }{2h} \ \lim_{h \to 0} \frac{\ln(1+h) + \frac{6+h}{1+h} + \frac{(6h+6)(1+h) - 3(h+1 )^2}{(1+h)^2} }{2} \ \lim_{h \to 0} \frac{\ln(1+h) + \frac{6+h}{1+h} + \frac{(6h+6) - 3(h+1 )}{(1+h)} }{2} \ \lim_{h \to 0} \frac{\ln(1+h) + \frac{6+h}{1+h} + \frac{6(h+1) - 3(h+1 )}{(1+h)}}{2} \ \lim_{h \to 0} \frac{\ln(1+h) + \frac{6+h}{1+h} + (6- 3)}{2}$

[jolly parrot]

938c2cc0dcc05f2b68c4287040cfcf71

[stoic imp]

did I messed up or no

@summer imp

[summer imp]

I don't think so

[stoic imp]

this was a very painful exercise

we applied lhopital like twice

product rule quotient rule chain rule power rule

It tested differentiability at a point

butI think taking both side limits was necessary

u see what I mean @summer imp

[summer imp]

No

This is the case when you can take the derivative on both pieces when they are both differentiable

Here, first of all, you have 3 pieces : x < 1, x=1 and x > 1.

And moreover you can't define differentiability on the singular point x=1

[stoic imp]

true dat

but in general

should be two limit comparison

no?

also I wanted to ask

só the function derivative at x = 1 does not exist then?

[summer imp]

As I explained, it depends on what you're dealing with. If the functions on either side of the "breakpoints" are differentiable, then you can differentiate them and take the limit on both sides, but only after you've shows it's continuous at that point.

In a way, for the derivative to exist in those cases, we can't have discontinuity, and we can't have a pointy bit, and that translates to the function being continuous and having the derivatives on both sides agree.

When the function has a specific point defined like in your problem, the breakpoints don't have derivatives defined so we have to resort to the actual derivative definition. (Note that in the previous case, you wouldn't need to use the limit definition of the derivative, just ensure that the the derivatives agree on both sides of the breakpoint)

[stoic imp]

yes but in this case the derivative at a point of both sides doesnt match

or wat

[summer imp]

The derivative is defined at x=1

It's 9/2, you've computed it

[stoic imp]

yes

[summer imp]

I guess you could actually check the derivative on both sides, but in the one point case like you have in your problem, you would end up computing the same derivative on both sides.
But then you would compute twice the same thing, and you'd also have to check for continuity, so it's just overdoing it

[stoic imp]

but so then what is the answer then?

I did the computations but my theory is bad

[summer imp]

You've found a value for the derivative. Therefore it is differentiable, with derivative 9/2

[stoic imp]

ohh

this exercises always tripp me up man for this little details I swear

@summer imp ty for the help

[summer imp]

Nw

[stoic imp]

.solved

[pearl pond]

Channel closed

Closed by @stoic imp

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.

[tardy dock]

Find the equations of the two lines which pass through the point (0,4) and form tangents to a circle of radius 2, centred on the origin.

[tardy dock]

So far what I have done is

implicitly differentiated the equation for the circle

x^2+y^2=4

and I got

dy/dx= -x/y

But I'm a bit lost with where to go from here

[summer imp]

You don't need calculus here

Unless you absolutely want/need to

[tardy dock]

Oh yeah I'm aware of the geometric approach

but what's bugging me is that

I'm unable to get it when I use calculus

So I'd like to still know the approach with calculus

[summer imp]

It's quite a bit longer than the usual approach where you use the discriminant.

The idea is that lines will have the form y = ax + 4 for some unknown a.
You can solve for the x coordinate of the intersection of the circle with the line, and
dy/dx has to match the slope of the line at the point of intersection.
This gives you a system of equations to solve for a

[tardy dock]

Ohhh

Okay I see

thank you

.close

[pearl pond]

Channel closed

Closed by @tardy dock

Use .reopen if this was a mistake.

[pearl pond]

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.

[copper mirage]

how was 3^x^2+5x changed into (3^2)^-3

[hard kite]

it wasnt

[versed ledge]

9^-3 was changed into that

[copper mirage]

I see

Where did the -6 come from

[versed ledge]

(3²)^-3 = 3^-6

[hard kite]

product of exponentss

[copper mirage]

where what

[hard kite]

$(a^b)^c = a^{bc}$

[jolly parrot]

kaue

[copper mirage]

ohhh 2 * -3 is -6

right

and that’s why it’s raised to that power

[hard kite]

yup

[copper mirage]

Then how did they get that product

Of x^2 + 5x + 6

[versed ledge]

Are you reading the text in that picture?

since the bases are the same we can now equate the exponents

What does this mean can you tell me?

[copper mirage]

idk

3^x^2+5x isn’t the same base as 3^-6

what

[hard kite]

if $3^a = 3^b$ them $a = b$

[jolly parrot]

kaue

[hard kite]

then

[versed ledge]

Where a is base 
b,c are exponents```

[copper mirage]

x^2+5x isn’t equal to -6

That doesn’t make sense

[hard kite]

it is

[copper mirage]

💔💔

it’s not tho

I don’t get that

[hard kite]

youre trying to find the x that makes it equal

[copper mirage]

wym

[versed ledge]

Have you studied quadratic equations yet?

[copper mirage]

maybe

[hard kite]

there is some number x that if you square it and subtract itself times 6, you get -6

[copper mirage]

right

[hard kite]

thats what it is saying

[copper mirage]

why by 6

[hard kite]

sorry, add itself times 5

[copper mirage]

if degree is -6

[versed ledge]

Did you understand this @copper mirage ?

[copper mirage]

no because x^2+5x isn’t equal to -6

it’s not

[hard kite]

it's not saying x is -6, its saying x² + 5x is -6

[copper mirage]

it’s not tho

what

So confused

[versed ledge]

Try putting x = -2 in x²+5x

What are you getting

[copper mirage]

-14

[versed ledge]

[copper mirage]

what are u getting at

[hard kite]

,ask solve x² + 5x = -6

[jolly parrot]

Results provided by WolframAlpha

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

Requested by wkaue

[versed ledge]

(-2)²+5(-2) ≠14

Not -2²

[copper mirage]

how would I know what number to plug in

[hard kite]

,ask (-2)² + 5(-2)

[jolly parrot]

Results provided by WolframAlpha

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

Requested by wkaue

[hard kite]

thats what youre trying to solve

its saying x² + 5x = -6, for what values of x does it work if you plug it in?

[copper mirage]

why where did the -2 come in

how would I know to plug in -2

[hard kite]

if you solve the quadratic equation you will find the somutions

solutions

[copper mirage]

so just exponents = exponents

[versed ledge]

If base is same

[copper mirage]

x^2+5x = -6

I see

Could’ve just said that …

.close

[pearl pond]

Channel closed

Closed by @copper mirage

Use .reopen if this was a mistake.

[pearl pond]

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.

[untold pebble]

Can someone please explain why does this inequality hold?

[untold pebble]

Hello

[summer imp]

The upper sum of a refinement can only go down, and the lower sum of a refinement can only go up

[untold pebble]

So U(f, P epsilon) <= U(f, P1) and L(f, P epsilon) >= L(f, P2), that is -L(f, P epsilon) <= -L(f, P2)

?

[summer imp]

Yes, because Peps is a refinement of both P1 and P2

[untold pebble]

Ok thank you!

.close