help-41

[rocky tendon]

it's not like this

somehow it's eqaul to this

how is the sqrt negative wtf

maybe it's a mistake what do you think

[trim crypt]

Incase of 1, 0 and fractions the square root will not be negative

Are you sure x is bigger than an ineger but smaller than a fraction?

[rocky tendon]

ohhh my bad but that's not the problem that i'm talking about

$0 \le x \le 0.5$

[grizzled pagoda]

RulzerFly

[rocky tendon]

yeah this

i replaced the 0 with a 1 without knowing

but still it gives me the same results

this

[rocky tendon]

instead of

[trim crypt]

The difference is the sign and place of the 1/2, review the process and see what are you doing with it

[rocky tendon]

can i show how i got it ??

[trim crypt]

tbh im not very familiar with this, but it’s generally good idea to show it

[rocky tendon]

$y^2 + x^2 = y \Rightarrow y^2 - y + x^2 = 0 \Rightarrow (y - \frac{1}{2})^2 + x^2 = (\frac{1}{2})^2$

[grizzled pagoda]

RulzerFly

[rocky tendon]

so this is a circle with a center of (0, 0.5)

so we're trying to get the part colored with red

so we write y in function of x

it gives

$(y - \frac{1}{2})^2 + x^2 = (\frac{1}{2})^2 \Rightarrow y - \frac{1}{2} = sqrt{\frac{1}{4} - x^2} \Rightarrow y= sqrt{\frac{1}{4} - x^2} + \frac{1}{2}$

$(y - \frac{1}{2})^2 + x^2 = (\frac{1}{2})^2 \Rightarrow y - \frac{1}{2} = \sqrt{\frac{1}{4} - x^2} \Rightarrow y= \sqrt{\frac{1}{4} - x^2} + \frac{1}{2}$

[grizzled pagoda]

RulzerFly

[rocky tendon]

look

[trim crypt]

The only confusion i have is, where did the the parentheses (y-1/2)^2 come from

[rocky tendon]

just to get a circle equation

i think i found where i'm wrong

the squared

look

$y - \frac{1}{2} \neq \sqrt{\frac{1}{4} - x^2}$

that's the problem

[grizzled pagoda]

RulzerFly

[rocky tendon]

it's abs

and the red part is the bottom one

so

$y - \frac{1}{2} = - \sqrt{\frac{1}{4} - x^2}$

[grizzled pagoda]

RulzerFly

[rocky tendon]

and

yeahhh that's ittt

$y = \frac{1}{2} - \sqrt{\frac{1}{4} - x^2}$

[grizzled pagoda]

RulzerFly

[rocky tendon]

like the solution

[trim crypt]

I be real

I was genuinely gonna advise some general stuff, but you went through the work again and got it

Seems you got it with no help anyway

[rocky tendon]

it's easy i'm just dumb :skul

[trim crypt]

Nah i still don’t understand how you got it

So im the dumb one

[rocky tendon]

thank for help bro

.close

[amber wasp]

Channel closed

Closed by @rocky tendon

Use .reopen if this was a mistake.

[trim crypt]

What help

[rocky tendon]

.reopen

[amber wasp]

✅

[trim crypt]

Anyways, good ya caught on your mistake

[rocky tendon]

yeahh

.close

[amber wasp]

Channel closed

Closed by @rocky tendon

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.

[glossy arrow]

Hi there!
I started studying Boolean algebra and it's still very confusing for me.
Do you think I wrote down the expression right?

[sinful sapphire]

sure

[frank zealot]

yeah

[glossy arrow]

Thank you! I will try to tackle the simplification, then. 🙂

[amber wasp]

@glossy arrow Has your question been resolved?

[glossy arrow]

What do you think, am I on the right track?

<@&286206848099549185>

[frank zealot]

yes

correct

[glossy arrow]

Thank you for your help!

.close

[amber wasp]

Channel closed

Closed by @glossy arrow

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.

[ebon temple]

find the area bounded by the curves y=sec^2x -1, y=8cosx-1 and the line x=pi/4 for the domain pi/4 < (and equal to) x < (and equal to) pi/3

[elder harbor]

what have u done so far

[amber wasp]

@ebon temple Has your question been resolved?

[ebon temple]

like i lwoeky kind of forgot

how to do it with three functions

[amber wasp]

@ebon temple Has your question been resolved?

[elder tangle]

maybe revising first is better then, do you remember how to calculate the area under a curve above the x axis?

[ebon temple]

yes

[elder tangle]

then first plot the curves

ig you can use desmos

can you tell what is the area you need to calculate?

[ebon temple]

uhmm

?

wait do i need to care about x=pi/4 at all bc the bounds

r already like

[elder tangle]

yeah turns out you don't need to

[ebon temple]

ohhhhh

okok tysm

i lowkey graphed it wrong

thats why i was confused

[elder tangle]

even without the bounds i think you can figure out the bounds yourself

[ebon temple]

ok yes

thanks

[amber wasp]

@ebon temple Has your question been resolved?

[inland oracle]

think its a little easier to imagine it if you use trig identity 1 + tan^2(x) = sec^2(x)

basically graph of tangent but everything is positive

[amber wasp]

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.

[fluid swallow]

Help

[fluid swallow]

The first is the question and the second is my attempt. I am not a math student so I am very clueless about the rigor, please help me

Mighty @patent raptor

Help me, I am really bad at math and have absolutely no clue if I have done it right

Anyone please help me

[quick spoke]

i'm kinda confused by ur working layout

[fluid swallow]

Which part I can explain ☺️☺️

[quick spoke]

btw ur answer isn't quite correct, g'_n doesn't converge uniformly

[fluid swallow]

Bcs im not really math student and this is my hobby so the layout can be pretty messy

[quick spoke]

yh that's valid

[fluid swallow]

On [0,1] though

[quick spoke]

yeah no it doesn't converge uniformly

we'll get to that

[patent raptor]

this explains it huh

[fluid swallow]

It doesn’t converge uniformly on [0,1] why though?

[quick spoke]

i think as a general principle, it's kinda to deciper ur work cus you have to prove several parts and it's not entirely clear what each part of your work is trying to prove - a good way to present your work is to do a claim-proof structure

so Claim: "stuff"
Proof: "stuff"

then what u've done jumps out a lot more

anyway that's just some general comments

[fluid swallow]

Yes that’s true bcs I ain’t trained in that sadly

[quick spoke]

i mean if ur not studying maths it's impressive ur doing this lol

[fluid swallow]

Is fun

[quick spoke]

i think some more words would be good to explain why g_n -> 0 pointwise but overall that's fine

[fluid swallow]

And these days those in Econ study real analysis too

[quick spoke]

(worth mentioning that i.e. g_n(x) >= 0!)

[quick spoke]

oh interesting

[fluid swallow]

Can’t x takes 0?

Since n is natural number x can take 0

[quick spoke]

depends on the convention

for set theory it can sometimes be helpful to think of 0 as a natural number

[fluid swallow]

Usually I will exclude n=0

[quick spoke]

a lot of times i think in like i.e. the US 0 is not natural

[fluid swallow]

since on rudins if we take 0 then it can have many problem

[quick spoke]

anyway here it doesn't make sense if n=0, cus then we have 1/0 so they just mean n >= 1

[fluid swallow]

Yes but here I really excluding 0 as a natural number

[quick spoke]

also i'm curious by how u've differentiated x^n/n lmao, chain rule with the exponential???

i mean it works but like power rule lol?

[fluid swallow]

Generalized power rule I learned from course cal 2

[fluid swallow]

You aren’t gonna to leave some short comments for enlightenment

[quick spoke]

oh right if u haven't done it in analysis makes sense

[fluid swallow]

Cal 2 includes generalized power rule

[quick spoke]

so you compute g_n'(x) = x^(n-1)

[fluid swallow]

Yes

[quick spoke]

what does this converge to pointwise?

[fluid swallow]

Yes you’re right it doesn’t converge uniformly

[patent raptor]

LY will enlighten u

[fluid swallow]

It goes to 1 whenever x=1 otherwise 0

I made a careless mistake

What’s the point of that epsilon - argument

That looks quite daunting already 😭😭

It converges uniformly on [0,1) eight

[quick spoke]

no unfortunately

[fluid swallow]

Is the rest correct I only need to delete the epsilon argument right?

[fluid swallow]

Why?

[quick spoke]

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

[fluid swallow]

On [x,1-delta]

This is correct right?

[quick spoke]

yeah so if we use the half open interval [0, 1), it doesn't converge uniformly because intuitively, no matter how big n is

[fluid swallow]

Forgot the neighborhood again not studying math makes me this dumb😭

[quick spoke]

x^n will be very close to 1 for x very close to 1

even though the limit should be 0

hence convergence is not uniform

[fluid swallow]

So if I fix it by saying it converges uniform on [0,1-delta] it should be correct right?

[fluid swallow]

Is the part a s proof correct? I actually used Dini theorem though

[quick spoke]

the part a proof is fine

it's a bit hard to judge ur proof cus it depends on what analysis results u already know

but i think it's fine to say x^n -> 0 as n -> infinity for |x| < 1

[fluid swallow]

Bcs I ain’t really math student so just assume as little as possible

[patent raptor]

you are still a pro

[fluid swallow]

Is that fine though? Shouldn’t I use m test, definition or dini theorem

[fluid swallow]

I am not

Is the convergence uniform on [0,1-delta]?

[quick spoke]

i mean if ur doing uniform vs pointwise convergence then i think ur beyond the point where you need to rigorously justify that i.e. 1/2^n -> 0

[fluid swallow]

And is the format or the way the epsilon argument is crafted fine?

[fluid swallow]

You’re right!

The inequality is so hard

[quick spoke]

i mean i mentioned my thoughts about ur formatting

[fluid swallow]

😭😭😭😭

Maybe it’s not to late to transfer to dept math

[quick spoke]

if u want i can write out what i think would be a nice way to present ur work?

[patent raptor]

say yes ema

[fluid swallow]

Please do it for me owwwww 🥰 you’re so nice!!!!
And again. Is dili Theorem valid for part 1 though?

[quick spoke]

i wasn't aware of dini's theorem but it looks like it's fine

[fluid swallow]

Is dini s theorem correct for part a? You’re like a pro right you solved that daunting integral

[patent raptor]

havent bothered looking yet

[quick spoke]

oh wait ur thing for showing g_n(x) is decreasing is kinda cursed lol

n is meant to take values in the natural numbers so differentiating it is a little bit cursed

but you can phrase it differently to make it less cursed

[patent raptor]

was about to say that

[fluid swallow]

You’re right I should use inequality directly

[patent raptor]

instead of the derivative you can just show g_n > g_(n+1) or g_n < g_(n+1)

[fluid swallow]

Then I qualify dini theorem

Or I use Bolzano weierstrass theorem which is easier right?

I will try to refine it a bit and be right be right back

[quick spoke]

oh wait ok so ur thing is correct, but it's ur method is a little bit overkill

[fluid swallow]

Please show me it I really wanna see 🥰🥰

[quick spoke]

it's like quite easy to show directly that g_n -> 0 uniformly

[quick spoke]

i'm writing it up now

[patent raptor]

I have a Lemma from my notes from last semester that says a function sequence f_n converges uniformly to f if and only if ||f_n - f||_oo -> 0 as n -> oo.

|| f ||_oo = sup|f(x)| denotes the supreme norm on D

[quick spoke]

i suspect the question is looking for something like that

[fluid swallow]

I revised mine till

[quick spoke]

dini's theorem requires ur limit function to be cts

so you should find the limit function as g(x) = 0 first then apply dini

[fluid swallow]

Yes [0,1] bounded and closed

What’s cts?

[quick spoke]

continuous

[fluid swallow]

I am reading yours 🥰🥰

so the order matter right?

[quick spoke]

you need to put a little more justification why
"2 limits" => not uniform continuity

[quick spoke]

yh

[fluid swallow]

That characteristic function h is so clever I love it 🥰🥰🥰🥰

Did you use sequential test too

I shall refine it again

Thanks so much you’re brilliant 🥰🥰

[amber wasp]

@fluid swallow Has your question been resolved?

[amber wasp]

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.

[tough mica]

The base-$10$ integers $36$, $64$, and $81$ can be converted into other bases so that their values are represented by the same digits $\triangle\Box\Box$, where $\triangle$ and $\Box$ are two distinct digits from $0$-$9$. What is the value of $\triangle\Box\Box$?

[grizzled pagoda]

938c2cc0dcc05f2b68c4287040cfcf71

[violet blaze]

notice

36=6^2
64=8^2
81=9^2

[amber wasp]

@tough mica Has your question been resolved?

[tough mica]

Triangle and box are 2 and 3?

[violet blaze]

no

10^2 = 100 is base 10, right?

[tough mica]

Ok

36 in base 6 is 6^2 + 0 + 0 = 100

100 in base 10 is 10^2 + 0 + 0 = 100

81 in base 9 = 9^2 + 0 + 0 = 9^2

Idk

[violet blaze]

81 in base 9 is 100

[tough mica]

100 typo

[violet blaze]

so triangke square square is ?

[tough mica]

100

[tough mica]

Idk, 100

[violet blaze]

yes

[tough mica]

Why is that

[violet blaze]

because they are all 100 in some base

which is what the qn is asking

[tough mica]

Because they are perfect squares

[violet blaze]

yes

[tough mica]

thanks

.close

[amber wasp]

Channel closed

Closed by @tough mica

Use .reopen if this was a mistake.

[amber wasp]

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.

[true lake]

The figure below represents the floor plan of an office. The owner of the room intends to install a granite strip to decorate the floor. This strip is the non-dotted part in the figure. Knowing that rectangles ABCD and EFGH are congruent, indicate how many meters of strip will be needed:

(consider sqrt(2) = 1,4

[amber wasp]

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

[true lake]

1

wait

2

i know i have to convert

[amber wasp]

@true lake Has your question been resolved?

[true lake]

😭🙏vro

[amber wasp]

@true lake Has your question been resolved?

[amber wasp]

@true lake Has your question been resolved?

Channel closed

Closed by @true lake

Use .reopen if this was a mistake.

[true lake]

.close

[amber wasp]

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.

[ruby dome]

$\int_0^{+\infty} \sin(x^2) dx$

[grizzled pagoda]

Task Bot

[ruby dome]

How to compute this ?

[thorny pewter]

the standard way is by complex analysis, if you're familiar

for a real approach you might want to look at https://math.stackexchange.com/questions/187729/evaluating-int-0-infty-sin-x2-dx-with-real-methods/190293#190293 for some methods

[ruby dome]

Thanks so much !

.close

[amber wasp]

Channel closed

Closed by @ruby dome

Use .reopen if this was a mistake.

[amber wasp]

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.

[near flower]

Hi for part b i dont get why the solutions absolute value the integral

and why they only consider the bounds from 0 to 1

this is what i started doing

[royal parcel]

what your doing makes more sense to me too

and i think it should be a + instead of a - between the two integrals

[near flower]

oh oops ur right

[royal parcel]

The absolute value is probably meant to be inside the integral rather than outside. then it would be the same as your working

[near flower]

were they meant to put a 2 in front of the entire thing? Cus its symmetrical?

[hollow salmon]

This is the enclosed region. Because the enclosed regions swap, if you did the integral f(x) - g(x)), it would likely zero out.

[near flower]

oh do you mean what i did in my working?

[hollow salmon]

You asked why the absolute value signs are there.

[near flower]

ohh

[hollow salmon]

If you subtract f(x) - g(x), you get this new equation.

As you can see, part of the bounded interval is negative.

[near flower]

Ah I understand, if you absolute value f(x)-g(x) then it gives you the entire area between 0 and 1

[hollow salmon]

Yes. That's not the usual way of doing this though. One would typically create two separate integrals on two different intervals and subtract the appropriate function from the other.

[near flower]

So basically what I did?

[royal parcel]

wouldn't this force him to separate them either way, if he does not have a calculator to evaluate the integral

[near flower]

wait what

[hollow salmon]

Almost, you would add the two integrals instead of subtracting them.

[near flower]

ye thats my mistake

alright thanks guys

.close

[amber wasp]

Channel closed

Closed by @near flower

Use .reopen if this was a mistake.

[near flower]

.reopen

[amber wasp]

✅

[near flower]

ok idk where i went wrong but i got a negative area

[hollow salmon]

The initial integrals are correct. You mathed wrong somewhere. I get 1/16.

[near flower]

Oh ok thats good to know I probably did something dumb

Thanks

.close

[amber wasp]

Channel closed

Closed by @near flower

Use .reopen if this was a mistake.

[amber wasp]

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.

[bleak cargo]

I need someone to help me understand this. I am confused as to how to divide this or even if I can factorize it.

[scarlet trail]

dividing polynomials

you should probably watch a video on how to do it if you dont know how

[bleak cargo]

i do know how to do that

[scarlet trail]

what specifically about this one are u unsure about

[bleak cargo]

i divide 12x^5 with 3x^3 right?

i am kind of confused about there being 3 digits, things, wathever they are called in the second polynomial

[scarlet trail]

wym 3 digits

[bleak cargo]

this

i have always had like X-1 or something

[scarlet trail]

what do you multiply 3x^2 by to get 12x^5

[bleak cargo]

4x^3?

[scarlet trail]

yea

so thats ur quotient so far

than u multiply the denom by 4x^3 and subtract it ffrom the original to get a smaller dividend

than u just go down the line

[bleak cargo]

like this?

[scarlet trail]

well u would multiply 4x^3 by 3x^2-x+2

than subtract that new thing from the orignal

of 12x^5

so it cancels

[bleak cargo]

so now i just subtract all of those above?

[scarlet trail]

wym all of those above

[scarlet trail]

this is really just long division with variables exact same process

[bleak cargo]

so like this?

[scarlet trail]

it would be 3x^4 - 4x^3 -x -2 wouldnt it

[bleak cargo]

yeah but i dont write those, but ig i should

[scarlet trail]

well than yea

than you continue

so what do u multiply 3x^2 by to get 3x^4

[bleak cargo]

so i repeat the same process? divide the 3X^4 with the 3X^2 and then multiply with the brackets?

[scarlet trail]

just work it out and ill tell u if ur right

i think u got it

[bleak cargo]

okay

[scarlet trail]

wouldnt it be negative 3x^3

[bleak cargo]

oh yeah you are right, mb

[scarlet trail]

yea besides that

looks perfect

[bleak cargo]

now i just have to correct it

[scarlet trail]

if you need anymore help with this feel free to ping me

[bleak cargo]

okay, i will ping you when i finish this

[scarlet trail]

👍

[bleak cargo]

@scarlet trail

i believe this is correct since it all just canceled out in the end

[scarlet trail]

if thats a -1 at the end

i got the same thing

[bleak cargo]

ye -1 right to the equal sign

[scarlet trail]

yep!

bravo

[bleak cargo]

tyyy

i do have a few more problems, not long, just practicing for an exam tomorrow, if it is not a problem

do i use just factorize it here?

<@&286206848099549185>

[amber wasp]

@bleak cargo Has your question been resolved?

[bleak cargo]

<@&286206848099549185>

[hidden basalt]

check the second line

you didnt distribute the negative

[bleak cargo]

oh okay, lemme correct it rq

wait, where exactly, i cant find anything

[bleak cargo]

like this?

[hidden basalt]

yup

[bleak cargo]

?

wait i messed it up

[amber wasp]

@bleak cargo Has your question been resolved?

[hidden basalt]

yeah no try again

[amber wasp]

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.

[vagrant acorn]

cant follow how this happend or what -1/3 means

[unreal rapids]

So, the steps are, move 1 over so it's 4x^3=1

Then x^3 =1/4

Now to get the x we raise the expression with ^(1/3)

So we have x = (1/4)^(1/3)

Now this doesn't really look nice

So we use the rule n/x = x^(-n)

Which showes x = 4 ^(-1/3)

This helps @vagrant acorn ?

[vagrant acorn]

wow

i was wondering how the hell a 4 got there

but this makes sense

thank you

[unreal rapids]

No problems :)

[vagrant acorn]

.close

[amber wasp]

Channel closed

Closed by @vagrant acorn

Use .reopen if this was a mistake.

[amber wasp]

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.

[steel notch]

Am I allowed to do this?

[hollow cape]

should be ok

[steel notch]

Thank you.

.close

[amber wasp]

Channel closed

Closed by @steel notch

Use .reopen if this was a mistake.

[steel notch]

.reopen

[amber wasp]

✅

[steel notch]

If I prove that the series of |an| is divergent, then does that also mean that the series of an will be divergent?

[compact yarrow]

No

Consider the alternating harmonic series

[steel notch]

Hm. Interesting

(-1)^n*1/n

|an| diverges using the p series test

But an converges

Using the liebniz test

Thank you.

.close

[amber wasp]

Channel closed

Closed by @steel notch

Use .reopen if this was a mistake.

[amber wasp]

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.

[sterile nymph]

What is f(x)?

[split sail]

oh mb

so since the thingy is in the middle

we reflect the left side of the y axis innit?

and vvertical stretch by 2

but the mark scheme says otherwise

[sterile nymph]

I'm not sure what is meant by "find the coordinates of"

Are they asking for where (x, f(x)) gets mapped to in the form of (x, f(|2x|)) or are they asking about (f(x), f(|2x|)) or something else? I'm not actually sure.

What does the mark schema say?

[split sail]

yea i think

[sterile nymph]

Ah

Weird ok

[split sail]

nvm understood it

sketch it and itll make it easier

.close

[amber wasp]

Channel closed

Closed by @haughty monolith

Use .reopen if this was a mistake.

[amber wasp]

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.

[steel notch]

This series is absolutely convergent, right?

Using the root test

[young needle]

yep

[steel notch]

Thanks!

.close

[amber wasp]

Channel closed

Closed by @steel notch

Use .reopen if this was a mistake.

[amber wasp]

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.

[meager gale]

this is what i did and i continued it but got the wrong answer

i put it in an integral calc, and the answer i got there was different to the answer given to me

i think theres something fundamentally wrong with how i set up my equation

[amber wasp]

@meager gale Has your question been resolved?

[weak zinc]

What did they get, and what did you get?

[meager gale]

i found the mistake dw

.close

[amber wasp]

Channel closed

Closed by @meager gale

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.

[steel notch]

Is this correct?

[distant herald]

yes, but you can simplify that further to just arcsin(x/a) + C

if a > 0, a / |a| is just 1, so that case is the same

and if a < 0, a / |a| is -1, arcsin is odd so the negatives cancel

erm did i mess up

[weak zinc]

Even though arcsin is odd, you don't get a negative sign introduced by that, do you

At best you'd get e.g. arcsin(x/(-a)) or something, unless I'm fried

[distant herald]

yeah this is what i was trying to go for lol

i guess it's technically best to leave it like this then

ah right if you graph an example of this with negative a, just arcsin(x/a) doesn't make sense. i suppose the reason arcsin(x/a) is always on integration cheat sheets is that they assume WLOG that a > 0 since (-a)^2 = a^2

[shadow stump]

well you can take a/|a| = sgn(a) (we are assuming a is nonzero anyway). then inside the arcsin we can write 1/a = sgn(a)/|a|, and the sgn comes out (odd function) and cancels with itself. so a more convenient (but equivalent) form would be arcsin(x/|a|) + C

[steel notch]

Thanks guys. Noted

.close

[amber wasp]

Channel closed

Closed by @steel notch

Use .reopen if this was a mistake.

[amber wasp]

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.

[keen pawn]

If $(x_n) \to x$ show that $\sqrt{x_n} \to \sqrt{x}$.
\
As $(x_n)$ converges, it follows that $\forall \varepsilon >0. \exists N>0,$ st $n> N \implies \abs{x_n-x} < \varepsilon^2$
\
We wish to show that this implies $\abs{\sqrt{x_n} - \sqrt{x}}< \varepsilon$.
\
We also find that $(\sqrt{x_n}+ \sqrt{x})(\sqrt{x_n} -\sqrt{x}) < \varepsilon^2$

[keen pawn]

now what

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[amber wasp]

@keen pawn Has your question been resolved?

[keen pawn]

<@&286206848099549185>

[sterile nymph]

Use the max of the two values

[keen pawn]

I also considered using boundedness

[keen pawn]

yeah, I did think of that, but that requires more than we have at our disposal , no?

[sterile nymph]

Hmmm true, I guess you can't just use the max of the two values.

[keen pawn]

AM>GM?

We know that $2\sqrt{x x_n}< \sqrt{x}+ \sqrt{x_n}$

[grizzled pagoda]

ƒ( wai ina teacup)= I don't know

[robust isle]

you need to break this up into two cases

one where x = 0 and one where x > 0

[keen pawn]

x=0 is done

[robust isle]

did you do that elsewhere

[keen pawn]

yes

[robust isle]

okay then you should capitalise on the fact that x > 0

[keen pawn]

How

I suppose AM>GM would work

I can cap \sqrt{x} + \sqrt{x_n} at 2x_n

[robust isle]

sqrt(x) + sqrt(x_n) >= sqrt(x) > 0

[keen pawn]

yes

how does that help

[robust isle]

you get to choose what |x_n - x| is less than

[keen pawn]

Ah

I see

[robust isle]

lets say $\abs {x_n - x} < \eta$
[ \abs {\sqrt {x_n} - \sqrt x} \abs {\sqrt {x_n} + \sqrt x} < \eta \
\abs {\sqrt {x_n} - \sqrt x} < \f \eta {\sqrt {x_n} + \sqrt x} \le \f \eta {\sqrt x}
]

[keen pawn]

yes

and by boundedness, \sqrt{x_n}+ \srt{x] < 2\sqrt{x_n}

ah

[keen pawn]

I see

yeah, that makes sense

Got it

tq

.close

[amber wasp]

Channel closed

Closed by @keen pawn

Use .reopen if this was a mistake.

[robust isle]

[amber wasp]

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.

[amber wasp]

@tough mica Has your question been resolved?

[amber wasp]

@tough mica Has your question been resolved?

[amber wasp]

@tough mica Has your question been resolved?

[grizzled pagoda]

ucheo

ucheo

[amber wasp]

@tough mica Has your question been resolved?

[main trail]

maybe translate that to english first and it will be easier for ur question to be answered

[amber wasp]

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.

[meager gale]

im to find a, but if i expand this, wount i be left with ln(-1)?

[tidal basin]

integral of 1/x is ln|x| not ln(x)

[meager gale]

ahhhhh

Thx

.close

[amber wasp]

Channel closed

Closed by @meager gale

Use .reopen if this was a mistake.

[amber wasp]

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.

[kind rose]

try finding the limit with respect to a, then solve the relatively simple resulting equation

[remote shore]

w.r.t 'a'...
can you explain a bit more

[hidden basalt]

what have you tried si far

[hasty yacht]

recall what e is

[kind rose]

solve the limit while leaving a as a constant

[hasty yacht]

i assume you're familiar with this form since you're solving this problem too

[remote shore]

yes

.close

[amber wasp]

Channel closed

Closed by @remote shore

Use .reopen if this was a mistake.

[amber wasp]

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.

[fierce edge]

for x = a, a - 2 in Dom(f):

f(x) at x = a evalutes to f(a)

and for f(x + 2) to evaluate to f(a), we must have x = a - 2

Thus, we can see that f(x + 2) is a translation of f(x) 2 units to the left

[fierce edge]

would an argument like this work?

[split sail]

Yes it will work

U can test it with y=x graph

I mean f(x) =y

[amber wasp]

@fierce edge Has your question been resolved?

[fierce edge]

hmm what?

[split sail]

What was ur doubt exactly, can u tell it again

Ig u were asking can I write it as some shift in the graph. Along x axis right?

@fierce edge .

[fierce edge]

I know it is a shift

I want to know if my argument is correct

It might be but like do i really need to specify x = a-2 in Dom(f) too?

[split sail]

yeah, so ur domain changes

u need to specify

[severe scroll]

a - 2 might not be in Dom(f)

but it's in Dom(g) where g(x) = f(x+2) as long as a is in Dom(f)

your argument is fine, and i would have said something similar. one might make explicit that this is literally the definition of what it means to "shift the graph left by 2", that is, (x,y) \in graph(g) if and only if (x +2, y) \in graph(f)

but that's exactly what you showed anyways

[fierce edge]

oh

i don't remember the solution but i recall them only mentioning a in Dom(f)

and nothing about a - 2 in the context of "domain"

but yeah okay we would have to say x = a- 2 is in the domain of g(x) right?

[fierce edge]

if we reason this way

[severe scroll]

yes but that's okay, because a - 2 + 2 = a ;)

[fierce edge]

😭 yeah i guess we don't need a - 2 for f

but we need it for g, no?

[severe scroll]

yes

that's why my comment was so cheeky, because try putting a - 2 into g

[fierce edge]

mhm you get f(a) so you only need x = a to be in Dom(f)

[severe scroll]

yeah

but that's good because we already assumed that a was in Dom(f)

because (a,f(a)) was in graph(f)

[fierce edge]

this makes sense, but like idk somewhere in the solution they only just talked about a and nothing else (no g(x) having x = a - 2 in the Dom or whatever)

maybe i'm misremembering

[severe scroll]

yeah, you should not trust solutions given in a solution manual as much as your intuition (hot take)

[fierce edge]

😭 oh

[severe scroll]

but like

[fierce edge]

I like looking at solution manuals cuz like the author is clearly better than me at this

but i guess my idea works as you affirmed

so meh

[red quarry]

hi

[amber wasp]

@fierce edge Has your question been resolved?

Channel closed

Closed by @fierce edge

Use .reopen if this was a mistake.

[amber wasp]

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 galleon]

what could be the example of one to one function that isnt strictly monotonic

[split kraken]

actually, hold on

I think I might be silly

[delicate void]

your example is correct i think

[vast scaffold]

If it’s not continuous then take any piece wise function

[split kraken]

I think f: R \ {0} -> R given by f(x) = 1/x would work, yeah?

it's injective, but not strictly monotonic

[oak galleon]

yes that seems to be correct

[craggy sundial]

isn't that strictly decreasing?

[vast scaffold]

Not when it’s negative

[craggy sundial]

no it's still decreasing

f' is -1/x^2, which is all negative

[delicate void]

it is monotonic in R+ and R- but not in the whole domain

[oak galleon]

i dont htink you can say that its decreasing on its whole domain

thus it isnt strictly monotonic? iguess

[wind summit]

f(x) = sin(x)

[delicate void]

exactly

[wind summit]

🙂 it does both

[delicate void]

but it is not injective

[oak galleon]

its not injective

[craggy sundial]

oh yeah
I thought that f' just have to have the same sign

[oak galleon]

alright thanks fot help

[delicate void]

that is right in case the domain was continous

aka an interval

[craggy sundial]

ah I see
bc then the slope across some interval is just the sum of all the f'

divided by the interval length

[delicate void]

i didnt get it

can you elaborate

[craggy sundial]

I mean like
$\frac{f(b) - f(a)}{b-a} = \frac{1}{b-a}\int_a^bf'(x)dx$

[grizzled pagoda]

Sepdron

[delicate void]

yes that an elegant way to see it

[craggy sundial]

so the domain doesn't have to be continuous right?
just that condition has to be true

[crisp stratus]

if you allow, piecewise functions, then
$$f(x)=2\lfloor x\rfloor-x$$
is a really nice example of this

[grizzled pagoda]

artemetra

[crisp stratus]

it's decreasing almost everywhere

[crisp stratus]

i don't think you'll find a continuous example though, because by IVT you'll be able to find points that would break injectivity

[delicate void]

I think it is mandatory to have a continuous domain to use that result using derivatives.

[crisp stratus]

or you'll have to work with really strange domains ig

but on an interval no, there is no such continuous function

[amber wasp]

@oak galleon Has your question been resolved?

[craggy sundial]

I moved to #help-4 so I don't take over this channel

[amber wasp]

Channel closed

Closed by @oak galleon

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.

[calm pewter]

i need help ik volume and stuff but idk how to start

[amber wasp]

@calm pewter Has your question been resolved?

[calm pewter]

<@&286206848099549185>

<@&286206848099549185> anyone?

[vivid current]

here

how can i help you

[arctic oriole]

First you need to calculate the volume of the juice given the position its already in at the start

Do you know how to do this?

[calm pewter]

so 20x6x10?

[calm pewter]

like this?

[arctic oriole]

That would be the volume of the carton itself

[calm pewter]

yh

[arctic oriole]

Remember the juice doesn’t actually fill the entire carton

we want the volume of the juice so you must account for the given depth

[calm pewter]

so 10x20x8?

[vivid current]

the box lies plain?

[arctic oriole]

The box originally lies on the 6x10 face

the height is the 20, we want to change that height for volume of the juice

[calm pewter]

waht do they mean by depth?

[arctic oriole]

Im not sure if they mean 20-8 or 8+0

Depth is usually measured top down

So I would assume it’s 12

[calm pewter]

depth

6x10x8 the amrk sheme says

[arctic oriole]

amrk?

[calm pewter]

mark

sry

[arctic oriole]

Well whatever, if we assume its 6x10x8 then its going to be 480

Does this make sense so far

[calm pewter]

no

[arctic oriole]

480 cm^2

[arctic oriole]

Which part is confusing you?

[calm pewter]

6x10x8

why dont we do

8x10x20

[arctic oriole]

Because the original orientation of the box is on the 6x10 face

The diagram shows this

[calm pewter]

is depth the height?

[arctic oriole]

Yes, I think so

[calm pewter]

yh

so

6x8x10

next

[arctic oriole]

Yes, but it depends on how they are measuring depth which they aren’t very clear on

[calm pewter]

yh

[arctic oriole]

It could be 20-8 (depth from the top of the carton) or 0+8 depth of the fluid itself

I would say just pick one and then if you’re wrong you’re justified to complain

[calm pewter]

yh isee

[arctic oriole]

I’d guess 8

[calm pewter]

les stick to this

[arctic oriole]

Sure

[calm pewter]

yh

[arctic oriole]

So its 480

[calm pewter]

whats the next step?

[arctic oriole]

Right, so when we turn the carton on its side, we expect the volume of juice to stay the same right? Just reorient itself with gravity?

[calm pewter]

yh

[arctic oriole]

Okay so we know the volume of juice when its in the original orientation must equal the volume of juice in the rotated orientation, this lets us setup an equation

[calm pewter]

how we set it up

[arctic oriole]

Recall that the original base of the carton (the bottom in the original orientation) is 6x10

[calm pewter]

yh

so 60

[arctic oriole]

Best to visualize it

This equation lets you solve for x

(The new depth)

[calm pewter]

yh ty

[arctic oriole]

does this make sense?

[calm pewter]

yh

[arctic oriole]

Alright, good. Any other questions?

[calm pewter]

no

now just solve for x?

[arctic oriole]

Yup!

[calm pewter]

so

x=4?

am i right

?

after this i have question abt some other topic

[arctic oriole]

Ye

Looks right to me

[arctic oriole]

Sure, what is it?

[calm pewter]

u know for this i have solved the inequality i got t is less then 5.5

the answer sheet says

the largest value is 5

i wrote 5.4

why is not 5.4

[crude kite]

Because is says t is a whole number

[arctic oriole]

Yeah

For part B

[crude kite]

5.4 is not a whole number

[calm pewter]

ohh

i see

[arctic oriole]

5.5 for A

[calm pewter]

it always the things like this tht get me in the exam

[arctic oriole]

5 for B

[calm pewter]

yh

[arctic oriole]

Yeah they get tricky

[calm pewter]

yh

anyway thx

.close

[amber wasp]

Channel closed

Closed by @calm pewter

Use .reopen if this was a mistake.

[amber wasp]

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.

[tacit apex]

Hello I have a logics question, it goes as follows:
Only Squares can have two or more Squares on their right side.
I constructed this sentance:
∀x: (∃a: (RightOf(a, x) ∧ Square(a) ∧ ∀b: (RightOf(b, x) ∧ Square(b) ∧ (a ≠ b))) ⇒ Square(x))
But it seems to be wrong for some reason?
I don't really see why and where

[tacit apex]

I started with abstracting it a bit
So considering only Squares can have this characteristic of having "two squares or more to the right", it has to be a subset of all squares

[grizzled pagoda]

Mephisto

[pseudo crescent]

sorry to interrupt you, but is this a typo?

did you mean exists there

[tacit apex]

is there a difference when defining "two or more"?

as in

[grizzled pagoda]

Mephisto

[tacit apex]

and

[grizzled pagoda]

Mephisto

[pseudo crescent]

This would be always false

[tacit apex]

what about

$\exists a: R(a) \land \forall b: R(b) \Rightarrow (a \not = b)$

[grizzled pagoda]

Mephisto

[pseudo crescent]

this one looks fine

[pseudo crescent]

This part says that if R(b), then a is different from b

[tacit apex]

yeah so if b is a square and is to the right of x (our original premise) it has to be a distinct square from a

[pseudo crescent]

which could be translated as not R(a)

[pseudo crescent]

thats not what we want

that would imply that a itself is not a square

[ebon cedar]

The formula does it for one square only I believe, and maybe because your quantifiers are all over the place

[pseudo crescent]

say that R(a) means "a is good"

[pseudo crescent]

then this translates to
"all good things are distinct from a"

therefore a can't be good thing

which is obviously not what we want

[tacit apex]

so it's a contradiction giving an empty set?

[pseudo crescent]

yeah, its a contradiction together with saying that R(a)

[tacit apex]

hm I see

[pseudo crescent]

Anyway we want 2 things:

1. existence of some a with R(a)
2. existence of some b with R(b) and b != a

[pseudo crescent]

This captures it well

[tacit apex]

I tried:
∀x: (∃a: (RightOf(a, x) ∧ Square(a) ∧ ∃b: (RightOf(b, x) ∧ Square(b) ∧ (a ≠ b))) ⇒ Square(x))
but it's still wrong :/

[pseudo crescent]

i need to count the parens, gimme a moment

[tacit apex]

We have access to LogicPalet through our university

when I run this sentance it generates this world as a counter example and proof that the statement is false

[pseudo crescent]

can you show me the proof?

[tacit apex]

idk if I it can generate a whole proof, it just generates an image for which the given statement still holds

[pseudo crescent]

oh, well

[tacit apex]

as a counter example

but it seems so confusing because how can there be triangle there if it's an implication

it's like the premise is correct, but the conclusion is false

hm maybe it's because I used an existential quantor for a and b?

[pseudo crescent]

Negation of this would be existence of object which satisfies the premise but isnt a square

[pseudo crescent]

Supposedly, its the triangle here

How exactly does RightOf work btw

[tacit apex]

RightOf(x,y) means x is to the right of y

hm I can just say not (Triangle(x) or Pentagon(x))

[pseudo crescent]

Would RightOf(x, x) be true

[tacit apex]

in the conclusion

[tacit apex]

ooh good question

[pseudo crescent]

Its the only thing that could fail here

[tacit apex]

ah okay in the description they say it's a non reflexive relation

[pseudo crescent]

Hmm weird

[tacit apex]

so I assume RightOf(x,x) would be false

hold on I'll try to generate a proof

I think it might be possible

Okay got it

Just had to name all elements

woops can't use a and b

x too...

🤦‍♂️

[pseudo crescent]

Wait can it name the objects here as well

[pseudo crescent]

Why do you have triangle there

[tacit apex]

in what part should I dig?

oh what

[pseudo crescent]

Verifying this please

[tacit apex]

yeah I copy pasted it from my application

ah I was executing the wrong one, my bad, I was testing something

here's the new proof

okay so

c and d are triangles

meaning Square(c) and Square(d) must be false

but the statement as a whole is true

so the premise must also be false

which should not be the case for c

[pseudo crescent]

It says its true? So it does workm

[tacit apex]

nono, the statement as a whole is true, i.e. there are no contradictions in it

[pseudo crescent]

Yeah

It works, no?

[tacit apex]

but it still doesn't generate a world where our original premise holds

"only squares can have two or more squares to the right of them"

[pseudo crescent]

Yeah, and we modeled exactly this statement

And it works just fine

[pseudo crescent]

It's true in this world

[tacit apex]

no, because a triangle has two squares to the right of it

[pseudo crescent]

Oh

[tacit apex]

which is true in our model

that's the issue

we get

∃a: (RightOf(a, c) ∧ Square(a) ∧ ∃b: (RightOf(b, c) ∧ Square(b) ∧ (a ≠ b))) ⇒ Square(c)
which is true. Why?

with c a triangle

considering the whole is true

[pseudo crescent]

Can you expand x=c?

[tacit apex]

and Square(c) is false

∃a: (RightOf(a, c) ∧ Square(a) ∧ ∃b: (RightOf(b, c) ∧ Square(b) ∧ (a ≠ b))) must also be false

[tacit apex]

yeah

I think it's a problem with the right of statement indeed...

considering RightOf(c,c) returns true

ohhh no wait

it returns true because both the premise and conclusion are false

essentially.... it's like our truth values are wrongly modelled

so putting a triangle on our premise side, should return true

meanig we should use implications again

[pseudo crescent]

oh wait

[tacit apex]

got something?

[pseudo crescent]

sorry, my dad called me so i was gone for a while

[tacit apex]

ah no worries

[pseudo crescent]

anyway, it seems like it interprets
∃a P -> Q
as ∃a (P -> Q)

if im not mistaken

and therefore an easy fix would be adding parens

[tacit apex]

not sure if I understand what you mean

[pseudo crescent]

fixed

i was just too lazy to find the ∃ symbol

∀x: ( ( ∃a: (RightOf(a, x) ∧ Square(a) ∧ ∃b: (RightOf(b, x) ∧ Square(b) ∧ (a ≠ b))) ) ⇒ Square(x))

added new parens

[tacit apex]

I'll try it out

OMG

[pseudo crescent]

did it work?

[tacit apex]

YES

OMG OFC

[pseudo crescent]

ahhhhhhhhhh

this hurts

[tacit apex]

it had to be a conjunction

[tacit apex]

yeah... it does

[pseudo crescent]

conventionally, ∃a P -> Q would be interpreted as (∃a P) -> Q not as ∃a (P -> Q)

[tacit apex]

yeah... otherwise ∃a (P -> Q) can be true for anything

that makes both P and Q false

[pseudo crescent]

yep

it's a different statemetn

what surprises me is that the software interpreted it like that

against the convention

the convention is that quantifiers have higher precedence

but the software decided to ignore it for some reason

[tacit apex]

yeah that's why I did what I did

I was following the conventions

[pseudo crescent]

It's like if calculator interpreted 5*3 + 4 as 5 * (3 + 4)

that's pretty wrong

[tacit apex]

yeah

I mean

I always use parenthesis after a quantifier

maybe they were just misplaced?

∀x: (∃a: (RightOf(a, x) ∧ Square(a) ∧ ∃b: (RightOf(b, x) ∧ Square(b) ∧ (a ≠ b))) ⇒ Square(x))

[pseudo crescent]

This is just
∃a: (P(x)) ⇒ Square(x)

it's correct and me and any sane person would interpret it as (∃a: (P(x))) ⇒ Square(x)

but LogicPalet decided to be illogical and interpret it as ∃a: (P(x) ⇒ Square(x))

[tacit apex]

I must say I was very confused

[pseudo crescent]

same

[tacit apex]

I always use sets to make sense of questions like these

so it's almost impossible to make errors

and my sketches were perfect

[amber wasp]

@tacit apex Has your question been resolved?

Channel closed

Closed by @tacit apex

Use .reopen if this was a mistake.

[tacit apex]

thank you

[amber wasp]

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.

[pulsar frost]

Hi

[pulsar frost]

#help i am having trouble to solve no 14

#help-41

@amber wasp help

[amber wasp]

@pulsar frost Has your question been resolved?

[pulsar frost]

Nope

[crisp stratus]

react to bot's message with "❌"

[amber wasp]

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

[pulsar frost]

Thankyou

[pulsar frost]

❌

[stray steeple]

bro . give a react

choose the option ❌

[pulsar frost]

Wdym?

[crisp stratus]

click on that

[pulsar frost]

Okay

Thanks to both of you

[crisp stratus]

you have that AB is shared between those two triangles

notice that angle CAB = angle CBA

thus angle DAB = angle EBA

[pulsar frost]

Okay

And then

?

[crisp stratus]

you have side and angle, so you need to either find another shared angle or side

[crisp stratus]

what have you tried?

[pulsar frost]

Hold on a minute

[pulsar frost]

Forgive my handwriting but is this going in the right direction

[pulsar frost]

@crisp stratus please speak something

[amber wasp]

@pulsar frost Has your question been resolved?

[pulsar frost]

.close

[amber wasp]

Channel closed

Closed by @pulsar frost

Use .reopen if this was a mistake.

[amber wasp]

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.

[ornate iron]

What is the answer to this question?

[amber wasp]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[ornate iron]

<@&286206848099549185>

[crisp stratus]

hint

f''(x) is positive

[ornate iron]

i am still unable to think of anything

could u pls help me

<@&286206848099549185>

[crisp stratus]

don't ping helpers several times

[ornate iron]

sorry i am new here

[crisp stratus]

i can try

[ornate iron]

wont do it now

help me pls

.close

[amber wasp]

Channel closed

Closed by @ornate iron

Use .reopen if this was a mistake.

[crisp stratus]

.reopen

[amber wasp]

✅

[crisp stratus]

nevermind it isn't always positive

but i think if it is then you can get the maximum

or actually nah

idk :(

.close

[amber wasp]

Channel closed

Closed by @crisp stratus

Use .reopen if this was a mistake.

[ornate iron]

ths for trying tho

[amber wasp]

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.

[soft comet]

Sin ^12?

[soft comet]

Literally no other condition is given on A B and C

Nvm I'll try it myself

.close

[amber wasp]

Channel closed

Closed by @soft comet

Use .reopen if this was a mistake.

[amber wasp]

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.

[shy moss]

Calculate $\frac{\partial f}{\partial x_k}, k = 1,2,3$ for the functions $(x=(x_1,x_2,x_3)) \ a) f(x) = \ln|x_1x_2+x_2x_3+x_3x_1|$

[grizzled pagoda]

Merineth 🇸🇪

[shy moss]

I'm not sure i understand this correctly

I want to find the partial derivative for first x_1 ?

[keen pawn]

yes, you first want to find the partial derivative wrt x_1

[shy moss]

$\frac{\partial f}{\partial x_1} = \frac{x_2+x_3}{x_1x_2+x_2x_3+x_3x_1}$

[grizzled pagoda]

Merineth 🇸🇪

[shy moss]

Seems right?

ye

.close

[amber wasp]

Channel closed

Closed by @shy moss

Use .reopen if this was a mistake.