help-49

[frail coral]

r u guys tying to solve it?

[pearl hull]

We’re awaiting you to make the first move

[frail coral]

bruh i have no idea what im doing

[pearl hull]

Let’s apply this, do you have any idea about what we are talking about?

Coordinate geometry

[frail coral]

bruh im cooked

[pearl hull]

Why?

[frail coral]

idk how to solve

ima try draw to scale lol

and see what happens

[pearl hull]

Not really a big deal given that I haven’t forsaken you 👍

[unborn oracle]

Ok, so you can lay coordinate system into the picture and then make some linear equations for the two lines. We’ll see from there

[onyx elm]

$\left [\frac{32}{7}+1,0+1\right]$

[grand pond]

fsuahiacsf

[midnight plank]

@frail coral Has your question been resolved?

[frail coral]

no

[fleet axle]

that doesn't mean no trig

[mystic condor]

But how can you use trig here

[fleet axle]

that is the intersection?

[fleet axle]

it doesn't mean you have to use trig, but, if you set up an (x, y) coordinate system

that would involve trig

i guess depending on how you do it

[humble gazelle]

I just divided the thing with a horizontal line

I think I found the solution

Wait a sec

[mystic condor]

Thats just like pythagoras and stuff theres no sin cos tan or anything

[fleet axle]

there are always multiple ways to do things

[fleet axle]

trig can be equivalent to that

like pythagoras' theorem is the same as sin^2 + cos^2 = 1

there are just different ways to do it, you definitely don't have to use trig

someone might prefer to define angles and use trig to get them

[humble gazelle]

I kind of checked to see if the calculations were right but I'm just going to go through it again and hopefully put a nicer image

[pearl hull]

,rccw

[fleet axle]

nice

[frail coral]

is it 522?

one of my friends got 538

[humble gazelle]

I mean, I got 522 but how did your friend do it?

I don't trust my arithmetic these days

[fleet axle]

ah splitting the diamonds into two triangles is a great idea

[humble gazelle]

Dang

This is why I usually don't put stuff in coordinates

It usually works though

[frail coral]

which answer is correct do yk?

[humble gazelle]

I think the B should be (45, 23) rather than (45, 33)

Because the side length is 45 and 45-22=23

[fleet axle]

45 - 22

i agree

[frail coral]

so urs is correct?

[fleet axle]

i trust impendingdoom more

since the image from your friend has an error for the coordinate of point B

but that's up to your own judgment

and impendingdoom doesn't trust himself

it's tough to trust yourself in math tho

[frail coral]

in the other photo it adds 23

[humble gazelle]

I was trying out the coordinates like your friend suggested but I can double check mine. I think the method I used should work though, since triangle area and ratios work pretty reliably for me in parallelograms

[frail coral]

ok

[fleet axle]

that is a good point

ideally you could check it yourself shatgpt

if you understand the method

[frail coral]

nah im lost

[fleet axle]

the area is made up of 4 triangles, you just need to find a base and height for each of them

and add up their areas (1/2 * base * height)

[fleet axle]

impendingdoom drew the triangles

[frail coral]

yeah

idk tbh

[fleet axle]

for example, 8 and 6 can be the bases of the bottom left triangles

,w y - 8 = (45 - 22 - 8)/45 x, y = 45/(45 - 4 - 6)(x - 6), solve for x, y

[grand pond]

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[fleet axle]

is this what we got for the point of intersection?

[frail coral]

thats what i got

[fleet axle]

ok cool

so then the two bottom triangles on the left, for example

one has a base of 8 and a "height" of 33/2

the other has a base of 6 and a height of 27/2

[frail coral]

yeah

[fleet axle]

,w 1/2(833/2 + 627/2 + 4*(45 - 27/2) + 22*(45 - 33/2))

[grand pond]

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[frail coral]

thats what i got

[fleet axle]

i think it's right

[frail coral]

same idk how it can be wronf

[fleet axle]

who said it's wrong

[frail coral]

the other guy got smth else

he got 522 remember

[fleet axle]

yeah but he wasnt sure of the algebra ig

[frail coral]

yeah

[fleet axle]

i think i trust our answer, at least i can't find anything wrong with it

[frail coral]

yeah same

well ty for ur help

[vocal escarp]

j

[lyric charm]

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[jade magnet]

i dont get the first question

[jade magnet]

so N is not just 3(3(3(3n+1)+1)+1)+1?

[lyric charm]

3n+1 becomes 2m

[jade magnet]

is it not 3m+1 becomes 2n? not that way round

idk if it would make sense for 8n to be 81m + 65 if 3n is 2m - 1

actually maybe i should start with what arthur does first

so arthur took (N-1)/3 bananas right

but since at the start they had N bananas so 3N/3 bananas

there should be [3N-(N-1)]/3 bananas left

so (2N+1)/3 bananas

but the orangutan took one so it's - 1 which is -3/3

so (2N+1-3)/3 so (2N-2)/3 bananas

and then did brenda take (2N-2-1)/9 bananas?

[lyric charm]

was a bit fast and loose with the letters and typoed sorry

i meant that 3n+1 turns into 2n at each step

[jade magnet]

dw it happens n and m are right next to each other on a keyboard anyway

[jade magnet]

ok yeah

i think what i shouldve done is not tried to work backwards here

[jade magnet]

well hopefully this is right at least after arthur sleeps

[lyric charm]

im gonna try and repro this once im home

[jade magnet]

aight

[humble gazelle]

I got something like this

[jade magnet]

hmm

yeah i shouldve done that

i got 8N = 81m + 57 just now 😭

[humble gazelle]

I'm just not sure how to prove the second part

Do you think this is okay?

[midnight plank]

@jade magnet Has your question been resolved?

[midnight plank]

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[steel cedar]

1.40

[steel cedar]

If it's an open interval

We can't use similar methods right? Since there is a possibility that sup(A) = an for some n. In which case the supremum isn't an element of the interval

[supple pilot]

If the an sequence becomes constant after some point then it can happen

Also the theorem is not true for open intervals, take (0, 1/n) sequence of intervals
They are obviously nested, 0 doesn't belong to any of them and no positive number belongs to all of them

[dreamy lichen]

I dont see how sup(A) = an would be related

but yeah, its not true for open intervals

[scarlet cave]

Did you end up reading all this?

[supple pilot]

I think the proof the book suggests is taking supremum of A as the constructed common element

[jade magnet]

yeah i did

[supple pilot]

Since supremum is smallest upper bound it is contained in every interval then

[dreamy lichen]

oh, yeah, thats quite probable

[scarlet cave]

gj I wouldn't have the courage to read all that

English is one of my biggest fears

[steel cedar]

Wait so nested interval property only applies to closed intervals?

What about things like (a,b]?

[dreamy lichen]

Yes, later youll learn about a generalized version which states that it applies to all compact sets

[steel cedar]

Or [a,b)

[dreamy lichen]

still doesnt work

(0, 1/n]

[supple pilot]

same counterexample i made but with (0, 1/n] or [-1/n, 0)

[dreamy lichen]

[(n-1)/n, 1)

[steel cedar]

I see

[dreamy lichen]

if you need to apply it on open intervals, try to choose some closed intervals which are subset of the open ones

im pretty sure it only fails on open intervals when one of the bounds is eventually constant

[steel cedar]

Why did you say sup(A) = an isn't related? Is there any proof that doesn't use supremum? (Or inf)

[dreamy lichen]

i just wasnt sure how its related, now i see it

but yes, there are several other proofs. It depends on what your main property defining reals is

[steel cedar]

oh okay, i just thought the proof in my book is a nonstandard

[dreamy lichen]

if its the existence of supremum, then the standard proof uses that

it can actually be proved that NIP and LUB property are equivalent

and there are several other equivalent properties / statements

[steel cedar]

yeah next section literally says nested interval property and completeness is equivalent

[dreamy lichen]

Yeah, so therefore if your fundation is completeness, you'll certainly have to use it within the proof

or at least use sth derived from completeness

[steel cedar]

the reason we can't just say a + b / 2 is an element of the interval is because we haven't proven that reals are closed under division or what?

[dreamy lichen]

whats a and whats b?

[steel cedar]

Oh yea, a is left end and b is right end

[dreamy lichen]

bounds of what interval specifically?

the first interval, the second, the thousandth?

[steel cedar]

nth?

[dreamy lichen]

yes, (an + bn) / 2 belongs to nth interval

but does it necessarily belong to all the intervals?

Is it a common element of all of them?

[steel cedar]

But it's a common element to I1, I2,... I n-1 isn't it?

[dreamy lichen]

Yes

but what about I_n+1?

[steel cedar]

Shi

[dreamy lichen]

thats why it doesnt help a lot

you'd have to take the limit (existence of which is again equivalent to LUB property)

and you'd also have to prove that the limit is indeed contained within all the intervals

[steel cedar]

okay one last question, can you always find such closed?

[dreamy lichen]

not always

(0, 1/n) is an example of that

you could start with sth like [1/4, 3/4] for n = 1

but then you'd have to push the right bound to the left

and the left bound to the left as well - but that would violate nestedness

[steel cedar]

(0,1/n) sure is a strong counterexample

That's it ig

Thanks all!

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[glad egret]

true

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[gray pumice]

What's the actual definition of a function, in terms of properties of a relation?
I've found (on various lecture slides, websites and such) all the following:

• A function is a right-unique and total relation
• A function is a right-unique and left-total relation
• A function is a right-unique relation
• A function is a left-unique and left-total relation (this one seems obviously wrong? f(x)=x² over reals is a counterexample, and obviously a function)

And at this point I'm so confused that I'm not sure I remember what a function should be.

Each value on the left must only occur at most once, so I'm going to go with "it's definitely right-unique", which is why we generally define the square root over reals as "only the positive solution". Do we generally assume that functions must be any kind of total at all?

[lyric charm]

a function needs to be total on the left in the sense that f(x) must be a thing for every x in its domain

this requirement is quite frequently flaunted in highschool however

where questions of the "find the domain of f(x) = 1/(x^2-1)" variety abound, despite being technically incorrect in terminology

right-totality has a different name when you talk about functions: we call it surjectivity

and left-uniqueness is called injectivity

(unless i am mixing up my left and right)

[gray pumice]

yes, and a right-unique relation is called functional and a left-total one is called serial

[runic hamlet]

who even remembers all those terms for relations

[gray pumice]

I don't

which is why I had to check, because I'm trying to explain this to someone else

[runic hamlet]

well dont explain it with those words

[gray pumice]

Meaning that f : R -> R f(x)=x² is not a function, but f : [0,infinity) -> R f(x) =x² is?

[runic hamlet]

no one can remember them anyway

[carmine sigil]

A function is any functional relation, using your definition above. (Right-unique)

[lyric charm]

f : R -> R f(x)=x² is not a function
whys it not a function

[gray pumice]

well, they need to know it in those terms for an exam once, then go on to forget it afterwards

been there, done that

[lyric charm]

if you're framing it in relational terms

the graph of f is the set {(x,y) ∈ R^2 : y = x^2}

[gray pumice]

I meant sqrt(x), not x²

[lyric charm]

buh

that kinda changes absolutely fucking everything

[gray pumice]

It really sort of does

[lyric charm]

then yes you cant declare f(x) = sqrt(x) with domain R

but domain [0, +∞) makes it ok

[gray pumice]

well I could... it's just no longer a function

[carmine sigil]

It's a partial function

[gray pumice]

So... "A function is a right-unique and left-total relation."?

[lyric charm]

a function is a trio of two sets and that between them

[carmine sigil]

You can have a non-left-total relation model a function on a reduced domain

[gray pumice]

I mean yes, but at that point the relation itself, when viewed as a whole, is not a function

[carmine sigil]

Well, where is the domain of the relation written exactly?

[gray pumice]

presumably in its definition, I would hope?

at least in cases where anyone might care about the domain

[carmine sigil]

So a relation can be modeled as a set of ordered pairs plus some extra information about the ordered pairs

[gray pumice]

do you even need extra information?

[carmine sigil]

Yes

[gray pumice]

Isn't a relation from A to B just a subset of AxB?

[carmine sigil]

That's the thing, how could you tell that the members of R are from AxB and not CxB where C is a superset of A?

[gray pumice]

ah, that's what you meant by extra information

yeah, so a relation is a pair of domain and codomain and then a subset of their cartesian product

which I guess you could view as a 3-tuple

[carmine sigil]

So if I am given a relation without information about the domain and codomain, I can verify that a function might exist by verifying right uniqueness, but I can't verify left totality. But what I can say is that there exists some function for a choice of domain and codomain that agrees with this relation.

[gray pumice]

okay, but if explicitly given a domain and codomain, then it has to be right-unique and left-total, or is otherwise not technically a function?

[carmine sigil]

Sure, if it's right unique and not left total you can say it's a partial function to be specific

But saying "f(x) = √x is not a function" risks being misunderstood.

[lyric charm]

which is exactly what i said

[gray pumice]

f(x)=sqrt(x) is a function, because we'd implicitly assume that it means
f : [0,infty)->[0,infty), f(x)=sqrt(x) or similar

[lyric charm]

a function is a trio of two sets and [that] between them
                ^^^^

[lyric charm]

a formula can have a function inferred from it

but formulas are not by themselves functions

[gray pumice]

but f : R -> R, f(x)=sqrt(x) is not a function

[gray pumice]

well yes, but when someone for some reason isn't explicit about domain and codomain, then this notation would generally make me assume "they mean a function".

And if they meant something mapping from quaternions to negative integers only, they should've specified.

[lyric charm]

yeah but your student(?) is taking a discrete math exam

so they need to be pedantic about it

[carmine sigil]

We can infer, but what if I intended the codomain to be (-5,∞)? What if I intended the domain to be (8,10) ∪ ℕ?

These are also valid choices

[gray pumice]

true

not what's generally implied with this notation, but technically possible

Anyways, I think this answered the question.
Thanks for your help!

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[graceful ferry]

Find for which values of p f(x,y) is differentiable on 0

[graceful ferry]

What am I doing wrong?

[graceful ferry]

P<-1/2*

[midnight plank]

@graceful ferry Has your question been resolved?

[steel crest]

how do you know you're wrong first of all

[graceful ferry]

Because that answer isn't in the options

But I found it out already thx tho

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[unkempt skiff]

If i have smth like lim x-> inf (x^2-x) is that indeterminate? Cuz it’s inf - inf right? Or does it = inf?

[austere blade]

it is indeterminate

[unkempt skiff]

rlly

[olive matrix]

it is an indeterminate form, but that's not the end of the problem

[unkempt skiff]

huh

[olive matrix]

indeterminate forms can (often/usually) be reduced to something more manageable

[unkempt skiff]

i need help W this, i have to use lhopitals but idk how, so far i simplified it by multiplying it by the conjugate, but that leaves me with a numerator of x^2-x which is indeterminate. Idk how to get it to a form where i can use lhopitals

[unkempt skiff]

How

[olive matrix]

well in this case you could factor it to x(x - 1)

and get inf * inf which is infinity

[unkempt skiff]

Cancel out the x?

I did that

[olive matrix]

not sure how you'd cancel anything

[unkempt skiff]

And ended up not having to use lhopitals at all

[olive matrix]

oh sure yeah that works

[unkempt skiff]

But i need to use lhopitals 😔

[unkempt skiff]

do yk how 😭

[olive matrix]

well you could not cancel the x

then you'd have something that goes to infinity on top and bottom

but like. that seems silly

and like a pain

[austere blade]

does the question say you need to use lhopitals?

[unkempt skiff]

yeah

Ngl this question is silly

when it could literally be solved without 🏥

[unkempt skiff]

yea for some reason

[austere blade]

they just want to torture you then

[unkempt skiff]

I LITERALKY tried everything 😭

[eternal pawn]

so many questions can be done without l'hopital though

[unkempt skiff]

😭

[unkempt skiff]

oh

Does anyone know how i can manipulate it into a form where lhopitals can be used

😭 💀

[vernal zenith]

technically you can use it whenever you have a fraction

[austere blade]

hailey said you don't cancel the x

[unkempt skiff]

?

I thought it has to be 0/0 or inf/inf

[unkempt skiff]

o

[austere blade]

No, i'm pretty sure you can only use the rule if you get an indeterminate form like 0/0 and inf/inf

[vernal zenith]

o yeah true

[unkempt skiff]

yea ok lemme try that

wait

is inf * inf indeterminate

It’s inf right

[eternal pawn]

yes

[austere blade]

yeah

[eternal pawn]

I guess the point of this limit was to get used to l'hopital which is great... but imo it's unnecessary and can make you learn bad habits

[austere blade]

yeah

[unkempt skiff]

Bruh

What is this

[austere blade]

I think they just wanted them to practice the differentiation aspect

[unkempt skiff]

Did i do it wrong

[unkempt skiff]

😭

[eternal pawn]

you forgot x

in the denominator

[unkempt skiff]

Where

Oop

💀

uhhhhhhhhhhh

did i do it right

so i can cancel out another infinity

[eternal pawn]

yes

[austere blade]

yeah

[austere blade]

no

[unkempt skiff]

huh

oh

mb it’s inf * inf

[austere blade]

it still ends up as indeterminate lol

[eternal pawn]

so I'm not sure what they expect you to do, but you could cancel x, then denominator goes to 1

but then, why not do it from the start lol

what this limit DOES teach is that l'hopital has its flaws

[unkempt skiff]

what

[unkempt skiff]

💀

Whattt

Did i do it wrong

[unkempt skiff]

so like

am I stuck in a loop

or like

[austere blade]

i'm not sure what you did there

did you do lhopitals twice?

[unkempt skiff]

huh

[unkempt skiff]

so we were here right

so like

I took

Derivative of this again

Is it not right

[eternal pawn]

but it's not inf/inf

[unkempt skiff]

W HAT

[eternal pawn]

denominator goes to 1

[unkempt skiff]

How

[eternal pawn]

second term goes to 0

and first goes to 1

[unkempt skiff]

inf/inf?

like 1

[rich mirage]

Try factoring out x?

[austere blade]

inf/inf isn't cancelled to 1 if that's what you are asking

[austere blade]

They did but the question wants them to use lhopitals

[rich mirage]

Oh gatekeepers smh

[eternal pawn]

$\frac{x}{\sqrt{x^2+1}} = \frac{1}{\sqrt{1+\frac{1}{x^2}}}$

[grand pond]

bloubbloub

[austere blade]

yeah as x approaches to infinity, 1/(x^2) will approach to 0

[eternal pawn]

btw you didn't even have to multiply by the conjugate if you factored x from the start

maybe it's what mistav meant

[midnight plank]

@unkempt skiff Has your question been resolved?

[balmy oar]

H

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[unkempt skiff]

Huh

[unkempt skiff]

How

wait im kinda confused

so i was here

and someone said inf/inf DOESNT simplify to 1?

[silent zodiac]

Yes

Inf/inf is not 1

[austere blade]

it doesn't cancel to 1 yeah

[silent zodiac]

its indeterminate

[austere blade]

I see you're still getting tortured by the problem @unkempt skiff

[unkempt skiff]

yea

[unkempt skiff]

okay

sorry so like

[unkempt skiff]

Are any of these steps unnecessary

[twilit jetty]

are you still trying to find $\lim_{x\to\infty}\sqrt{x^2+1}-\sqrt{x+1}$?

[grand pond]

mtt

[unkempt skiff]

yes did you see me from before

[austere blade]

the question apparently wants them to use lhopital rule

[twilit jetty]

no, I scrolled up

thats stupid

you can do this in one step by factoring out an x

[unkempt skiff]

exactly

[austere blade]

exactly

[unkempt skiff]

😔

[twilit jetty]

well if youre stuck using l'hopital, we have to find an easy cheese use for it

[unkempt skiff]

my prof wants us to practice 🏥 i guess

[twilit jetty]

how about you multiply it by x/x then use l'hopital on that or something

[unkempt skiff]

how

[unkempt skiff]

From the beginning?

[twilit jetty]

just anywhere, so you get 1/1 and then youve technically used l'hopital

[unkempt skiff]

what

huh

[eternal pawn]

$$\sqrt{x^2+1} - \sqrt{x+1} = x \left(\sqrt{1 + \frac{1}{x^2}} - \sqrt{\frac{1}{x} + \frac{1}{x^2}}\right)$$

now we have
$$x \longrightarrow +\infty$$
$$ \sqrt{1 + \frac{1}{x^2}} \longrightarrow 1$$
$$ \sqrt{\frac{1}{x} + \frac{1}{x^2}} \longrightarrow 0$$

so the whole thing is $+\infty \times 1 = +\infty$

[grand pond]

bloubbloub

[twilit jetty]

you can pretend to use l'hopital by multiplying by $\lim_{x\to\infty}\frac xx$

[silent zodiac]

When u take out the x

[grand pond]

mtt

[silent zodiac]

It comes as

[unkempt skiff]

huh I can’t do that tho 😭

[silent zodiac]

|x|

[twilit jetty]

then use l'hopital on this to get $\lim_{x\to\infty}\frac11=1$

[eternal pawn]

ok sure

[grand pond]

mtt

[silent zodiac]

U cant take it out like x

[unkempt skiff]

😭

uhhhhhhh

[twilit jetty]

thats a cheese use of l'hopital so you can then just factor the x out like a normal person and move on with your day

[eternal pawn]

the whole thing is positive though so no big deal

[unkempt skiff]

I hate |x|

[unkempt skiff]

idt I can do that tho

plus

I would never have thought of that anyway

☠️

[austere blade]

you thought of the better method which is to factor out the x at least

[twilit jetty]

none of this is reading as a obvious joke to you, alr

[unkempt skiff]

help

😭

forgive

[unkempt skiff]

after rationalizing?

[austere blade]

No like when you first posted the question

like way back

[unkempt skiff]

oh

lmao

yea cuz THATS what id do before I learnt abt lhopitals

[twilit jetty]

the problem with l'hopital is you need an indeterminate form, but this question diverges so theres no indeterminate form to be found here

[austere blade]

yeah

[eternal pawn]

yes and please continue to do so

[unkempt skiff]

But anyway can someone explain this again this confuses me since there’s an indeterminate form

[twilit jetty]

how about you ask your professor about this

[unkempt skiff]

um

[unkempt skiff]

🤓

I might be a tad late

[silent zodiac]

Bro skipped limits first class

[unkempt skiff]

i will if it DIDNT say to use lhopitals but 🙇

[twilit jetty]

"it" says to use it?

[eternal pawn]

sure

[unkempt skiff]

was lhopitals taught at the beginning for u guys?

[twilit jetty]

go screenshot the source you found this problem

[unkempt skiff]

my assignment yes.

[austere blade]

I never learned it actually

[silent zodiac]

No

[unkempt skiff]

it’s lit a doc typed by my prof

[silent zodiac]

U start with the basics

[unkempt skiff]

one sec

[unkempt skiff]

what

[twilit field]

same, I may cover it in RA, but never did in calc

[unkempt skiff]

?

[austere blade]

Different education systems

[austere blade]

Same with me

[unkempt skiff]

O

[silent zodiac]

Also i just use expansions and taylor series and sandwhich for the most part

[unkempt skiff]

whats ra

[silent zodiac]

[austere blade]

real analysis

[twilit jetty]

they teach you taylor series but they dont teach you l'hopital

that sucks

[twilit jetty]

l'hopital is the easiest way to let students abuse taylor series to immediately solve a problem

[silent zodiac]

No i know l hospital well

[twilit jetty]

ah fuck its right up there in the image

[austere blade]

it's a more rigourous version of calculus

[twilit jetty]

we are so screwed

[unkempt skiff]

Yep

[eternal pawn]

why not use taylor then? it's not long anyways

[twilit jetty]

I forgot

[silent zodiac]

Me stopping every nerve in my body to not use series expansions :-

[austere blade]

just erase the word l'hoptial rule with your pen

[twilit jetty]

you dont have to introduce taylor series to abuse its power, when you d/dx the top and bottom youre really moving on to the next term in the taylor series to compare

[twilit field]

Bernouilli's theorm may work
gives you x^2-√x

[silent zodiac]

Is the answer not just 0?

[twilit jetty]

as a reminder, the answer is infinity

[silent zodiac]

Oh

[austere blade]

it's infinity

[silent zodiac]

yea

[twilit jetty]

the simplest approach as we've all found is to factor an x out

[austere blade]

it diverges

[twilit jetty]

this is because the first term is degree 1 essentially, and the second term is degree 1/2 essentially

1 > 1/2

[twilit field]

a friendly reminder that (1+x)^n≥1+nx

[twilit jetty]

which gives us the idea that it ought to diverge and then to do a cheesing strat like this

[eternal pawn]

yeah, it amounts to the same thing, but taylor is more general, especially in cases where you need to do some shit before getting to 0/0 form + it gives more intuition imo

[unkempt skiff]

clearly wants to cook us

[silent zodiac]

Lets gooo

L hospital is the biggest scam there is

[eternal pawn]

me on my crusade against l'hopital

[silent zodiac]

All my homies use taylor series 🗣️🗣️

Me when the denominator is 7 degree polynomial and my professor asked me to use l hospital:-

[twilit jetty]

this seems like a shaky reason to use this

its more of that (1 + x)^n ~ 1 + nx

instead of >=, since then youre attempting to bound the limit in one direction and then the other which doesnt work

[twilit field]

I made a mistake, yeah

[unkempt skiff]

my wifi is ending me

[unkempt skiff]

send me to the hospital atp

😭

[unkempt skiff]

?

whats *is for

can someone pls actually save me from this

how do i use lhopitals bruhhhhhhhhhhhhhh

with what i have rn

was I getting any closer

え

e

the connection is finally back

[unkempt skiff]

is there any way out of this

[eternal pawn]

Yo

Take the exp

[unkempt skiff]

what exp

[eternal pawn]

Nvm what was I cooking

[unkempt skiff]

nah u good

this question hurts me

I’ve been stuck on it for 5 days

cuz idk how im supposed to use lhopitals

when you don’t need it at all 🤓

[twilit jetty]

@unkempt skiff heres a potential approach

[eternal pawn]

Maybe you divide by sqrt x+1

[eternal pawn]

Then you square the fraction

[twilit jetty]

you multiply by x/x
then this time the fraction on the right is indeterminate, so you use l'hopital
then simplify by dividing the left fraction by x/x
this is enough to plug in infinity and get infinity as a result

[eternal pawn]

Like $\frac{\sqrt{x^2+1} - \sqrt{x+1}}{\sqrt{x+1}} = \frac{\sqrt{x^2+1}}{\sqrt{x+1}}-1$

[grand pond]

bloubbloub

[eternal pawn]

Nvm

I am truly smoking smth

Nvm x2: you square the first term and find its limit using l'hopital, which show that this goes to infinity, then note that the original limit is this times sqrt x+1 which also goes to infinity

[silent zodiac]

The living urge to just ignore those 1s

[twilit jetty]

this may not have a formal reason to work, since to focus on a specific aspect of a limit you have to evaluate all other parts of it

that being said I also like that, it should work:

your professor likely wouldnt like it

[eternal pawn]

It works because i am saying that sqrt x+1 = o(sqrt x^2+1) therefore the difference goes to infinity

But again this is just an exercise in "who can get around the rules the best"

[eternal pawn]

Am i smoking again

[unkempt skiff]

no,dip

hold up*

[unkempt skiff]

Isn’t this inf - inf

How can i use lhopitals when that is there 😭

[eternal pawn]

Lmaooo

[unkempt skiff]

😭

[unkempt skiff]

Am i smoking smth too

My e i am

Maybe

This question is so cooked

i asked my classmate and someone told me :
multiply by conjugate and you get inf/inf

??

[unkempt skiff]

Lhopitals wasn’t used right

[lapis lynx]

I would solve this by taking an $x^2$ out of the first square root and $\sqrt{x}$ out of the second one. Then factor a $\sqrt{x}$ out of the expression and plug in infinity to get that it diverges

[grand pond]

cytos

[unkempt skiff]

i have to use lhopitals tho

it’s a must

[lapis lynx]

[unkempt skiff]

☹️

[lapis lynx]

teachers always stifling creativity nowadays

[unkempt skiff]

yea

someone should just send make to the hospital instead

😔

ok can i verify again

[twilit jetty]

alr this should work

theres a typo in there

alr here we go

[unkempt skiff]

does inf^2-inf really not give you inf

is it truly indeterminate

cuz if it gives me infinity no other problems would exist

Oop

[twilit jetty]

cat, your image is outdated

[lapis lynx]

do this and rewrite it as $\frac{\sqrt{1+\frac{1}{x^2}}-\sqrt{1+\frac{1}{x}}}{x^{-\frac{1}{2}}$

[unkempt skiff]

yep i figured mb

[lapis lynx]

Fuck

[twilit jetty]

if youre stuck typing it up, use desmos to type it then copy-paste it here

[unkempt skiff]

Wait this is allowed?

[twilit jetty]

desmos by default has its expressions be latex

[twilit jetty]

its the same problem as over here, and the answer is "Im not sure"

[unkempt skiff]

😔

[twilit jetty]

there doesnt seem to be an easy way out of this

[unkempt skiff]

ts pmo

💔

[twilit jetty]

pmo?

[unkempt skiff]

yes

[twilit jetty]

had to google that

[unkempt skiff]

🙀

[twilit jetty]

yikes

[unkempt skiff]

what the hell

[twilit jetty]

jk

[unkempt skiff]

uh

are you by any chance

a millennial

🙏

[twilit jetty]

dont do this to me

[lapis lynx]

just do this but move the sqrt(x) that you factor out into the denominator as x^(-1/2) then use L’Hôpital’s

[unkempt skiff]

Hey are you secretly a prof

Millennial prof

jk

bro

my wifi

HELPP

hello

[unkempt skiff]

what

i can randomly move it to the denom?

[twilit jetty]

3 = 1/(1/3)

[bold beacon]

what is your question?

[twilit jetty]

it works

following your steps, youre doing this

[lapis lynx]

yes if you invert it

[twilit jetty]

Im going to add, this is doing in 3 steps what couldve been done in two

[unkempt skiff]

must use lhpotals

[bold beacon]

The image earlier that you posted. mtt has used l'hopital rule

[twilit jetty]

however, this limit is infinity / 0 and so we cant use l'hopital on it

[unkempt skiff]

THATS a kit of roots

[twilit jetty]

it was not used correctly

[unkempt skiff]

?

Where

[twilit jetty]

so it wasnt allowed

[unkempt skiff]

Can u reply to their pic

Oh yea

ok guys

can we take a break from this

it hurts me

[twilit jetty]

yea you would lol

we're actually very close here

[unkempt skiff]

i actually have another question

[unkempt skiff]

really

[twilit jetty]

cat you still need to go through this one

its not going to answer itself

[unkempt skiff]

i feel like close yet far

[twilit jetty]

think of it this way

so far we just need an infinity / infinity

[lapis lynx]

oh yeah this question is goofy since you shouldn’t been be using L’Hôpital’s for it

[unkempt skiff]

im waiting for l hospital

[twilit jetty]

however the fact that the top infinity has more power than the bottom one we can hide

as long as we see infinity / infinity

[unkempt skiff]

exactly

[unkempt skiff]

ok

ok wait

no one responded to my quesiton from before

Are y’all SURE

that

inf^2- inf

is INDETERMINATE

[twilit jetty]

by itself it is

itd be infinity - infinity

but it heavily suggests a method which would quickly not make it indeterminate

in either case, its not infinity by itself which is what we need

[unkempt skiff]

not inf??.”

?

Huh

nahh my wifi

[unkempt skiff]

can yiu show me how

maybe we can get it to infinity

[twilit jetty]

oh here we go

[unkempt skiff]

so we get inf / inf after rationalizing

[twilit jetty]

the infinity we were talking about was x^2 - x

factor an x out, then its x(x - 1)

infinity * (infinity - 1) = infinity^2 = infinity

[unkempt skiff]

WHAT

WAIT

[twilit jetty]

since l'hopital is being used on the whole thing instead of a part of it, we should be fine

[unkempt skiff]

aren’t we done then…?

[twilit jetty]

this has to be it

[austere blade]

I feel like this has been going on for a long time and maybe you should just skip the question and ask your professor @twilit jetty

[twilit jetty]

yep

[unkempt skiff]

it’s due

[twilit jetty]

how can you say that when we've just finished

[unkempt skiff]

like

t e

Tmr

Haha

[austere blade]

oh

nvm

[unkempt skiff]

it’s already 8

pm

[austere blade]

ignore what I said

[unkempt skiff]

bro mtt

ty

[twilit jetty]

np

[unkempt skiff]

saviour

[twilit jetty]

the key here is that for infinity / infinity, we cant have infinity - infinity

[unkempt skiff]

my saviirurrrrrr

[twilit jetty]

so rationalizing it gets rid of that, mostly

from there, you can do l'hopital

[unkempt skiff]

my saviirurrrrrr

[unkempt skiff]

ok so whenever we have inf-inf it’s always indeterminate then?

[unkempt skiff]

procrastination gets me

l te time

um

[twilit jetty]

yep, this is known as one of the seven indeterminate forms

[unkempt skiff]

okay ty

wait

wait.

IM SO SEUOUD

i

[midnight plank]

@unkempt skiff Has your question been resolved?

Channel closed

Closed by @unkempt skiff

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>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[blissful trench]

why its wrong?

[carmine sigil]

The total area of the shape is the area of blue + area of yellow - area of both blue and yellow

Do you see why?

[blissful trench]

nope

[carmine sigil]

The overlap is counted twice

If you simply add them

But we want to count it only once

[blissful trench]

$A_{total} = A_{blue} + A_{yellow} - A_{overlap}$?

[grand pond]

アキラ (>⩊<)

[blissful trench]

idk whats overlap here

go on

no lol

i added two shapes

ya

it was like this

how easy?

can u explain why its wrong?

ok

k

now what

how did u get 3?

5-2?

let me guess i need to add another shape right?

[carmine sigil]

Wait you're trying to find the rectangular shape, not the odd shape with the triangle base?

[blissful trench]

I have 3 shapes now

how would u find the area of this shape?

[blissful trench]

it asking to find the area of the shape

[blissful trench]

this shape

[carmine sigil]

You'll want to delete the triangle, it isn't helping things right now

[blissful trench]

ok

[blissful trench]

ok i think i got it, thanks a lot

.close

[midnight plank]

Channel closed

Closed by @blissful trench

Use .reopen if this was a mistake.

[blissful trench]

.reopen

[midnight plank]

✅

[blissful trench]

I have another question

how many shapes can u do with this?

[carmine sigil]

3

[fathom onyx]

er... 2 rectangles minus 2 triangles

[carmine sigil]

You can do it with 2 rectangles and 1 triangle

Tru

[fathom onyx]

oh now I see it tho

[blissful trench]

can u get out i dont need ur help 🙂

[soft glade]

This is true

[blissful trench]

no but rather i dont want 3 ppl at the same channel

[fathom onyx]

FYI, this is equally rude - be careful saying this

[fathom onyx]

yeeee

[blissful trench]

ill ask a linear algebra in a bit so feel free to help if u can lol

either help or stop being rude

I dont want u if keep doing like this

[carmine sigil]

Can we stop with the slap fight please

[blissful trench]

whats next

[fathom onyx]

Well, the rectangles' areas should be pretty easy

[blissful trench]

in the pink i see 2x4 but the yellow and blue are quite confusing

[fathom onyx]

Since the top part of the pink rectangle and the bottom part of the pink rectangle are... opposite sides of a rectangle...

what should this remaining part of the yellow edge be?

[blissful trench]

2

[fathom onyx]

yee

so the yellow one should be doable now

[blissful trench]

ok so for pink we have 4 and 2, for yellow 3, 2, 3

do I need to add them or multiple?

[fathom onyx]

Well what's the area of a rectangle?

[blissful trench]

length x width

[fathom onyx]

right

So the pink one's length and width are...?

Thus its area is...?

Similarly, for the yellow rectangle...?

[blissful trench]

pink shape is 8 and yellow is 72?

[fathom onyx]

Pink is right

Where did 72 come from?

[blissful trench]

3x3x2x4

[fathom onyx]

What's the length of the yellow rectangle?

[blissful trench]

same as this

but for pink it says wrong

yellow too

[fathom onyx]

Again, this question please

[blissful trench]

its not length x width?

wait

[fathom onyx]

I'm asking for the LENGTH of the...

[blissful trench]

its 8?

[fathom onyx]

yeee

[blissful trench]

i see

[fathom onyx]

And its width?

[blissful trench]

4

[fathom onyx]

So the yellow rectangle's area is...?

[blissful trench]

32

it says wrong again

why

[fathom onyx]

yellow is wrong?

The pink one is, but the yellow one should be right

[fathom onyx]

Okay those numbers are right

Maybe if we fill in the rest it'll update correctly

[fathom onyx]

The pink one - the base, we should now know, right?

@blissful trench Still here?

[blissful trench]

yes

[fathom onyx]

^

[blissful trench]

8 and 3?

[fathom onyx]

yeee

So the area of the triangle is...?

[blissful trench]

base * height/2 which means 12?

[fathom onyx]

yee

So the area of the whole shape should be...?

[blissful trench]

52

[fathom onyx]

yeeeeeeee

[blissful trench]

thanks man :D

[fathom onyx]

hopefully the website should stop bugging out like that lol

[blissful trench]

every question just gets more complicated

[mortal mirage]

dear god

[fathom onyx]

It is just a matter of breaking them down into shapes whose area you can recog-...

Dear lord

Rectangle minus 5 triangles?

I'm not sure how this site wants you to approach this

i.e. what inputs it'll expect

[fathom onyx]

I'd go for this

[blissful trench]

it keeps asking what is the area of this shape

[mortal mirage]

[blissful trench]

i still have like 5 more

i solved 3 only

[fathom onyx]

yh but I mean it doesn't give these demarcations or anything?

[blissful trench]

nope

just like that

[mortal mirage]

it (the website) wants you to do that??

[blissful trench]

ya

[mortal mirage]

which minion of satan designed this 😭

[fathom onyx]

My proposal was this

Purple rectangle minus each of red, orange, yellow, green and blue triangles

[blissful trench]

wait lemme try this

[fathom onyx]

This requires the area of a trapezium (for the purple shape there), and while the bottom length of that trapezium is possible to get, it's difficult to justify without some strong geometric intuition at play

Like, I can see it, but I struggle to explain it, iykwim

[blissful trench]

no worries

[mortal mirage]

how would you get the shorter base tho

[blissful trench]

the first one is 8 and 4 right?

for blue

[fathom onyx]

You'd argue via a lot of symmetry

[mortal mirage]

yea ig

its a lot harder than your method tho

[fathom onyx]

Oh the site does allow it!?

Nice

[blissful trench]

yep

[fathom onyx]

Both blue triangles have the same area

[mortal mirage]

for the areas?

[blissful trench]

yea

if they have same area that means i just need 4 and 2?

[fathom onyx]

For their side lengths, I'm guessing? Then yh

[blissful trench]

that worked gg

for yellow is only 2

[fathom onyx]

(you gotta say "area" at least, so it's clear you're referring to that and not a side length)

[blissful trench]

pink and orange are wrong

[fathom onyx]

You're right, the yellow area is 2

[blissful trench]

i got it

[fathom onyx]

Well what're your heights for each of them?

[blissful trench]

for pink it only says 6

[mortal mirage]

but you can deduce the height

[blissful trench]

how

[mortal mirage]

well the tip is 5 cm away from the other side right?

and the total is 8 cm

[blissful trench]

how did u get 8

[mortal mirage]

-# first diagram on mathcord that's actually drawn to scale

[mortal mirage]

it's given in the problem

[blissful trench]

oh

idk actually

[fathom onyx]

(look at the bottom of the shape)

[mortal mirage]

it's a rectangle, so the length of the base "carries" through the whole shape

[blissful trench]

im looking for pink and it states 6 and 5?

[mortal mirage]

yes, but the 5 isn't the height, is it?

the total segment has length 8

[blissful trench]

ya

[mortal mirage]

and it's broken up into two segments: one of length 5 and the other is the height you are looking for

[blissful trench]

wouldn't that be 15?

[mortal mirage]

how come?

[blissful trench]

5x6/2

[mortal mirage]

not really, the 5 isnt the height of the triangle

[blissful trench]

oh fair

[mortal mirage]

do you understand this? ^^

[blissful trench]

not really

how did the yellow just said 2 when pink didnt

[mortal mirage]

how did you get that the height for yellow is 2?

it's the same method for finding pink's height

[blissful trench]

luck

[mortal mirage]

uhh

ok?

u sure it was luck

[blissful trench]

yes

[mortal mirage]

ah

[blissful trench]

¯_(ツ)_/¯

[mortal mirage]

alr gimme a few mins to make a diagram bc im on computer

[blissful trench]

sure

i think pink area is $\frac{1}{2} \times 6 \times 2 = 6 , \text{cm}^2$?

[grand pond]

アキラ (>⩊<)

[blissful trench]

nvm its also wrong

[fathom onyx]

[Where's that 2 come from there?]

[mortal mirage]

ok so

after 5 mins of battling with my computer

you see how the whole segment is 8?

[blissful trench]

just a guess

ya

[mortal mirage]

alr now

part of that segment is 5

and do you see how the other part is the height that we are looking for?

[blissful trench]

yes

its 6 right?

[mortal mirage]

the height?

there are no 6s in this diagram

[blissful trench]

oh

[mortal mirage]

you have a segment with total length 8, and part of it has length 5

5

oh my god

i hate my keyboard

what's the other part gonna be?

[blissful trench]

so 8 and 5 divide by 2?

[mortal mirage]

uhm

[blissful trench]

i hate geometry

[mortal mirage]

do you see how it's just 8-5?

[mortal mirage]

me too, dw

[blissful trench]

yep

[mortal mirage]

ok good

so the height is...

[blissful trench]

3?

[mortal mirage]

yes!

[blissful trench]

or 13?

oh

so what will be the pink shape

[mortal mirage]

mk so what's the area?

[blissful trench]

9

[mortal mirage]

yee :)

[blissful trench]

holy it worked

only orange is left

[mortal mirage]

orange is pretty straightforward tho

let's start easy: what's the height?

[blissful trench]

4

[mortal mirage]

yh

ok now the base is a bit trickier

what's the total height of the entire rectangle?

you should be able to figure this out from the right side

[blissful trench]

8?

6+2

[mortal mirage]

close!

i think you're forgetting a 2

[blissful trench]

oh

10?

[mortal mirage]

yes!

ok now

so the height of the rectangle should be the same on the left side as well, right?

[blissful trench]

yes

[mortal mirage]

so the height is...

base

sorry

[blissful trench]

np

[mortal mirage]

^^

[blissful trench]

so will that be 20?

[mortal mirage]

uh

the total height of the rectangle is 10

and you subtract away 2 from the blue triangle

[blissful trench]

i did 10 x 2 and then divide by 2

i mean 4 not 2

10x4 divide by 2

[mortal mirage]

well the base isn't 10

10 is the total

you havta subtract away 2

because the blue triangle occupies a bit of the height as well

[blissful trench]

16?

[mortal mirage]

yes!

[blissful trench]

so the final area for all is 35?

[mortal mirage]

i need to do the arithmetic, but i think you got it

[blissful trench]

it says wrong 😭

[mortal mirage]

w h a t

for which?

[blissful trench]

8+2+9+16 gives 35

for all