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[celest coyote]

pls help i dont understant

[silent crater]

I think (f-g) (x) is the same as f(x)-g(x)

so (f/g)(x) is the same as f(x)/g(x)

[celest coyote]

so how do i get answer

do i combine terms

?

[silent crater]

the second one is easy, It's the last answer

because you cannot simplify it any further

for the first one it would look like 2x-1-(x^2+x-2)

[celest coyote]

so do i just substitute?

[silent crater]

you substitute the given functions in for f(x)-g(x)

if f(x)=2x-1

and

g(x)=x^2+x-2

then it would be

2x-1-(x^2+x-2)

you would get -x^2+x+1

[celest coyote]

i'm sorry

how did that work

[silent crater]

ok, so the term (f-g)(x) is the same as what?

[celest coyote]

f(x)-g(x)

[silent crater]

alright

and what is given for f(x)?

[celest coyote]

2x-1

[silent crater]

and for g(x)?

[celest coyote]

xsquared + x - 2

[silent crater]

ok so subtract those 2

[celest coyote]

how do i that

sorry

[silent crater]

2x-1-x^2-x+2

then group like terms

-x^2+2x-x-1+2

here let me put it into a calculator to write it because I don't know how to use the tool in here

[celest coyote]

oke

[silent crater]

it will look like this

is that easier to read?

[celest coyote]

yes

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[unkempt swift]

@grim nebula hi u alive?

[grim nebula]

no im

in a meeting lol

[unkempt swift]

Oh

Okay i shall wait

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[weary edge]

I'm confused

[weary edge]

do I just convert them to base 10?

Or just solve in base 7?

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[weary edge]

Second unanswered quesiton today 🥲

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[sudden osprey]

how do you find the limit of a function?

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[sudden osprey]

like with wolfram alfas limit calculator or anything

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[radiant citrus]

Problem:
Given vector b_x = -20m and b_y = 40m.
Calculate the length of the b vector.
What is the angle for b with its positive direction on the x-axis?

i have no issues with calculating the length of the vector, as its a simple substitution and knowing the formula.
my problem is that when i am asked to calculate the angle of a right triangle, i have no idea which trigonometric function i could use
i have the theory that if the excercises gives me the x and y components, then maybe i need to take that to heart, and use tangent and cotangent only
but even then, the solution is: (44,7 m, 117°)
hence the angle i am looking for is 117 - 90 = 27˚
.
.
.
what is the best way to think about this?
how can i find the direction of a triangle?
how do i know i have the correct drawing when working with trig. functions?
and how can i make extra sure that i am calculating the right angle for the excercise, when i have all of the available data for using all 4 trig. functions for this type of problem?

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[tall mango]

i'd draw everything out like this:

It's my fault, but i'm not sure what you mean by "the angle for b with its positive direction on the x-axis". Which angle is it referring to

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[radiant citrus]

yes this is the correct drawing

sry about the english, cuz i had to translate it and no idea how to properly

i was asking about how you came to the conclusion that this is what the triangle looks like

and which angle to calculate

[copper dagger]

Hi, have you learnt about dot product for vectors?

Regarding the triangle, when given the coordinates of a vector, it is usually with reference to the origin. So it is safe to sketch the triangle by noting the negatives and positive of the x and y coordinate.

Regarding to calculate the acute, obtuse or even negative angles. I do not have an answer. It would be safer to check with your professor as the question is not specific/ confusing in english

[tall mango]

yep, guess this explains it

[radiant citrus]

im sorry i didnt reply yet, on a lecture, will reply when available

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[radiant citrus]

@tall mango, @copper dagger

i asked my professor to explain, turns out it doesnt matter which you use in terms of the solution since if you know either of the 2 unknown angles

you can very easily calculate the other angle too

thank you for your patience and help!!!

[tall mango]

Glad to help!

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[violet widget]

Isnt the summation undefined for n =1 ? https://cdn.discordapp.com/attachments/1025113502182031361/1026539120895467540/unknown.png

[strange shore]

It is

[violet widget]

okay

what would the answer be?

the series doesnt exist?

[unique aspen]

i'm really not sure what the question could be asking

[violet widget]

Same, they gave a hint so i’m guessing the series should exist

I think it could be a typo

[unique aspen]

yeah but i'm just not sure what the typo is exactly

maybe they just want it to start from n = 2 or something

[violet widget]

my guess n=2

yea

I’ll ask my teacher

[unique aspen]

good idea

[violet widget]

thx for all the help!

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[hot surge]

I am working on a custom set notation for my conlang and I'm wondering if this notation is simple and fluid enough to be easily understood by set-theorists (which I have still only newly become).

A set of x-number of objects {x} is still 1{x}. Therefore, {1 + 1} = 1{2}

The simple change that I have made is the use of an inverted pair of set-notational brackets to identify or represent the liminal/unbounded set. So for any set {x}, }{{x}}{. This is because for set {x} we can always envision that which contains {x}. In an infinite set, there must be infinite sets within an unbound infinite "set" represented as }...{{x}}...{

Consider:
}{{{{{{{{your body} your room} your house} your neighborhood} your city} your state} your country} your planet} nonliminal infinite space{
Or just consider:
}nonliminal infinite space{

Does this notation make simple and proper since for a conlang system of mathematics?

I am also interested in the limits established within/upon nonliminal space established by the limits of the boundaries of the sets which it contains. Perhaps represented as {y} in }...{y}...{{x}}...{

[hot surge]

So }x{ might represent any set with imaginary limits/boundaries. Are those a thing? I need to look that up.

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[hot surge]

Is this correct?
{A} ∈ A/(x → ∞)

I'm confused. Does (x → ∞) = [x(∞) → ∞]? Can that be?

I'm struggling with the concepts infinitesimalism and its inverse, where if x → ∞ =! ∞ is x infinitely approaching but never reaching infinity. This means x → ∞ =! ∞ must contain its own infinity of x → ∞. So then does that infinity actually = the infinity that it doesn't =, proving a contradiction to be true, or would that infinity be its own unique infinity to the one being apprached? This all sounds like a recursive recursive infinity to me. Which is a little confusing and actually kind of scary.

@grim nebula good afternoon math friend

u halp me pl0x?

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[hot surge]

.reopen

[final saddle]

✅

[hot surge]

thx

[unique aspen]

pinging random people is frowned upon

none of this seems rigorous enough for anyone else to understand

i'm not convinced any of this is useful or interesting in any way

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[tranquil pine]

I think I might be taking the derivative wrong

[tranquil pine]

The derivative is h(t) = ln t / t^2 + 1

I did the quotient rule

[amber holly]

Seems to be correct though

[vale silo]

[tranquil pine]

I can simplify this rigut?

[vale silo]

don’t need to if the question only want it at t=4

can punch it into the calculator hahaha

but yea can simplify

[tranquil pine]

Oh I’m doing linear approximation

So ye I need to plug in 4 I guess

Uh this is a super nasty number

I got@like -0.0236

[hot surge]

.reopen

fuck

[hot surge]

Snow is my friend, not a random person. It is not "rigorous" because I just began on set theory today. And your level of interest is really not my primary concern, though I will note that you were interested enough to reply in the first place.

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[sleek flicker]

Hi, will the square of a normal distribution centred at 0 give me a gamma distribution or need it be centred at 0 for that?

[muted prairie]

Need what be centered at 0?

Yeah I think you get like Gamma(2,1/2) or something

I'm not sure

Normal dist needs to be centered at 0 and have stdev 1

[sleek flicker]

The original normal distribution centred at 0

But you also get a gamma distribution when centred at -1?

I'll show you what I mean

For 2b you have a normal distribution X centred at 0 and then Y is the square of the normal distribution centred at -1

Not sure how to go about getting from there to the pdf of Y

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[muted prairie]

Do you have techniques for transforming pdfs in general?

If you're getting questions like these you should have been taught how to turn a pdf of X into a pdf of f(X) for any f

Sadly I don't think there's a way to utilize the connection to X² being a gamma dist

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[cobalt bane]

I keep getting enormous answers like “8+h/16h^2+128h+256”

[cobalt bane]

Finding the derivative is fine, the main problem is using the “f(x+h)-f(x)/h” definition to do it

[sweet summit]

hi there. One moment, let me look

[cobalt bane]

Tyvm

[sweet summit]

can you share the work you've done to get to 8+h/16h^2+128h+256

[cobalt bane]

Alright lemme just take a pic

[sweet summit]

ty 🙂

[cobalt bane]

My handwriting is abysmal, sorry

[sweet summit]

great! let me take a look 🙂

hmm

I think you're double dipping here

one sec I'm writing it out

okay soory

It might be easier to just solve for f'(x)

then plug in your value

[cobalt bane]

Hmm ic

Ohhhh I get it now, it makes more sense to start with the definition

[sweet summit]

yep! 99% of the time it'll work out better that way 🙂

[cobalt bane]

Tysm!!

[sweet summit]

yep np!

[cobalt bane]

I have another quick question if you don’t mind! When I have to discover the equation of a tangent line I can always use the “y-y’= m.(x-x')”formula right? (With y’ and x' being the points given and m being the derivative of f(x'))

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[pliant gyro]

Hi, I'm taking Calc 1, and I'm looking for advice: Should I pay special attention to proofs?

[pliant gyro]

I know they can be practically ignored as long as you follow the rules, and that's what my professor advocates for but I'm curious if not even trying to understand the underlying derivation of everything will come back to bite me in later math classes

[desert mantle]

well for some of them, maybe

for others maybe you won't ever see them again or you'll prove them again next time

it will obviously never hurt to deeper understand stuff

and trying to understand some of the proofs will prepare you for proof based courses later

[pliant gyro]

That's what I need to know, thanks!

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[buoyant eagle]

how would i find the interval

is it just (-inf, +inf) cause each term is continous over all R

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[buoyant eagle]

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[inland badge]

can someone help me w a few of these i’m not sure how to do them

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[restive badger]

can anyone help me with the answer to this? and explain why

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[restive badger]

<@&286206848099549185>

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[unkempt swift]

im not good at tis ill just make a guess lol

0

the first two rows add up to 9

last two rows add up to 18

im legit just guessing LOL

this is a pattern spotting type of question right?

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[midnight tartan]

Hello, I tried doing the exercise. Is it correct ?

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[muted prairie]

Is the goal here just to write f(y) = Bg(x) + h

for some functions f,g and constant h?

[midnight tartan]

Sorry, what is bg(X) ?
I was told that I need to write as the following form :
Ab + e

[muted prairie]

beta times some function of x

like you have here beta times log(x)

[midnight tartan]

Ah yes

A is a matrix I think

[muted prairie]

would it be valid for the second problem to subtract epsilon from both sides first

[midnight tartan]

Ok thank you I will try that !

[muted prairie]

all right

i'm not 100% on what the problem means so it might somehow be wrong

[midnight tartan]

Like this ? xD

[muted prairie]

Beta shouldn't be alone

what happened to the x

Other than that good

[midnight tartan]

Oh yeah sorry

But what about the e

How do I bring it to the right ?

[muted prairie]

well it says linear in the parameter β

in a sense we've done that idk if we need ε or what

I really don't know what counts as a valid "transformation" into a linear equation

and tried looking it up, nothing

[midnight tartan]

I was told it's like AB+e

[muted prairie]

ah

then probably not possible

[muted prairie]

though here you have something other then ε added so who knows

[midnight tartan]

Okay thank you

I'll just wait for the teacher to correct the exercise ;_;

Thanks :)

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[fair rain]

is this right am confused

[hollow iron]

Remember that division by 0 is undefined

(I am assuming you're trying to find the domain, right?)

[fair rain]

am trying to find the domain of Dfog

f(x)=-1/(x+1)

g(x)=2x

[hollow iron]

Find f(g(x)) first.

[fair rain]

but the teacher told us that we should always find the domain first

[hollow iron]

What

Well I guess she means you think about it this way:
Find the domain of f, and find where g(x) equals a number that is not in the domain of f.

[fair rain]

ok thanks

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[hollow iron]

No problem!

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[indigo timber]

I must be overlooking something, but how does this simplify to what my teacher got? I know K=1/4\piE_0 but don't know how it jumped from 1/k(R1-R2) to k(R2-R1)/R2R1 i need to nap

[indigo timber]

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[thin girder]

Any ideas on this one guys?

[thin girder]

My prof has only taught us the derivitives of trig functions, and not really much else

so not sure how to go about this one

[grim badger]

csc(x) is a trig function

[pale wind]

cosecant

1/sin

[thin girder]

Right right

I know the regular derivitive is -cotxcscx

I have no idea what the powers in the derivitive mean though

[pale wind]

you take derivative twice

[thin girder]

Oh ok, well how do u take the derivitive of a trig function twice

just do derivitive of 1/sin?

Or derivitive of -cotxcscx

[pale wind]

this

[thin girder]

So u apply product rule here

[pale wind]

yep

[thin girder]

Well now I dont know what the derivitive of -cot is

-csc^2 maybe?

or positive csc^2

Nice I figured it out, it was just positive csc^2, thanks for letting me know that squared means take the derivitive twice

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[teal mesa]

I have no idea how to do this and I have a test tomorrow

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[onyx saddle]

Hi

[onyx saddle]

I need help

9x - 7i > 3 (3x - 7u)

How to solve

.close

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[unkempt swift]

hi if ur free can we go thru the AM-GM equality

[unkempt swift]

like i actually wanna learn that

[tired walrus]

how much generality are we talking

only the 2-term one? or for n terms? or maybe n terms with weights?

[unkempt swift]

im not sure lol snow just mentioned AM-GM equality and im quite curious as to what that is

[unkempt swift]

ok nvm i think n terms

[tired walrus]

$\frac{x_1 + x_2 + \dots + x_n}{n} \geq \sqrt[n]{x_1 x_2 \dots x_n}$

[soft zealot]

Ann

[tired walrus]

so this?

[unkempt swift]

yeaa

[tired walrus]

the name stands for "Arithmetic Mean - Geometric Mean"

[unkempt swift]

ahh okay i see

can i briefly understand the proof for this

like the intuitive idea of it

i googled and saw two proofs based on

1. lagrange multipliers
2. jensens' equality

not quite sure wat those are but im curious XD

[tired walrus]

there are many ways to prove this inequality

...jensen's inequality is a generalized version of the definition of convexity, if you're familiar w/ that.

there are also some inductive proofs of this

[unkempt swift]

ermm im not familiar lol

[unkempt swift]

is there like a quick runthrough of these on youtube or smth

[tired walrus]

probably not

lagrange multipliers are kind of a beefy subject

[unkempt swift]

ah i see

what level is that

calc 2?

[tired walrus]

far above

[unkempt swift]

oh wat

analysis?

[tired walrus]

uni-level analysis-ish

[unkempt swift]

o.o

is there no way to get a brief idea of it without fully understanind lagrange multipliers

cuz the equality looks rly interesting lol

[unkempt swift]

how about jensen's inequality

[tired walrus]

im trying to find a proof that involves neither of these concepts and is just plain induction

but i forgot where i had it

[unkempt swift]

ah

maybe we can find it online

instead of ur notes or smth

actly thats probably wat u meant

nvm

[tired walrus]

ok i found it

[unkempt swift]

yay

[tired walrus]

the proof proceeds by means of first proving the special case where the numbers are 'normalized' multiplicatively

also im gonna be proving a slightly stronger version

[tired walrus]

namely that if the x_i are not all equal to each other then this inequality is strict

so the normalized case is this: for $x_1, x_2, \dots, x_n > 0$ which are not all equal to each other and which satisfy $x_1 \dots x_n = 1$, we have $$x_1 + \dots + x_n > n$$

[soft zealot]

Ann

[unkempt swift]

right

[tired walrus]

and we prove this by induction

the base case is n=2, which can be proved directly-ish: $(x_1+x_2)^2 = (x_1-x_2)^2 + 4x_1x_2 = (x_1-x_2)^2 + 4 > 4$ therefore $(x_1+x_2)^2 > 4$

[soft zealot]

Ann

[unkempt swift]

lemme just send this again

[tired walrus]

we will get to that in due time

[unkempt swift]

ah okay yes

[unkempt swift]

[tired walrus]

okay, and now on to induction

take $n+1$ positive numbers $x_1, \dots, x_{n+1}$ which are not all equal and whose product is 1.

[soft zealot]

Ann

[tired walrus]

then there exists a number among the x_i that is less than 1 and a number that is greater than 1

we can reorder them so that $x_n < 1$ and $x_{n+1} > 1$

[soft zealot]

Ann

[unkempt swift]

um

ah okay

[tired walrus]

from this we get $(1-x_n)(x_{n+1}-1) > 0$ and thus $x_nx_{n+1} < x_n + x_{n+1} - 1$

[soft zealot]

Ann

[unkempt swift]

yes

[tired walrus]

now apply the induction hypothesis (normalized AM-GM for $n$ terms) to the numbers $x_1$, $x_2$, \dots, $x_{n-1}$, $(x_nx_{n+1})$, whose product is 1

[soft zealot]

Ann

[tired walrus]

though note that they might end up being all equal, so we must replace the inequality by a nonstrict one

thus $x_1 + \dots + x_{n-1} + x_nx_{n+1} \geq n$

[soft zealot]

Ann

[tired walrus]

however when we then apply $x_nx_{n+1} < x_n + x_{n+1} - 1$ we get $$x_1 + \dots + x_{n-1} + x_n + x_{n+1} - 1 > n$$

[soft zealot]

Ann

[unkempt swift]

wait im slightly lost lol lemme look at it again

ok right

[grim nebula]

curious proof

[unkempt swift]

[tired walrus]

to get the general case, apply normalized AM-GM to $x_1/m, x_2/m, \dots, x_n/m$ where $m = \sqrt[n]{x_1 \dots x_n}$

[soft zealot]

Ann

[unkempt swift]

yes

erm

[tired walrus]

if theres any part of the proof that is unclear just ask

god knows my presentation here was somewhat haphazard

[final saddle]

@unkempt swift Has your question been resolved?

[unkempt swift]

i sort of get the idea yes

i wanna get the idea first

then try it later

on my own

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@unkempt swift Has your question been resolved?

[dawn elk]

there’s one geometric proof iirc

but ig it’s for 2 numbers

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[hasty heron]

Let α > 0, β > 0, γ > 0 be three arbitrary angles such
that α + β + γ = π/2. prove that
tan α tan β + tan β tan γ + tan γ tan α = 1.
Note: The argument must be valid for any triple of values ​​of α, β and
γ that satisfies the given conditions.

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[tired walrus]

@hasty heron have you made any progress on this?

[hasty heron]

α + β + γ = π/2 then

2α + 2β + 2γ = π

then

α = -β - γ + π/2
β = -α- γ + π/2
γ = -α-β + π/2

[tired walrus]

...ok so that's a little bit walking in circles

consider that tan(gamma) = 1/tan(alpha+beta)

[hasty heron]

tan α tan β + tan β * 1/tan( α + β) + 1/tan( α + β)* tan α = 1

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[tranquil pine]

help

[tranquil pine]

help

any1 ther???

hello??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

any1 ther plssssss

[tranquil pine]

hey

[strange rune]

if your total number is called A

what is A in function of x and y?

[tranquil pine]

no

but

we hv to form

a

equation out if it ryt

[strange rune]

28 = 10*2 + 8

45 = 10*4 + 5

so A=?

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[brazen rover]

I want 210,000 apple.

• Every 15 minutes I get 50 apples

How many minutes/hours/days is it going to take to get 210,000 apples?

[thorn grotto]

210,000 / 50 = 4,200 times 15 minutes

4,200 * 15 = 63000 minutes

[brazen rover]

ohh ok, tysm!!!

i will now close this help channel

tysm i hope u have good dat

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[cedar tapir]

What does this mean?

[hollow iron]

Limit arithmetic.

[cedar tapir]

yeah, but I don't know what is O

[hollow iron]

For example, the first one (top left) states that if you have a limit of the form "positive/0+", then that limit is infinity.

Okay let me give you an example.

$\lim_{x \to 0} \frac{1}{x^2}$

[soft zealot]

RedstonePlayz09

[hollow iron]

Can you tell me what x^2 approaches when x approaches 0?

[cedar tapir]

would that be like 0.0000000000001

[hollow iron]

No, I'm asking what it approaches.

It's true that you can plug in very small values,

but what does it approach?

[cedar tapir]

0

[hollow iron]

Correct,

and more specifically it will approach 0 from the positive side.

So when you plug in values very close to 0, your function will be something small and positive.

In addition, the numerator is just one

So you have a limit of the form "$\frac{1}{0^{+}}$"

[soft zealot]

RedstonePlayz09

[hollow iron]

By your table, this limit will be equal to infinity.

[cedar tapir]

oh

now I understand

Thank you!

[hollow iron]

No problem!

[cedar tapir]

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[peak maple]

hey guys

i have a couple questions but i dont even want some1 to do them can you just tell me what i should search up to learn it

like ion even know what to search

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[copper trail]

I’m stuck on all of these questions since I wasn’t here for a week and I need help but please don’t go to in depth in it

[copper trail]

<@&286206848099549185>

please help me out

anyone please help me out

i'm really having a hard time with this

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[ornate sun]

Just looking for some quick confirmation: a matrix in REF form cannot have a leading -1, correct?

[strange rune]

yeah by definition of ref form

the leading values should be ones

[ornate sun]

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[karmic garnet]

(I have minimal math skill and want to know how to even approach my problem)

In my board game, there are 7 "board" locations. Players likely have a preference/desire to interact with a specific location. Players are considering cards to play, where the cards affect one location. I need to calculate a weighted mechanical value for cards that offer 1 location / multiple locations / any locations for the single card effect to activate. For example: (screen capture). This shows that if a player is offered 4 specific locations to do something, there's a 57% chance than their desired location is offered.

I'd like to assign these rows a rating of "value". For example, being offered only 1 option is a "1" value. Being offered 7 options seems (at first glance) to be a 7 then, 7 times as useful as only 1 option. However, this isn't true. If your only need is to play location X and the 7-option card is 7x harder to play than the 1-option card, you would be better off considering 4 * 1 option cards (and odds are you would find Location X on one of these, 57%). The "value" rating should increase more slowly than flat multiplication, likely at an exponentially diminishing amount. The higher over 3.5 options you go, the less each additional option offered to you matters / adds value.

How would I calculate (based on the 1 / 7 being a 1 value) the diminishing returns on value for each additional option?

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[karmic garnet]

<@&286206848099549185>

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[harsh bay]

does u have to be x+2?

it would be much easier if u was x+1

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[little haven]

.reopen

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✅

[little haven]

but then I would be left with a number like u^5/5 + u^4/4 (somethign along those lines) and subbing u = x+2 but Im just not 100% sure that is right

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[hexed copper]

Can anyone help me calculate the value of this ( with no calculator ofc )
arctan(2)+arctan(3)+arctan(2+sqrt(3))

[hexed copper]

<@&286206848099549185> please help

I think I know the answer for arctan2 + arctan3 but the problem is in arctan(2+sqrt(3))

[jaunty turret]

You can apply the formula for sum of arctan

[hexed copper]

There is a formula for arctan a + arctan b, but not for arctan(a+b)

[jaunty turret]

Assume that a+b=x

Then proceed

[hexed copper]

The problem is in order to apply this formula you nees to prove that arctan a + arctan b belong to the ]-pi/2 ; pi/2 [ interval

Which can't be done directly in this case

I did calculate the tan of that expression, and i get :
(1+sqrt(3))/(3+sqrt(3))

How to find a number whose tan is this result

[jaunty turret]

I don't mean the formula for arctan(a+b)

I mean apply the formula for arctana+arctanb to whatever the sum of arctan2+arctan3 is and arctan(2+sqrt3)

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[viscid kestrel]

hi, how do i do this question?

[tired walrus]

do you know what a geometric progression is?

[viscid kestrel]

yes

do i use ar^n-1?

[dawn elk]

so use it

you know a_4 is -12/5

a is 300

n =4

find r

[viscid kestrel]

ohh ok i got the answer now haha i got confused at first

thanks!

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[dawn elk]

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[tranquil pine]

Hi. Could someone please explain to me how I get the part circled in red

[tranquil pine]

🙏🏾

[gleaming ember]

this seems impossible to me they are essentially saying $-y\epsilon^{-x} \sin{y}= y\epsilon^{-x} \sin{y}$

[soft zealot]

Bonjoeri

[tranquil pine]

Ohh

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[prime ember]

Hello, I was wondering if anyone could help me determinate all the n in N that verifies: 3^n > n^3

[prime ember]

Other than that

[deft ravine]

That is one of the easiest way of doing this. Another method could be noting that the derivative of (3^x-x^3)>0 for x bigger than 3 and then checking x=1,2,3

[prime ember]

Thanks ! We didn’t introduce derivatives in my analysis class so I guess I gotta stick and adapt to what the professor gave us

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[celest juniper]

sin1 x cos2 x tg3 x ctg4 how to know if this has positive or negative value?

[void valley]

just signs of trig functions in I quadrant

all of them are positive, hence value is ...

[wraith crater]

Is this in radians or degrees?

[celest juniper]

degrees

[wraith crater]

Okay then follow this explanation

[celest juniper]

Thx

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[potent scaffold]

are these correct

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[hidden frigate]

3 and 4 are good, but not 5

Do you want to go through it?

[potent scaffold]

yes pls

am confused

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[hidden frigate]

Okay

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[prisma drift]

Could i please have help with LaTex, for some reason i have 2 images which can fit on 1 page but they go on two different pages

[prisma drift]

<@&286206848099549185>

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[tranquil pine]

Hi

[final saddle]

Please don't occupy multiple help channels.

[tranquil pine]

compounded anually

i know my equation is
A = Pe^rt

so would it be

A = 10000e^(0.09)(20)

?

i dont get the difference between compounded anually and monthly in this equation

or even weekly

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[naive palm]

Super new to this

I'm not really sure what I'm doing

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<@&286206848099549185>

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[hexed garnet]

given z complex. Why is it that $\int_{\gamma_1} \bar{z} dz \neq \int_{\gamma_2} \bar{z} dz}$? Given that $\gamma_1$ and $\gamma_2$ has the same end points, they just have opposite directions. Even though $\int_{\gamma_1} z^2 dz = \int_{\gamma_2} z^2 dz}$

[soft zealot]

soda
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[final saddle]

@hexed garnet Has your question been resolved?

[final saddle]

@hexed garnet Has your question been resolved?

[rain compass]

i assume you’re asking why $\int_{\gamma_1}z,dz\ne\int_{\gamma_2}\overline{z}, dz$

[soft zealot]

maximo

[rain compass]

@hexed garnet am i wrong to assume that

if so, notice that we have $$\int_{\gamma_1}\text{Re}(z), dz + i\int_{\gamma_1}\text{Im}(z), dz$$

which means if equality were to hold: $$\int_{\gamma_1}\text{Re}(z), dz + i\int_{\gamma_1}\text{Im}(z), dz = \int_{\gamma_2}\text{Re}(z), dz - i\int_{\gamma_2}\text{Im}(z), dz$$

[soft zealot]

maximo

maximo

[rain compass]

since gamma2 is just gamma1 backwards, we can take the negative integrals on the right and find that this is true only if z is pure imaginary

for a simple example, consider $\int_0^1,dz=1$ and $\int_1^0,dz=-1$

[soft zealot]

maximo

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[hexed copper]

Hello

[hexed copper]

How can I evaluate this limit ?

Without using l'hopital's rule or any derivative

[strange shore]

at +infinity, arctan(x) approaches pi/2

[hexed copper]

yep

I tried to write (pi/4 - arctan(x/x+1)) as (arctan(1)-arctan(x/x+1))

[strange shore]

and what did you get ?

[hexed copper]

and then I used the fact that arctan(a)-arctan(b) = arctan ((a-b)/(1+ab))

[strange shore]

yea

[hexed copper]

which gives me (arctan(1)-arctan(x/x+1)) = arctan (1/(2x+1))

but this doesn't get me anywhere

[strange shore]

true

hmm

[hexed copper]

you don't have a clue ?

[strange shore]

sadly no

[hexed copper]

we also know that the limit of arctan(x)/x when x approaches 0 is 1

idk if we can use it here

by evaluating the limit when u approaches 0, with u = 1/(2x+1)

[strange shore]

x approaches infinity here, unless you found some u-sub somewhere

[strange shore]

if u = 1/(2x+1), then what is x^5 ?

[hexed copper]

it's (1/2X) - 1/2

or (1-x)/(2x)

and arctan(1/2x+1) is arctan(u)

[strange shore]

all of this to the power of 5

[hexed copper]

yep

times arctan(u)

[strange shore]

$\left( \frac{1}{2u} - \frac{1}{2} \right)^5 \arctan(u)$

[soft zealot]

Ｈｅｒｅｌｓ

[strange shore]

this ?

[hexed copper]

yep

but again I don't get to the answer because I get infinity * 0

[strange shore]

arctan(u) at 0 is 0 sadly

you will have infinity x 0

[hexed copper]

if I divide and multiply arctan(u) by u

we'll have u * arctan(u)/u

is there a way to factorize by u ?

I wanna use the limit arctan(u)/u = 1

[strange shore]

you will have u(1/(2u) - 1/2)^5

infinity x 0 again

[hexed copper]

don't think so

u((1-u)/2u)^5 = u((1-u)/2u) * ((1-u)/2u)^4

which is (1-u)/2 * ((1-u)/2u)^4

which is infinity

and multiplied by arctan(u)/u, it's positive infinity

isn't it ?

@strange shore ?

[strange shore]

I guess you found it

it should work

,wolf x^5 (pi/4 - arctan(x/(x+1)))

[soft zealot]

Results provided by WolframAlpha

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Requested by Ｈｅｒｅｌｓ#1420

[strange shore]

i guess its infinity, yea

[hexed copper]

alright

I got it finally

would you mind helping me with a last one ?

I've already tried it but didn't find the answer

[strange shore]

im going to eat

[hexed copper]

okay

[final saddle]

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[lyric garden]

are these functions asymptotically equivalent?

[inland bison]

do you remember the definition for two functions to be assymptotically equivalent?

[final saddle]

@lyric garden Has your question been resolved?

[lyric garden]

Big theta must hold

[inland bison]

well there is an easier test than that

in this case, note that the function 16x/ln(x) is not zero for all x that is near infty here, which means we can explicitly define this equivalence by the limit $\lim_{x\to \infty} \frac{f(x)}{g(x)}=1$ where $f(x)=x\ln(x)$ and $g(x)=\frac{16x}{\ln(x)}$

[soft zealot]

waler

[inland bison]

well you can switch f(x) and g(x) here, it does not matter really, what matters is that g(x) must not be mostly 0 for most x near the limit bound

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[fair ginkgo]

$\f:\mathbb{R}\rightarrow\mathbb{R}
\f(x) = \pi\cdot x^{3}
\\text{What's } (f\circ f\circ f\circ f\circ ... \circ f)(1) \text{ n times?}$

[soft zealot]

Thunder7

[desert mantle]

what about n=1

n=2

n=3?

[fair ginkgo]

for n=1 it's pi
for n=2 it's pi^4
for n=3 it's pi^13
for n=4 it's pi^40

[desert mantle]

ok. so we notice that during those steps we always multiply by 3 (and then add 1)

so maybe a good idea is to look at powers of 3

what are the first few powers of 3

(only looking at the exponent)

[fair ginkgo]

1, 3, 9, 27, 81?

[desert mantle]

ok. do you see any connection between those and the exponents we have

[fair ginkgo]

oh yeah, for example n=2's exponent is 3^1 + 3^0

[desert mantle]

does that same pattern also hold for the other ones?

[fair ginkgo]

for n=3 it's 3^2 + 3^1 + 3^0

so yeah

[desert mantle]

and the next one?

[fair ginkgo]

same

[desert mantle]

ok so we are looking at sums of the form 1+3+3^2+3^3+....

have you encountered sums like that before

[fair ginkgo]

no

[desert mantle]

hmm

does the term geometric sum/series/sequence mean anything to you?

[fair ginkgo]

I actually just think my professor meant to say that f(x)=x*pi so that the result would have been pi^n, but I still want to know what the result is with f(x)=pi*x^3

[desert mantle]

ok. lets do a bit of theory

a sum of the form $1+r+r^2+r^3+\ldots+r^n$ is called a geometric sum

[soft zealot]

Denascite

[desert mantle]

we can calculate a closed form of that

it is given by $1+r+r^2+\ldots+r^n = \frac{1-r^{n+1}}{1-r}$

[soft zealot]

Denascite

[desert mantle]

can you verify that this is true by multiplying both sides by 1-r ?

[fair ginkgo]

yes I understand what's going on there

[desert mantle]

ok

in our case have r=3

can you calculate the closed form for 1+3+3^2+3^3+...+3^n ?

[fair ginkgo]

(1-3^{n+1})/(-2)

[desert mantle]

thats the wrong sign

[fair ginkgo]

ok

[desert mantle]

yes now its correct

or more commonly you'd factor a -1 out of the top and write it as 1/2*(3^(n+1)-1)

[fair ginkgo]

ok

[desert mantle]

and if you want you can verify that this is indeed correct and gives the correct answers

[fair ginkgo]

but for my first case n is now 0?

so it's actually $\pi ^{\frac{3^{n}-1}{2}}$?

[soft zealot]

Thunder7

[desert mantle]

dont forget about subtracting the 1

[fair ginkgo]

right

[desert mantle]

$\pi^{\frac{3^n-1}{2}}$

[soft zealot]

Denascite

Thunder7

[fair ginkgo]

alright, perfect, thank you a lot

[desert mantle]

as an exercise if you want, try it with $f(x)=\pi x^2$ and $f(x)=\pi x^4$

[soft zealot]

Denascite

[desert mantle]

btw technically we would still need to prove that this pattern actually holds forever

[fair ginkgo]

how so?

induction?

[desert mantle]

yes

if you already know induction then this is just a short easy exercise

[fair ginkgo]

I don't, I just know it's a thing

[fair ginkgo]

so for the first it's $\pi ^{2^{n}}-1$
and for the second it's $\pi ^{\frac{4^{n}}{3}}$

[soft zealot]

Thunder7

[desert mantle]

did you forget a -1 there again?

[fair ginkgo]

yes...

both -1

lol

i forget it when typing it out in latex

anyway, thanks a lot

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[vagrant quest]

How do you answer number 7

[vagrant quest]

Is it just 23 /57

Just a guess

Haven’t learnt it yet

Or the other way around

[thorn grotto]

don't you think it depends on gravity as well?

[vagrant quest]

Oh yeah

That’s true

[thorn grotto]

I am a bit confused because the questions below seem way easier

[vagrant quest]

It’s a whole review package kind of thing

[thorn grotto]

okay

so what would the vertical component of velocity be when you launch the object?

*projectile

[vagrant quest]

Lemme find that

Approx 19 m/s

[thorn grotto]

yeah

if you would plot the y-position of the projectile versus time, what would the shape be?

[vagrant quest]

Does that tell us the height of the max?

[thorn grotto]

oh, and have you ever heard of the derivative?

[vagrant quest]

From the quadratic formula?

[thorn grotto]

yeah its a quadratic

[vagrant quest]

Ohhh okay

Ohhhh

Okok

[thorn grotto]

so y(t) is a quadratic

[vagrant quest]

I get how to solve this now

Right

[thorn grotto]

what would y(0) be?

y(t) = at^2 + bt + c, you basically need to find a b and c now

[vagrant quest]

Okay

Thank you

[thorn grotto]

if you got the answer, you can post it, so I can check if it's correct

[vagrant quest]

alright

Or would informal velocity be 0

Initial*

Wait nvm

I found this way to be easier and I got the same answer

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[vagrant quest]

.close

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[wheat helm]

3\1/2_
How would you prove that angle 3 and 2 are complementary if angle 1 is a right angle

[quaint sail]

what do all the angles add up to

[wheat helm]

180

oh i see

.close

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[tranquil pine]

Can someone help me understand this theorem of inversions? I think the first one (part a) says if we invert a point that's on a line which also contains the center of the circle, the point we inverted will remain on the line. Please confirm with me if that's correct.

I don't understand parts b,c,d and the moreover part

[tranquil pine]

I think this is how part b visually looks... Still doesn't make sense

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[unkempt swift]

@grim nebula hello

[unkempt swift]

.close

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[main pulsar]

NO

I need help

explaining

what is d/dx?

I am new to this

[bleak drum]

Derivative no? Also pewsky help 12 is still on by you. Can you do close please

[shell mountain]

<@&268886789983436800>

[hasty heron]

So funny dude!!!

[main pulsar]

I tried closing

[bleak drum]

Ok well thank you

[main pulsar]

I am very new to calc

d/dx means derivative

what is a derivative?

all the explainations dont make sense on google

it means a change in the graph?

[rugged rampart]

it means rate of change

[main pulsar]

got it

so the equation

I dont understand at all

nvm guys

.close

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[crude current]

Hello

[crude current]

Does anyone know how to sketch this?

[final saddle]

@crude current Has your question been resolved?

[long beacon]

if only something related sin and cosine together

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[wise coral]

Can I get help with this problem im really stuck and confused. Ill post my work here in a sec.

[wise coral]

How I got my derivative:

(and confirmed it with an online derivative calculator its the same.)

<@&286206848099549185>

[vital crag]

This is too hard to follow

[vital crag]

Maybe you just need to simplify

[wise coral]

Yeah sorry about that. I tend to use whatever blank spot is nearby to jot down my work.

[wise coral]

Honestly that is as simple as I know how to make it. Im on the brink of losing my sanity its been a couple days on this problem.

And some other problems like it too.

[vital crag]

You can write $3\sqrt{3}=3^{3/2}$

[soft zealot]

riemann

[wise coral]

Ok

(The sidenote is for me its not a part of the problem/simplification)

Is this even accurate?

It feels like it is not.

I forgot the -2 at the end

I still wrong riemann

[wise coral]

Actually wait no 3/2 is impossible. 3/2 comes from a power of 3 and a square of 2. Wheres the power of 3 coming from when there is no power of 3????

You know what forget it. I have to do this problem by a certain time. You guys are too busy right now. I also cant wait I have to complete this im outta here. 😭
.close

.close

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[pale arrow]

I cant figure out how to do this

[robust sedge]

Use a change of coordinates and determine the jacobian of the transformation.

[pale arrow]

what wuld i change the coordinates to?

i can use (x,y,z) = (au, bv, cw) but where does a unit circle come in?

unit sphere*

nvm

.close

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[raw burrow]

Hi

[raw burrow]

Ik that it’s the 3rf one

3rd

[wary helm]

The third one is correct, but there's also another which is correct

[raw burrow]

I squared root 16 and 9

I found 4 and 3

I square rooted 16x9

[wary helm]

The easiest thing to do would be to just evaluate both sides of each equations to see whether they match.
You can also use radical properties to find the answers

[raw burrow]

I found 144

[wary helm]

That's correct, as I told you. But there's another option which is correct

Two correct options

[raw burrow]

Mhm?

[raw burrow]

How

[deft ravine]

Go through each individual option and check if it is correct

[wary helm]

Do the calculations

[raw burrow]

How

Give me example

For the first one

[wary helm]

.

[wary helm]

You need to do what you did before for the third option

Btw, those are all the radicals properties I talked about before, and you should learn them by heart since you're going to use them a lot in the future

Second and third one in particular for your problem

[raw burrow]

Ok

[wary helm]

Evaluate left and right side:
√16 + √9 = ?
√(16+9) = ?
If they're equal, you have a correct equation

That's the first option

[raw burrow]

Ez

Hsnksss

Thankssss

[wary helm]

Yw

[wary helm]

If you're done you can close the channel, if you find your answer and want to ask here to check whether it's correct you can close it later

Ping me if you want me to check your answer though

[raw burrow]

Oof I tried again and didn’t get it

[raw burrow]

I followed this

@wary helm

Sorry , can you clarify it more

[wary helm]

Have you tried evaluating those two expressions?

What's √16 + √9?

And what's √(16+9) instead? If for both you get the same answer, that option is a correct answer, otherwise it's not

@raw burrow

[raw burrow]

Yes

I did

[raw burrow]

7

[wary helm]

.

[raw burrow]

19

Ig

[wary helm]

How did you find 19?

√ is outside the parentheses, so you should solve what's in them first, 16+9, then find its square root

[raw burrow]

25?

Bro idrk

@wary helm

This is actually kind of hard

To understand