help-13

[strong dawn]

does someone know the name of this formula? It's used to project points from a cube to a cubesphere

[cedar kiln]

@strong dawn Has your question been resolved?

[warped coyote]

It’s a specific coordinate transformation, Normally they’re written in the form x’ = Ax but it looks like this is already solved https://en.wikipedia.org/wiki/List_of_common_coordinate_transformations

But actually not really because it’s a projection onto the sphere not redefining the coordinates, so something is normalized, presumably rho=1

[strong dawn]

yes but, this formula was created to have a more uniform distribution of points, I've used it in my project for school and if there is like someone who invented it I should probably refference it. but I don't know how it's called

[warped coyote]

Where did you find it?

[strong dawn]

on youtube

https://www.youtube.com/watch?v=sLqXFF8mlEU&t=205s : 1:50

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[lone dune]

for this problem wouldn't I technically be able to convert it into a diff equation and solve it normally

because y prime is dy/dx right

,rotate

[mortal grove]

you could, but that's not what the question asks lol

but that is just a separable ODE

[lone dune]

yeah ik I was just curious

thanks though

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[undone onyx]

im a little confused about how to use the wronskian to show linear independence of t and t^2

so i calculuate W(t) = t^2 wehich makes sense, but there is this idea that my professor mentioned in class that if there is a t0 is in the interval s.t. W(t0) = 0 then W(t) = 0 for all t in I (and likewise for not equal to 0) but i am confused since t can take on values that both equal to 0 and not euqal to 0? For instance W(0) = 0 but W(1) = 1.

Let me know if you know whats wrong with my reasoning, thanks!

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[undone onyx]

<@&286206848099549185>

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[jade sonnet]

hi, im trying to find $r_x$ given $r(x,y,z) = \sqrt{x^2 + y^2 + z^2}$

[wraith dagger]

lewis_f04

[jade sonnet]

i assume i can set $f(x,y,z) = x^2 + y^2 + z^2$, and then $r_x = \frac{1}{2}f(x,y,z)^{\frac{-1}{2}} \cdot \frac{\partial f}{\partial x}$

[wraith dagger]

lewis_f04

[jade sonnet]

is this correct? as in does the chain rule work this way in partial derivatives, ive consulted google and my lecture notes but they use examples where x y and z are functions of t, which is not the case here which makes me doubt

<@&286206848099549185>

[pine grove]

Okay, respectfully, what the fuck is that math (I’m not saying it’s wrong I’m just shocked lmao) 😭 sorry but I couldn’t even begin to help with this. This makes me feel so dumb lmao.

[jade sonnet]

weirdness 🙂

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[slow rock]

In the second to third line where does the h at the complete bottom disappear

Cause at first everything is over h

Then the h goes away I don't understand why

[carmine bronze]

The h is at the very end of the denominator.

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[devout frost]

can recursive equation terms change to continuous function?

like a gamma function

[sour horizon]

any function just defined on positive integers can be extended to the real numbers and be continuous

but there are many ways to do it

[devout frost]

is that really possible?

[sour horizon]

like one thing you can do is just connect the points with lines

but is that any use to you, idk

[devout frost]

hmm.. i just wonder how imaginary number works

that equation is same as this

here's some examples

any positive number converges, but negative is not

It sounds like natural but it interests me

[devout frost]

it generates random numbers!

my point is, i want make this to continuous function like a gamma function, but i don't even know how to approach this problem

Is there anyone who can solve this problem?

[devout frost]

.

[devout frost]

i forgot one more thing, that this equation results in different graphs depending on the initial value

It's not a hardest problem on you guys, right...?

i think it seems there's no pattern even when using Taylor series

[cedar kiln]

@devout frost Has your question been resolved?

[cedar kiln]

@devout frost Has your question been resolved?

[cedar kiln]

@devout frost Has your question been resolved?

[devout frost]

I guess that all difficult problems stem from simple ones

https://www.youtube.com/watch?v=jUTwjVAYXcU

even an elementary school student can calculate this problem, so can you solve?

can you find a pattern?

My math skills are worse than a patrick

[devout frost]

i found something funny!!

[devout frost]

this equation

is same as

this!

because of substitution

i think this is a big hint for this problem

it's chaos

this equation term graph looks like this

it has a pattern

https://media.discordapp.net/attachments/858590847192399885/1202048030753169459/200.gif

i am waiting for you guys...

i really really want to make continuous function with recursive equation terms

[worldly chasm]

@devout frost a different recursive equation that might help you come to terms with this question is the logistic equation.

$$
x_{n+1} = r x_n (1 - x_n)
$$

This particular recursive equation's behavior varies as a function of the free parameter $r$.

[wraith dagger]

全能の存在

[worldly chasm]

And exhibits chaotic behavior if r is large enough.

You have simply discovered another chaotic, nonlinear recursion.

[devout frost]

https://tenor.com/view/crying-cry-sad-flaque-alone-gif-13147324

damn

then, is it almost impossible to make continuous function?

[worldly chasm]

Essentially. Because of your recursion's sensitivity to initial conditions.

[devout frost]

alright

thank you so much

[worldly chasm]

Though

[devout frost]

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[worldly chasm]

If you really want to try hard

You might be able to do at least some investigating using generating functions

But I doubt you will make much headway

Best of luck!

[devout frost]

👍

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@wraith mauve Has your question been resolved?

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[crimson sedge]

<enumitem>
We are given the following five facts about a discrete-time signal $\bm xn$ with $z$-transform $\m Xz$:
\begin{enumerate}[label=\alph*), font=\bfseries]
\ii $\bm xn$ is real and right-sided 
\ii $\m Xz$ has exactly two poles
\ii $\m Xz$ has two zeros at the origin
\ii $\m Xz$ has a pole at $z = \412e^{j\omega \ff\pi3}$
\ii $\ds\m X1=\483$
\end{enumerate}
We need to determine $\m Xz$ and specify its region of convergence

[crimson sedge]

Okay, so my logic with this is that: Since x[n] is real, the two poles must be complex conjugates of each other

So like

I am thinking something like [
\m Xz = \4{Az^2}{\p{z-\412e^{\ff{(j\pi}3}}\p{z-\412e^{\ff{(-j\pi}3}}}
]

[crimson sedge]

A is a constant to be determined™️
but is this right structurally so far

[sacred grail]

™️

[crimson sedge]

anyways doing some

algebruh

you get A = 2

for the region of convergence im guessing its like

$\abs z >\412$

[crimson sedge]

because its right-sided

ok i think its right

bonk me if im not @sacred grail

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[sacred grail]

i dont remember how this stuff works so good luck

[crimson sedge]

bruh

you always tell me

you are a FOURIERER

[sacred grail]

[crimson sedge]

Ok tbf the z-transform is whatever the fuck so

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[meager pike]

for number 2,

ive created a set Ap = {|u| in X | f(|u|^p > c^p}
then i say integral_x f dm >= 1/c^p (integral_Ap f dm) >= m(Ap)

Could I also say this is an increasing sequence of sets that converges? so i could create a simple function that goes 0 <= g <= u

[mighty drift]

I don't think the inequality you wrote holds

Also there is no function f

[mighty drift]

These are both, in fact, just an application of Markov's inequality, and a potential simplification

[meager pike]

its the markov inequality

i get that 😛

[mighty drift]

By that I mean there's simpler than what you're trying to do
Which I either didn't understand, or understood to be wrong

[meager pike]

im just following my notes from a proof that uses the markov inequality from lecture

i get i made a mistake with the set notation

[mighty drift]

Well then try to correct it

[meager pike]

doing it

ive created a set Ap = {x | f(|u(x)|) > f(c^p)}

then by markovs inequality right? m(Ap) <= 1/c^p integral f(|u(x)|)dm

[mighty drift]

That's one f too many but yeah

[meager pike]

show me please, so i can be precise

[meager pike]

im not sure where the one too many f is 😛

[mighty drift]

f(c^p) is just f(c) or c^p

[meager pike]

rgr, thank you very much!!!!

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[upbeat token]

how do you find the standard deviation?

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<@&286206848099549185>

[hearty arch]

isn't it the average distance each point is away from the mean?

so you take the square of each points distance from the mean, and sum up those values. Then divide that by the number of data points, and take the square root of it.

so if you had a set like: 1, 2, 3, 6. it's average is 3.
Then (3-1)^2+(3-2)^2+(3-3)^2+(3-6)^2=4+1+0+9=14. Divide that by the number of values which is 4, so 14/4 or 7/2. Then you take the square root of 7/2 which is around 1.87 and that's your standard deviation

now do that but with your data set

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[cedar kiln]

@real tree Has your question been resolved?

[real tree]

<@&286206848099549185>

[lucid stump]

Not sure but it might be about 6.7 or something
Cus OA=OB

[real tree]

Its not an option

[lucid stump]

What are the options?

[real tree]

12root20

12root17

9root17

9root10

[lucid stump]

I got 15√17

[normal yew]

9 root 17

[real tree]

9 root 17 is an option

How tho?

[normal yew]

wait a mint i'll send you a full solution

[real tree]

kk thx

[normal yew]

yes its true

[real tree]

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[vast fable]

alrighty so as long as I am not stupid Ive set up the Lagrangian functions and differentiated in regard to x, y and lambda but I am kinda stuck on how to solve this set of 3 equations.. i assume its simple as hell and im just being stupid but im like actually lost rn haha

[cedar kiln]

@vast fable Has your question been resolved?

[vast fable]

<@&286206848099549185> :3

[alpine rune]

it won't always be simple. it goes long pretty often

[vast fable]

it was a mock exam question with 10 points so it should be solvable within 10 minutes - the solution is x=20 and y=24 but im struggling to get there...

[alpine rune]

yeah I got those values

let me tell you a shorter way out

[vast fable]

sure thx

[alpine rune]

it didn't take even 2 minutes here lol

alright so first differentiate the equation wrt x.. and then differentiate the constraint wrt x and multiply the value by lambda

then equate those

that'd be your first

(its the exact same thing but it just goes faster)

do the same with y, same variable lambda

equate both by taking y/x as t and then you get a value of t, which you use to develop a relation between x and y (which I did get), then substitute in the constraint and you'll get the x = 20 and y = 24

try what I said first, else ill simplify it

because I did that and it happened

[vast fable]

aight ima give that a try, only problem i see is that my prof made it very clear that we need to use the method he told us to use and not go different routes if we want to score points on the exam

so id assume he would want me to actually write it down the way i did in the 2nd pic and go from there

[alpine rune]

its lagrange multipliers but just simplified it down

[vast fable]

aight aight oke gimme a sec then

ty alr

[alpine rune]

ok

[vast fable]

ignore the msg just now, I'm all set thx for the help :))

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[fickle arrow]

I need help with this sequence im stuck with this question for almost 2 hours now

i tried arithmetic sequence but it doesnt work

[livid hound]

hint: explicitly express 1 and 2 as fractions with a numerator of 2

[fickle arrow]

hmmm

[livid hound]

wait

[fickle arrow]

alr

[livid hound]

misread the value

[kind gust]

yea maybe its meant to be 1/2? there are nothing i could think of with this little terms thats not crazy

[livid hound]

there doesn't actually seem to be a clear rule here

[fickle arrow]

thats why im stuck here for almost 2 hours trying to figure this out

[livid hound]

potentially some typo somewhere,
skip imo

[kind gust]

lmao i think they wanted to write 3/2 and 5/2

[fickle arrow]

perhaps yeah

let me try with those values

[limpid glacier]

it could be 50

if switched

[fickle arrow]

yeah i think its 50.5 if switched

[limpid glacier]

interesting

[fickle arrow]

oh well it is what it is thanks guys

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[gaunt badge]

Can someone please help with this question?

[kind gust]

do you know about AM-HM inequality

[gaunt badge]

I don’t think so no, could you please explain?

[kind gust]

what about AM-GM

[gaunt badge]

Also no, sorry

[kind gust]

the full name is arithmetic - geometric mean inequality

what inequalities do you know

[gaunt badge]

None I think 😓 I haven’t done them formally, I’m trying to do that now with a textbook. So far all I’ve been taught is that I should try using square numbers, knowing they are greater than 0 and rearranging

The hint tells me to let 1/x = u etc and go from there, but I don’t see how that would help me?

[cedar kiln]

@gaunt badge Has your question been resolved?

[cedar kiln]

@gaunt badge Has your question been resolved?

[candid coyote]

@gaunt badge you know the fact that x+1/x>=2?

Its the same as
$$ (x+y+z)(1/x+1/y+1/z) >= 9 $$

[wraith dagger]

A shot

[candid coyote]

Opening it you get $$ 3+x/y+y/x+x/z+z/x+y/z+z/y >= 9 $$

[wraith dagger]

A shot

[candid coyote]

And it is easy to prove

[cedar kiln]

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[crimson sedge]

how come?

[crimson sedge]

how did they get that exponent

when i multiply x-1 and -(4/x) i get that

[chrome flax]

You’re adding x-1 and -4/x

That’s what you should be doing^

[crimson sedge]

a^x * a^y = a^(x+y)

?

[chrome flax]

Yes

[crimson sedge]

let me try

[chrome flax]

(a^x)^y = a^(xy)

[crimson sedge]

yup i got it cheers

thanks

[chrome flax]

Np

[crimson sedge]

am i expected to use the quadratic formula on this noe

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@crimson sedge Has your question been resolved?

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[fervent pike]

am I supposed to give an explicit formula?

How do I start this question

do I do prove by induction and prove n+1?

hm

I found some videos that might help

I'll try it out first

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

working on it now

[azure horizon]

there's a reasonably obvious pattern

try making a formula for the pattern and then proving that it's the correct formula

by induction

[fervent pike]

the bottom left, I tried to write a formula based on the relationship between numerator and denominator

I need to replace n with somth else

n is just placeholder for now

either that, or on the right side, I tired writing a formula based on relationship between the terms

Im sort of stuck on that idea, so Im going with the bottom left idea... trying to find smth to replace the placeholder rn

[azure horizon]

that ain't it

here's a hint: look at the differences between the terms and 1

notice the pattern

[fervent pike]

difference is alternating series

and denominator of each term is doubled from previous

[azure horizon]

ok

so can you try and describe that with a formula

[azure horizon]

almost right

wait no that is right, i thought it would start at n = 0 not n = 1

wait no

ok

so try n = 3

then that would be -1/2^2 + 1

which is 3/4

so it's not quite

[fervent pike]

that should be easy fix

instead of 2^(n-1) do 2^(n-2)

[azure horizon]

sure

then in fact you can also say (-1)^(n-2)

and make it just

(-1/2)^(n-2)

because (-1)^(n-2) = (-1)^n, to be clear

[fervent pike]

ahh ok

(-1/2)^(n-2)+1 now I should do a proof by induction to verify the formula

would you assume an with the formula I found? or use the given..

@azure horizon

[azure horizon]

yeah just shove it in

[fervent pike]

so suppose an=(-1/2)^n-2+1 and prove an=(-1/2)^n+1-2+1?

oh wait

let me try it out first

[fervent pike]

damn

ism making some sort of error

@azure horizon

I dont know I cant see it???

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

skipping that question for now..

would this be a fibonacci sequence? and finding an explicit formula... its prob best to just remember it right

<@&286206848099549185>

also, if someone can please help with the last one it'd really appreciated

[fervent pike]

AHHHHHHHH

I got it

I think for both questions

ohhmyyygooodness

yea so for the last one, I was supposed to use n-3 not n-1 for exponent (you can see at the start of calculation) and this one, yes its fibonacci, I use char root method to solve the recurrence relation

BOOM

lol okokkokok

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

i’ll have to go somewhere

closing channel for now

.close

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[blissful summit]

how can i prove values of p

[mental trail]

What have you tried

[blissful summit]

tbh i dont even know

how to start

i thought of doing the integral test

then isolating for p for values that converge maybe?

not really sure though tbh

[mental trail]

Integral test is the right idea

[blissful summit]

alright ill do that from 2 to inf

ok i have no idea if i did this right at all

i got lim n approaches inf of p(ln((lnx)^p) bounded by 2 to n

nvm

i got 1/1-p of the integral bounded by 2 to inf of u^1-p

thats definitely right now

[mental trail]

Not really

The bounds should have changed

[blissful summit]

yeah mb

i substituted ln x again

to make it original bounds

[mental trail]

And you did u = lnx right?

[blissful summit]

yes

i fixed that

idk what to do here though

[mental trail]

So it's not u^1-p

[blissful summit]

its ln x^1-p yes

[mental trail]

Where does the 1 come from?

[blissful summit]

integrating 1/u^p

power rule

[mental trail]

So don't say 'integral' when you ve already integrated

[blissful summit]

alright

what is the proper term then

[mental trail]

Just .... evaluated at bounds ....

[blissful summit]

alright cool

[mental trail]

Just one final problem

Your integration doesn't cover p=1 case

[blissful summit]

right

ok thanks i got it

.close

[cedar kiln]

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[cedar kiln]

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[vocal mauve]

how did they get from this to that?

[vocal mauve]

and i dont understand how to use little o notation

i know what it is but i dont understand how can it be useful

<@&286206848099549185>

[hasty dome]

Easy

[vocal mauve]

oh ok thx

is it thanks to taylor

[hasty dome]

So first I want you to get in the zone, mentally prepares

Train your mind, jog ur memory with some meditation for 5 mins

After that

[vocal mauve]

what

[hasty dome]

Watch this video

[mortal grove]

he's trolling, ignore him

[hasty dome]

All explained above ^^

[vocal mauve]

isnt this bannable

[hasty dome]

Chill

I'm just joking

So first you wanna make it integrative right

Integratable *

So u know ur limits right?

[mortal grove]

what they did here is used $\sum_{i=1}^{\infty}x^n = \frac{1}{1-x}$

[wraith dagger]

doaby

[mortal grove]

replace x with $-t^{-1/2}$

[wraith dagger]

doaby

[mortal grove]

this should start from i = 0, my bad

[vocal mauve]

hmm

ohh

ok so they took out the t^-1/2

and they used taylor on that

but why is there little o?

i dont understand how to use it

[mortal grove]

yep! but that formula is only valid for $|x| < 1$, so gotta be careful

[wraith dagger]

doaby

[vocal mauve]

careful of what

[mortal grove]

like if your range for t is outside of that interval, equality doesn't hold

so depends on your bounds of integration

but that's being pedantic lol

[mortal grove]

little o notation goes like this. say you have this series:

$\sum_{i=1}^{\infty}x^n$

you can rewrite this as

$1 + x + x^2 + x^3 + o(x^3)$

[vocal mauve]

this was the question

[wraith dagger]

doaby

[mortal grove]

little o is just like saying ... after the x^3

it means powers higher than 3 in this case

[vocal mauve]

wait couldnt i use taylor right here in the beginning

x=-sqrt(t)

[mortal grove]

using taylor series here is actually a bad idea

[vocal mauve]

huh

so

it is a way to say like ...

like 3 dots

[mortal grove]

pretty much

[vocal mauve]

why

[mortal grove]

because that formula i showed you here is only valid if |x| < 1

but your bounds of integration depend on x, which is going to infinity

so if x is like 10 for example, your integral goes from 0 to 20, which is outside of this interval

[vocal mauve]

im not rlly understanding the reasoning

so ifu get that question

from the beginning

what would u notice?

[mortal grove]

i would start by probably just multiplying by the conjugate

since i see something added to a square root in the denominator

or you could try some u-substitution shenanigans, just anything to eliminate the square root

[vocal mauve]

so the steps i sent at the beginning arent the best?

[mortal grove]

no, and in fact they'll give you the wrong answer

[vocal mauve]

huh rlly

[mortal grove]

by the reasoning i gave above

[vocal mauve]

my prof did this

[mortal grove]

is he trying to approximate the integral? or find an exact value?

[vocal mauve]

it says calculate

[mortal grove]

this is the most handwavy argument i've ever seen lol

it might've worked out in the end but it could've easily gone very wrong

[vocal mauve]

so u saying that guy is a lucky boy

or myb he just saw its gonna work

but ye i dont understand anything and i wanna cry but i got no time to cry

[mortal grove]

i just did the integral in like 2 seconds using u substitution

[vocal mauve]

so u r saying that i should try to get rid of the square root

i tried to use u sub before but i got nowhere

myb i didnt do it correctly idk

should i try multiply by the conjugate

[mortal grove]

let u = 1 + sqrt(t)

try that and see where you get

[vocal mauve]

ye

i did that

i got nowhere

[mortal grove]

oh where did you get

[vocal mauve]

hmm

[mortal grove]

worked for me

[vocal mauve]

ok then im just bad

[mortal grove]

i'm sure it was just an algebra mistake

[vocal mauve]

wanna hop on a call rq

[mortal grove]

it happens

[vocal mauve]

imma share my screen

[mortal grove]

no i'm busy irl

[vocal mauve]

no im just bad cuz idk how to do this stuff

aight

[mortal grove]

just send a ss of your work

[vocal mauve]

wanna hop on a call no mic just so u see my screen

imma do it on paint with a graphic tablet

just the integral

nah man i got it wrong cuz idk how to actually do it

thats the way i did it but its obviously wrong

i cant have a sqrt(t) there

but idk how to do it

@mortal grove ping

[mortal grove]

almost but you want everything in terms of u. so what is sqrt(t) in terms of u?

[vocal mauve]

ohh bruhhhh

ye aight imma try it

??? does this make sense

am i still missing sometihng

oh ye lmao

wait

i got this?

[vocal mauve]

now i think its correct

and now i got that does it make sense

@mortal grove i hope its fine if i ping u

[mortal grove]

that looks right to me. now just substitute t back in and plug in your limits

[vocal mauve]

nice so its good

[mortal grove]

then take the limit as x -> infinity and that'll give it to you

yep

[vocal mauve]

dont i have to do the integral before?

[vocal mauve]

is the last step even correct?

cuz the integral was from x to 2x

[mortal grove]

everything you did is fine. but now you have to evaluate that at your limits. to do that, you need to convert back to t since your limits depended on t

alternatively, you can change your limits of integration using u = 1 +sqrt(t)

so at t = x, u = 1 + sqrt(x)

and at t = 2x, u = 1 + sqrt(2x)

those would be your new bounds

both ways are valid

[vocal mauve]

i got that plugging in t

oh so now i just plug in 2x instead of t

minus the same but with x

and then i do the limit

im stuck again

i got to here

[vocal mauve]

(there's missing a 1+ in the log)

[cedar kiln]

@vocal mauve Has your question been resolved?

[cedar kiln]

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[civic coral]

At

[civic coral]

Except from these two green points, that you are able to find it after putting in a corresponding inputs.

.close

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[rigid dust]

Can someone help me with logarithms?

[pliant atlas]

waddup

[rigid dust]

I’m looking for a simple explanation I can give ya a precise example 😭

[pliant atlas]

alright

[rigid dust]

You know how it is in math class when the teacher got a thick accent?

[pliant atlas]

yuh

[rigid dust]

I’m struggling

[pliant atlas]

right

[rigid dust]

Alr alr hollup

These are my teachers notes, do you think you could explain it to me a bit?

[pliant atlas]

I forgot

Log laws

My bad

[rigid dust]

All good

[pliant atlas]

[rigid dust]

I’m trynna see if I can find any other notes

Text is blurry asf golly

This what I’m looking for?

[plucky owl]

Good video btw https://www.youtube.com/watch?v=oVUJMVR1JpA&ab_channel=TheOrganicChemistryTutor

[rigid dust]

Ty ty

https://tenor.com/view/there's-nothing-we-can-do-gif-14390726165144583214

[cedar kiln]

@rigid dust Has your question been resolved?

[rigid dust]

No

[cedar kiln]

@rigid dust Has your question been resolved?

[cedar kiln]

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[fast arrow]

Can someone please check my work

[fast arrow]

<@&286206848099549185>

[cedar kiln]

@fast arrow Has your question been resolved?

[fast arrow]

<@&286206848099549185>

.close

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[gloomy delta]

Can someone tell me how can I even start this?

[livid hound]

apply factor theorem

[gloomy delta]

Thank you, will research

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[sick fossil]

idk what I'm getting wrong here

[digital cliff]

seems you have an uninvited guest

called x

[sick fossil]

should just be a number right?

[digital cliff]

should be t

[sick fossil]

t?

[stark blaze]

yeah because where did the x come from?

[digital cliff]

think the derivative is wrong too though

actually nvm

but yeah, your stuff has t's, there was never an x

[sick fossil]

oh

wrong variable

used to doing math with x

is there a diff between f'(a) and f'(t) then?

[digital cliff]

yeah

just replace t with a

its like if it asked for f'(5)

a is just some number

[sick fossil]

no

just find f'(a)

[digital cliff]

what??

[sick fossil]

no yeah it was just to find f'(a)

no number

[digital cliff]

i... know?

idk what youre talking about

i was giving an example

[sick fossil]

oh

mb

how do I start?

ik it's smth along the lines of finding a slope but along where?

Im assuming 40-60

[digital cliff]

you could ig, i would just draw the tangent line, if thats possible

but since its quite straight there, relatively

itll give a good enough estimate

[sick fossil]

Id only get the slope out of it no?

or is that enough info to proceed?

slope is 25

@digital cliff ?

[digital cliff]

slope is all it wants

,calc (710-200)/(20)

[wraith dagger]

Result:

25.5

[sick fossil]

so the slope is f'(50)?

[digital cliff]

well, the slope of the line joining the the points at x=40 and x=60 is an estimate for f'(50) which is the slope of the tangent to f at x=50

its an estimate, not the value itself

it only works because f is almost linear between 40 and 60

[sick fossil]

ic

ty

[cedar kiln]

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[rose tinsel]

Hey just wondering where I went wrong in this problem. I did not get the right solution doing the problem this way but doing it a different way I did find the right solution. I just want to know what is wrong about this way.

[rose tinsel]

This is the way that yields the correct answer and the only difference is factoring one more time in the denominator before moving to partial fraction decomposition

[rocky harness]

If you substitute $x=sec(\theta)$, you get $\int \frac{sec(\theta)tan(\theta)dx}{sec^{2}(\theta)-1}$

[wraith dagger]

smidgin

[rose tinsel]

ah i see

i accidentally brought in the sqrt

[rocky harness]

Yep

[rose tinsel]

is there a way to solve that integral using trig sub or nah

i mean i know that integral is equivalent to inverse tanh but i forget how to get there

[rocky harness]

$\int \frac{sec(\theta)tan(\theta)dx}{sec^{2}(\theta)-1}=\int \frac{sec(\theta)tan(\theta)dx}{tan^{2}(\theta)} = \int cosec(\theta)dx$

[wraith dagger]

smidgin

[rose tinsel]

would i use u sub sec maybe?

ah real

so just go about it without the root

makes sense

[rocky harness]

Yes, and don't mind the dx instead of dtheta

[rose tinsel]

nvm this is stupid this would take me back to where i was

[rocky harness]

Yeah, you just did the sub x=sectheta so you'll just undo your u sub

[rose tinsel]

yep

Yeah so then I get this

only difference is inside the natural log but you can flip the sign of the numerator and denominator due to the absolute value right

so then you get the same answer as the other method

Alr cool thanks just a simple mistake in the end

.close

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[rocky harness]

!status

[cedar kiln]

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

[rocky thunder]

1

[rocky harness]

Do you know that when speed is constant, speed=distance/time?

[rocky thunder]

sure

[rocky harness]

Use that here, write what is given into equations

[rocky thunder]

what is the distance and speed

[rocky harness]

They have given us a relationship between the times taken, in the second case.the time taken is 4.5 hours lesser when his speed increases by 2kmph

[rocky thunder]

ye

so what do i write

[rocky harness]

Ok, so first start off by rearranging this to get
time = distance/speed

[rocky thunder]

ok

[rocky harness]

Ok, so suppose the time taken in the first case is x and in the second case, it is y

What is the relation between x and y?(hint: it takes 4.5 hours lesser when the speed increases by 2 kmph)

[rocky thunder]

idk

[rocky harness]

x-4.5=y

Do you see why?

[rocky thunder]

oh

yea

[rocky harness]

We aren't told what the speed is either, so let's say the speed is s

[rocky thunder]

aight

[rocky harness]

x=108/s

[rocky thunder]

yup

[rocky harness]

Do you agree?

[rocky thunder]

yuhh

[rocky harness]

Now let's increase the speed to s+2. we know when the speed is s+2, the time taken is y

So y=108/(s+2)

[rocky thunder]

ye

[rocky harness]

Put x and y here

[rocky thunder]

ok

[rocky harness]

(108/s)-4.5=108/(s+2)

[rocky thunder]

ye

roger that

[rocky harness]

Can you solve this equation now?

[rocky thunder]

lemme try

ok i got it

tysm

ur a legend

.close

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[cedar kiln]

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[marsh lake]

how do u find the distance between the intersecting points of red and blue?

[marsh lake]

the pic is just an example

[short blade]

what do you mean by distance

like the difference in x values, or the length of the curve

[marsh lake]

distance of each intersecting point between each other

[short blade]

did you make up this question

if not, do you have the original question

[marsh lake]

-5<x<5, 8sinx+3=0

[short blade]

i mean like a picture

[marsh lake]

its the answer

[short blade]

why did you send me the answer

[marsh lake]

because i dont know how to do it?

[short blade]

i mean

i asked you to send me the question

and you sent me the answer

i dont understand what is happening

[marsh lake]

this is the question

[short blade]

that is not a question

also, i asked if you could send a pic

to clarify

[marsh lake]

8sinx+3=0, -5<x<5, find all values of x

the answer solved it graphically

[cedar kiln]

@marsh lake Has your question been resolved?

[cedar kiln]

@marsh lake Has your question been resolved?

[cedar kiln]

@marsh lake Has your question been resolved?

[marsh lake]

<@&286206848099549185>

[tame zodiac]

do you have any x values that meets 8sinx+3=0?

[hearty arch]

Find the x values of the intersection points, say x1 and x2, and the distance between them for this particular instance (one of the functions is a horizontal line) is |x1-x2|

[cedar kiln]

@marsh lake Has your question been resolved?

[marsh lake]

ohh

thanks

[cedar kiln]

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[undone crypt]

What is the solution to this?

[undone crypt]

I got one answer, wolfram got a diffirent and my professor got a diffirent

[vague rapids]

well show your working

[vague rapids]

The answers may be same, it could be possible that the way of representation is different

[undone crypt]

eller means or

[mental trail]

pi/2 and -11pi/2 are congruent mod pi/2

so they give the same answers

[wanton grove]

this is same as wolframs answer

[mental trail]

replace n by n+2 in the first set of solutions WA gave you to convince yourself of that

[undone crypt]

ok, but what is my professor doing that i am missing?

[mental trail]

and in your working, the reason why your answer is different is because (2x+pi/3) = arccos0 + 2pin or
-(2x+pi/3) = arccos0 + 2pin

you forgot to distribute the minus sign

or wait let me rewrite it

very much likely because arccos0 = pi/2

and 5pi/6 very much cannot be written as pi/6 + 2pin

[undone crypt]

Oh

But then

[mental trail]

and furthermore

it's not 5pi/6

it's -5pi/6

forgot the minus sign

[undone crypt]

And i guess i can rewrite that as 7Pi/6

[mental trail]

yes, mod 2pi

[undone crypt]

I dont know what mod is

But it seems like its the most basic answer for a periodic function

Ok but still now

I dont have the same solutions

[mental trail]

well now you have those

so divide by 2

[undone crypt]

At the very last part of my professors solution they have +Pi/2n, where does that come from?

[mental trail]

it's just this part

distinguish between the cases "n is even" and "n is odd"

[undone crypt]

what?

[mental trail]

Before we continue, you now have the solutions on the left of "eller" correct?

[undone crypt]

Correct

[mental trail]

so start from the right, x = pi/12 + pi/2*n

if n is even, n = 2p

and so x = pi/12 + pi*p

if n is odd, n = 2p+1

so x = 7pi/12 + pi*p

here are the two cases, brought into a single one

[undone crypt]

Wait so the left side of ”eller” means the same thing as the right side?

[mental trail]

yes

[undone crypt]

Ahhhh

Thank you

Ahhh that was confusing

He basicly said: ”its ok to answer like this too”

?

[mental trail]

yeah

because in both cases you give explicitely the correct values of x

it's just that the second answer (right side) is more compact

it's like answering "x is an even integer or x is an odd integer" instead of "x is an integer"

[cedar kiln]

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[cedar kiln]

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[subtle hinge]

can somoen help me with 2

[cedar kiln]

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[subtle hinge]

.reopen

[cedar kiln]

✅

[subtle hinge]

can someone pls solve that

[cedar kiln]

@subtle hinge Has your question been resolved?

[cedar kiln]

@subtle hinge Has your question been resolved?

[quaint forge]

the no. of distinct terms will be the highest power of x +1

[cedar kiln]

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[fervent pike]

how is it that 1/(sqrt(n+1)+sqrtn) < 1/2sqrt(n)??

what

[crystal raptor]

sqrt(n+1) + sqrt(n) > 2sqrt(2) might help you, try and see why

[fervent pike]

oh wait

yea so deno is bigger hence why the value is smaller

damn

ok

thanks

.close

[cedar kiln]

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[fervent pike]

.reopen

[cedar kiln]

✅

[fervent pike]

so I’m going to go back to a question I did yesterday

I used a different method to find a closed formula for the recurrence relation

and now I’m trying to prove my formula is correct by induction

I would like some guidance as to if my methods and process are correct

and how I can simplify my equation to get a_n+1

[azure horizon]

wtf are you doing

where did 12 come from

what is 5

what happened to the other formula

[fervent pike]

yea so im trying a new method I found on youtube, characteristic root technique

[azure horizon]

the thing isn't right though

like try n = 1

wait no

wait yeah

try n = 2

12 (-1/2)^2 + 5 = 3 + 5 = 8

check your workings

[fervent pike]

n=1, n=2 is provided tho

this formula needs to work with the given values too right

[azure horizon]

yes

[fervent pike]

wtf so this method is wrong??

[azure horizon]

no

you probably did the workings wrong somehow

so the characteristic root method lets you say

a_n = A(-1/2)^n + B right

you got that?

did you get that

so you just need to substitute

[fervent pike]

i see

[azure horizon]

a_1 = -A/2 + B = -1

a_2 = A/4 + B = 2

and then you shouldn't get 12 and 5

[fervent pike]

got -12 and -7 this time...💀

idk

oh

ohhmyyyywhy

[azure horizon]

did you get it?

[fervent pike]

4 and 1

should be an = 4(-1/2)^n+1

yea

thats right

also, this is gonna sound really stupid but how can I simplify this? to match 4(-1/2)^n+1 +1

[dire geode]

,tex .exp rules

[wraith dagger]

riemann

[fervent pike]

i cant get it to match for some reason🥲

oh

YASSSSSSS

ok

we good

lol thank you guys soooo much

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

staying here for now

in case of more questions

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

if a sequence (an) has finitely many terms outside the interval (a-eps, a+eps) and infinitely terms inside, that would be convergent?

and divergent is if the above property does not hold?

[dire geode]

is eps fixed?

[fervent pike]

what do you mean?

[dire geode]

is there a $\forall \eps > 0$ somewhere

[wraith dagger]

riemann

[dire geode]

or is it a fixed number like $\eps = 0.01$

[wraith dagger]

riemann

[fervent pike]

Im trying to understand what its saying here

Im gonna try to read more about it...

not really understanding whats happening here

[cerulean sail]

What they're saying is that if you have this, that there are only finitely many terms of a(n) outside the interval, the sequence converges to the limit a...

But saying that there are infinitely many terms in that interval doesn't necessarily imply that there are only finitely many outside the interval

Assumedly they took the sequence (-1)^n as their example 4.1? Note that for that, you have all the even terms as 1 and the odd terms as -1

So you have infinitely many terms "close to 1" and infinitely many terms "close to -1", but, if you shrink your interval small enough (say being within eps = 1), then you have infinitely many terms that are in each interval, and infinitely many terms that aren't

[fervent pike]

that would be divergent tho, no?

[cerulean sail]

Yes, (-1)^n is not convergent

[fervent pike]

so what I'm saying here is true?

[cerulean sail]

If you can't find any a so that you have this true (for any eps > 0), then sure

(however, be a bit careful: if you have a specific "a" such that it isn't true, that doesn't mean the sequence doesn't converge, all it means is that it doesn't converge to the specific "a" you chose)

[fervent pike]

ok, so then that would just mean you chose the wrong 'a' then

so by definition, convergent sequences that converges to a has infinitely many terms inside (a-eps,eps+a) and finite outside

and if not, then its divergent or you chose the wrong a

[cerulean sail]

Not convergent to [that] a

[cerulean sail]

(it might be, either you chose the "wrong" a, or that there might be no such a where it's true, it could be either one)

[fervent pike]

if you have no such a where it is true then wouldnt that be divergent then?

[fervent pike]

made an edit

[cerulean sail]

Better

[fervent pike]

and if you have set of numbers in a sequence denoted like this, {an}, its not the same thing as a set right? because you can have numbers repeating

no it is written like a set

right

thats what was confusing me

[cerulean sail]

Strange they're mixing their notation, the (a(n)) and {a(n)}

You are right that terms in a sequence do not need to be distinct

[fervent pike]

back in an hour or two

[cedar kiln]

@fervent pike Has your question been resolved?

[cedar kiln]

@fervent pike Has your question been resolved?

[fervent pike]

i just went to a meeting and then took a longggg break

damn i really need to get back to work

exam tmr😱

[fervent pike]

would this be right?

again theres no solutions to the textbook im using

I dont know what to doooo

<@&286206848099549185>

[cerulean sail]

[fervent pike]

idk😭 😭