help-0

[modest zinc]

Now do I integrate?

[wind cloak]

You should have u^2 - 1

Other than that you're good

And yes integrate

[modest zinc]

okay, this is where I’m lost. I got everything else! This is where i need help

[wind cloak]

Where are you lost?

[modest zinc]

Integrating. You’re just doing the anti-derivative right?

[wind cloak]

yes

[modest zinc]

I’m going back through my notes😭

[wind cloak]

$\int x^n \dd{x} = \frac{x^{n + 1}}{n + 1} + C$

[ocean seal]

NEONPerseus

[wind cloak]

This is all you should need to know

[modest zinc]

??

[wind cloak]

You need to remove the integral sign

And also the 1 = x^0

you need to integrate that as well

[modest zinc]

So what about the 8?

[wind cloak]

keep that out its a constant multiple

[modest zinc]

Okay.

And isn’t the anti-derivative of 1….just 1?

I’ll figure it out. I gotta get to class. Thank you a bunch for doing this! This helped a bunch!

Gotta go!

[wind cloak]

its u

$\int 1 \dd{x} = \int \dd{x} = x + C$

[ocean seal]

NEONPerseus

[modest zinc]

AHHHH😭😭😭

Okay. Thanks a bunch!!

.close

[lone heart]

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[tidal ingot]

i really am stuck here and not sure how to caulcate the expected value

[tidal ingot]

what are the values of X we use to get the weights?

[noble sinew]

Find the PMF if needed first

[tidal ingot]

for which values?

thats my main issue

X is discrete

[noble sinew]

A PMF is defined for all real numbers

[tidal ingot]

hm

[noble sinew]

P(X=x)=1/2 for x=1,2 and 0 otherwise is a PMF for example

[tidal ingot]

yes

p(X=x) = p(X<=x) - P(X<=x-1)

idk how to use this property here

hold on do i even need it?

[noble sinew]

Thats not true in general

[tidal ingot]

yes only for discrete no?

this is discrete

[noble sinew]

Can you tell me P(X=0)? P(X=1)? P(X=-1.6261671),…? Notice anything thats similar for all these?

[noble sinew]

Still no

[tidal ingot]

0.1 no ?

[noble sinew]

Are they all 0.1? How did you get that?

[tidal ingot]

it is cdf so 0.1 is the sum of all their probabilities

[noble sinew]

P(X=x)=1/2 for x=1, 1.1 and 0 otherwise. Then P(X=1.1) is not equal to P(X<=1.1)-P(X<=0.1)=1-0=1. So it doesn’t hold for any discrete RV

[noble sinew]

???

[tidal ingot]

hmm

im really confused how do we get PMF for all real numbers here

and how are you giving X real number values example when its discrete

[noble sinew]

You just said yes to an example where I said PMF is for any real number

So which one is it

[tidal ingot]

X is a discrete RV here

[noble sinew]

So was the one I gave an example of

[tidal ingot]

yeah

[noble sinew]

So?

[tidal ingot]

im not sure where u got the values 1,2 from

where do we get them here

[noble sinew]

An example

EXAMPLE

[tidal ingot]

yeah where do we get them here

for x = -5, -6 .... p(x) = 0

[noble sinew]

1 thing at a time

So agree or disagree its defined for every real number

No matter if discrete or continious?

[tidal ingot]

yeah but its 0 if its like 1.1 for example?

[noble sinew]

Discrete means countably many values where the density is non zero

It doesn’t mean integers only where its non-zero

[tidal ingot]

alright

so then?

here

[noble sinew]

Well how did you find P(X=0)?

[tidal ingot]

i usually do the rule we took in class as mentioned before

[tidal ingot]

.

but now that u said its not necessarily integers

that hold non zero values

i dont think this works anymore

[noble sinew]

Indeed it doesn’t

[tidal ingot]

so what in the world do i do

[noble sinew]

Could P(X=0) be say 0.1?

[tidal ingot]

i dont see a reason why not

[noble sinew]

We are given P(X<=x)=0.1 for -4.5<=x<3

If P(X=0)=0.1 could the above be true?

[tidal ingot]

P(X<=x) is equal to the sumation of all porbabilities of X <= x

right?

[noble sinew]

Yes

[tidal ingot]

yes it could be true

[noble sinew]

You are told P(X<0)=0.1=P(X<=0) for example from that

If P(X=0)=0.1 wouldn’t we have P(X<=0)=P(X<0)+P(X=0)=0.2?

[tidal ingot]

oh yeah that is true

how does this benefit us?

[noble sinew]

So what must P(X=0) be?

[tidal ingot]

0

[noble sinew]

What about P(X=1)? What about P(X=0.5)?

Notice anything in common with all these?

[tidal ingot]

just a second where are we told that P(X<0)=0.1=P(X<=0)

where exactly

[tidal ingot]

how did u derive it from this

[noble sinew]

P(X<=x)=0.1 for any x in [-4.5,3)

Is what that means

So I just picked some values in that interval

[tidal ingot]

so P(X<=2.5) = 0.1

same thing for

[tidal ingot]

these

[noble sinew]

= and <= is not the same

[tidal ingot]

P(X<=x) = P(x) + P(X < x)

right?

[noble sinew]

Yes

[tidal ingot]

p(x=1) is 0

[noble sinew]

What about P(X=0.5)? What about P(X=pi-1)? Notice anything in common with all the values I picked if you look at the given CDF?

[tidal ingot]

for eample for P(x=0.5) , p(x<=0.5) is equal to p(<0.5)

and its the boundary values that have non zero probability on them?

well not all of them

P(X=6) is 0.3

p

(x=-4.5) is .1

thank you dude everything makes sense now

[noble sinew]

Yep

[tidal ingot]

.close

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[river bough]

Hey so I get the difference between an lebm and a rebm but I don't get why how we choose the different models

it makes sense that the rebm is e^x/x^3 since that's the most influencial powers

but why is the lebm x^-10/ x^3?

isnt e^x much much more "powerful"?

[lone heart]

@river bough Has your question been resolved?

[river bough]

<@&286206848099549185>

🙏

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@river bough Has your question been resolved?

[lone heart]

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[lone heart]

@vernal kindle Has your question been resolved?

[keen pasture]

What did you try?

[versed escarp]

2 ways:

bottom edge - top edge = ?
Use the scale

[lone heart]

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[versed escarp]

You don't have to answer but just asking what grade you're in

[lone heart]

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[autumn tartan]

how will i do the bottom 2 questions?

i think i filled in all the missing data correctly

.close

[lone heart]

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[alpine sable]

I need help

[alpine sable]

With p win and p lose

[tacit arch]

what grade are you in

[alpine sable]

I’m in the uk year 11

My spelling trash

@tacit arch you there ?

[tacit arch]

show what you tried

[odd coyote]

i need help with 5446x45 can someone help

its broken

[tacit arch]

go back to your channel

[odd coyote]

brruh im new on tthis serv

[alpine sable]

Back

I tried adding them all

[lone heart]

@alpine sable Has your question been resolved?

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[olive canyon]

i need someone to explain what this expression means

[olive canyon]

i know that eventually this is the identity operator for psi

but i still don't understand what the bras and kets and the summation mean

it becomes this

[tacit arch]

why do you need to know

[olive canyon]

and i believe this means the dot product of vector j with its hermitian counterpart, multiplied by psi

[tacit arch]

the document you're reading from should explain it

[olive canyon]

it's a powerpoint with no context

[tacit arch]

show the whole slide

and a few slides before too

[olive canyon]

professors have the tendency to esplain stuff without giving context

it's i ndutch

[tacit arch]

that's fine

[tacit arch]

and for what purpose do you need to learn

[olive canyon]

are you familiar with dirac nottion?

[olive canyon]

quantum mechanics

[tacit arch]

are you learning qm?

[olive canyon]

yeh

[tacit arch]

do you know what hilbert spaces are?

is this finite or infinite dimensional?

[tacit arch]

is the sum j finite?

[olive canyon]

it's finite

it represents the number of rows/colums in a row/column vector

[tacit arch]

$| j\rangle$ are the eigenbasis

[ocean seal]

riemann

[tacit arch]

right eigenvectors, specifically

$\langle j |$ are the left eigenvectors

[olive canyon]

see the thing is

[ocean seal]

riemann

[olive canyon]

i don't know what eigenvectors are

i know about eigenvalues

but not eigenvectors

[tacit arch]

linear algebra is definitely a pre-requisite for quantum mechanics

https://www.khanacademy.org/math/linear-algebra/alternate-bases/eigen-everything/v/linear-algebra-introduction-to-eigenvalues-and-eigenvectors

[olive canyon]

which is why i'm not really following with what the prof is saying

[tacit arch]

deeper linear algebra resource http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/751LinearAlgebra.pdf

[olive canyon]

eigenvalues i know, it's a number that scales a vector in the same way a matrix does

but i'm not familiar with eigenvectors

or i forgor

[pseudo ice]

Eigenvectors come paired with eigenvalues

Do you have a definition of eigenvalues you’re used to? Almost always I see eigenvectors immediately defined at the same time

[olive canyon]

A v = x v

with A a matrix, v a vector and x a scalar

and x is the eigenvalu

[pseudo ice]

That v is the eigenvector corresponding to the eigenvalue x

[olive canyon]

so eigenvectors are just vectors corresponding to an operation in which the vectors are just scaled and not rotated

in other words all eigenvectors share the same direction

is that right?

the thing that makes this so confusing for me is that i have done much of this math, but not with complex numbers

[pseudo ice]

Pretty much, your eigenvectors just get scaled under multiplication by your matrix (or equivalently under applying your linear map) and how much you’re scaled by is your eigenvalue

For more detailed explanations I’ll probably have to defer to other resources

[pseudo ice]

And for the most part it’s similar (hah!) but with a lot more benefits when you work under complex numbers (for example more matrices being diagonalisable)

[lone heart]

@olive canyon Has your question been resolved?

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[dark ibex]

Make a table of values and find the limts of
lim e^x
x->0

[dark ibex]

Did I do it right?

[lone heart]

@dark ibex Has your question been resolved?

[dark ibex]

<@&286206848099549185>

[delicate hearth]

make x closer to zero

[dark ibex]

Now?

[delicate hearth]

make closer in both sides, and see numerical view

[dark ibex]

?

how do see numerical value

[delicate hearth]

which software are you using?

[dark ibex]

Desmos graphing calculator in a browser

[lone heart]

@dark ibex Has your question been resolved?

[dark ibex]

<@&286206848099549185>

[delicate hearth]

it should be something like that

[dark ibex]

Oh ok

A lot more closer to 0

.close

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[pallid creek]

I might be wrong but

[pallid creek]

Like

Let's say ln(2)

That's

2^e = x right?

So e x ln(2) = x

Therefore x = whatever

But doesn't that also mean ln(2) = eln(2)

[exotic belfry]

$e^{ln 2}=2$

[ocean seal]

ThM

[tacit arch]

this whatever is what you're confused about

[pallid creek]

I need to think hard about this

ln(2) is log base e of 2 right?

Meaning

2^e = x?

And u can move the e to the front

So u get eln(2) = x

But x is also ln(2) no?

[dense jacinth]

yes

[exotic belfry]

logarithm of x with respect to base 2 is not ln(2) if this is your question.

[dense jacinth]

where does x come from

[pallid creek]

Idek

Just making it into an equation

Or no?

Would it just be 2^e

[dense jacinth]

ln(e^x) = x

[pallid creek]

Where did ur x come from

[dense jacinth]

its an identity

for any value of x

[pallid creek]

Oh right

I see I see

So e^x = 2?

[dense jacinth]

ln(e^2) = 2

[exotic belfry]

this

[pallid creek]

So ln(2) is the same as ln(e^2) = 2, or they are seperate equations?

[dense jacinth]

seperate

[pallid creek]

So what happened to ln(2)

[dense jacinth]

ln(2) is irrational

ln(e^2) is just 2

which is an integer

you can't simplify ln(2) any further

but ln(e^x) is simply just x

[pallid creek]

Wait wait that equation is 2 because the ln and e cancel?

[dense jacinth]

this?

yes

[exotic belfry]

thats the definition of ln

[dense jacinth]

e^ln 2 = 2 has the same effect aswell

[pallid creek]

Yea bc u can move ln to the front right?

[lone heart]

@pallid creek Has your question been resolved?

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[maiden narwhal]

How do I calculate the primitive function of 6 ÷ √x?

[tacit arch]

power rule

,tex .int rules

pain i removed it

$\int x^n dx = \frac{x^{n+1}}{n+1} + C$

[ocean seal]

riemann

[maiden narwhal]

ah, how would the numbers go in this case?

[tacit arch]

$\frac{1}{\sqrt{x}} = x^{?}$

[ocean seal]

riemann

[maiden narwhal]

what's the question mark supposed to be?

[tacit arch]

for you to figure out

[last ether]

He wants you to solve for the question mark

[maiden narwhal]

thats what i cant do

[tacit arch]

,tex .exp rules

[ocean seal]

riemann

[tacit arch]

use negative exponent and fractional

[last ether]

You're so cool Riemann

[maiden narwhal]

i wish i was riemann

so 1/x^0.5 = x^-0.5

and 6/x^0.5 is 6 times that?

[tacit arch]

correct

[maiden narwhal]

and primitive function of that will be 12*x^0.5

[tacit arch]

,w diff 12x^0.5

[ocean seal]

Results provided by WolframAlpha

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Requested by riemann#2529

[maiden narwhal]

thanks! i appreciate it a lot

.close

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[strong dirge]

The graph is a similar shape to sqrtx so it can't ever be concave upwards

what would the interval notation be?

[serene junco]

hm, I'm not so sure about that second derivative

For parametric equations, $\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dx}{dt}}$

[ocean seal]

tatpoj

[serene junco]

Is this what you used?

[strong dirge]

I did that

[serene junco]

Hm

I think you missed a factor of 2 somewhere?

and to find where the graph is concave upward, you need to find where $\frac{d^2y}{dx^2} > 0$, so you can just solve the inequality

[ocean seal]

tatpoj

[serene junco]

It is concave up for some values of t. If you don't see any on the graph, I suspect you're only considering positive values of t, but the problem doesn't specify t>0

[lone heart]

@strong dirge Has your question been resolved?

[strong dirge]

Oh ok so it would be (-infinity,0]?

yeah that's the answer bruh

but the second derivative is incorrect

got it

had 2 instead of 4 in the denominator

Could you try this question out of curiosity?

I found it extremely difficult to integrate

[lone heart]

@strong dirge Has your question been resolved?

[fallen iron]

if I multiplay twenty why are these 20 (denominator) gone?

[lone heart]

@strong dirge Has your question been resolved?

[brave knot]

2y-x=5

i dont get thatttttt

[lone heart]

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[fickle owl]

Can anyone help with real analysis?

[fickle owl]

Bottom 5 questions

Quite high level

<@&286206848099549185>

Mainly 2,3,4

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[lone heart]

@fickle owl Has your question been resolved?

[lone heart]

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[vapid shuttle]

mwuahaha help-0 is mine

Here is what I tried doing for this question, the correct answer is p = <1 , 2, 3, 0 > and P is the same matrix as mine but with a zero row below it

I don't understand where I went wrong

could someone take me through from the beginning perhaps?

isn't the projection of b onto A a 3D vector anyways? So I understand that in space <1, 2, 3, 0> and <1, 2, 3> are the same, but why would the answer include a 0 fourth component

<@&286206848099549185>

[echo forum]

u can think of it as mapping the input vector from 4 dimension to 3

[vapid shuttle]

yes

[echo forum]

so basically keeping everything except

last feature

[vapid shuttle]

is there then a real difference between <1, 2, 3> and <1, 2, 3, 0 > as an answer for the projected vector?

[echo forum]

well 1 is in R^3 and the other is in R^4 if that makes sense

[vapid shuttle]

and should our projected vector be in R3 or R4

we are trying to project it into the columnspace of A

so I would assume that to be R3? since A is 4x3 ?

but supposedly the answer is <1 , 2, 3, 0>

[echo forum]

well thte projection matrix is actually

4 x 4

[vapid shuttle]

sure

but aren't we projecting onto the column space of A

[echo forum]

WEll recall for the formula

of the projection space

is defined as P = A(A^TA)^-1A^T

[vapid shuttle]

and, when I tried to find the projection matrix using the formula I found it to be 4x3, so can you tell me if I have the proper formula or if I just messed up

[echo forum]

just try multipying it out

u fidn that A^TA

= I

and that P = AA^T

[vapid shuttle]

yes I got that

[echo forum]

as a result of that

[vapid shuttle]

wait

Doesn't P = A(I)A^T

[echo forum]

u should get P = 4 x 4 matrix where first 3 columns

[vapid shuttle]

and the identity is 3x3

that's where I got mixed up it seems

[echo forum]

ya but u will find that u will basically get A

when u multiply if my mental calc

r collect

so u get AA^T

and then multiplying Pb

yields the proper projection u desire

[vapid shuttle]

So I did all of these steps in my work

and the reason I am basically missing a dimension

from the projected vector b

and the projection matrix

is because I multiplied by the identity matrix

which was 3x3

[echo forum]

well it should be 4 dimension

[vapid shuttle]

and it brought down my dimensions

[echo forum]

if u did it right

u messed up ehre

[vapid shuttle]

how

because I should have a zero row

right

[echo forum]

it should haave another row at bottom w all 0s

ya

[vapid shuttle]

but

where did I lose that row

is my question

because the step above I multiplied a 3x3 by a 3x4

that's why I got what I got

the 3x3 was the identity

from ATA

[echo forum]

from what it looks i think u mssed up here since A = 4 x3 so
A A^T = 4 x 3 x3 x4 = 4 x4

[vapid shuttle]

4x3 times 3x4

is 4x4 ?

[echo forum]

well u get 4 x4 matrix

right as output

cuz it

''s outer dimension

that determine the output dimension

of matrix operation

[vapid shuttle]

wait

AT was 3x4

and A was 4x3

[echo forum]

ya

[vapid shuttle]

and I was performing

ATA

so shouldn't I have gotten 3x3

like I did

[echo forum]

well u still messed up

[vapid shuttle]

wouldn't that produce a 3x4

[echo forum]

3 x 3

the problem here is that ur missing

features of A

even if u did it correctly

either way u ahve to calculat efor AA^T

[echo forum]

3 x4 x4 x 3 = 3 x3 output

[vapid shuttle]

ohhh it looks like I forgot to multiply by A aswell

[vapid shuttle]

this here is 3x3 and 3x4

[echo forum]

ya

[vapid shuttle]

I will try this again

thank you

[echo forum]

also ya ur right it should be 3 x4 i trolled

sorry if that threw u off

[vapid shuttle]

no worries

this channel is occupied

read #❓how-to-get-help

[echo forum]

hint: when u just have length of side = x
area = (x)^2 perim= 4x
when u have length of side = 4x
perim = 16x area = (4x)^2 = 16x^2

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[stable night]

hi can someone tell me if this is the simpliest form

.close

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[lone heart]

@rich basin Has your question been resolved?

[rich basin]

<@&286206848099549185>

[alpine sable]

slope is undefined

you need to give the equation

it will be x = 1

[rich basin]

how come?

[strange meadow]

Because it’s a vertical slope

And it’s at x=1

[rich basin]

okay

[strange meadow]

x=k is a vertical slope where k is a constant

[alpine sable]

tan of 90 degree is undefined which means slope is undefined

[rich basin]

right, thanks

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[buoyant depot]

i'm slow

b-a/n(f(x0)+2(x1)+4(x2)+2(x3) etc

right?

but wrong?

[lone heart]

@buoyant depot Has your question been resolved?

[jagged cobalt]

$\frac{b-a}{2n}[(f(x_0)+f(x_n))+2(f(x_1)+f(x_2)+...+f(x_{n-1}))]$

[ocean seal]

AℤØ

[buoyant depot]

over 2n?

so what i have is correct just needs to be 6/14 not 6/7?

[jagged cobalt]

i would usually write it as h/2 where h=(b-a)/n
im not sure since you have a 4(x2) here? where'd the 4 come from?

[buoyant depot]

wait delta x over 3

isnt it

delta x / 3 (x0 + 4(x1) + 2(x2) etc

oh wait hm i see

i’ll give it another go but

[jagged cobalt]

wait, i think we're talking about different things - are you talking about simpsons or the trapezoid?

[buoyant depot]

simpsons

i got simpsons wrong havent given trapezoids a go yet

sorry i should’ve specified

[jagged cobalt]

ah i see, ive been talking about trapezoids since the box was empty😅 one sec

[buoyant depot]

is it just my delta x / 3 which is wrong?

[buoyant depot]

no worries sorry

my fault

i can see the confusion

my delta x is 9-3/7 i believe? so 6/7

[jagged cobalt]

i think you have your 4 and 2 the wrong way around.
should be b-a/3n (f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+.....+2f(x_n-2)+4f(x_n-1)+f(n))

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[buoyant depot]

i think thats what i did

but i didnt multiply denom by 3

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[buoyant depot]

so that could be it

[buoyant depot]

fucker tried booting me

😭

cause 2.1 + 42 which is my x0 + 4x1

i think its just my initial delta x / 3 which is incorrect tbh

[jagged cobalt]

what did you have for it?

[buoyant depot]

6/7

but i think it should be 6/21

because n is 7 i believe

but i didn’t multiply that by 3

[jagged cobalt]

its b-a/n which is 9-3/6

[buoyant depot]

wait is my n 6?

i thought it was 7

[jagged cobalt]

the 3 corresponds to x_0, the 9 is x_n so n is 6

[buoyant depot]

ahhhhhh

but i have to divide that by 3

so its 1/3 then what i have

not 6/7

[jagged cobalt]

yeah

[buoyant depot]

i see okay

thank u very much

simpsons trips me up

its so similar to trapezoidal too

well kinda

[jagged cobalt]

I never even heard of it until a few days ago😅

[buoyant depot]

hahaha

well

seems like ur getting it better than me

thanks mate

[jagged cobalt]

np

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[prime vapor]

hello

[prime vapor]

I need help with homework

i really dont know how to solve it

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[hard mountain]

The Hessian is a matrix with the second partial derivatives of f. You can find it by first finding the jacobian of f, and then taking the partial derivatives of the jacobian

[prime vapor]

i need to be explained like a primary school child

im really bad at maths, currently having it in uni and hessian matrix doesn't really serve any purpose for my career anyways

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[alpine sable]

stats has null set?

[alpine sable]

what does it do?

ping me pls

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[tired fox]

ok so the rationals are not real?

[marsh rapids]

Q != R

[last ether]

Q is a subset of R I guess

[marsh rapids]

a classic example of this is {x in Q | x² < 2}
its sup in R is sqrt(2), but in Q it doesn't have a supremum

[tired fox]

oh ok

but if A = Q, Q is a subset of the reals and must therefore satisfy this definition?

[marsh rapids]

it has a sup in R

which in this case would be +inf (the sup in general is in R U {+inf], hence why they say A is bounded)

[tired fox]

okay, think I understand now

thanks

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[formal cairn]

hello

[formal cairn]

can i get help on this?

[pliant cedar]

What have you tried

[formal cairn]

im not sure what to do

because the height is the whole bollard

and i cant work out seperate heights for the cylinder and hemispher

[pliant cedar]

What is the distance from the center of the hemisphere to the tip

[formal cairn]

its not specified

[pliant cedar]

You know the diameter of the hemisphere

[formal cairn]

yep

ohhhh

[pliant cedar]

Yah

[formal cairn]

ohh i got it haha

thanks a lot u were a lot of help

.close

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[formal cairn]

wait

isnt this the formula i should use

for the question above

[formal cairn]

^

and it said 3sf

so i wrote 29800

.reopen

[lone heart]

✅

[formal cairn]

?

[woeful pulsar]

29900

round

[formal cairn]

ohh thanks

.close

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[compact kestrel]

how do I get arc PS

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[alpine sable]

can anyone explain why 0! = 1?

[remote heron]

i feel like youre missing some here @grizzled raptor

[lone heart]

@grizzled raptor Has your question been resolved?

[dense meadow]

5! = 5 x 4 x 3 x 2 x 1 = 120
4! = 5!/5 = 120/5 = 24
3! = 4!/4 = 24/4 = 6
2! = 3!/3 = 6/3 = 2
1! = 2!/2 = 2/2 = 1
0! = 1!/1 = 1/1 = 1

Idk if this would help

[alpine sable]

ty

[remote heron]

how about the last one?

i think some you can just rule out as false

like, the fourth

thats probably what i would do for the last one

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[remote heron]

just make a counter example

.reopen

[lone heart]

✅

[remote heron]

can you think of a function that is normal at x=1 to x=inf

but blows up at x=0

not quite

whats our prototypical function that has 0 as a problem value

think back to algebra or pre algebra

hows division by 0

yea

what happens near 0 with 1/x

$\int _0 ^ \infty \frac 1x \dd x$

[ocean seal]

jan Niku

[remote heron]

do you think this will converge

the point is

we found a counter example

theyre saying if f(x) is positive and continuous

and $\int_1^\infty f(x) \dd x$ converges

[ocean seal]

jan Niku

[remote heron]

then you can always extend the bounds down to 0 and it will still converge

we are saying that is false

for example, f(x) = 1/x

it only takes one counter example to make something false

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[remote tulip]

@minor needle

[remote tulip]

I don’t see how you exactly got the answer

Let me take a picture

I don’t see how your able to cancel that put

I know that cos(arccos(x))=x

But once you sub in I don’t see how your able to cancel out the arccos

The answer makes sense that it is that way but I don’t see the property since I can’t separate sqrt(1-cos^2x) to make it just cos(x)

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[remote tulip]

.reopen

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✅

[lone heart]

@remote tulip Has your question been resolved?

[lone heart]

@remote tulip Has your question been resolved?

[remote tulip]

@minor needle

[minor needle]

what

[hexed relic]

I have a triangle where there is the angle b and 2 angles equal to how can I find the sin(b) knowing that sin(a) = 0.6

[lost lichen]

what do you mean with 2 angles equal to?

[hexed relic]

yeh

[lost lichen]

two angles with the same size?

[hexed relic]

yes

[lost lichen]

alright so the sum of all angles in a triangle is always 180°

[hexed relic]

yeh

[lost lichen]

so a + 2*b = 180°

to get a you can do arcsin(0.6)

[hexed relic]

but without using calculator ?

cuz i have to do an exam without calculator

is there a way to resolve it without calculator ?

[lost lichen]

phew

im afraid i can't help you with that I'm sorry

[hexed relic]

thank you all the same

😄

[remote tulip]

Can you look at my question above

On how you exactly got that answer after subbing in

The answer makes sense that it would be like that but I want to know how exactly do if I get something similar but slightly different I know exactly how to get the answer

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[remote tulip]

.close

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[vast arrow]

Having some troubles with this

[vast arrow]

I know the basics to where we can set it up

because I know that a is =1 but when I double check my work in desmos its not correct

unless i did something wrong

[jagged cobalt]

f(x) is of degree 4, not 3

[vast arrow]

but I am only given 3 x cords

[jagged cobalt]

one of those 3 brackets needs to be ^2

[vast arrow]

that would be -3

got it

[jagged cobalt]

Yeah, the (x+3) should be (x+3)^2 - then you need a constant at the front that brings the y intercept to 1

[vast arrow]

got got, the final answer is 1/36(x+3)^2(x-1)(x-4)

[vast arrow]

thanks for clarifying I totally forgot about the ^2

[jagged cobalt]

looks about right👍

[vast arrow]

Awesome Thank you!

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[tacit flint]

can someone explain a please, ik it’s something to do with finding P(Q n T) but idk how to find it

[fading citrus]

got them

[tacit flint]

ban this man

[hybrid zenith]

dudes 14

[tacit flint]

id love some help please lol

just not sure how to find P(Q u T)

i need this to find P(Q n T) which is the final answer

P(Q u T) should equal 0.6 but idk how to get to it ;-;

for question a

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@tacit flint Has your question been resolved?

[tacit flint]

<@&286206848099549185> save me

[finite gorge]

i am not sure how to do this

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@tacit flint Has your question been resolved?

[tacit flint]

nvm i got it, thanks invisible helpers 😔😔😔

.close

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[fallen iron]

is alpha and beta alternating angle?

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[hexed relic]

i solved it

[lost lichen]

Ohh yeah i figured you could do it this way later

Great job though!

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@fallen iron Has your question been resolved?

[fallen iron]

is alpha and beta alternating angle?

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[alpine sable]

can someone help me with this

[lone heart]

Please don't occupy multiple help channels.

@alpine sable Has your question been resolved?

[lament forge]

what's the context? idk what any of these symbols mean

[alpine sable]

It's logic

Thankfully I solved it by myself

[alpine sable]

Logic is more of a niche subject its only not as general as calculus etc

its only skimmed over in most ocassions

[lament forge]

well i know about logic, i just haven't seen these symbols before

and i also don't know what the goal is here, there's just a sequence of statements

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[lunar ingot]

For part b, is it just the probablity is 1?

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[gusty gorge]

hmmmmmmm perhaps, perhaps not

depends on how you define grandson

after all, you could have a daughter and then she has a son

but the daughter marries a Yale man

[lunar ingot]

lol I think in a question it takes about onlyh males only?

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@lunar ingot Has your question been resolved?

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[tawny crown]

Yes you can, since multiplication is commutative for real numbers

[vale wigeon]

well, can we?

or does your teacher forbid the use of the commutative law of multiplication?

[lone siren]

I know that. But is that became a convention?

cuz I find everyone writes this way

[lone siren]

not actually. but the just don't write like this

[vale wigeon]

don't put that much weight into it.

[tawny crown]

Both are the same thing, you can use either

[lone siren]

oh I see

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[lone siren]

.close

[lone siren]

I don't think so. Cuz it's still opened :/

@lone heart, close it

.close

[vale wigeon]

it will close in a few minutes, be patient.

[lone siren]

oh, sorry 😓

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[barren depot]

Only just need to know how to seperate the (1+t) in (1+t)u'(t)

I can solve the rest

[delicate hearth]

$1+t=\cfrac{-u(t)}{(u'(t)-1)}$

[barren depot]

Appreciate it 🙏

[delicate hearth]

missed - sign

[barren depot]

.close

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[ocean seal]

yeahnote

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[visual depot]

how to make connection with the unit circle

[visual depot]

ok so

It’s easy but

I don’t understand the numerator

like how is the numerator 7pi/6 in the third quadrant

how is the numerator 5pi/4

[gusty gorge]

wdym numerator

[tawny crown]

Pi rad = 180 degrees

that will clear everything up

and one quadrant = 90 degrees = pi/2 rad

[rocky grove]

Well 7/6 = 1.167 and 5/4 = 1.25 so it increases the more you rotate throughout the circle.

[tawny crown]

think of it like 7pi/6=pi+pi/6. so its 180 degrees and then another 30 degrees, going anticlockwise. so you would end up in third qudrant

[rocky grove]

And eventually you will reach 2 lots of π

And 2π = full turn which gets you back to 0

[lone heart]

@visual depot Has your question been resolved?

[visual depot]

omg am is tupid

wait so

[visual depot]

so like

oh

ok hgot it thanks

[lone heart]

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[hearty gulch]

How do i do this?

[lone heart]

Please don't occupy multiple help channels.

[hearty gulch]

plz help i was there is only 1 value of a that works

[sleek pasture]

a=0,b=1

[hearty gulch]

how is a = 0 tho?

is it not undefined if it's 0/0

[carmine reef]

it would be yeah

that's why when you plug in x=1 you get the other case instead

can you imagine what a graph of the function might look like?

[hearty gulch]

so these are the only values

how do i show this mathematically

[lone heart]

@hearty gulch Has your question been resolved?

[molten pivot]

for all real numbers a other than a=0, there exists a pole at x = 1 for the function a/(x-1). so we know that a = 0, and that the left limit of f(x) as x goes to 1 must equal 0.

now we can solve the equation:
0 = ln(b)

i'll leave the rest to you, sir

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[snow cliff]

hello, how do you start the problem to C?

i don't understand what it's asking for?

i know it's something to do with linearization with the formula z = f(a,b) + f_x(a,b)(x-a) + f_y(y-b)

[lone heart]

@snow cliff Has your question been resolved?

[snow cliff]

@crisp iron

[lone heart]

@snow cliff Has your question been resolved?

[snow cliff]

.close

[lone heart]

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[molten pivot]

how do i "pull out" the constant

is it a^m or just a

$$A^m(a\vec{v} + b\vec{u}) = $$
$$A^m(a \vec{v}) + A^m(b \vec{u})$$

[ocean seal]

Mr. Gamer

[molten pivot]

= $A^{m-1}(A(a\vec{v})) + A^{m-1}(A(b\vec{u}))$

[ocean seal]

Mr. Gamer

[molten pivot]

$=A^{m-1} (2a \vec{v}) + A^{m-1} (3b \vec{u})$

[ocean seal]

Mr. Gamer

[molten pivot]

??

[gilded vessel]

is A meant to be a vector?

[gilded vessel]

you can keep applying it

$A^m \cdot \vec{v}$ = $A^{m-1} \cdot 2\vec{v}$ = $A^{m-2} \cdot 4\vec{v}$

[ocean seal]

dog.

[molten pivot]

yeah just figured that out lol

[gilded vessel]

$A^m \cdot \vec{v} = 2m\vec{v}$

[ocean seal]

dog.

[molten pivot]

if Av = 2v
then AAv = A(2v) = 2(Av) = 4v
so on and so forth

[molten pivot]

A is a matrix

[gilded vessel]

ah makes sense

[molten pivot]

but what do i do with a and b

[worn fox]

Just a. A^m is still a linear map so constants can be pulled out

[molten pivot]

so:
Av = 2v
A(av) = 2av
AA(av) = A(2av) = ?

= a A(2v) = a.2.A(v) = 4av i suppose then

so final answer:

$$2^m a \vec{v} + 3^m b \vec{u}$$

[ocean seal]

Mr. Gamer

[worn fox]

Looks good

[torn forge]

Looks amazing

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@molten pivot Has your question been resolved?

[lone heart]

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[opal topaz]

How am I supposed to solve for the work done by the child? All I could find online is people finding the work done by the frictional force, but that's not what I'm looking for. Given just the frictional force as well as the distance, I feel like it's impossible to compute for the work done by the child, especially since time is not given.

[delicate jacinth]

This is not math

[opal topaz]

It's not?

[delicate jacinth]

But a fast internet search gives me that work is the force times the distance

[opal topaz]

I will look for a physics discord then, I apologize.

[opal topaz]

You can't find the force of the child cause you aren't given acceleration and stuff

.close

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[outer lark]

This is on earth presumably ?

[fast lichen]

they dont say 💀

[outer lark]

Mars child

[fast lichen]

on a mars sidewalk

never know

[delicate jacinth]

Yeah but you would still have to assume that the force used by the boy is equal to the friction

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[jade hollow]

hi,
how would i plot the graph of
sin(|z|) <= 0 and |arg(z)| <= pi/4
on argands plane

[limpid spade]

!t

[delicate jacinth]

how arg(z) is defined in your book

specifically the counter-domain

[lone heart]

@jade hollow Has your question been resolved?

[jade hollow]

what does that mean?

[jade hollow]

the angle made by a complex number, z with the positive real axis

(argument)

[delicate jacinth]

arg(z) can return either 0:2pi or -pi:pi

[jade hollow]

0, 2pi

[delicate jacinth]

So |arg(z)| <= pi/4 would be a line

[jade hollow]

a straight line on real axis?

[jade hollow]

and in the 4th quadrant

right?

[delicate jacinth]

no

anything besides that line has an argument bigger than pi/4

[jade hollow]

modulus arg z

[delicate jacinth]

0:2pi

can't be negative

[jade hollow]

right right right

[delicate jacinth]

if it's -pi:pi

[jade hollow]

it might be principal

im not too sure

[delicate jacinth]

would be this

[jade hollow]

but this works

[delicate jacinth]

your book should have the definition

[jade hollow]

this all the possible values of z right

[delicate jacinth]

yeah excluding the other restriction

[jade hollow]

ok cool

[delicate jacinth]

sin(|z|) <= 0

When is sin(x) less than 0/

[jade hollow]

sin|z| will only lie on real axis right? from [-1,0] in this case

sin|z|, not z

[delicate jacinth]

yes

sin(|z|) in -1:1

because |z| is real

[jade hollow]

yea

[delicate jacinth]

When is sin(x) less than 0/

[jade hollow]

then this

[delicate jacinth]

no

If z = pi/2

we have sin(|z|) = 1

wait

[jade hollow]

yea

[delicate jacinth]

So it's not [-1,0], it's [-1,1]

[jade hollow]

you mean z = pi/2 or |z| = pi/2?

[delicate jacinth]

z = pi/2

z = pi/2 -> |z| = pi/2

[jade hollow]

sin|z| belongs to [-1,1]?

[delicate jacinth]

yes

[jade hollow]

but that contradicts sin|z|<=0

[delicate jacinth]

yes

we have to restric z more

When is sin(x) less than 0/

[jade hollow]

so sin|z| => [-1,0] is the minimum condition

[delicate jacinth]

yes

When is sin(x) less than 0/

[jade hollow]

go ahead

[lone heart]

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[solemn geyser]

Can someone help me with this question please :
What are the coefficients of P=(1+X+X^2+…..+X^n)^2

[solemn geyser]

I’ve been stuck on it for a while now

Yes

[errant herald]

I have an equation that is n/k + n/k + n/k … is there a way to set this up in summation notation?