help-23

[faint seal]

im pretty sure the log term is an outcome from some sec substitution

oh?

as in, $\int \frac{e^{-x}}{\sqrt{1+4e^{-x}+e^{-2x}}} dx$

[flat frigate]

kheerii

[calm bridge]

yeah

[faint seal]

so I could substitute e^-x=u

[calm bridge]

and let e^-x = u

yes

[faint seal]

which would make it super simple

ahhhhh

okay, thanks so much!

[calm bridge]

[faint seal]

i see where the x term comes in here too

it's from log e^x

from the common denominator

[calm bridge]

right

[faint seal]

okay tysm

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[eternal carbon]

fascinating

that does indeed shave off like 3 minutes

[calm bridge]

btw op mentioned jee, so isn't this a competition problem?

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[cobalt sentinel]

I think i found the proper terms for the antiderivatives but its telling me that the syntax is incomplete

[cobalt sentinel]

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[dark marlin]

got it down to cot(x) + 2ln(5x)

my right side feels wrong

i know bring the 2 down

so i think its

2 * ln(5x) * 5 / 5x

so 2 ln(5x) * 1/x

right?

[rose plume]

ye

[dark marlin]

2ln(5x) / x?

oh ok it just felt weird

thanks

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[lavish bear]

Someone help meh

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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

[lavish bear]

1

Broo

[tranquil ore]

If you invest in the personal bank, how much will you have after one year?

If you get 2% interest

[lavish bear]

Ummm

£27,750.59

Im stupid. I dont deserve to live 😭

[tranquil ore]

Relax lol

[lavish bear]

Am.i wrong?

[tranquil ore]

Yes but don’t worry

Just look up compound interest

Each year you multiply by 1.02

Cause you increase by 2%

[lavish bear]

25,000 x 1.02 squarwd by 2? Let me get a calculator

26,010

Is what i got

@tranquil ore

[tranquil ore]

^3 cause it’s three years

The important idea to understand here is that you’re getting interest on your interest

Each year you get a bit more interest because you have a bit more money from last years interest

[lavish bear]

I see

Then how do i eork out the "Secure Bank" one

Thats what looks rlly confusing

@tranquil ore

[tranquil ore]

Just do it year by year

[lavish bear]

£26,622.82

@tranquil ore

[tranquil ore]

I got something close

What calculation did you do

[lavish bear]

I did 25,000 x 1.046^1 = 26,150
Then, 26,150 x 1.009^2= 26,622.82

[tranquil ore]

Oh it’s just 1.043

You got the right ideas

[lavish bear]

Ohh shi

I cant read. Im tired

Sorry for wasting ur time @tranquil ore

[tranquil ore]

lol np

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[pulsar pecan]

Hi

[pulsar pecan]

Time in hours and concentration

[devout shale]

!xy

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[pulsar pecan]

its in multiple parts and in another language

so im trying to split it into multiple parts to explain

how do I find the values of a1, a2 and w using the differential equation and table?

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[frail beacon]

Hi

[frail beacon]

How to do this?

I tried 5x + 20 = 12000 but it’s wrong

[dusky sky]

so

how much money did we pay at the beginning

12k right

[frail beacon]

Yes

[dusky sky]

wait

i misread

ok i got it

so we are in 12k debt rn

we need to make that much money

for every game we make we lose

5 dollars

but we also earn

20

[frail beacon]

Yes

[dusky sky]

so how much profit do we do with one game

[frail beacon]

15

Dollars

[dusky sky]

yes

so

lets say the number of games we sell is

x

so we make 15 dollars for 1 game
how many dollars for x games

[frail beacon]

I did 12000 divide 15 and it’s 800

800 games?

[dusky sky]

yea

good job

[frail beacon]

Tysm

[frail beacon]

I have another question

Is it ok?

[dusky sky]

ok

[frail beacon]

I don’t know for this

[dusky sky]

so

i am bad at math terms in english but

i feel like perpendicular means 90°

between those lines

right?

[frail beacon]

Yes

90

[dusky sky]

okok good

so

if two lines are

perpendicular

that means their slopes multiplied by each other is

-1

do you know this

[frail beacon]

Nope

[dusky sky]

ok so for example

y=2x

slope of this is 2

and y=-1/2x

slope of this is -1/2

if you multiply them

2 x -1/2 = -1

so that means they are perpendicular

so you need to do the same first

with that line given

[frail beacon]

Oh ok

So 2/3 is the slope

And I multiply with each possible answer?

[dusky sky]

yes

no just find the number that would make 2/3 times it = -1

[frail beacon]

Oh ok

[dusky sky]

and that is

?

[frail beacon]

-3/2 maybe?

[dusky sky]

yes!

you could just

reverse the fraction

and add a -

just telling yea

but yeah so after we've found that the slope of the line is -3/2

we can write our line like this

y=-3/2x + a

we dont know "a" yet we need to find it

[frail beacon]

Yes

[dusky sky]

so the question says

it goes through the point (3, -2)

which means if i put x=3 and y=-2 our line should confirm that

i mean the equation of the line

does that make sense

[frail beacon]

This one?

[dusky sky]

yes

[frail beacon]

Ok ok

[dusky sky]

because the point is on that line

you can do this with any point on that line

like for example lets say point (n, m) and if you know its on that line

the equation should work

[frail beacon]

Oh

When I did -2 = -3/2 times 3 + a it was -2 = -4 1/2 + a

[frail beacon]

I put x = 3 and y = -2 into here

[dusky sky]

yes

so what is a equal to

if you solve that

[frail beacon]

2 1/2?

Wait

No

Or yes

[dusky sky]

yes

so

now we know the equation

its

y = -3/2x + 5/2

but we need to

[frail beacon]

Why 5/2

[dusky sky]

2 1/2 = 5/2

[frail beacon]

Okok

[dusky sky]

yes

[dusky sky]

make this look like one of the options

https://media.discordapp.net/attachments/903481106819612714/1229906618938818571/IMG_7575.jpg?ex=663162cc&is=661eedcc&hm=c00a6f70d880f7a2b5bf1c4210e14be37a244c1ada6c5da9d6a21f863a63131b&

i feel like theres an easier way lmao

we could just

try the ones that have -3/2x

put x=3 and y=-2 on them

whichever one is true is the answer

[frail beacon]

Oh okay

[dusky sky]

but yea the other method is for finding the equation yourself

this one is easier for this question because it gave us options lol

[frail beacon]

I’m not sure how to do that

Like turn it into standard form?

[dusky sky]

have you found the answer

[dusky sky]

i can explain that aswell

[frail beacon]

Nope when I put them in it equaled weird stuff

[dusky sky]

i feel like the answer is A

because

try it

[frail beacon]

I see

Stuff cancels out

[dusky sky]

yes

remember its slope needs to be -3/2 and you can just try the point given after

like we did here

[frail beacon]

Yeah

[dusky sky]

yes

[frail beacon]

I got it Tysm

[dusky sky]

i kinda explained jt bad lmao

hope it helps

[frail beacon]

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[devout shale]

Is the hint true because of an application of Cauchy Goursat's theorem?

And if so, could anyone help me see how that is?

[hardy lion]

w is outside the circle of radius R

that might help

[devout shale]

Then f(zeta)/(zeta-w) is holomorphic inside the circle of radius R

[devout shale]

ABCD

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[hardy lion]

did that actually help

[devout shale]

yah because I just need to have that f(zeta)/(zeta -w) is holomorphic over C_R(0) which it is (given to us to be) unless zeta=w but zeta cannot equal w if |zeta|<R and |w|>R

[hardy lion]

im so cool

[devout shale]

basically no divide by 0 is what ur saying

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[soft blade]

how would i set up a question like this

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[echo hemlock]

Can someone help me with 10

I’m so confused idek what I did

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[astral bison]

I'm trying to solve for t in equation 2sin(2t)=0

Is t=arcsin(0)/2 the correct way to go about it?

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[stoic dune]

What solution interval are they asking for?

arcsin(0)/2 = 0 is one of the solutions, but there's infinitely more.

@astral bison

[astral bison]

I was doing it in the context of a parametric equation, so I guess -10 to 10?

I was trying to solve for the vert tangent

[stoic dune]

So you're trying to get dx/dt = 0?

[astral bison]

yeah

[stoic dune]

You want to solve 2cos(2t) = 0 in that case

[astral bison]

I just realized I did the derivative incorrect

But I'm guessing that solving for the inverse of the trig function would only give me one solution?

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[wild hamlet]

How would you get rid of the 2 in sin2x?

[rose plume]

sin(x+x)=sinxcosx+sinxcosx

or wait

[timid ridge]

double angle identity

$\sin 2\theta = 2\sin \theta \cos \theta$

[flat frigate]

mochaccino

[wild hamlet]

Thank you

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[keen venture]

Doing basic calculus for the first time, could someone walk me through finding the derivative of 1/the cube root of X. The answer is -3x^4, however I'm coming to a different answer so i'd like to see how this answer is reached

[timid ridge]

that is the wrong answer

[keen venture]

oh damn

[timid ridge]

$-3x^4$?

[flat frigate]

mochaccino

[keen venture]

yeah this is the answer given by my lecturer

wait no

-3x^-4

is what is given

[junior smelt]

And you were given $\frac1{\sqrt[3]{x}}$, right?

[timid ridge]

for $\frac{d}{dx} \frac{1}{\sqrt[3]{x}}$??

[flat frigate]

mochaccino

[keen venture]

yes

[timid ridge]

hell nah thats also wrong

[keen venture]

aint no way

[timid ridge]

what did you get

[keen venture]

-1/3x

thanks for the confirmation ill find the answer eventually. cheers guys

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[vocal glade]

A spherical balloon is being deflated so its volume decreases at a constant rate of x .
what is its outer area decrease rate When its radius is r ?

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[lean otter]

Hi

[frigid spruce]

that's a weird question 💀

[split fulcrum]

this is so true

[light shoal]

it just keeps getting weirder

[split fulcrum]

bungo

i call upon ur intellect

to solve these

[light shoal]

no i cannot

[split fulcrum]

you totally smashed the last few

[light shoal]

i must defer to my sir

[split fulcrum]

dyssrupt

[lean otter]

Nvm

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[dense tiger]

Hello, I have a math question (Calculus II)

[dense tiger]

I pretty much get how to solve this but the 1 circled

How do you get the 1 ?

[light shoal]

just factor out 123/10^3 from all of the terms after the 4

[dense tiger]

im sorry how would you do that if you dont mind

my brain is not working rn lol

[light shoal]

try going in reverse

carry out this distribution

and see that you get what you had on the previous line

[dense tiger]

Am I multipling 123/10^3 by the 1 ? to get 123/10^3 again ? Cause there is a 1/10^3 after that

[light shoal]

it's just the distributive law of multiplication

123/10^3 times 1 is 123/10^3

123/10^3 times 1/10^3 is 123/10^6

etc

[dense tiger]

got it

so basically the 1 represents 123/10^3 going into itself ?

[light shoal]

yea you could think of it that way

[dense tiger]

but you will always have 123/10^3 on the outside as well correct ?

as seen here outside the brackets

[light shoal]

not after you multiply it out

[dense tiger]

referring to like this

and I assume 1/10^3 is always the n1 ?

if x is < 1

[light shoal]

what do you mean by n1

[dense tiger]

Basically (1+1/10^3+1/10^6+1/10^9) its N = 0 , 1 , 2 ,3

If the value is < 1 it'll always be the N = 1 value ? such as 1/10^3 to input in the parenthesis

Here’s another example

What am I doing wrong here? I have a feeling it has to do with the 0

@light shoal

[light shoal]

that's correct

what's your concern?

[dense tiger]

oh ok awesome. So the 1 will always be a 1 and theres no circumstance where this value would change as its just 27/10^2 into itself ?

thats the only thing throwing me off. Even though this is simple

[light shoal]

yea that's right

[dense tiger]

ok awesome thank you

If I have any other questions ill be in here in a little bit

trying different examples

[light shoal]

nw, i'm heading to bed but i'm sure someone will be able to help

[dense tiger]

👍 good night. Thanks for your help

[light shoal]

yw, cheers

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[thorny dust]

I'm having some trouble seeing how to approach this one

Text says: "knowing that the sum of a_n converges/diverges (a/b) determine the convergence of [given series]"

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[lean otter]

A line L1 is parallel to the line y = (1/2)x + 7 and passes through the point (−2, −2). Another

line, L2, has the equation y = −3x + 27.
a. Determine L1's equation.
b. Determine the coordinates of the intersection of L1 and L2.
c. Lines L1 and L2 form a triangle with the x-axis. Determine the area of ​​this triangle.

[versed wave]

!status

[safe radish]

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

[lean otter]

1

[versed wave]

derivative of a function on $x_0$ is the slope of its tangent on that point

[flat frigate]

فطر

[lean otter]

wdym

[versed wave]

well you need to find L1 equation

since its a linear equation its relatively easy

you got the slope, now just find a point where it passes

[lean otter]

it passes through -2

do i put -2 on y

then solve it

from there?

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[lean otter]

can you show how to do

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[trim hawk]

i need help with this question, i know the formula here is AE • EC = BE • ED

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[trim hawk]

im still looking for help on this one

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@trim hawk Has your question been resolved?

[trim hawk]

1

i need help with this question, i know the formula here is AE • EC = BE • ED

<@&286206848099549185>

[naive ember]

I am unfamiliar with this sort of question, but I could try to help. How do you know this is the equation?

[trim hawk]

when you texted my professor finally responded to me so i’m just gonna close this one now! thanks anyways for the response !

[naive ember]

Well cool. I am glad he finally got back to you. Good luck! 🙂

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[lean otter]

<@&286206848099549185> I need help reading this, long story short it's for an essay

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[lean otter]

They can have it

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[flat frigate]

faiyrose

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[median vigil]

both lower triangular and upper triangular matrices have the same property of having the determinant be the product of the diagonals

it's more common to make it upper triangular because gaussian elimination is usually used to make a matrix upper triangular, but that's not a requirement necessarily

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[lunar lagoon]

For 5

[lunar lagoon]

I got up to

80

How do I make the ln part

Bln3

How do I answer 5b

[summer crow]

what did you find for part a?

,rotate ccw

[lunar lagoon]

A is one

B is 6

And c is -29

I inter grated b to get 80 -29ln(12) + 29ln(4)

But I have no idea how to get it into the form it wants

[summer crow]

assuming you've done the integration correctly, then the procedure is fairly simple

hint:

$\ln(a \cdot b) = \ln(a) + \ln(b)$

[flat frigate]

lgkoo

[timid ridge]

hint: 12/4 = 3

[lunar lagoon]

🤦

I see it now

Ty for the help

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[rain hawk]

can someone expain how you get-5/3 i got 5/3

[rain hawk]

for the line eqn

[summer crow]

can you show your work?

[timid ridge]

well i mean not really math but if you think about it it has to be negative not positive slope

[rain hawk]

^

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[delicate patio]

what was the trick to finding h' = 0

when the denominator = 0?

[delicate patio]

actually when thats the case division would be impossible, would that be a perforation?

x = -1 would be a perforation, or some edge case, but when is the result of h' = 0?

[delicate patio]

when the numerator is 0 id guess

so x = 0 in this case

[steel gulch]

Yeah, in this case is not differentiable when x=-1

[steel gulch]

Ah okay

[delicate patio]

yeah makes sense, is that a perforation, since its like a gap

in the graph

[steel gulch]

Yeah, graph it in desmos if you want

When the numer=0, h'=0 like any other function

Sorry, I should be more specific, just like any other function defined at 0

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[high lagoon]

Hi I’m doing power series for convergence or diverge and was testing my intervals of -1 and 1. Can I just use the alternating series test for both values ?

[junior smelt]

For the x = -1 one, you're missing some , and when you account for those, the series is not actually even alternating

[high lagoon]

Oh even if we have the (-1)^n-1?

[junior smelt]

[it does converge, by your p-series, but you can't use the alternating series test for the first one when it doesn't alternate

[junior smelt]

that's exactly why it's not alternating: you cancel that out with the (-1)^n, and that becomes -1

[high lagoon]

Ah yeah right

If I use p series is it a certain test? Or can I just say it converges by p series

[junior smelt]

Well I mean it's just p-series, and of course being absolutely convergent is enough to conclude the series is convergent

[high lagoon]

Got it

Thank you!

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[wooden fossil]

Could someone help me understanding this proof. Essentially it's supposed to prove that if a kernel is such that K(x, t) for vectors x and t = <phi(x), phi(t)> i.e., inner product between feature mapped vectors for some feature map phi then K is positive semidefinite

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[quasi meadow]

So after I find the series for the mclaurin series how do I approximate to 6 decimal places

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[stoic dune]

You'd find the error term that's 6 decimal places accurate, then evaluate that many terms

I imagine you're allowed a calculator for this?

[quasi meadow]

yes

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[mellow mountain]

im confused

shouldnt part C just be that the function is less than 0 when x<1?

[hushed tendon]

its equal to 0 at x=-1

[mellow mountain]

oh right

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[noble brook]

can someone help me with this pls. idk where to start

<@&286206848099549185>

[brazen viper]

u want to subtract the integrals of both and take the absolute value

[noble brook]

so find integral of each first and subtract?

anyone??

[brazen viper]

yes

and then take the absolute value

[noble brook]

how to find Integral of g

[brazen viper]

u sub

[noble brook]

.close

gotit thx

.close

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[stiff solar]

I am working on a Real Analysis II problem that is stated as:
Suppose V is finite dimensional. Let $f \in B(V,R)$ (the space of continuous linear functionals) and $T(f) \in V$ be the Riesz Representation of f. Say $T(f) = v_0 \in V$. Prove that T is continuous.

[flat frigate]

Chase Foxen

[stiff solar]

So, the hint we were given was to consider an orthonormal basis of V. Let's call this ${ b_1, b_2, \dots, b_n }$

[flat frigate]

Chase Foxen

[stiff solar]

My thinking is that we can express $T(f) = v_0 = \sum_{j=1}^n \langle v_0, b_j \rangle b_j$. And since $\langle v_0 , b_j \rangle $ is the Riesz Rep. of f, then this inner product is continuous. So, for some $f_1.f_2 \in B(V,\mathbb{R})$ we would w.t.s. that for all $\varepsilon > 0$ there exists a $\delta > 0$ s.t. $|f_1 - f_2| < \delta$ implies that $|T(f_1)-T(f_2) | = |v_1 - v_2 | < \varepsilon$.

[flat frigate]

Chase Foxen

[stiff solar]

But where I get stuck is how to use the continuity of f to imply this condition. The continuity of f only allows us to show that the outputs of the same functional are close, not that two functionals in $B(V,\mathbb{R})$ are close together, which is what we need to have in the $|f_1 - f_2| < \delta$ "step".

[flat frigate]

Chase Foxen

[stiff solar]

close

.close

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[winged girder]

Hello

[winged girder]

How can i find the v.asy for this function

Vertical asymptome

[icy lance]

when is the denominator 0
and factor the numerator

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[fathom island]

Can someone tell me if this problem is good solved in Decarta2D?

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[random rivet]

i dont get the right part

abt sin

[solar hazel]

[unkempt geyser]

Law of sines, side a/sin(A) = side b/sin(B)

Then you solve for whatever your looking for

[solar hazel]

i have that exact pic in my pfp collection lmaooo

[random rivet]

this is rhe law of sines

isnt it

[unkempt geyser]

Yes

[random rivet]

why did they put sin a

on denominator

[unkempt geyser]

It can go in either, bc if you raise both sides to the power of -1 it’s still equivalent

[random rivet]

okk

[unkempt geyser]

Anything else?

[random rivet]

i did the other way

but

didnt get the answer

[unkempt geyser]

Did you do sin^-1?

[random rivet]

yea

[unkempt geyser]

Could I see your work?

[random rivet]

the other example did this

and it worked

[unkempt geyser]

Looks like you’re working with vectors, did you forget to account for that?

[random rivet]

what does that mean

[unkempt geyser]

Not sure, haven’t done vectors yet. Lemme find a video

Watch this: https://youtu.be/ZN7YaSbY3-w?si=ZjOrLb2-BnwRT42r

[random rivet]

okk

that video is simple info

ik that alr

im asking abt the sin law

[random rivet]

bec this vid is just multiplying

[unkempt geyser]

So basically it just took the values and applied it to law of sines, ig that it used some vector math to change the | |3x-5y | | into smth, prob solved for the values

[random rivet]

how r those related

im so confused

😭

[unkempt geyser]

I’m so sorry, I don’t know anything about vectors, I’m grabbing at straws run

Do you know how the vectors work?

[random rivet]

yea

im just having trouble

with the sin law

i got the first pary

not the sin part

[unkempt geyser]

So what they did is solve for x and y ig, and then cross multiplied so | |-5 y| | * sin(30) = | |3x-5y| | * sin a

The divided so (| |-5 y| | * sin(30))/| |3x-5y| | = sin(a)

Then took the inverse sine of that

[random rivet]

for the inverse

where did 5 sin 30

come from

and the square roots on denominator

[unkempt geyser]

Idk, again, no knowledge on vectors

[random rivet]

its the sin rule

pnfmfeegmsgjese

okay wtv

ill ask someone

thanks

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[steady river]

I need help solving for c(t)

[dull sequoia]

What have you tried

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[misty ice]

1.Two points A and B are on the same horizontal line. A motorist departs from point A towards point B with a speed of 28.8 km/h and an acceleration of 160 cm/s². Two seconds later, a cyclist departs from point B towards point A with a speed of 61.2 km/h and a deceleration of 80 cm/s². If the motorist catches up to the cyclist 150 meters from point B, find: a) The distance between points A and B. b) The velocity of each one.

[misty ice]

can someone please walk me through this kinematic problem, i am just starting with the topic.

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@misty ice Has your question been resolved?

[steel stag]

you have initial speed, acceleration, and distance traveled for B, so you can use x=vt+1/2at^2 to find the time
with time you have 3 variables for A which is enough, so use x=vt+1/2at^2 to find the distance A travels, whihc solves a)

any equation works for b) if it has vf, like vf-vi = at

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[oak whale]

Hey ! I was doing some maths for fun, and came across an intzgral in the form of ∫sqrt(a-x²)dx

So of course, I thought of trig sub to solve it, BUT

I end up with ∫sqrt(cos²(θ))cos(θ) dθ

Every solutions I ever found just simplified this as ∫cos²(θ) dθ, but I don't understand how this is possible...

|cosx| × cosx insn't the same as cos²x... Does anyone know any answer ?

[junior smelt]

Implicit assumption on the values of theta, most likely (e.g. assuming that you're in [a subset of] something like -pi/2 to pi/2)

Often the positive square root just gets assumed in these types of problems, for better or for worse

[oak whale]

Well, yeah here my integral is definite between -π/2 and sin-¹ of something so i'm good

But even for indefinite integrals

We just assume θ is like in a [-π/2 ; π/2] range ?

[junior smelt]

Well, it makes life easier so people tend to do it

[oak whale]

Ohh I see it

Since we set x = asin(θ)

We just set the rznge we want for θ

Okk thank you very much!!!

[junior smelt]

I mean, another way you probably could do it is to use the fact that the absolute value is just the "original thing" multiplied by its sign, that might make things better in general

[oak whale]

Thank you!

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[floral cliff]

i don't get the steps in this solution

[full oar]

what step don't you get specifically? or the entire thing?

[floral cliff]

the entire thing

[full oar]

ok i see

[floral cliff]

i get you can break up the numerator and thus the integral

i just don't know how to get TO the 2nd line and onwards

(i can see that you can pull out a 1/2 etc)

i also understand completing the square

mostly what i don't get

[full oar]

oh

the solution computed the integral by a simple u sub where w = x^2 + 12x + 40, dw/dx = 2x + 12 (cancels the numerator). therefore, 1/2 integral(1/w)... (note i didn't use u here because u is used in the second fraction)

would you like me to expand on that a bit more?

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[floral cliff]

no, that makes sense. tanks

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[drifting condor]

is this legal? i think so, as i used l’hopitals due to it being infinite both in the numerator and denominator, but it felt very off

[drifting condor]

disregard the equals between lim and (6/2)

[lean otter]

in the numerator

is it

3x^2

or 3x

[drifting condor]

3x^2 yes

[full oar]

lgtm

[drifting condor]

thanks

[full oar]

everything is legal, is there anything else you needed help with?

[drifting condor]

for the time being, no. appreciate it

[full oar]

:) feel free to close this ticket then

[drifting condor]

.close

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[alpine grove]

I can't make sense of this explanation... I'll need a second explanation for a changing of basis with transformations.

Anyone can help?

[alpine grove]

I'm suspecting this would be similar to the matrix of passage

[raven heart]

une matrice de passage, c'est un cas particulier de matrice de transformation linéaire qui est définie ici

avec T = identité, t'as exactement tous les changements de base

[alpine grove]

Donc grosso modo, c'est exactement la même chose de ce que l'on parlait plus tôt?

Mais qu'on applique dans le concept de transformations.

[raven heart]

c'est plus général encore

mais très similaire oui

[alpine grove]

Qu'entendez-vous par plus général?

[raven heart]

ce que je viens de dire au-dessus

t'es pas obligé d'avoir T = identité dans ta définition là

pour n'importe quelle transformation linéaire T tu peux parler de sa matrice dans les bases B1, B2

[alpine grove]

Oh,

Serait-ce pour obtenir la transformation d'un vecteur dans des coordonnées de base 2, on doit convertir la matrice associée à la transformation?

[raven heart]

qu'est-ce que t'entends par la matrice associée à la transformation ?

[alpine grove]

Voici un exemple:

Transformation géométrique : Symétrie orthogonale d'axe X.

La matrice associée est
1 0
0 -1

[raven heart]

ok donc tu parles de la matrice exprimée dans la base standard

[alpine grove]

Ouais c'est une transformation dans la base canonique/standard.

Mais si on voulait fair ela même transformation, mais dans une autre base, on devra convertir cette matrice.

Avec un changement de base

[raven heart]

ouais

changement de base qui sera légèrement plus compliqué que pour des simples vecteurs

mais ça devrait arriver dans la suite ça de toute façon

c'est du classique

[alpine grove]

Pas sur de voir pourquo c'est plus compliqué.

[raven heart]

read up

and you'll know

[alpine grove]

Alright!

Donc juste pour clairer.

Soit on nous donne une transformation en base canonique.
On a un vecteur dans une base quelconque différente de la base canonique.
On veut transformer le vecteur avec la transformation.

Avant de pouvoir faire la transformation, on devra convertir la matrice de la transformation.

Avec un changement de base.

[raven heart]

oui

[raven heart]

l'idée très grossière c'est que cette "conversion" impliquera un changement de base du côté input et du côté output de ta transformation

léger spoil

c'est pour ça que je dis que c'est plus compliqué

[alpine grove]

Ah je vois. je crois que je peux m'Épargner de ce détail si je comprends ce que je viens d'énoncer ci-dessus.

[raven heart]

ils vont pas te l'épargner ce détail dans tes slides

[alpine grove]

On parle de matrices semblables peu après.. Est-ce ceci?

[raven heart]

oui c'est lié

[alpine grove]

C'est ceci qui est expliquée si je comprends bien?

[raven heart]

oui c'est exactement la conversion dont tu parles

[alpine grove]

Je vais me prendre un break et je me relance là-dedans maintenant que je crois suffisament comprendr epour le décortiquer dans une tête fra¸iche.

Merci encore

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[earnest python]

is this $\Re$ symbol related to the function Re(..)

[flat frigate]

pyrate

[raven heart]

yes they should be the same thing

what's the context behind this?

[earnest python]

just when I am taking notes I type \Re and this pops up,,, i am just wondering if it was a symbol for Re() or something else

[raven heart]

ah ok

well yeah it's a funky symbol for Re(.)

[earnest python]

i would look it up, but i dont even know what to call that weird R

[raven heart]

$\mathfrak{R}$

[flat frigate]

aPlatypus

[earnest python]

huh

thanks

[raven heart]

fraktur font

[earnest python]

thank you

I think ill stick to Re....honestly its kinda ugly

but good to know

tahnks again

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[storm quest]

i have no clue what im doing, my teacher just started covering this topic today and we have an exam on it Friday 😭

[storm quest]

got it

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[unkempt shadow]

Is this true ?

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@unkempt shadow Has your question been resolved?

[raw meadow]

I think its true🤔

[unkempt shadow]

But is writing this like this in an exam subject valid u think ?

[raw meadow]

Im not sure I understand. This looks like two 'claims'. This does not look like an explanation

If it is a math exam, its allowed to type like this of course

[junior smelt]

Also it isn’t: even taking them piece by piece, -1 > -2 but 1 is not strictly greater than 4

[raw meadow]

Yes, if these were fractions it could also be not true i think. Be careful what kind of numbers the variables are.

[unkempt shadow]

Ok thank you

Mb if you misunderstood my english is nor very good

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[tender dawn]

hello

[tender dawn]

any tips on how to solve this?

im stuck

its integral btw

[jolly shard]

$$\int{\frac{1}{1+x^{1/2}}dx}$$

[flat frigate]

Pixelius

[tender dawn]

yes

how do i solve that?

[jolly shard]

U-sub ?

U=x^{1/2} and partial fractions should solve it

[tender dawn]

but

if u = x^{1/2}

then

du = dx * 1/2 * x^{-1/2}

but the integral does not contain the x^{-1/2} term

[modern elm]

you can do u = 1 + x^{1/2}

x^{1/2} = u - 1

x = (u-1)^2

dx = 2(u - 1)du

then plug in

[tender dawn]

wow

@modern elm how did you come up with that

[modern elm]

i just kept u subbing

idk if it's the most clever way of doing it but

i guess it works

cause i couldn't put in dx so i just isolated it

[tender dawn]

i always thought u cant u-sub if the integral doesnt contain a factor of the x-derivate

for example if 2x / (1 + x^2)

you can u = 1+x^2

because we have 2x factor

[modern elm]

right yea those are the nice ones

[tender dawn]

well thank you, very helpful

[modern elm]

of course man

glad i could help!

[tender dawn]

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[celest topaz]

hello, can anyone explain to me what goes on between these 2 lines

[celest topaz]

why is 1/s^2 factorised out instead of 1/s

do you multiply it by s/s to leave an s inside and rip an s outside?

[steel stag]

either way is fine

factoring out 1/s makes it -1/s [ (m+1/s)e^... - 1/s ]

which makes it -1/s [ 0 - 1/s]

[celest topaz]

which multiplies back to 1/s^2

fair enough

[steel stag]

yea

[celest topaz]

so its just the way the author decided to go about doing it then

and isnt something inherent to do with the laplace transform

[steel stag]

right

[celest topaz]

noted

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i dont remember the thing

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[celest topaz]

.reopen

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✅

[celest topaz]

@steel stag wait isnt the 2nd -1/s^2 a product of -1/s and 1/s so if you factorise -1/s out then you have a positive 1/s inside?

[steel stag]

uh 1/s vs 1/s^2 won't change any signs

so just do whatever's there

[celest topaz]

mind confusion

mild

also where did the -1 at the end come from

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[still trout]

can someone help me do the explain and also draw the 2 possible triangles out i should be able to solve them no problem but idk how to start that’s it

[still trout]

this is what i have so far

<@&286206848099549185> could someone assist

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[inner shuttle]

can someone help me with integrals. Heres the first problem.

[inner shuttle]

can you explain to me.

[meager merlin]

Wait, does it provide a step?

nvm

[inner shuttle]

im suppose to use riemann sum to express the integral

[meager merlin]

It asks for expressing

[inner shuttle]

i just need help comprehending the concept

why things work the way it do

[meager merlin]

Intergral provides u the area below a graph right?

So Riemann sum instead of solving the intergal, provides u a geometry way to getting the area by calculate the sum of the area of rectangles

[meager merlin]

these rectangle

But, as u can see, it just an approximation

But

[inner shuttle]

hm yes

[meager merlin]

If the delta x getting smaller and smaller

The Riemann sum provides a better approximation (the error is getting smaller)

[inner shuttle]

so thats why we use the interval [2,5]

[meager merlin]

If delta approaches 0 (by using limit) we can say the Riemann sum provides the EXACT value

[inner shuttle]

5-2/n

hmm

[meager merlin]

The interval is just the area between these value

[inner shuttle]

ah

[meager merlin]

Here's an example

the interval is like the limit point where we want to calculate the area

[inner shuttle]

yeah from 2 to 5

only the shaded area

[meager merlin]

Yep

In case they give u a step

Lets say 1

Then the riemann sum is the area of those 3 rectangles

But if the step getting smaller (delta x approaches 0)

Then the riemann sum is the exact area

[inner shuttle]

im gonna be able to access desmos graph

[meager merlin]

Here's the illustration

The more steps, the more accurate the approximation gets

[inner shuttle]

the question says do not evaluate the limit , so the answer would be the graph drawn?

[inner shuttle]

i get what you mean

[meager merlin]

I think whats it asking u is to write down the expression

[inner shuttle]

the summation mark ?

alrighty

[meager merlin]

its probably something liks this

But u need to modify this

So it goes from 2 to 5

And f(x) is cos(x^2)

[inner shuttle]

ah okay

so the answer would be

can you help me with one more

[meager merlin]

Yep

Looks correct

[meager merlin]

Since g(x) is a function of x and the RHS is dz

So u need to do the intergral

And take the derivative then

[inner shuttle]

so i need to do the integral first

[meager merlin]

Usually, if its dx, u can assume this

[inner shuttle]

huhh

[meager merlin]

Oops

[meager merlin]

I mean in case u meet this form

[meager merlin]

But for this, u need to do the integral

[inner shuttle]

i mean i get that, dz or dt or any sort of d_ is still dx

but the thing is

[meager merlin]

bruh

[meager merlin]

Whoever give u this task is a monster

[inner shuttle]

which one

[inner shuttle]

oh

[meager merlin]

To intergral this whole term

[inner shuttle]

i thought i had to use substitutionh

its FTC1 with substitution/chain rule

this is just a practice exam

[meager merlin]

Do it then

[inner shuttle]

yo thx for the help

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[fathom jewel]

chain rule left the chat

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[lean otter]

I have a quick question, is a vertical asymptote a discontinuity?

[drowsy jolt]

yes

[lean otter]

All of them?

[drowsy jolt]

because u must pick up your pen

yes

horizontal isnt

vertical is

[lean otter]

And the holes are also discontinuities

[drowsy jolt]

yes

[lean otter]

Is anything else a discontinuity?

[drowsy jolt]

we have point discontinues (piece wise functions, when one value of the function is completely away from the others), removable discontinuities (holes) and VERTICAL asymptotes

[lean otter]

Ok

[drowsy jolt]

if you need to pick up your pen to draw the function its not continous

[lean otter]

I have a different question, should I close this one and reopen it or just put it again

[drowsy jolt]

why?

[lean otter]

Ok I think that's calc

I just need algebra 2