help-10

[tired bough]

alr

thank you bro

❤️

can i still access this channel after ive closed it?

[shut lagoon]

It won’t erase anything but some other stuff will be posted after

So maybe just remember it was channel 10

Or search for yourself in the search bar

[tired bough]

alr, great

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Hello, i struggle with this type of exercises, where i have a fraction and absolute value, how do i know what numbers i should use (where i put question marks) to proceed with calculating the limits of the function?

[restive gorge]

You wanna evalaute the limit as x approaches 1?

[timid silo]

I know that it has to be someting with 1 because with 1 i can bring the denominator to zero

[timid silo]

Yes

[restive gorge]

Well the absolute value can stay, actually

just consider the limit from both sides tho

the numerator is alsways positive anyway, so observe the denominator for close values around x=1

You can also make the argument, that since x=1 is a root of the denominator but not of the numerator, it is therefore a pole / vertical asymptote

[timid silo]

But after i have split the funtions like in the picture, i need to use a number for x which is in one case higher and in the other case lower than one. How do i know for which of the two functions if X needs to be higher or lower than 1.

[restive gorge]

And since (x-1) = (x-1)^1 has odd power the sign switches at the pole meaning, from one side it goes to +inf, other -inf

and testing some numbers it is clear from the right it approaches +inf because the denom stays positive, and from the left it becomes negative

it is a "1/0" situation basically resembling for example something like 1/x

[timid silo]

So i dont need to split the funtion like this at all?

[restive gorge]

no

it's redundant

[timid silo]

Oh

Ok

I think i got it

Thank you

.close

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[latent quiver]

At a certain pizza shop, a pizza sold has mushrooms with probability p = 2/3. On a day in which 100 pizzas are sold, let N equal the number of pizzas sold before the first pizza with mushrooms is sold. What is the PMF of N?

[latent quiver]

I am tempted to say this is simply 2/3 * (1/3)^(n-1), but the sentencing of the question is throwing me off

Am I correct? Or is there something i am missing?

[fossil crag]

so P(X = n) = that?

unfortunately with that PMF you'll find that X = 101 is possible for example

you need to adjust for that

[latent quiver]

Sorry I dont know how to use the Texit bot, but I meant to say that equation holds from n = 0 to 100 and 0 otherwise

[fossil crag]

ah, but in that case, is the sum of probabilities really 1?

[latent quiver]

you do raise a good point

but that formulation is the standard geometric distribution

which i would assume to hold in such instances

[fossil crag]

but geometric distributions are valid when the experiment can be repeated an infinite number of times

[latent quiver]

Oh right

Okay, so how should I reevaluate this?

[fossil crag]

in fact it isn't "standard" since you don't allow n> 100

[fossil crag]

well, imagine if even after 100 pizzas we didn't sell a mushroom pizza

[latent quiver]

yeah

[fossil crag]

consider Y the variable that counts the number of non-mushroom pizzas we would have sold before a mushroom pizza, if the store doesn't stop selling pizzas until it sold a mushroom pizza

it's like "ok we sold 100 pizzas, let's pretend we're selling more..."

[latent quiver]

alright

[fossil crag]

X has the same distribution as Y for n <= 99

then, when we reach X = 100

all the hypothetical Y = 100, Y = 101, Y = 102... are condensed into this value of X = 100

so the probability X = 100

is the same probability that Y >= 100

[latent quiver]

Oh wow thats a very cool way to visualise this, thank you!

ok but maybe lets focus on finding what the values are for Y < 100 first

My formulation might still be wrong i believe

At P(N = 1), i assume it is (1/3) * (2/3) as it could be either

At P(N = 2), we condition on the fact that there was a non-mushroom pizza so (1/3)^2 * (2/3)

So; P(N = n) = (1/3)^n * 2/3 for N < 100 if i got this right

[fossil crag]

why ^n now?

wait sorry

you're correct

[latent quiver]

I am visualising a tree-diagram

[fossil crag]

carry on

[latent quiver]

At N = 100, I think this would read as "We have sold 100 non-mushroom pizzas by this point"

Restaurant doesnt do anymore pizzas

[fossil crag]

yes so (1/3)^100

[latent quiver]

so the piecewise representation is

2/3 * (1/3)^n, for n = 1, ... 99,
(1/3)^100, for n = 100,
0, for otherwise

[latent quiver]

Ok thanks a bunch!

Do you mind if you could help me with another

.close

[obtuse pebble]

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[waxen swan]

How do I convert this into (x-h)^2/a^2 + (y-k)^2/b^2 = 1 format?

[brazen viper]

You need to complete the square

Do you know how to complete squares?

[waxen swan]

Ohhhh

That’s it?

[brazen viper]

almost

,rccw

[waxen swan]

Oh

Wait I didnt see that part

[brazen viper]

you dropped your -9

[waxen swan]

Yeah

[brazen viper]

You added and subtracted 9

used the +9 and forgot about the -9

[brazen viper]

,rccw

[waxen swan]

Always make the rhs 1 right?

[brazen viper]

this looks correct to me.

just remember that your form is (x - k)^2 / a^2, so it might be useful to write 9 as 3^2

[waxen swan]

Oh yeah, for the graph part

But okay I get it now, thank you

.close

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[spiral sleet]

Calculate the Taylor polynomial T3(x; x0) at the expansion point x0 = 1 for the function f(x) = 4e^x · ln(x). What approximation does this result for f(0.8)?

my solution: -0.8e + 0.08e - 0.016e / 3

is this correct?

[tardy epoch]

show your work

[obtuse pebble]

@spiral sleet Has your question been resolved?

[tardy epoch]

,w taylor series (4e^x * log(x)) at 1

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[tardy epoch]

looks like you're off by a factor of 2 on the cubic term

[obtuse pebble]

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[rich thunder]

Hello

[rich thunder]

I legit get up to 125/216

How do I get 19 wtf?

[subtle sinew]

You find a common denominator

So you can do 125/216 - 2/3

[rich thunder]

Omg

I have to do 3 X something

What’s the quickest way to do that?

[subtle sinew]

A common denominator is just multiplying the denominators together. You'll just have to simplify

[spiral sleet]

Oh ty I see now, I had the wrong value for f'''(1), it's -e and not 4e

Sry for interrupting

[rich thunder]

Ur good

[rich thunder]

I don’t get it

How do I find what to multiply by fast

[subtle sinew]

.

[rich thunder]

I can’t 215 x 3?

[subtle sinew]

You'll have bigger numbers, and need to simplify

[subtle sinew]

You mean 216?

[rich thunder]

Yes

[subtle sinew]

Yes you can do 216 * 3 as a common denominator but in the end, you're going to have to simplify

[rich thunder]

What’s the easiest way to simplify

Do u have any tips and tricks on calculator?

😃

[subtle sinew]

Do you know how to simplify fractions in general?

[rich thunder]

I usually just divide them with way smaller numbers

I don’t think I’ve attempted to simplify a huge fraction

[subtle sinew]

Small or big numbers, the process is the same

[rich thunder]

Omg I just do 216/ 3

X 72 by each side

LETS GO

I’m stuck on this part now

[subtle sinew]

Yes you could do that, but what if 216 was not divisible by 3?

[rich thunder]

I have no idea

[subtle sinew]

Where are you confused?

[rich thunder]

Because the X used to be negative

[subtle sinew]

Do you know how to add/subtract fractions?

[rich thunder]

Yeah the basic stuff

Usually I square root

Or like divide with whatever

[subtle sinew]

Where exactly are you confused with this step? You just subtract the fractions

[rich thunder]

Ok u know what ur right

I think I have this down now

Maybe minus the fraction part

LOL

Jokes aside I have figured it out and im grateful thank u!

[subtle sinew]

And that's my point of saying, you can multiply the denominators together to get a common denominator. It's not going to be the lowest common denominator but it will be a common denominator

[rich thunder]

Yeah idk how to simplify from 500

And also I thought I was supposed to flip the fraction when I move it to the other side

Am I being lied to

Dammit!

Oh my gosh only 2 more questions to go

[subtle sinew]

So you're telling me that you don't know how to simplify from here?

[rich thunder]

No idea

Please show me!

[subtle sinew]

You know how to subtract fractions, right?

[rich thunder]

1 more question left 😈

[rich thunder]

Yum yes

I don’t know when I’m supposed to add or subtract

I know when I’m supposed to multiply and divide

For some reason I’m bad at the easy stuff??

[subtle sinew]

There's a minus sign in between the fractions...

[rich thunder]

But why sir

Is it because X was negative

We had to flip to other side

[subtle sinew]

You had 2/3 - x = 125/216, initially, correct?

[rich thunder]

Yes

[subtle sinew]

If you wanted to isolate for x, what should you do to the 2/3?

[rich thunder]

Put it on the other side

But wouldn’t that be 3/2 idk

Idek

Don’t trust me

[subtle sinew]

No

Because it's not (2/3) * x

[rich thunder]

Oh

My god

It’s all makes so much more sense

Thank u so much!

[subtle sinew]

If you have x - 23423 = 2346246, what would you do?

[rich thunder]

Ahhhhh

Wait

Then why not add fractions

Because aren’t u supposed to do opposite

[rich thunder]

I have no idea

[subtle sinew]

You want to isolate for x

[rich thunder]

Oh add the other side

Right?

[subtle sinew]

Why add?

[rich thunder]

Because u have to cancel them

Is it cause of the stupid variable?

[subtle sinew]

Why not subtract 23423?

Why are you adding?

[rich thunder]

To cancel them

[subtle sinew]

So you add to both sides

Same thing with
2/3 - x = 125/216
How do you want to isolate for x?

What should you do with the 2/3?

[rich thunder]

Minus

Other side

[subtle sinew]

So what would that look like?

[rich thunder]

2/3 is positive

Oh my god

Oh ok

[subtle sinew]

So what would the equation be if you subtracted 2/3 on both sides?

[rich thunder]

I’m on this question now

Was going to use this technique

But this is only used for determining restrictions

[subtle sinew]

What do you think you should do?

[rich thunder]

Honestly I was thinking about pulling off that 1

So I can get to the square root

[subtle sinew]

If you have $\frac{1}{2x} = 15$
What can you do first?

[warm shale]

CaptainNova22

[subtle sinew]

You want to "remove" that fraction, right?

[rich thunder]

This one right here I would do 15x2

[subtle sinew]

If you multiplied by two on both sides, you'll get 1/x = 15 * 2

That x is still in the denominator

[rich thunder]

Divide the other side by 1?

Hmmmm

[subtle sinew]

How is that going to help?

[rich thunder]

I’ve never had to deal with this I don’t think

….

The square root is restricting me from doing anything

Should I square Both sides

I hate the one on top

What do I do for that wtf?!!

[subtle sinew]

Go back to this, you want to "remove" the denominator, right?

[rich thunder]

I have to get rid of the square first tho

Ok let me try 😈

The one is throwing me off

Ngl

[subtle sinew]

I'm not asking you to focus on your problem. I'm trying to show you what to do with a simplier example

[rich thunder]

Oh

Thank u

[subtle sinew]

Now once again, you want to "remove" the denominator, what should you do?

[rich thunder]

Is this correct so far?

[subtle sinew]

No

[rich thunder]

….

Damn

I’m guessing it was divide by 2 first

If it is imma be mad

[subtle sinew]

Squaring both sides was fine

The next step was wrong

[rich thunder]

Oh

[subtle sinew]

You have $\frac{1}{2x+4} = 144$
You have a fraction, how would you get rid of it?

[warm shale]

CaptainNova22

[rich thunder]

Flip the fraction

[subtle sinew]

What would that look like?

[rich thunder]

2x+4 -1?

[subtle sinew]

You're significantly making this much harder

That's why I was trying to show you a simplier example but you kept avoiding it

[rich thunder]

Ofc it’s the last question

Ahhhhhh

[subtle sinew]

That is why I was trying to show you an easier example

[subtle sinew]

No

Not exactly correct

[rich thunder]

This is embarrasing

[subtle sinew]

You flipped one side of the equation but did nothing to the other

Why?

[rich thunder]

Wait what

Oh

I’m supposed to

I’ve never had to do this

I forgot other side too

Dammit

[subtle sinew]

.... And that is exactly why I was trying to do an easier example

[rich thunder]

I’m sorry

[subtle sinew]

Where did minus 4 come from?

[rich thunder]

Moving stuffs around

Seeing if it’s correcto

[subtle sinew]

Are you saying $\frac{1}{144-4}$ or $\frac{1}{144}-4$?

[warm shale]

CaptainNova22

[rich thunder]

Oh

Is it supposed to be the right one

lol

[subtle sinew]

Which one was your work showing?

[rich thunder]

1st

Never had to do this

[subtle sinew]

Also if you subtracted 4 from both sides, why is it still on the left side?

[rich thunder]

I’ll never forget this

[subtle sinew]

Another thing to note, what's anything divided by 1?

[rich thunder]

Oh forgot to throw 1 out the window

Had it there just incase I had to cross multiply or something lol

[subtle sinew]

So you have $\frac{1}{144}-4$ what should you do?

[warm shale]

CaptainNova22

[rich thunder]

I’ve never solved an equation like this

With fractions like this

Very interesting

Imma guess and say multiply the bottom?

By negative 4

[subtle sinew]

Common denominator

[rich thunder]

Ok so I multiply the bottom

With 4

Gives me the top

Then I multiply the 2 with the denominator

Wow

I actually didn’t know this

Pretty crazy stuff

I didn’t know i flip fractions on both sides

That is so dumbbbbb

@subtle sinew thank u so much!!!!!!

.close

[obtuse pebble]

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[young gust]

shouldnt this be -6?

[young gust]

the answer itself says that F is in the opposite direction from n

is it a typo or am i missing smth?

btw the question asks to find the flux using geometric methods

[obtuse pebble]

@young gust Has your question been resolved?

[obtuse pebble]

@young gust Has your question been resolved?

[obtuse pebble]

@young gust Has your question been resolved?

[obtuse pebble]

@young gust Has your question been resolved?

[acoustic rain]

idk anything about this but its been like 4 hours you can ping helpers
<@&286206848099549185>

[obtuse pebble]

@young gust Has your question been resolved?

[young gust]

<@&286206848099549185>

Someone pls help

[obtuse pebble]

@young gust Has your question been resolved?

[worn coyote]

Likely a typo, yes. F is certainly pointing in the opposite direction from n and therefore F n = -3 sqrt(2)

And flux = -6

[young gust]

This is a practice problem from MIT ocw

The course is multivar calculus

I'm not sure tho

My reasoning seems to be right

[young gust]

Ah thank you, glad to know I'm not missing smth

.close

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[quasi island]

im struggling to understand what that notation actually means. theres nowhere in the notes that explains it

[red ice]

which notation?

the piecewise function definition?

[quasi island]

uh, the p(x) = ...........

[red ice]

oh that just means the probability density function

X is a random variable

[quasi island]

whats the significance of the 1/(b-a) being above the 0, have

[red ice]

p(X) gives you the probability density for each value of X

[red ice]

when a < X < b, p(X) = 1/(b - a)

otherwise, p(X) = 0

[quasi island]

ahhhhhh right

alright thanks alot

[red ice]

no worries!

.close

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[unreal nexus]

Hello

[unreal nexus]

Could anyone explain what's 3x lined equal sign, and what's mod 4?

[unreal nexus]

Choose another channel, pal

[ember frost]

congruent to 0 modulo 4

let $a, b\in\mathbb Z$ and $n\in\mathbb N$. $a\equiv b\pmod n$ iff $n\mid(a - b)$

[ember frost]

in other words, a modulo n = b modulo n

[quick totem]

in that case it means just that x is divisible by 4.

[ember frost]

to really answer your question though, the 3x lined equal sign is the equivalent symbol. in your case specifically, it is what i just said

[unreal nexus]

What's | sign?

[ember frost]

divides

for example, 3 | 9 because 9 is divisible by 3

[ember frost]

mod means modulo, which is a binary operation. for example if you have integers a and b, then a mod b returns the remainder of a/b

but in your case, it is helpful to think about clocks

this clock has 4 hours on it, so its modulo 4

you go 1, then 2, then 3, then 4, like a clock would

normally you go 5, but here you loop back to 1

thus 5 is congruent to 1 modulo 4

[unreal nexus]

That's interesting

But what does it have to do with the task?

[unreal nexus]

Thank you for that very much

[ember frost]

well you asked what modulo congruence means

idk what your task is

[unreal nexus]

This is the task

[ember frost]

yeah but like, what do you want to do

[unreal nexus]

So that's basically that system on the picture, right?

[unreal nexus]

Print all the elements of the set

[ember frost]

all?

uh, there are infinite of them

i suppose you only need like 5 and then slap ellipsis on both sides

[ember frost]

using the information i just gave, can you list some integers that are congruent to 0 mod 4?

[unreal nexus]

Not like literally, but yeah

[unreal nexus]

I've seen the answer of the task, so there's no sense in doing it

Just needed to get the meaning of that

So thank you

[obtuse pebble]

@unreal nexus Has your question been resolved?

[obtuse pebble]

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[royal edge]

Why is this wrong. I thought I can apply the distributive property here

[polar fossil]

,rccw

[polar fossil]

• inside the parentheses

not times

[royal edge]

Oh thanks

.close

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[fleet crow]

just need help with 7c only. i forgot what it means when something is due south/north

[sand bough]

hi

In a 2D coordinate system, "due south" of the origin means that the airplane's x-coordinate is 0. In other words, it is directly below the origin on the y-axis.

[fleet crow]

hmm i see

[sand bough]

yea?

[fleet crow]

so to find the time would it be: 1540 + t(-220) = 0?

then rearrange to find t?

[sand bough]

let me cal

wait a sec

1540 m + (-220 m/s * t) = 0

this is mine

according to Initial x-coordinate + (x-component of velocity * time) = 0

[fleet crow]

that makes t = 7?

[sand bough]

t = 1540 m / 220 m/s = 7 seconds

whats your ans

[fleet crow]

im so dumb

i did the other one

and set the airplanes y axie = 0

was wondering how i got 6.25

[sand bough]

ok

[fleet crow]

thankyouu

[sand bough]

yea

!done

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

[sand bough]

🙂

[fleet crow]

.close

[obtuse pebble]

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[sudden sage]

how do I write the formal definition for lim x to ♾️ of f(x) = ♾️ ?

[obtuse pebble]

@sudden sage Has your question been resolved?

[obtuse pebble]

@sudden sage Has your question been resolved?

[tardy epoch]

https://math.libretexts.org/Bookshelves/Analysis/A_Primer_of_Real_Analysis_(Sloughter)/05%3A_Limits_and_Continuity/5.03%3A_Limits_to_Infinity_and_Infinite_Limits

[sudden sage]

what im confused about is how does infinity fit in here

do i just replace |f(x)-L| with f(x) > e

cause subbing L as infinity doesnt make sense

[tardy epoch]

It doesn't. You skipped your actual question

[sudden sage]

the exact question was in the exercise

and the first one used x -> a

[sudden sage]

.close

[obtuse pebble]

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[obtuse pebble]

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[vivid mirage]

Could someone walk me through a full solution of this problem?

[restive gorge]

Use the equation they provided and try to simplify it, is there something that you can then tell?

[vivid mirage]

3v2=2v1

They are linearly dependent

[restive gorge]

yup

one is multiple of the other

v_2 = (2/3)v_1

[vivid mirage]

Right

Thank you 🙂

.close

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[open spoke]

What is L1 norm, L2 norm, L 3 norm, ... ,L infinity norm ?

[foggy quail]

kind of depends on the setting

[alpine bison]

you are the one who made argue some helpers about the question on $\pm$

[warm shale]

everg

[open spoke]

Eyyy whats up

[drifting wraith]

" the Lp norm is the pth root of the sum of the entries of the vector raised to the pth power"

(a+b+c)
sqrt(a²+b²+c²)
cbrt(a³+b³+c³)...

[foggy quail]

that assumes the entries are nonnegative

[obtuse pebble]

@open spoke Has your question been resolved?

[drifting wraith]

yeah that feels like it's not on purpose

like it's supposed to be absolue values, and google lied

anyway it's different ways to add several numbers into one, L2 corresponds to how distances in irl space work

[obtuse pebble]

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[untold harness]

Can someone answer check?

I think I might have gotten it???? I don't know

[wary badger]

show your work

[untold harness]

wait nope nvm

[alpine bison]

let's hope it is not close, but no cigar

[untold harness]

so it's asking for rate of change of radius in terms of time, right?

dr/dt

[wary badger]

yea dr/dt

[untold harness]

ok

i can find that by multiplying dr/dS by dS/dt, right?

[wary badger]

first can you tell me the formula for the surface area of a sphere

[untold harness]

4pi * r^2

[wary badger]

yep

so

$S = 4\pi r^2$

[warm shale]

knief

[wary badger]

just differentiate dt

S and r are both functions of t

[untold harness]

so i differentiate that, and that's dr/dS, right?

[wary badger]

we are given $\frac{dS}{dt} = -0.1$

[warm shale]

knief

[wary badger]

what

[untold harness]

wait no

no

[wary badger]

^^

it’s like implicit

[untold harness]

i'm not sure what you mean

[wary badger]

implicit differentiation

bro what

[untold harness]

the fuck was that 💀

[misty zodiac]

sorry for that

[wary badger]

who knows

all good tony

!help

!help

[obtuse pebble]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[misty zodiac]

hii i am tony stark ceo of starc industries

how can i help you

[untold harness]

^

[wary badger]

build me an arc reactor

[scenic zenith]

whats your answer?

[untold harness]

yeah i lied i thought i had one. i don't

[wary badger]

brother differentiate this dt

[untold harness]

help im stupid how

my brain has kind of melted

[scenic zenith]

do you understand chain rule?

[untold harness]

yes

[wary badger]

do you know implicit differentiation

[untold harness]

yes

[wary badger]

ok it’s the same thing

[untold harness]

i am just overwhelmingly fatigued in life rn, im so sorry

[wary badger]

treat it like S and r are y sort of

[scenic zenith]

substitute the value and find dr/dt

[wary badger]

all of life is suffering and convincing ourselves that it is worth it.

[untold harness]

chipotle

[wary badger]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[untold harness]

its fine man 💀

no

[scenic zenith]

ok lol

[untold harness]

why

[wary badger]

because you can’t just copy answers

[untold harness]

i

...ok

[wary badger]

it’s cheating

[scenic zenith]

right

my bad

[wary badger]

all good fish tank

[misty zodiac]

To find this, we first need to differentiate the surface area formula with respect to time (t), which gives us dA/dt = 8πr(dr/dt). We can then substitute the given values into this differential equation as follows: -0.1 = 8π*(20/π)*(dr/dt). Solving this equation for dr/dt gives us the rate at which the radius of the sphere is changing, given the conditions in the problem statement.

[wary badger]

💀💀

!nogpt

[obtuse pebble]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[wary badger]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[untold harness]

its ok i think i got it

[misty zodiac]

sorry budy u know what happend if viplash

[wary badger]

lame

[misty zodiac]

i would give an internship at starc tower

or avengers building

but be careful with hulk he dosent like math

[untold harness]

this is very funny and yet a tad distracting

[wary badger]

nah bruce banner can control it now

[untold harness]

mayhaps stick to other channels if you dont mind

thank you mr stark

[misty zodiac]

sory guys you please carry on

i want to let you guys know i am a professional tutor.
i work at University of south florida as Teaching assistant

[untold harness]

that's wonderful

good for you

[misty zodiac]

my name is rohith

nice to see bunch of nerds together

[wary badger]

fire

[untold harness]

they say my grades on fire but at least im iced out

[untold harness]

ok so i was instructed to differentiate this

but that would give us dS/dr

so how do i turn that into dr/dt

@wary badger sorry for ping but i am uh still confused

[obtuse pebble]

@untold harness Has your question been resolved?

[untold harness]

.close

[obtuse pebble]

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[worldly bay]

is writing {X∈ℝ, x ≠ 3, 4} the same as writing {X∈ℝ, x ≠ 3, x ≠ 4}

[gilded needle]

yes

normally one would write : or | instead of the first comma

[opaque mesa]

instead of , i would use the and symbol

[worldly bay]

ohh true

[worldly bay]

oh what

i thought u meant &

[dark stirrup]

$x\in\bR$, not $X\in\bR$. Case matters

[warm shale]

SWR

[worldly bay]

right

[worldly bay]

so the lil triangle without the bottom line is and??

[opaque mesa]

i guess

[dark stirrup]

As mentioned earlier, ${x\in\bR|…}$ is preferred over ${x\in\bR,…}$. Specifically because the comma can get confusing with the commas that follow. The pipe can be interpreted as “on the condition that”

[warm shale]

SWR

[worldly bay]

oh alr

would putting {x∈ℝ | x ≠ 3 or 4} be wrong

like is there a symbol for "or" or something

[opaque mesa]

why or?

are you not sure if x is not equal to 3?

[worldly bay]

x is any real number on the condition that its not equal to 3 or 4

[opaque mesa]

.

[worldly bay]

just outta curiosity how would i type that on a keyboard

or what would i need to look up to copy and paste it

[opaque mesa]

x ≠ 3 ʌ 4

[worldly bay]

alr thanks

[dark stirrup]

I would recommend against this

[dark stirrup]

$x\ne3,4$ I would understand if I were grading your paper, but $x\ne3\wedge4$ reads very awkward

[warm shale]

SWR

[dark stirrup]

Best is $x\ne3\wedge x\ne4$ or you could do $x\notin{3,4}$. Best would be simply $\bR\setminus{3,4}$

[warm shale]

SWR

[worldly bay]

Alr thank you

[alpine bison]

np

[obtuse pebble]

@worldly bay Has your question been resolved?

[wary badger]

you’re welcome

[obtuse pebble]

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[molten forum]

Hi, we have to express the shaded area in terms of number a. I got 2sin(a) - a^2, is this correct?

[viral blade]

looks right

[obtuse pebble]

@molten forum Has your question been resolved?

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[sand radish]

how to 6x2 = 0

[sand radish]

I already solved most of it but I'm stuck at 6x square equals 0

I asked chatgpt and somehow he told me I could divide both sides by 6

but how does that work?

[restive gorge]

Can you show your work?

[sand radish]

.

ignore x2 = 6

im dumb

[restive gorge]

Just divide by 6

you did so well

[sand radish]

but like

how does that work?

why is it that allowed?

[restive gorge]

because 6 is a factor

[sand radish]

oh

[restive gorge]

you are allowed to add, subtract stuff

[sand radish]

so how should I write it?

[restive gorge]

as divide and multiply (except 0)

they way I do is
6x² = 0 | : 6
x² = 0

| is like a command line

saying what you are about to do next

[sand radish]

and then i just get rid of the x square

correct?

@restive gorge

[restive gorge]

yes by pulling the square root

[sand radish]

okay

thank you

.close

[obtuse pebble]

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[frozen crow]

Hello Guys! I just wanted to ask if what does this problem want to find?is it Present Value(PV), Future Value(FV) or Periodic Rate(P) this topic is Annuity

Problem:How much is the monthly amortization on an automobile loan of P900,000.00 to be amortized over 5-year period at a rate 9.5% compounded monthly?

[frozen crow]

<@&286206848099549185>

[frozen crow]

At first I thought it was asking for the future Value but my other classmates insisted that the future vale is the 900,000 in the given.

I did some research and it says its looking fir the amortization? <@&286206848099549185> is that right?

[pastel tide]

??

[frozen crow]

?

nvm I got the answey after some self studying

.close

[obtuse pebble]

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[frozen crow]

.reopen

[obtuse pebble]

✅

[frozen crow]

My classmate said my first answer was correct, it was finding (P) but I don't know if P or Amortization

can you guys help me

[obtuse pebble]

@frozen crow Has your question been resolved?

[obtuse pebble]

@frozen crow Has your question been resolved?

[obtuse pebble]

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[sterile stratus]

Can someone help with this question? This is all I’ve done so far.

[sterile stratus]

@ me when someone answers thanks

[timid silo]

@sterile stratus

[sterile stratus]

Yes

[timid silo]

A great starting point would be to write everything in terms of f(x)

[sterile stratus]

I tried solving it

Wdym tho

[timid silo]

wait I'll show you how

just gimme like two minutes

[sterile stratus]

Oki

I also tried using the fact that f(-1) =2f(1) , we could say (I think) (-1,y) and (1,2y)

[main stream]

umm

f(x) is odd function

[sterile stratus]

o

[main stream]

h(x) is even function

[sterile stratus]

I mixed it up with h(x)

nvm

[main stream]

soo because f(x) is odd

f(1) = -f(-1)

[sterile stratus]

no that’s for even functions

[main stream]

but it is also given that f(-1) = 2f(1)

ohhh

yess sorry my bad

[sterile stratus]

yaur

it’s oki

[sterile stratus]

Yes now

[timid silo]

Qiqi are you sure this question is correct?

especially the part about

[main stream]

so f(1) and f(-1) both must be zero

[timid silo]

f(x) = 3 - h(-2)

[sterile stratus]

About how f(x)=3-h(2)

Yeh

I was confused too

Cuz there’s no x

but a horizontal line ?

[timid silo]

can you send the original question is possible?

perhaps we're missing ut on something

[main stream]

f(1) and f(-1) are both zero right?

[sterile stratus]

Nvm it can’t owo

[timid silo]

Qiqi do you have the original question?

[sterile stratus]

A classmate gave me that question idk wheee they got it from :(

[timid silo]

I am fairly certain we are missing out on something here

f(x) = 3 - h(-2) seems wrong

[sterile stratus]

Yeah and horizontal lines can’t be odd

[timid silo]

Yeah

And it can't be a horizontal line in the first place

[main stream]

what if... f(x) = 0

[timid silo]

I think that could work

[main stream]

f(x) = 0

[timid silo]

3(f(-1)) = [h(2)]^3 - k

[main stream]

so you get

h(2) = 3

[timid silo]

yup

[main stream]

so answer should be k = 27

[timid silo]

3 * 0 = 3^3 - k

k = 27

yup

I think that could work

[main stream]

:)

[timid silo]

@sterile stratus

[sterile stratus]

oki lemme c

[timid silo]

good thinking @main stream

[main stream]

thank you sir

[sterile stratus]

THANKS GUYS

[timid silo]

THank yoobie

I didn't contribute much

[sterile stratus]

It’s ok still thanks to u 2

but guys if f(x)= 0 then why would they give f(-1)=2f(1) like the answer would still be correct but like why would they give that info

[timid silo]

hmm tru

if it works tho

I guess its fine

since 0 = 2 * 0

[sterile stratus]

Yeh

[main stream]

yes thats the reason

with the help of that we were able to determine that f(1) and f(-1) were zero

[timid silo]

yup yup

its kinda intuitive

but yeah

[red ice]

fun fact this trick applies in a lot of situations

[timid silo]

oh south is here

[red ice]

I remember working with tensors and basically you had to show that x = -x

so that x = 0

[timid silo]

Kewl!

[sterile stratus]

I don’t get it how

[red ice]

add x to both sides so that 2x = 0

anyway that was just an example

[sterile stratus]

ohhh

Oki thank u guys again I appreciate it

.close

[obtuse pebble]

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[fickle oasis]

How can i solve this question?

[red ice]

it's separable

expand the brackets on the RHS and move all the terms containing T to the left

then integrate both sides

[fickle oasis]

I might've done smtg wrong

Could you check for me?

[obtuse pebble]

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[queen yew]

Statistics class, called OMIS 600. Example problem on the image is not given in the book but was copied during class. I need to know everything about it. From the formula(s), to how to work it, what each individual letter/variable in the formula means, etc.

[obtuse pebble]

@queen yew Has your question been resolved?

[queen yew]

<@&286206848099549185>

[obtuse pebble]

@queen yew Has your question been resolved?

[obtuse pebble]

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[cunning breach]

Say a diffenrential equation $$xy'=y+xy$$ we can make it as $$\frac{y'}{y}=\frac{1}{x}+1$$ Where the solution to it is $$y=\pm Dxe^x$$ where D is a constant besides 0. Since $y\neq0$ from the initial equation, why can we conclude that D is a arbitraty constant?

[warm shale]

Good

[cunning breach]

Like how could we suddenly conclude that D could be 0, when we excluded y = 0 and x = 0 at the beginning.

[obtuse pebble]

@cunning breach Has your question been resolved?

[cunning breach]

<@&286206848099549185>

[obtuse pebble]

@cunning breach Has your question been resolved?

[cunning breach]

.close

[obtuse pebble]

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[warm shale]

Bean Man

[timid silo]

what is the || here ?

[tired mica]

Some norm

g is a function from R to R

So abs

[timid silo]

ok because a norm on a real number was weird

hm do u have context ?

[tired mica]

The only other information is that g is C1

[timid silo]

maybe calculate the derivative with the limits ?

[timid silo]

on R ?

[tired mica]

yes

[timid silo]

ok isee

if u do lim when x->0

of (f(x)-f(0))/(x-0)

=f(x)/x

and f(x)/x <Mx

so tend to 0

[tired mica]

Thats what I got

Alright thank you

.close

[obtuse pebble]

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[crimson geyser]

Someone please help me evaluate that lim x-->infinity ( (1 + 10/x) ^ (e^x)) = infinity

[crimson geyser]

im stuck and only found the indeterminate form of type 1^infinity

stuck on ln y = e^x • ln(1 + 10/x)

[wary badger]

can you use lhopital

bring the e^x down

[crimson geyser]

yes this is lhoptial

[wary badger]

$\frac{\ln(1+\frac{10}{x})}{\frac{1}{e^x}}$

[warm shale]

knief

[crimson geyser]

OHH I SEE

[wary badger]

this will be 0/0

[crimson geyser]

Nvm im stuck again

[polar fossil]

writing that denominator as 1/e^x is mildly deranged

[wary badger]

i was just making the point

i thought it was more clear than e^-x

[crimson geyser]

do i set y = f(x) now?

[wary badger]

generally we would write L

[crimson geyser]

L = y?

[wary badger]

no

L = limit

[crimson geyser]

ohh

[wary badger]

you’re solving for L

y makes it seem like a function

[crimson geyser]

So L = lim x-->inf (f(x)?

[wary badger]

yea

$L = \lim_{x \to \infty} \left(1+\frac{10}{x}\right)^{e^x}$

[warm shale]

knief

[wary badger]

then you do the whole ln(L) thing

and eventually you’ll go back and solve for L

after lhopital

[crimson geyser]

Something like that? @wary badger

[wary badger]

well did you write undefined?

you’re supposed to use lhopital from there

0/0 is met

$\lim_{x \to \infty} \frac{\ln(1+\frac{10}{x})}{\frac{1}{e^x}}$

[warm shale]

knief

[wary badger]

are you unfamiliar with lhopitals rule?

[crimson geyser]

no im just confused with this particular problem for some reason my brain just turns off

[wary badger]

derivative of numerator/derivative of denominator

[crimson geyser]

ill apply it now

[wary badger]

if $L = \lim_{x \to \infty} \frac{f(x)}{g(x)}$ results in 0/0 then $L = \lim_{x \to \infty} \frac{f’(x)}{g’(x)}$

[warm shale]

knief

[wary badger]

@crimson geyser what did you get

[crimson geyser]

i got lim ( (10/(x(x+10))/ (e^(-x))

so i think

10 / (1/(e^x) * (x(x+10))

[wary badger]

$\lim_{x \to \infty} \frac{\ln(1+\frac{10}{x})}{\frac{1}{e^x}} = \lim_{x \to \infty} \frac{\frac{-10/x^2}{1+\frac{10}{x}}}{-e^{-x}}$

[warm shale]

knief

[crimson geyser]

bc (a/b) / c = a / (b*c)

WAAAT

[wary badger]

$\lim_{x \to \infty} \frac{\frac{-10}{x^2 + 10x}}{-e^{-x}}$

[warm shale]

knief

[wary badger]

$\lim_{x \to \infty} \frac{10e^x}{x^2+10x}$

[warm shale]

knief

[wary badger]

what do you get

[crimson geyser]

10e^x / 2

holy crap

Now i solve for L

[wary badger]

well

lim at infinity though

[crimson geyser]

thank you

i think i was confused bc i took the deriv wrong at first thinking i did it correctly

i can apply this now to my problems

[wary badger]

well what did you get btw

[crimson geyser]

I got ln (L) = lim x->inf (10e^x / 2)

ln (L) = inf

L = e^inf = inf

[wary badger]

so L is

yea or just say it diverges

[crimson geyser]

havent touched series yet lol

thank you so much

[wary badger]

it has the same meaning

it’s not exclusive to series

[crimson geyser]

i see

[wary badger]

limits diverge

are you taking ap calc?

you generally don’t want to use arithmetic with infinity

they deduct points

[wary badger]

they’d take off points for this

[crimson geyser]

calc I college

and they dont really mind

[wary badger]

so maybe they won’t take off points then

[crimson geyser]

yeah just a lab

[wary badger]

yea don’t worry about it then

[crimson geyser]

thank you knief!!!

.close

[obtuse pebble]

Channel closed

Closed by @crimson geyser

Use .reopen if this was a mistake.

[wary badger]

you’re welcome sir

[obtuse pebble]

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[mortal sierra]

hello

[mortal sierra]

can someone helep me to understand the generalized binomial theorem

i understand the binomial theorem quite well

[timid silo]

@mortal sierra hi

[mortal sierra]

but i am really confused regarding the generalization

[timid silo]

What's your elo

[mortal sierra]

in chess?

[timid silo]

Yeah

[mortal sierra]

like around 1800 rapid in lichess

lol

okay but im here for math

have an exam tommorow

[timid silo]

Oh I'm 1700 rapid chess.com
I used to

[timid silo]

Okay

[mortal sierra]

does someone understand the generalized binomial theorem and is willing to explain?

:((

[timid silo]

I will ask others to come and help you

[tardy epoch]

Just do practice problems from your homework or practice tests

[mortal sierra]

thing is, i don't understand it

[timid silo]

It's available for free on the internet?

[tardy epoch]

Do one problem at a time

Then show it here when you're stuck

[mortal sierra]

yes, many things about it are, but i dont undertsand them either :((

[timid silo]

That's sad

[mortal sierra]

i know

;(((

[timid silo]

I always use AIs to help my Quirky brain to understand everything

[mortal sierra]

yeah guess ill have to use those

[timid silo]

Good luck

[mortal sierra]

if anybody comes here and understand the binomial theorem with negative and. fractional exponents, ill happily apreciate ur help

[mortal sierra]

thankss

[tardy epoch]

Why can't you just do problems

One

[worn yoke]

it's the maclaurin series of (1 + x)^n, what else is there to explain?

[mortal sierra]

what is a maclaurin series

0_0

[tardy epoch]

If you never learned it, you don't need to know it

[mortal sierra]

can u explain it only from prior knowldage of the normal binomial theorem, and infinite geometric series?

[mortal sierra]

cause i want to understand it

[tardy epoch]

That's the problem with vague questions, nobody knows what math you're allowed to use

[tardy epoch]

Doing problems is exactly how you learn

[mortal sierra]

no, i just want an explenation, noto direct help with the exam

[tardy epoch]

What exam

[mortal sierra]

i dont think so, you might learn how to solve problems, but not why things work

[tardy epoch]

What exactly is your question on the exam then

[mortal sierra]

ignore the exam for now lol

im just confused about the generalization

[tardy epoch]

What exactly

[mortal sierra]

like, does it only work for x + 1 to the power of rational number?, where x is between -1 and 1

or does it work for any numbers?

how tf does it work?

like for the normal binomial theorem, it cause combinatorics of the terms

[tardy epoch]

the right side only converges for the x you mentioned

But the exponent can be any real number

https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_(Morris)/02%3A_Enumeration/07%3A_Generating_Functions/7.02%3A_The_Generalized_Binomial_Theorem

[mortal sierra]

oh okay okay, i saw some places that they represnted it like a+b

and therefore got confused cause some other places wrote it as x+1

and it wasnt clear

.closed

thans for the help

.close

[obtuse pebble]

Channel closed

Closed by @mortal sierra

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

[pine sapphire]

i don't rlly understand question b

idk how to start it either

it kinda gave me an equation and idk how they got that!

[unreal musk]

Did you understand part a?

[pine sapphire]

yup!

[unreal musk]

and they tell you that "The lawn covers 4 times as much area as the flower beds", and the diameter of each lawn semicircle is 10m, and the radius of the flower beds are (5 - x/2)m

[pine sapphire]

OH SO U TIMES IT BY 4?!

4(5 - x/2)?

[unreal musk]

Not quite like that but there will be something multiplied by 4