help-0

[remote heron]

okay

so the desire is to end up with like

$g(\bar x) - g(\mu) = g( \frac{1}{\hat \lambda}) - g( \frac{1}{\lambda}) = \hat \lambda - \lambda$

[ocean seal]

jan Niku

[remote heron]

is this right?

this seems further away

or did we want that $\hat \lambda - \lambda = \frac{1}{\bar x} - \frac{1}{\mu}$

[ocean seal]

jan Niku

[remote heron]

and its good

why not

oh if we want xbar then

its wrong

we want $g(\hat \lambda)$

[ocean seal]

jan Niku

[remote heron]

not g(x bar)

or wait

idk im so lost

[ocean seal]

IAttemptToIntegrate

[remote heron]

that were estimating? yea

[ocean seal]

IAttemptToIntegrate

[remote heron]

yea

no

[ocean seal]

IAttemptToIntegrate

[remote heron]

g(\mu) is lambda

expression of parameter

[ocean seal]

IAttemptToIntegrate

[remote heron]

yes

so you just find like

some g where when its applied to x bar

you get the parameter you are trying to estimate

then it doesnt matter what happens to mu

it goes into g too

?

so $\sqrt n (g(\bar x) - g (\mu) \to \dots$

yea

[ocean seal]

jan Niku

[remote heron]

im confused about both sides but

i think left side i almost get

but we just put g(mu) right

but it matters right

i mean we cant just put whatever we want in

why not g(lambda hat) and g(bar x)

idk

[ocean seal]

IAttemptToIntegrate

[remote heron]

i dont want to get sidetracked but i also want to get the part thats easy right

okay

okay

and we care that g(x bar) turns into our mle

and thats it

its not important here that g(mu) = lambda

or is that important

if it didnt equal lambda would it be wrong

the final conclusion

idk ill make a note to ask my teacher

i dont want to stick

lambda the parameter of the distribution

im assuming it matters that like

g(bar x) - g(mu) = MLE - parameter mle is trying to estimate

thats all im trying to confirm

[lone heart]

@remote heron Has your question been resolved?

[ocean seal]

IAttemptToIntegrate

[lone heart]

@remote heron Has your question been resolved?

[remote heron]

i appreciate the write up I am working through it slowly

❤️ 🙇‍♂️

[lone heart]

@remote heron Has your question been resolved?

[remote heron]

almost

$\cdots$

[alpine sable]

Theres a 8 sets, each set gets given a random unit, there are 25 different units, there are 7 good units, an individual good unit can be only used once, what are the chances of getting all 7 good units in a set

[remote heron]

Recall that the Delta method states, provided some estimator $\hat \theta$ for some parameter $\theta$, and some function $g$, continuous and differentiable at $\theta$, and $g'(\theta) \neq 0$, that $$\sqrt n ( g ( \hat \theta) - g (\theta)) \longrightarrow N(0, g'(\theta)^2 \sigma ^2)$$
Clearly $\sqrt n ( \bar x - \mu ) \longrightarrow N(0, \sigma ^2 )$ by Central Limit Theorem. Then it follows $$\sqrt n ( g ( \bar x) - g (\mu)) \longrightarrow N(0, g'(\mu)^2 \sigma ^2)$$
Recall our MLE $\hat \lambda = \frac{1}{\bar x}$. This implies that $g(x) = \frac 1 x$ is a goo definition for $g$. Clearly $g$ satisfies all other required criteria. We note that under the mapping $g$:
\begin{align*}
g(\bar x) &= \frac{1}{\bar x} = \hat \lambda \
g(\mu) &= \frac{1}{\mu} = \lambda
\end{align*}
and observe $g'(\mu) = - \lambda ^2$ while $\sigma ^2 = \lambda ^{-2}$.
This ultimately provides that the asymptotic distribution of our MLE mapping $\bar x$ is
$$\sqrt n ( g ( \bar x) - g (\mu)) \longrightarrow N(0, \lambda ^2)$$

[ocean seal]

jan Niku

[remote heron]

is it too wordy enough @alpine sable

😊

thank you again for your patience and help

🙇‍♂️

[lone heart]

@remote heron Has your question been resolved?

Channel closed

Closed by @remote heron

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[topaz notch]

Ayo quick math question

[ebon condor]

Ayo

[topaz notch]

If I had a^-2/b^3 and I wanted to flip it to make the exponent of "a" positive, then would the exponent of "b" become negative?

Like: b^-3/a^2

[buoyant kayak]

i mean you could do that

or you could just bring a to the denominator with b

you don't need to move b at all as long as you negate the sign of the exponent and flip a's position

[topaz notch]

Ic. So I could do 1/a^2 (b^3) ?

[buoyant kayak]

$\frac{1}{a^2b^3}$

[ocean seal]

a disappointing son

[buoyant kayak]

if that's what you mean

yeah

[topaz notch]

Gotcha

Ye

Thx

[lone heart]

@topaz notch Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[jovial lantern]

helppppppp

[jovial lantern]

.close

[lone heart]

Channel closed

Closed by @jovial lantern

Use .reopen if this was a mistake.

[wary stream]

If you want help, you need to post the problem you are stuck with

[jovial lantern]

ok mabey tommorow

[buoyant kayak]

[bleak ridge]

[wary stream]

[jovial lantern]

ok

ummm

please close channel

[glass lichen]

You already closed it...?

[jovial lantern]

.close

.close

.close

[wary stream]

It's already close

[glass lichen]

Read what I just said and stop spamming.

[jovial lantern]

oh

ok

um

[glass lichen]

Just stop typing.

[jovial lantern]

sorry im new

[wary stream]

Then read #❓how-to-get-help

[jovial lantern]

.reopen

[lone heart]

✅

[wary stream]

So are you here to ask a question now?

[jovial lantern]

umm yes

This expression containing 26 term starts a+2b+4c+8d+16e+...
what is the sum of all the coefficients?

[glass lichen]

what have you tried?

[jovial lantern]

idk

[glass lichen]

you don't know what you tried....?

[wary stream]

Maybe start by determining the pattern

[jovial lantern]

do u have to use the quadratic fomula

[glass lichen]

Do you see a quadratic anywhere?

[jovial lantern]

yes i do

[glass lichen]

Ok, where

[jovial lantern]

ummm

[glass lichen]

Cause I don't

[jovial lantern]

i do

[glass lichen]

Ok, tell me where the quadratic is then

[jovial lantern]

an^2 + bn + c

[wary stream]

It also says sum the coefficients

[glass lichen]

without bsing one into existence

[jovial lantern]

ur not helping

[gray isle]

where are you seeing

an^2 + bn + c
in
a+2b+4c+8d+16e+...

[jovial lantern]

no where

hmmm

[wary stream]

So why are saying use the quadratic formula if there is no quadratic?

[jovial lantern]

hmmm

[gray isle]

if you really have literally no idea just say so instead of trying to make something up

[jovial lantern]

becuase

no no i do have idea

[glass lichen]

Probably trolling cause that's their message history

[wary stream]

As mentioned, it helps to determine the pattern first

[jovial lantern]

umm the second diffrence

[glass lichen]

what's the coefficient of f?

[jovial lantern]

of f

its

32

[glass lichen]

why is it 32?

[wary stream]

And you determined that how?

[jovial lantern]

cuz 16 x 2

[glass lichen]

so do you see the pattern of the coefficients?

[jovial lantern]

omg

yayayayayay

wait

nvm

ok cool

help

HEELPPP

[gray isle]

so do you see the pattern of the coefficients?
yes/no?

[wary stream]

What did you get stuck on?

[glass lichen]

Yes cause we're all telepathic and know what exactly you need help with from "HEELPPP"

[jovial lantern]

yes

[gray isle]

what's the pattern

[jovial lantern]

x2x2x2x2x2x2x2x2

idk how to write the fomula

let me try

uhhh

UHHH

SORRY

[gray isle]

?

[glass lichen]

Idk how you could be confused by their well worded comments \s

[gray isle]

that tells me nothing about what you tried and whether you succeeded

[lone heart]

@jovial lantern Has your question been resolved?

Channel closed

Closed by @jovial lantern

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[wheat prism]

My problem is. I want to prove this

[wheat prism]

What I have tried is using the definition

Of both limits

But I don't know how to continue since we have different signs in the inequalities

[vague coral]

I can't read what you have written

[wheat prism]

Let me take another pic

[vague coral]

or use a pen

[wheat prism]

Yeah there's that

I want to find that adding up both function I'll find that the limit as x approaches infinity

Is infinity

[vague coral]

$$L -\varepsilon < g(x) < L + \varepsilon$$ and $$f(x)>R$$
If you add $f(x)$ to $g(x)$, you are left with $$f(x)+g(x) > L-\varepsilon + R$$ I think

[ocean seal]

Herels

[wheat prism]

Yeah yeah but umm is that L-epsylon +R greater than 0?

[vague coral]

R>0, and I think epsilon shouldnt be greater than L, but im not sure

[wheat prism]

Yeah that's the weird thing about this one

Idk

Maybe how I approached it is wrong

[lone heart]

@wheat prism Has your question been resolved?

[lone heart]

@wheat prism Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[tacit arch]

It's just algebra

Can you be specific which division

What's wrong with it

There's nothing being claimed, it's just a fraction

Yes and yes

Yes

[tacit arch]

This

1/(sqrt(a)-sqrt(b)) = (sqrt (a)+sqrt(b))/(a+b)

[lone heart]

Channel closed

Closed by @fast gyro

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[rich quartz]

Hey guys is there anything I can do after this to get to substituting?

Stuck

[tacit arch]

What's f(x)?

Ah nvm that's a y in the beginning

Your f(2+h) is wrong from the start

[rich quartz]

oh yeah

okay thanks

.close

[lone heart]

Channel closed

Closed by @rich quartz

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[strong hornet]

so if im getting this right, what this is saying is that there can only be one area under a curve, and if there can be more than 1 value that area can be, then that function is not integrable?

[strong hornet]

could someone give me a little geometric interpretation of this? I'm having a hard time seeing what the step functions would look like in relation to some f(x)

[lone heart]

@strong hornet Has your question been resolved?

Channel closed

Closed by @strong hornet

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[vapid sinew]

yo

[vapid sinew]

if i have 3 things

like anything

and theres a 15 percent chance of gettign something

and i get that something 3 times in a row

what are the odds of taht

[tough pond]

.15^3

[vapid sinew]

ty

[lone heart]

@vapid sinew Has your question been resolved?

Channel closed

Closed by @vapid sinew

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[limber aurora]

I need help factorizing f(x) = 81x^4 - 72x^2 + 16

[limber aurora]

"Hint: First express f(x) as the square of a quadratic expression"

[tough pond]

let u = x^2
81u^2 -72u + 16. factor now

[limber aurora]

tywsm

[lone heart]

@limber aurora Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[sweet parrot]

Can i ask inventory management questions here? Ping me

[lone heart]

@sweet parrot Has your question been resolved?

[lone heart]

@sweet parrot Has your question been resolved?

Channel closed

Closed by @sweet parrot

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[alpine sable]

This is an interesting question

@crystal crown where are you stuck at though

[crystal crown]

I do not understand anything, have done nothing so far

[alpine sable]

I see

So you understand the dashes on AM and MD?

[crystal crown]

yeah

i just dont know how to solve this im bad at geometry

[alpine sable]

They mean that AM = MD

They're of equal length

[crystal crown]

ik

[alpine sable]

Oh

By the way, only this much information is given?

[crystal crown]

yeah

my teacher said its hard to solve

[alpine sable]

Let me try to solve it, I'll get back to you in some time

[crystal crown]

alr thanks

[hasty elk]

is ABCD just a random (convex) quadrilateral?

or is it a parallelogram or trapezoid?

it's actually quite simple if BC//AD

[alpine sable]

Yeah

But that information isn't given at all which it hard to go around this problem

[hasty elk]

it can't be true in the general case

probably

not sure

maybe the equal lengths actually force it to be doable without the parallel assumption

[alpine sable]

Hmmm

What if we connect points L and M

Since they both are midpoints

So they'll divide the quadrilateral into equal areas

[hasty elk]

that's exactly how you prove it in the BC//AD case

[alpine sable]

Yes

[hasty elk]

i had that thought, but there's no guarantee both sides will have equal areas cause AB and CD may not be equal in length

[alpine sable]

Oh yeah

[pale kestrel]

coordinate geometry time?

[alpine sable]

I think we might try to solve special cases first

[alpine sable]

But we don't have any data (the coordinates)

How we would proceed then

[pale kestrel]

with variables lol

it was a joke though

[alpine sable]

xd

I mean

[pale kestrel]

But since the teacher said it was hard

[crystal crown]

none its just random

[pale kestrel]

this might be a sure fire way to do it

[alpine sable]

Let's try then

[pale kestrel]

lol u try, ill come back in a few hrs

and u be swimming in algebra 😂

[alpine sable]

Alr

xd

[hasty elk]

BC//AD: use 1/2 base height, done

[pale kestrel]

it might not be so bad, though on a serious note

BC//AD isnt even generally true is it?

[crystal crown]

nope

[alpine sable]

Yeah

[crystal crown]

so this is it?

[hasty elk]

that's a special case

[lone heart]

@crystal crown Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[buoyant pebble]

hiiii i need help in a limit

[buoyant pebble]

i have done most of it but not sure if its true at the end

here it is

$\frac{2\sin{x} - \sin{2x}}{3x^3}$

[ocean seal]

itsalivenger

[buoyant pebble]

when x approaches 0

i factored a bit like this

[pale kestrel]

Consider the bounds of the numerator

[buoyant pebble]

$\frac{2}{3x^2}(\frac{\sin{x}}{x} - \frac{sin{2x}}{2x})$

[ocean seal]

itsalivenger

[covert agate]

then..?

[pale kestrel]

u dont need to do anything like that though

[pale kestrel]

.

[covert agate]

wdym bounds

[buoyant pebble]

same question 😦

[covert agate]

i’d use sin 2x = 2 sin x cos x and 1 - cos x = 2 sin²(x/2)

[buoyant pebble]

am not very good when it comes to english

$\sin{2x} = 2\sin{x}\cos{x}$ and $1 - \cos{x} = 2\sin²{\frac{x}{2}}$

[ocean seal]

itsalivenger

[covert agate]

yes

these identities help

[pale kestrel]

what?????

[covert agate]

yea

[pale kestrel]

you dont need to do any actual algebra

[covert agate]

..?

[pale kestrel]

what is the range of sin x?

[buoyant pebble]

1 and -1 ?

[pale kestrel]

yes

so your numerator

is always between -100 and 100 clearly

yes?

i picked 2 obvious bounds

[buoyant pebble]

DEFINITELY

[pale kestrel]

I can make it better if I bothered to think algebra

yes ok but it is good enough

ohh wait i said this all wrong

ok no but still no math

aaa how do i describe this

[alpine sable]

The answer will lie between that, but it's not the exact interval of the numerator

Just as an assumption for analysis

[pale kestrel]

You can see the numerator can always hit 1 and -1

for x tiny, that means the graph must keep going between -1/x and 1/x

does that make sense?

[buoyant pebble]

no 😦

[pale kestrel]

no

[buoyant pebble]

yes that is true

[pale kestrel]

not for x under 1

[alpine sable]

Oh yeah sorry

It's approaching 0

[buoyant pebble]

that would mean its bound by infinity

[pale kestrel]

basically im trying to justify why there is no convergence

yes

+-infinity

[alpine sable]

What shuri is saying that for very small x inside sin(x), it's always between 1/x and -1/x

[pale kestrel]

Your numerator does not converge, but your denominator converges to 0

The numerator is always oscillating

[buoyant pebble]

yes true

[pale kestrel]

If I sketch the graph, I will know the numerator will always be hitting points like -3, -2, 1, 2

i think

If it keeps hitting these points then the function must go between stuff like
-2/x

2/x

1/x

even for very small x

,plot (2sin x - sin x)/(3x^2)

[alpine sable]

,query graph (2sin x - sin x)/(3x^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pencil#9129

[pale kestrel]

ohhh wait im confusing things in my head

ok no =.=

@buoyant pebble nvm u have to use math ahahaha

[buoyant pebble]

xDDD

[pale kestrel]

$\frac{2}{3x^2}(\frac{\sin{x}}{x} - \frac{sin{2x}}{2x})$

[ocean seal]

Shuri2060

[pale kestrel]

this is a good step

i think there is an error though

$\frac{2}{3x}(\frac{\sin{x}}{x} - \frac{sin{2x}}{2x})$

[ocean seal]

Shuri2060

[pale kestrel]

its this right?

[buoyant pebble]

yes

[alpine sable]

Yeah it should be that

[pale kestrel]

oh wait

[buoyant pebble]

wait

no

[pale kestrel]

how did we get sin2x

$\frac{2}{3x^2}(\frac{2\sin{x}}{x} - \frac{sin{x}}{2x})$

[ocean seal]

Shuri2060

[pale kestrel]

is it this?

[buoyant pebble]

no

wait

[buoyant pebble]

e

$\frac{2}{3x^2}(\frac{\sin{x}}{x} - \frac{sin{2x}}{2x})$

[alpine sable]

$\frac{2}{3x}(\frac{\sin{x}}{1} - \frac{sin{2x}}{2})$

[ocean seal]

itsalivenger

Pencil

[covert agate]

use these

[pale kestrel]

$\frac{2}{3x^2}\left(\frac{\sin{x}}{x} - \frac{\sin{2x}}{2x}\right)$

[covert agate]

you should arrive at answer fairly easily

[ocean seal]

Shuri2060

[buoyant pebble]

yeees

[pale kestrel]

are u sure?

i think that is just 3x

ohhhh nvm misread

ok i see original

$\sin{2x} = 2\sin{x}\cos{x}$ and $1 - \cos{x} = 2\sin²{\frac{x}{2}}$

[ocean seal]

Shuri2060

[little drum]

$\frac{2\sin x - \sin 2x}{3x^3}$

[ocean seal]

Ansh

[buoyant pebble]

exactly this one

also i tried on desmos and it seems like it converges to 1/3

[pale kestrel]

you still have 1-1 in here so that form doesnt help right?

[buoyant pebble]

no 😦

[alpine sable]

$$\frac{2 sinx} {3x^3}(1-cosx)$$

[ocean seal]

Pencil

[pale kestrel]

sorry my bad earlier, what a waste of time. I was thinking the limit was infinity lol

[alpine sable]

After using double angle identity

[buoyant pebble]

oh no in that case that would be 0 instantly

[buoyant pebble]

wait am just checking

[covert agate]

this is the crucial step

[alpine sable]

$$\frac{4sin(x)sin^2(\frac{x}{2})}{3x^3}$$

[ocean seal]

Pencil

[covert agate]

uhh yea i guess

[alpine sable]

I believe we can work out with this now 🤔

[buoyant pebble]

how did you go from this

[little drum]

You can without it too though

[buoyant pebble]

to this

[pale kestrel]

You can also aproach with sin approximation up to x^3?

[little drum]

(1-cosx)/x^2 is a standard limit

[alpine sable]

Oh yeah

[buoyant pebble]

idk tbh

[alpine sable]

$$(1-cosx) = 2sin^2(\frac{x}{2})$$

[ocean seal]

Pencil

[alpine sable]

But no need of that

[alpine sable]

Because this converges to 1/2

So you'll have $\frac{2sinx}{2x}$

I believe you now know where this goes to

[pale kestrel]

,query graph (2sin x - sin 2x)/(3x^3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Shuri2060#9525

[buoyant pebble]

see

it has to converges to 1/3

[pale kestrel]

You havent done lhopital or series?

[little drum]

[buoyant pebble]

oh yea i forgot abt l'hopital

let me try

[pale kestrel]

hahaha

[alpine sable]

So you'll have $\frac{2sinx}{6x}$

[ocean seal]

Pencil

[pale kestrel]

lhopital makes so many of these easier

[alpine sable]

Yeah now we can proceed lol

Yeah

Omg XD

[buoyant pebble]

how can i derive cos(2x)

i mean sin(2x)

[pale kestrel]

sin 2x

goes to 2cos2x

?

[buoyant pebble]

that's what i thought

[alpine sable]

Wait nvm

[pale kestrel]

what

[buoyant pebble]

it still diverges

[pale kestrel]

im differentiating

then u can do lhopital again

not diverges

its indeterminate

0/0

right?

[buoyant pebble]

yeaaaa undetermined

[pale kestrel]

You can do lhopital again and again

each time u get this form

[alpine sable]

Yes ^

[alpine sable]

Or just end with this, use L'Hôpital's rule once and boom. Done

[pale kestrel]

(2cos x - 2cos2x) / 9x^2

[buoyant pebble]

yea how did you get that btw

[pale kestrel]

(-2sin x + 4sin2x) / 18x

[buoyant pebble]

if you got here no need for hopital

[alpine sable]

We need once

[pale kestrel]

(-2cos x + 8cos2x) / 18

[alpine sable]

Or you can also do what shuri is also doing

[pale kestrel]

i think i bodged my signs

[buoyant pebble]

because $\frac{sin{x}}{x} = 1 $ when x approaches 0

[alpine sable]

Using the rule again and again

[alpine sable]

Are you sure

[buoyant pebble]

yes

[alpine sable]

,query sinx/x x approaches to 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pencil#9129

[pale kestrel]

yes lmao

[alpine sable]

Oh

[buoyant pebble]

so how did you get there ????

[pale kestrel]

i cant do math today lol but anyways

They did double angle formula right?

[alpine sable]

Yes

Wait I'll show

[pale kestrel]

'(1-cosx)/x^2 is a standard limit'

We had this

it is standard or you can check with lhopital

[buoyant pebble]

i only know it by taylor series

can you write with the bot please

[alpine sable]

Also yes ^

[alpine sable]

i think you can also derive the identity by taylor series

But it's this

$$sin(2x) = 2sinxcosx$$

[ocean seal]

Pencil

[buoyant pebble]

i understand now

GOd i really need to remember trigonometric formulas

[alpine sable]

👍

[buoyant pebble]

thank you ssssooo muuuuuuuuch

THANKS ALL

.close

[lone heart]

Channel closed

Closed by @buoyant pebble

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[amber iron]

I need to solve $y' = 4-y^2$ by infinite summation

[ocean seal]

ykj3

[glass lichen]

you mean integration?

[amber iron]

like this

[glass lichen]

oh power series

[amber iron]

first problem is i dont know how y^2 will expand

<@&286206848099549185>

[lone heart]

@amber iron Has your question been resolved?

[little drum]

Did you have any examples in your textbook?

[amber iron]

not with y^2

[little drum]

Show me?

[lone heart]

@amber iron Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[rich rose]

Hello

[lone heart]

@rich rose Has your question been resolved?

Channel closed

Closed by @rich rose

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[grand karma]

How would I go about solving the question?

Sorry if this is simple

[tight locust]

@grand karma

i have created three new points

or rather just labeled them

but this is helpful

[grand karma]

How so?

[tight locust]

gimme a sec i'm drawing something

alright

by symmetry we have that angle POQ = angle ROQ = 60

the shaded region is composed of three sectors and six triangles

first we find the area of the sectors

the sectors form half the area of the circle

so 1/2 x pi x 2^2 = 2pi cm^2

then we find the area of the triangle OAR

OR = 2cm, OA = 1cm, angle ROA = 30

A = 1/2 b h = 1/2 x OR x sin(30) = 1/2 x 2 x 1/2 = 1/2 cm^2

there are 6 triangles so 6 x 1/2 = 3

so the answer is 2pi + 3 cm^2

[tight locust]

that clear it up?

[grand karma]

one second

are sectors the big triangles?

OHHH

I see it

thanks

[tight locust]

this is basically what you should be seeing

[lone heart]

@grand karma Has your question been resolved?

Channel closed

Closed by @grand karma

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[warped spruce]

claim

[warped spruce]

my teacher did derivative to this function

and I didn't understand why it works to just put the dominator in power of -1, what is the logic behind it?

[wary stream]

So you can use power rule instead of quotient rule

[warped spruce]

yes but why it works?

[wary stream]

Because $$\frac{1}{x} = x^{-1}$$

[ocean seal]

dldh06

[wary stream]

It's an exponent concept

[warped spruce]

alright but why it becomes derivative after you do it in power of -1

[wary stream]

What exactly are you asking?

[warped spruce]

I understood that he can do this line

[wary stream]

The problem is to find the derivative so doing power rule is easier than quotient rule

[warped spruce]

but why from here it becomes derivative

[wary stream]

Because you're finding the derivative of that function

[warped spruce]

you use something that called power rule

[wary stream]

That's what it's called

[warped spruce]

alright, Thank you bro

have a nice day 🙂

.close

[lone heart]

Channel closed

Closed by @warped spruce

Use .reopen if this was a mistake.

[warped spruce]

wait bro can you do it with this function too @wary stream ?

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[surreal sinew]

first factor out the constant

[lone heart]

@surreal sinew Has your question been resolved?

[alpine sable]

Can anyone help me with this?

It was supposed to be a revision for my test tmrw but our teacher didn't send us the correction

[surreal sinew]

Can you translate to english @alpine sable

[alpine sable]

1)a) calculate A^n

b) knowing that that matrix equals 5 we need to find the determinants I and ii

2. we need to find the rank of A depending on the different values of a

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[alpine sable]

3)a) we need to find the matrix X so that C.(A+X).B=I

[lone heart]

@alpine sable Has your question been resolved?

[tardy flume]

Hi guys

I have a question.
If someone would like to help me.

[tacit arch]

#❓how-to-get-help

[tardy flume]

I'm student of Pharmaceutical Chemistry.
2 year.
Doing great on Chem. Love it.
But there's something that I've come up with.
I'm understanding that math us important not really for Organic Chem (if you consider the daily lab or organic synthesis) But is important for the understanding of Quantum Physics applied for the models used in Chemistry.

What I've realized recently is that for me to ace (even if I'm only a student still) at Chemistry I would need also Math and Physics.

In the future job I'm saying.

Not for the grades. Doing great without any special deep knowledge of math

Is here someone who can guide me ?

I want to start studying Math on my own.

From the principals. To fully understand the thing. Not just doing some calculus without knowing what I'm looking for.

I would like to have a good knowledge on Math.
Is here someone who can guide me?
From where I should start ?

Pls 🙏🏼

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[wary stream]

Find the x and y components then add it up, then find the resultant and direction

The angle is measured CCW from the x axis

Counterclockwise

That 30 degree angle, yes, that's 30 ccw from x axis

That's not the resultant angle though

It's telling you what direction is measured positive

CCW from the x axis, is the direction for positive

This is what I mean about direction

If the resultant is 45 degrees, measuring CCW, it's 45, but making CW positive, its 315 degree or -45 degrees

[lone heart]

@midnight ferry Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[inland fable]

Which 1 do I pick?

[inland fable]

I did tan-1 -5.300 on calculator

I got -79

[inland fable]

?

oh hi riemann

I remember you from yesterday

so

could you help me out with this 1

Because I know it shouldn't be in the 1st quadrant but the first quadrant is 0-90

and from my notes it says anything that's tan negative would be in second or 4th quadrant

[tacit arch]

Both work

[inland fable]

so either 1 would mean I got the right answer?

2nd or 4th

the number wouldn't matter then

[tacit arch]

In general, tan(x) = tan(x+ pi) = tan(x+2pi) = ...

Just be sure you keep consistent with radians vs. degrees

[tacit arch]

I don't see an answer here?

[tacit arch]

Try tan( of this number plus 180) if degrees

[inland fable]

so

179.90etc?

[dense heron]

cant you select both?

[inland fable]

that's what I'm sayin

lol

so many numbers

ehhh

[dense heron]

lol

[inland fable]

I guess I'ma do the

4th quadrant

see if it works

[tacit arch]

Did you take the tangent of this value

[inland fable]

yeh

I got 179.9072328

tan of that number then + 180

weird

[dense heron]

you didnt have to deal with the numbers tho
they said that the tan is negative so the angle is either in the second or the fourth just like what reimann said

[inland fable]

true true

the number don't really matter it's just if it's tan or not and if it's negeative or not

[dense heron]

i mean

[inland fable]

wait a sec

it said I was wrong

it isn't 4th

[dense heron]

they didn't ask for any angles just what quadrant

[tacit arch]

tan(-79...+180) =tan(100...) =?

[inland fable]

wait

[dense heron]

can you choose 2 options?

[inland fable]

it allows me to put

yeh

2 options

[dense heron]

then 2nd and 4th

[inland fable]

so 2nd and 4th

[tacit arch]

You mismatched the parentheses

[inland fable]

ye

[dense heron]

ye

[inland fable]

what about cos= -0.0500

I got 92

and I put answer 1 and 4

[dense heron]

nein

is he asking for the quadrant again?

[inland fable]

ye

[dense heron]

so cos= adjacent / hypotenuse
if its negative that means that the adjacent side is negative / the -ve x axis
so it will be 2nd and 3rd

at least thats how i see it

[inland fable]

alr

lemme try that

mb

I mised up the negative and possitive

I see

[dense heron]

wut

[inland fable]

I thought the

answer would be possitive

but it is negative

questions

this 1 just says

sin theta=0 and tan theta= 0

X_X

subbject to both given conditions

I'm guessing it's asking for which quadrant they both have the same value?

so it would be 1 and 4 right?

[dense heron]

i have no idea

if the sin is 0 so the angle is either 0 or 180

[inland fable]

they both 0

[dense heron]

oh

if the question says <0 this means -ve number

0 +ve number
if the tan is +ve that means that its either the first or the third
since the sin is -ve so the first is eliminated

[inland fable]

ohh

ok

so

if it's <

it means negative

positive

[dense heron]

ai

[inland fable]

alr

third quadrant it is

hey

round to 2 decimal places mean like

52.22

right?

or is it just 52

big man wolf

you here?

is this correct?

it said I was wrong

<@&286206848099549185>

[tacit arch]

There are two answers again

[inland fable]

oh

uhh

hmm

third and 4th quandrant

right?

[tacit arch]

sin(x)=sin(180-x)

[inland fable]

alright so

sin (180-53.18743639)

sin theta =126.8125636

yeh?

that's my final answer I think

[tacit arch]

Take the sine of that angle and see

Theta is 126.81

[inland fable]

alr

nope

wrong answer X_X

"Check the value of the trigonometric function and note the sign. Locate all quadrants that the function is in. Check to make sure that the calculator is in degree mode. Recall any formulas for reference angles."

soo

<@&286206848099549185>

what's the right answer?

[tacit arch]

Oh your first answer is wrong since it's not in the specified range

[inland fable]

I put

126.81

[tacit arch]

There are two answers

[inland fable]

so what should I put in the box?

[tacit arch]

Use properties of the sine function to find it

[inland fable]

so 360-126.81?

[tacit arch]

sin(x)=sin(x+360) is the other one

[inland fable]

oh ok ok

mb mb

so I was supose to do

the 180-x and then do the 360- x

so 306.81

126.81, 306.81

ye?

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[tacit arch]

Yes it is

[inland fable]

alr

do I need to put

the ","

too?

noo

it's wrong againn

X_X

the real answer is 233.19, 306.81

eh eh eh eh eh

howww

[blissful ether]

Instructions say theta is between 0 and 360

-53.19 can't be correct

[inland fable]

126.81, 306.81

X_X

ok

lemme try the next simular question

hold up brb using washroom

[lone heart]

@inland fable Has your question been resolved?

[inland fable]

<@&286206848099549185>

so

do I just do cos?

instead of sin

same method?

[cunning trout]

This is a trigonometric equation @inland fable

So for that question when cos goes to the other side it because cos inverse of that number

[inland fable]

I just do the cos x on calculator and then do 180-value of x

and then do 360- value of x

ye?

[cunning trout]

So on your calculator do cos inverse of 0.7993,

[inland fable]

oh oko ok

lemme try

36.93669083

[cunning trout]

36.94 degrees

[inland fable]

should I use the full numbers

when I do

180-x

and 360-x

or use 36.94

[cunning trout]

I doesent say that from what I can see so I think just that

Unless it’s an ambiguous case

[inland fable]

oh

so it's just 36.94

?

huh ok

nope

maybe I do need to do the 180 and the 360

ok

basically that's the example

so

my answer in the back is wrong

<@&286206848099549185>

can someone help me figure this out

[inland fable]

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @inland fable

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

Channel closed

Closed due to the original message being deleted

[dark pelican]

Can someone help me with my geometry?

<@&286206848099549185>

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[dark pelican]

Uh

[dark pelican]

With the x+22 + x^2+28518=151390

I’m confused with x squared

What is the x^2 + x?

Or do we even do that at all?

It’s the segment addition postulate

<@&286206848099549185>

Can someone walk me through the problem please

33 minutes of wait bruh

[merry depot]

So you add up the two things and get a quadratic. So what's confusing you?

[dark pelican]

I’m stuck on the x+x squared part

How do we combine it

[merry depot]

You can't add them, they're different degrees

[dark pelican]

Oh

[true pulsar]

It would be like adding 6 apples to 5 oranges

[dark pelican]

So we will have two answers?

[merry depot]

more than likely you have 2 solutions, only one makes sense in the situation

Since x is a distance, it wouldn't make sense for the moon to be "-10000 km away" for example

[dark pelican]

I see

[lone heart]

@dark pelican Has your question been resolved?

Channel closed

Closed by @dark pelican

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[supple laurel]

can somebody check these descriptions and mapping rules and equations to see if they are right

[supple laurel]

in the red circle

[lone heart]

@supple laurel Has your question been resolved?

[lone heart]

@supple laurel Has your question been resolved?

[lone heart]

@supple laurel Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[formal vortex]

The velocity-time graph is shown in figure. The total distance travelled by the motor cycle in 60 sec is

[formal vortex]

<@&286206848099549185>

[quartz rapids]

What is the problem asking?

[formal vortex]

distacne

distance covered in 60 secs

[formal vortex]

.

[quartz rapids]

What math are you in rn?

[formal vortex]

11

graade 11

[quartz rapids]

Are you doing calculus?

Like derivatives and integrals?

[formal vortex]

ys

yes

but i dont know a thing

and pls do it fast

5 mins left

[quartz rapids]

You gotta divide the problem into 3

The easiest is the middle portion: the velocity is constant over time, so the position is a linear slope up

The first is a curve up and the last is a curve off to 0 slope

Treat each as a different problem and add them together

[formal vortex]

1000m
1125 m
1250m
1500m

there are the options btw

[quartz rapids]

Im not solving it for you, you have to try it yourself

Ill give you the middle one: with a slope of 25 m/s over 30 seconds, the distance covered there is 750m

[formal vortex]

thanks

.close

[lone heart]

Channel closed

Closed by @formal vortex

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[visual plinth]

...

[merry depot]

For what values of $\theta$ does $\sin\theta = \frac{\sqrt{3}}{2}$?

[ocean seal]

Zybikron

[visual plinth]

Solving for x has confused me here

Would these two be valid solutions? as when I type the inputs into the sin function they produce a negative output.

idk what im even asking , just if you were to solve this question what would the solutions of x be

[lone heart]

@visual plinth Has your question been resolved?

[merry depot]

all of those are valid solutions for x

[lone heart]

@visual plinth Has your question been resolved?

[visual plinth]

@merry depot

even tough the two solutions i boxed don't equal to squareroot 3/2 ?

they equal -squareroot 3/2

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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>.
• Type the command .close to free the channel when you're done.
• 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.

[uncut depot]

is it possible to say that there are infinite numbers between 2 numbers

[uncut depot]

sorry

.close

[lone heart]

Channel closed

Closed by @uncut depot

Use .reopen if this was a mistake.

[uncut depot]

ic

is it possible to say that there are infinite numbers between 2 numbers

for example $1 - 2$

[ocean seal]

azorfus

[echo socket]

I mean why not

[uncut depot]

yeah

[echo socket]

Okay 1 - 2 is definitely not infinite

[uncut depot]

no sorry i meant

a line

[echo socket]

But the amount of numbers between 1 and 2 are

[uncut depot]

ic

okay

thanks

.close

[echo socket]

This channel is already closing

[lone heart]

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>.
• Type the command .close to free the channel when you're done.
• 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.

[covert agate]

how dow we get sec u

and not |sec u|

[echo socket]

To integrate 1/cos, consider rewriting it as cos/cos^2

[carmine mica]

it's squared?

[echo socket]

Which is the same as cos/(1 - sin^2)

[covert agate]

??

[echo socket]

Then you can do u-sub

Let u = sin

[covert agate]

i’m not concerned about integrating secant

[echo socket]

Obviously it's not |sec u|

[covert agate]

tan²x + 1 = sec²x correct?

[echo socket]

Yes

Oh wait

[covert agate]

so we have sec²/√(sec²) = sec²/|sec|

= |sec|

[echo socket]

You meant why is there sec and not |sec|

[covert agate]

shouldn’t we obtain |sec u| instead

[echo socket]

I guess it's removed because while doing integrals we can just break up the interval into parts where sec is either positive or negative

[covert agate]

so in reality we’re integrating |sec|?

[echo socket]

I guess so

[covert agate]

how do we do that

[echo socket]

How do we integrate sec?

[covert agate]

|sec|

(and abs. value function, in general)

[echo socket]

If it's definite integral

[covert agate]

(if antiderivative of f is F can we get antiderivative of |f| in terms of F?)

[echo socket]

Then just use linearity of the integral

To break it up into intervals