help-27

[pure cedar]

THATS THE NORMAL VECTOR

🙏🏻

[blissful comet]

oh yeah normal vector ( perp to plane)

n

yeah

[blissful comet]

koi hindi mein samjhayega

[pure cedar]

lmao ok

[vital sedge]

Try to think of the blue point as the arrow going from the red paper to the blue point

[pure cedar]

kaha tk samajh aaya abhi 😭😭

[blissful comet]

normal vector agaya

[vital sedge]

there are infinite of these arrows perpendicular to the red paper right

so just find the one that's in line with the point we ar trying to find

which is 5,7,1

[pure cedar]

dekh
pehle plane ka normal vector aagya
fir question me diya hai ki jo line hai vo bhi plane ke perpendicular hai
to basically line ka bhi direction vector , normal vector hi hogya

bs fir to ho hi gya

line ka point pta hai ek

[blissful comet]

oh tou matlab 2 normal vectors

[vital sedge]

does that make sense?

[pure cedar]

direction pta hai

[blissful comet]

oh han

[pure cedar]

haan mtlb ese samajh skte hai

[mortal tendon]

the language shifted

[pure cedar]

uske baad to kuch ni krna

[mortal tendon]

crazy

[blissful comet]

yeh basically aesa hai na keh bhot saari imaginary lines parallel ja rahi ek doosre ke but plane ke perpendicular

hain

[vital sedge]

ongad @mortal tendon

[pure cedar]

haan exactly

[blissful comet]

yar thanku bhai god bless u

samajh agaya

[vital sedge]

fr

[mortal tendon]

crazy

[pure cedar]

bro said god bless u 😭😭😭😭

[pure cedar]

thanks meri jaan 🥀🥀

[blissful comet]

arey arey

ap kaha se ho

[pure cedar]

lmao

this is not for small talk

come to

[blissful comet]

oh han

[pure cedar]

#chill

!done

[devout snow]

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

@blissful comet Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[velvet coral]

It seems they are applying the order of zeros theorem separetely to each term in the denominator, is it possible to apply it to the whole denominotar at once? (i.e. the whole function $\sin(\pi z) (z^2 - 1)$) to obtain the same asnwer?

[bitter abyss]

Hello

[woven radish]

LXDL

[devout snow]

@velvet coral Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[potent compass]

Can you explain this one

[deft tapir]

It's because trig functions have waves which repeat and cycle after a set value

[potent compass]

Ooooo

[deft tapir]

In this case you have tan x

You see how it has a repeating graph?

So every 180° which is π, the graph repeats

[potent compass]

YES

please help me w this too

[deft tapir]

That's why in general, you only study those functions from [-π; π] or [0; 2π]

[deft tapir]

This one is just showing you how to draw -2tanx

[potent compass]

Where would the amplitude be

How do Ik which place Is the max and min

[deft tapir]

So since it's negative, it's symmetric to the center of the wave, and then it's srretched vertically

[potent compass]

Wait what?

[deft tapir]

So generally, you can just plug in the last value of your wave

Remember when we said that the graph repeats?

[potent compass]

Yes

[deft tapir]

So it starts at -90° which is -π/2 and ends at π/2

[potent compass]

No no I mean the amplitude for this

I don’t get it

I don’t understand how it works for tan

[deft tapir]

See how the graph is going up? It reaches it's highest value at π/2, you can calculate your highest value from there

If you have a function in the form of: atanx, where a is a constant, it just expands your graph vertically, but not the wave itself

[potent compass]

How do Ik it reached 2

[deft tapir]

What do you mean by that?

Like the value 2?

[potent compass]

Yes

I still of t get what the amplitude is for tab

Ik it’s the max and min for sine and cosien

*cosine

[deft tapir]

I don't remember ngl, but I'd assume you just input the highest value in the wave

[potent compass]

I kind of understand

The normal one has a amplitude of one and -one

So it passes through it?

[deft tapir]

It says it there that you get a repeating cycle every 180°, it's safe to assume that tan(180°=π) is your highest value (which converges to inf)

That's for tanx at least

Altho I don't think tanx had exact values, I think it had limits approaching inf and -inf

[potent compass]

I don’t get this

I don’t understand w the pi

[deft tapir]

180 is in degrees, π is in radians

It's just a different metric

180° = π rad
90° = π/2 rad
And so on

It's just a more common terminology

[potent compass]

Ok

[devout snow]

@potent compass Has your question been resolved?

Channel closed

Closed by @potent compass

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[hollow crest]

Hey so I have just started learning about the Sine rule, I understand it when I'm dealing with right angled trangles but I don't understand this. Is there like a formula or something to figure out the height of the triangle? Any help would be appreciated 🙂

[last parrot]

Looks fine

[summer summit]

they're just using the classic SOH-CAH-TOA identities, where that stands for sine = opposite/hypnotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent

[last parrot]

You need to use either sin, cos or tan that involve h

[summer summit]

the height "h" splits the triangle into two different right triangles

[hollow crest]

OHHH

Ok thankss

.close

[devout snow]

Channel closed

Closed by @hollow crest

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[devout snow]

Please don't occupy multiple help channels.

[stone stump]

<@&268886789983436800>

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[round orchid]

why is the settings for that even opened

it should be disablled

[stone stump]

for sharing links?

yeah that could never be useful

[round orchid]

no

invite links

[stone stump]

there are other useful discord servers

eg those in #old-network

[round orchid]

those are useful

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[prime sphinx]

the answer is got is 88degree is that correct?

[tepid stag]

yes you are correct

[prime sphinx]

thankss

.close

[devout snow]

Channel closed

Closed by @prime sphinx

Use .reopen if this was a mistake.

[tepid stag]

wait is H centre?

[prime sphinx]

no

well i mean

it doesnt look like it

do i close it

.close

[tepid stag]

no

you already did close dw

[tepid stag]

well i thought it was center at first glance and said yes but probably they didnt mention its not center so wouldnt be any problem ig idk

[prime sphinx]

https://giphy.com/gifs/yes-agree-indeed-GuDU8r5CnUoYtbS2CR

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[serene forge]

Hellooo for no 10 is this how you do it?
Range is y value

1×=1(0)=0?

[serene forge]

Oops the solution is right there

I don't understand still

[pure cedar]

any exponential function has range (0,infty)

[serene forge]

Ouh! Okie2 thank you

Evem if the exponents is like 5 or 3 etc

?

[pure cedar]

doesnt matter the number
every function of the form a^x

is always gonna go from (0,infty)

[serene forge]

Okay tysmm

[serene forge]

Oh I've seen an inequalities question

Its like
Log2 (3-x)<0

Do i just plug in the 2 in the graph?
The 2 is small btw

[pure cedar]

thats not how you solve a logarithmic inequality

what did you do

[devout snow]

@serene forge Has your question been resolved?

[serene forge]

I made the graph & just plug the numbers in qwq

[pure cedar]

plug what numbers in

[serene forge]

And since it says <0

+-+ i choose -

[serene forge]

2 & 3

From log2 (3-x)

[pure cedar]

why 2 and 3

[serene forge]

Because the question says log2 & 3-x so i thought u just input those numbers in the graph

[pure cedar]

nah mate

,w log inequality

log inequality works the same way

you just have to find root

and apply wavy curve method

or +-+-+ whatever

[serene forge]

Ah

,w log inequality

[woven radish]

Results provided by WolframAlpha

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

Requested by mugnes

[pure cedar]

dont see this

[serene forge]

Oh

[pure cedar]

this is trash

[serene forge]

Oh ok

[serene forge]

Uhm

Fund the root of log2?

[pure cedar]

its not log 2 mate

its $log_2 (3-x)$

[woven radish]

parthisjoking

[serene forge]

Oh

[pure cedar]

2 is the base of logarithm

[serene forge]

Is this how i write ut?

[pure cedar]

no thats square root lad

[serene forge]

?

[pure cedar]

try using

if y<0
then a^y < a^0

[serene forge]

A is the 2 in log?

[pure cedar]

yes

hey no

2 is the base of the log

a is taken to be 2

but a is not the 2 in the log

[serene forge]

Y=3
But 3 is larger than 0 so its a different formula?

<@&286206848099549185>

[chrome sorrel]

hello

uhm wats problem

[last parrot]

Which question

[fervent flame]

O to 1

0*

[chrome sorrel]

Huh

wat

[fervent flame]

Q10

[chrome sorrel]

ah, i see

[serene forge]

This one

[fervent flame]

What's the domain of the function?

[serene forge]

Oh I've already got that one helped

[fervent flame]

Oh ic

What ya need help with

[chrome sorrel]

uhm yeah das right

[serene forge]

The question is just log2(3-x)<0

Inequalities

[fervent flame]

What u gotta find ?

[chrome sorrel]

Whats up wid da ineuqlieyies?

[fervent flame]

Only x ?

[chrome sorrel]

Inequalities

[serene forge]

Wait

[chrome sorrel]

wow ure uhm

screaming

yes

[fervent flame]

X is (2,3)

[serene forge]

The solution set of the inequality log2(3-x)<0 is ()

[serene forge]

Indeed

[fervent flame]

First of all 3- x > 0 then
3-x < 1

[serene forge]

How'd u get 1?

[fervent flame]

2^0 = 1

[chrome sorrel]

Uhm

yes

das right

[fervent flame]

Remove the base

[chrome sorrel]

whyd u tell the answer straight away bro

[fervent flame]

i didn't got the question and straight up started solving

[serene forge]

Oh so if its log the way u find it is by #^0?

[chrome sorrel]

oh okay, das sumn id do as well

[chrome sorrel]

Yeah

the goal is to put x in like one spot

[fervent flame]

Yup

[chrome sorrel]

how does one do that?

well u can start getting rid of log

[fervent flame]

Basically inverse of log

[serene forge]

Wait2

[fervent flame]

Y = loga(x) is x = a^y

[chrome sorrel]

yknow, the more ive done calculus

the less i see of like log

its more ln

[fervent flame]

Yup

[serene forge]

Lik this?

[fervent flame]

No 3-x > 0

Coz argument is always +ve

[serene forge]

What's+ve 😭

[mystic scarab]

Positive

[fervent flame]

More than 0

[chrome sorrel]

is that how usability is spelt?

thats a word?

Oh sorry, thats out of topic

[fervent flame]

After argument is check then u have to get rid of log

By exponential increase

[fervent flame]

.

[serene forge]

Uhh the argument is
3-x≠0
3-x>0??? I don't get it 🥲

[fervent flame]

No it can't be 0

[serene forge]

Ouhhh ok

[fervent flame]

Always more than 0

The number within the bracket is +ve for real number

[serene forge]

Oh ok

So it has to be >0

[fervent flame]

Yup

[serene forge]

Unless its x-3

?

[mystic scarab]

Wdym?

The argument is 3 - x and it must be positive

[fervent flame]

Yus

[serene forge]

But the question is 3-x 😭

[mystic scarab]

My bad

[fervent flame]

Ohh yup srry i didn't see u inverted

My bad

[serene forge]

It's okay

[fervent flame]

Then u were r8

[chrome sorrel]

Uhm what

[fervent flame]

X - 3 < 0

[serene forge]

The symbol just flups right?

[chrome sorrel]

what did bro do?

[fervent flame]

Yes

[mystic scarab]

Whatever is between brackets (aka argument of the logarithm) must be positive @serene forge

[fervent flame]

Ya ik

[mystic scarab]

Wrong tag 😬

[fervent flame]

Np

After the argument check ,u gotta solve the actual inequality

[chrome sorrel]

mugnes, what do u know about logarithms?

[serene forge]

Oh okk thankss
Bc I've seen it become negative like
(X-3)(X-2) It becomes
(X-3) =
X-3≠0
=X=3

Etc

[mystic scarab]

This is wrong as written

[serene forge]

Or (x+3)
=X+3≠0
=x=-3

[chrome sorrel]

uhm

whats the ≠ for?

[last parrot]

Bro dont interfere let the helpers help

[serene forge]

Only the
Log (ab)=loga+logb
Log(a/b)=loga-logb
Etc

[fervent flame]

Yes

[mystic scarab]

!xyp

[devout snow]

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

[chrome sorrel]

Im tryna understand how she looks at the problem

or he?

[serene forge]

This as an example

That's how my tutor taught me

[chrome sorrel]

Okay and, did u know about it being the inverse of like exponents?

[serene forge]

No..

Never heard of that 😭

[chrome sorrel]

Ahh, i see

wait do u know what an inverse is?

[serene forge]

Like u move it's position

[chrome sorrel]

Ahh

[serene forge]

And when u do
Like from lefthand/righthand the +/- changes

[chrome sorrel]

Okay if i said like

wait do u know what a function is?

[serene forge]

Yeah :)

Kinda

[chrome sorrel]

Okay thats great

so f(x) is a function

u plug something into x and u get an output

the inverse would be

lets say the inverse is like g(y)

u plug something into y and u get ur input x

thats basically the point of log to like exponentials

[serene forge]

Ahh i see2

[chrome sorrel]

for example

32

u wanna find out how many 2s u wanna multiply together to get 32

so u take log2(32)

and u get like, 5?

2⁵ is 32 right

2⁵ is an exponential thing

so its basically doing the opposite

u get me?

[serene forge]

Yes

[serene forge]

Ohh

[serene forge]

Yesyes

U basically just find the exponent

[chrome sorrel]

Yeah

[serene forge]

Ah i see

[chrome sorrel]

so if u got uhm 1

what kinda exponent would u need

to get 1?

[serene forge]

Uh

0?

[chrome sorrel]

yeah

[serene forge]

Ouhh

[chrome sorrel]

and so uhh

thats what happens with ur problem

[serene forge]

Log2(3-x)<0
Log2(0+3-1)?

[chrome sorrel]

And also notice this

[serene forge]

Hm

?

[chrome sorrel]

log2(32)=log2(2⁵)=5

so like it just brings down

the exponent

[serene forge]

Ohh okiee

[chrome sorrel]

uhm yeah?

interesting way of writing that down

[serene forge]

Ah-

[chrome sorrel]

Lets backtrack here

[chrome sorrel]

log2(3-x)<0

what is ur thought process after u see that?

i just wanna see how u see it

[serene forge]

X becomes 1 since its a variable
Exponent of 2 is 0

So we put it in the bracket
Log (3-1+0)

[chrome sorrel]

Okay

why do u think x becomes 1?

[serene forge]

I assume its because we want a number for the solution

And a variable itself is equal to 1

[chrome sorrel]

Well u see

its an inequality

so..

ure guna hav a range of numbers

not just a number

Anyway lets plug in 1 and see what happens

log2(3-1)=log2(2)=1

and 1<0

hmmm yes

[chrome sorrel]

I think at this very moment, u should think of what the goal is here

the goal here is to like, just isolate x

put it on one side and all the other things put on one side

and just try ur best to do that

[serene forge]

Wait log2(2)=1??

How

I thought its 2 because log2(2)=log4=2

[serene forge]

Mkayy

[chrome sorrel]

Well uhh, whats 2s exponent hav to be so that it equals 2?

[serene forge]

OH

oh yeah mb

[serene forge]

Uhm

[chrome sorrel]

Uhh

wow

Okay

before i say anything

[chrome sorrel]

do u believe this is the answer?

[serene forge]

Not rlly ;-;

Bc i didn't move the x anywhere

🥲

[chrome sorrel]

Ah okay, thats a relief

[chrome sorrel]

So uhm, what was ur goal here?

[serene forge]

Make the inequalities/domain

[chrome sorrel]

Okay so uhm

log2(4) isnt equal to log(2)

[serene forge]

Huh?

But 2²=4

🥲

I don't get it

[chrome sorrel]

Oh

i see

log2(4)=2

not log(2)

[serene forge]

Oh!

Ok

[chrome sorrel]

Okay great

now uhh, solve the inequality

[chrome sorrel]

is that supposed to be x?

Lets approach this problem in a different way

log2(3-x)<0

[serene forge]

I guess so

[chrome sorrel]

lets get rid of that 3-x

and solve a simpler problem first

log2(x)<0

what does x hav to be so this is true?

[serene forge]

0?

Or a negative

Wait that doesn't make any sense

Uhm

-1??

[chrome sorrel]

yeah, figure it out

[serene forge]

Hn

[chrome sorrel]

oh really, theres an exponent thatll make 2 negative somehow

come on now

[serene forge]

0 is my best answer

But it'll be 1

So that can't be qwq

[chrome sorrel]

lets interpret this question

[chrome sorrel]

this is asking u to find out the numbers, such that when u turn them into 2 raised to some power, that power will be lesser than 0

and example would be 1/2

how do u get 1/2 from raising 2 to some power u may ask

2^(-1)=1/2

And -1<0

okay now analyze that interpretation

and do the problem again

log2(x)<0

[serene forge]

But 2^1/2 is 1 not -1

[chrome sorrel]

2^1/2 is √2 bro

2^0 is 1

2^(-1) is 1/2

do u know why 2^(-1) is 1/2?

[serene forge]

No

Is it because its less than 2 Bc unlike a normal exponent the number goes down instead of up

[chrome sorrel]

yeah it is

I think i see why ure struggling here

i think u should study exponents and logs more, like understand them

[chrome sorrel]

do u know about uhm

like

like exponent addition

i forgot what it was called but basically if u hav to numbers with the same bases and u multiplied them

[serene forge]

Oh ok

[chrome sorrel]

u add together the exponents

[serene forge]

Oh yeah

[chrome sorrel]

so

[serene forge]

Log(ab)=loga+logb right?

[chrome sorrel]

oh not that one

like a² multiplied with a³

gets a⁵

2+3

[serene forge]

Ohh

Yeah ik that one

[chrome sorrel]

so

2^(-1) times 2

what do u think that is?

-1+1 = 0

and 2⁰ is 1

that means that 2^(-1) MUST be 1/2

u get me?

[serene forge]

I'll just memorize that 😭

[chrome sorrel]

Bro dont memorize, this is math

u gotta understand

[serene forge]

Bc it doesn't make sense since -1+1= 0
Gone
2⁰ is 1

So how

Is it 1/2

[chrome sorrel]

2^(-1) is 1/2

das why when u multiply 2 to it

u get 1

[serene forge]

Log2(8)=3
Log10(100)=2
-# ignore this

Its 1/2 because its half of 2?

[chrome sorrel]

uhmm

well

first of all 1 is the half of 2

Okay wait bro

how did u learn this stuff

did u start with exponents and then logS

or logs then exponents?

[serene forge]

Exponents first then logs

In school

If that's what u mean

[chrome sorrel]

Okay

[devout snow]

@serene forge Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[pure cedar]

i used this method

i seated everyone in 2 rows

facing each other

and i make them shake hands with the person on their right

each time i do this

their number gets reduced to the number of handshakes that they can do now

and i partition it after a move

how do i prove that i can do this indefinitely

also

if i prove this for infinite number of couples

can it hold for 7125

i also thought about making a regular 2n-gon , idk howd that work out tho

the vertices could be handshakes maybe

[brave plaza]

I think you should use induction

[pure cedar]

how

[dusty comet]

unrelated but do u do math every day

[pure cedar]

everyone does math everyday

no?

[brave plaza]

so they shake hands with their neighbours correct?

in a row

everyone

[pure cedar]

yes

[brave plaza]

so what are the numbers after 1 round of this

the numbers of handshakes needed left

[pure cedar]

got it

i think i got it

[brave plaza]

explain

[brave plaza]

5 shakes hands with 4 only no?

or with eveyrone

in their row

[pure cedar]

the largest member from each row shakes hand with everyone from his row and the opposite sitting guy

this removes both 1 and 5

and reduces the number on everyone in between

this reduces the size of the row by 2

and the number on each guy is reduced by 1

and we can do this infinitely

to get to just 2 guys

facing each other

and in the end

they shake hands

[brave plaza]

it doesnt seem obvious to me that you can always do this

[pure cedar]

where is the problem

what case do you think can cause a problem

[brave plaza]

nvm it does work

I see it now

so the number of handshakes left on each person decreases by 1, except for the last person who is out

[pure cedar]

and the first one too

so the handshakes never repear also

[brave plaza]

oh yea since its 0

[pure cedar]

but this is not a proof🥀

[brave plaza]

you can easily make this into a proof

[pure cedar]

its just "look professor i made this cool diagram"

[brave plaza]

nono

[pure cedar]

how

[brave plaza]

they do repeat what

wait

oh

maybe not

[pure cedar]

no they dont

cuz we eliminate the guy who is having all the handshakes

[brave plaza]

yeah

ok this is nice

[pure cedar]

and then we get a fresh set

[brave plaza]

so this basically reduces the problem from n to n-2

[pure cedar]

ahhh

recursion

[brave plaza]

yes

[pure cedar]

but recursion might help us find how many handshakes were done , or maybe how many moves it took
but it wont tell us if its possible or not

oh but

ahh

got it

if its possible for n

its possible for n+2

and since its possible for both 1 and 2

its possible for all integers

by inductions

is this correct?

[brave plaza]

yes

You dont actually need induction here its enough to just say well for every n we can keep reducing the problem to n - 2, so we will end up at n = 1 or n = 0.

but what you said is also fine

[pure cedar]

thanks

.close

[devout snow]

Channel closed

Closed by @pure cedar

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[kindred mauve]

hi, the method i would use to answer this would be to find f(x) f'(x) f''(x) and sub into the maclaurin seri

[kindred mauve]

however this method is long

so is there another quicker method?

yh

[obsidian nebula]

nvm I was high

anyways I think you use f(x), f''(x) and the 4th derivative if you are doing maclaurin

because f'(0) is 0

and ''' is also 0

[kindred mauve]

how do we know secx is a even function

[red grove]

sec x = 1/cos x, so you could also develop 1/cos x

[mystic scarab]

Because cosx is an even function

[kindred mauve]

.close

[devout snow]

Channel closed

Closed by @kindred mauve

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[bright night]

hello, i am searching for a solutions book for stewart calculus 9th edition, can someone help me find one, preferably not broken like quizlet

[woven vale]

in the future, please leave your first channel open :)
these are free-to-use solutions so i think i'm okay posting these

just realized you said 9th edition and not 8th ._.

[bright night]

Oh ok

[bright night]

Yea I got the 9th edition and now I can’t find anything for it :

[supple knot]

Don't abuse help channels for looking for illegal resources

.close

[devout snow]

Channel closed

Closed by @supple knot

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

Please don't occupy multiple help channels.

[mystic scarab]

<@&268886789983436800>

[devout snow]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[bright night]

i wasnt looking for illegal resources, i am just looking for a resource that has the answers, i want to be able to check answers to a book. it doesnt need to be free, and i never said so.

[bright night]

so um i still kinda need it tho

[supple knot]

Yea still abusing help channels. It's not a math question

.close

[devout snow]

Channel closed

Closed by @supple knot

Use .reopen if this was a mistake.

[faint zinc]

@bright night any resource that would have the answers is going to run afoul of copyright claims against it.

[bright night]

oh

i didnt know that

so how do people check answers then?

[faint zinc]

If it's not in the back of the book, then they check their answers by comparing it against other students, some professors allow this some do not, or they simply double check their work and make sure everything is solid.

[bright night]

im self studying

i dont havea prof or peers

lemme check the book

[faint zinc]

For clarity, this is referring to 3rd party source of the answers. 1st party sources, i.e. the solutions manual, are restricted distribution. You generally need to demonstrate that you are teaching a course in order to get it.

You would get it directly from the publisher, typically.

.reopen

[devout snow]

✅ Original question: #help-27 message

[faint zinc]

anyway, I reopened the question so it wouldn't automatically lock

while I explained this

but it really is out of scope for the help channels.

So all we can recommend, due to Discord TOS, is attempting to get the solutions manual from the publisher, but I don't believe that you'll be able to do that.

There are other ways, but not ones we can help you with here.

I'll be closing this again.

@bright night best of luck. Self study isn't easy.

maybe try #study-discussion for general methods of checking your work to ensure it is correct.

.close

[devout snow]

Channel closed

Closed by @faint zinc

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[kindred mauve]

can someone help me with the first step for this

do we find tanx and tan^-1x

[faint gorge]

tan^-1 notation is so evil

[kindred mauve]

sorry

[faint gorge]

ig u can do what u did before, apply taylor series

or lhopital

tho i think herr taylor is cooler

if you manage to get terms up to 6th degree

[willow helm]

What is .

Multiplication?

[kindred mauve]

yes

[willow helm]

Interesting

[kindred mauve]

should i just memeorise tanx and arctan

[willow helm]

What do you mean memorize

[last parrot]

. is multiplication

[kindred mauve]

like would it make it easier to memrise

like sinx and cosx

[willow helm]

Memorize what

Or as opposed to what

[kindred mauve]

to finding them

calculating them

[willow helm]

Uh

Sorry I have no idea what you mean 🥲

You can't just memorize the entire tanx function

[faint gorge]

probably meant the taylor expansions

[unique monolith]

remember op wants to know first step

[deft tapir]

Memorizing maths

[kindred mauve]

idk

i was given a table with taylor series for sinx, cosx

suggesting to memorise these

[willow helm]

Oh I see

[willow helm]

Right

Well I am not the right person for this as I have never used the Taylor expansion for tan(x) in my life

[faint gorge]

how would you solve the limit without it

[willow helm]

Who doesn't like suffering with L'Hôpital

6 times

[kindred mauve]

thanks

.close

[devout snow]

Channel closed

Closed by @kindred mauve

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[fast solar]

@pseudo kettle

[last parrot]

?

any questions?

[last parrot]

!done

[devout snow]

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

@fast solar Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[zenith olive]

hello

[zenith olive]

So i am having very big issues at Cx

should it be -infinite?

[devout snow]

@zenith olive Has your question been resolved?

[zenith olive]

no

[devout snow]

@zenith olive Has your question been resolved?

[supple knot]

Very difficult to read and understand when you don't show original question

[cursive totem]

there is a horizontal asymptote at x/x-1 = 1

[last parrot]

just do "!xy"

[zenith olive]

The orange text is the question

We are at Power series

[cursive totem]

can you actually say y=1 though if its not true for any x values

[supple knot]

A series alone does not make a question

[zenith olive]

To give more context, we rn at uni are doing converges/diverges tests

Ratio test, leibniz etc

So here i should find if it converges or diverges

For two values of x

[cursive totem]

in that case your cx interval does make sense, take a look at the graph

[zenith olive]

So its all correct?

[cursive totem]

my interpretation of your notes are that cy is some desired region you want to find x values cx for which the series converges.

if so then it looks good

but you should post question to make sure

[zenith olive]

I see, thanks

[devout snow]

@zenith olive Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[terse jacinth]

can you guyz help me with this

[restive river]

f(x) is a 4degree polynomial , f(x) = (x-2)^2.g(x) so g(x) is a secod degree polynomial

if you write g(x) = ax^2 +bx +c
f(x) = (x-2)^2(ax^2 +bx +c )

sub x = 0 you will find c

[ripe grove]

similarly m(x) is a second degree polynomial

but thats not super useful here

[brave plaza]

sub x = 2 and x = 0 into the second equation

[ripe grove]

One could also use f(i)

[devout snow]

@terse jacinth Has your question been resolved?

[terse jacinth]

yah you are right but when itz come to find a and b idk how to get

[last parrot]

Use the second equation

[terse jacinth]

i find a different way to solve this by using long division

[last parrot]

Have you found c yet

Huh thats long and not robust

[ripe grove]

this is true

[terse jacinth]

yes but i guess that's the only way to solve this i already try the way to say before

[last parrot]

So have you found c

[restive river]

use this you wont need g(x)

[last parrot]

If you found c thats good

[terse jacinth]

x^4 -4x^3+7x^2 -12x +12 is f(x)

[terse jacinth]

may i send the way i fix it

[last parrot]

Thats correct

👍

[restive river]

you can if you want

[rain summit]

and get a system of your own

[terse jacinth]

but i use long divition is there any short way to get it

[last parrot]

Have you found c

I asked 3 times

[terse jacinth]

oh sorry i didnt notice c=3

[restive river]

too lengthy

[last parrot]

Good then f(x)=(x^2+1)m(x) + (6-8x) right?

Using 2nd eq

[terse jacinth]

yes

[last parrot]

then this tells us that f(x) divide by (x^2+1) gives remainder of 6-8x

[terse jacinth]

okey

then how am i able to find a and b with 2nd eq

[last parrot]

Then this implies that when you subs x=i

X^2+1 will be 0

[terse jacinth]

hola i get it

[last parrot]

Then solve from here

Hola is hello btw, you should say claro

[terse jacinth]

yah this way is too odd

[terse jacinth]

hey but there are only 2 eq we can get but there 3 known variables

[last parrot]

U suppose to find a b

And already got c

[terse jacinth]

then 1 eq and 2 unknown variables

[last parrot]

?wdym

They are known if u solve them

[terse jacinth]

we only know f(i),f(0)

using f(0) we can get c when we use f(i) we can get 1 eq to find and b then ?

[arctic jacinth]

@terse jacinth Are you done?

[terse jacinth]

i fix it my own way but itz too long you can see how did i get my answer from here

but is there any way to fix it i mean short way

[arctic jacinth]

hey dude, can you tell me whats the current situation?

I think i got the answer

[terse jacinth]

can you tell me the way

[arctic jacinth]

Yes Sir i can

Okay first of, we know that the f(x) is the polynomial of degree 4

right

[terse jacinth]

yes

[arctic jacinth]

and in the first provided equation

it is written that

f(x) = (x² - 1)g(x)

right

[terse jacinth]

yes

[arctic jacinth]

So can i say that the g(x) will be a quadratic polynomial

[terse jacinth]

yes you are right

[arctic jacinth]

Good

can i say the same for m(x) ?

[terse jacinth]

sure

[arctic jacinth]

Excellent

do you observe that in first equation

[arctic jacinth]

(x - 2 )²

completely divides

the f(x)

[terse jacinth]

yes

[arctic jacinth]

so can i sa that

[terse jacinth]

simply f(2)is a factor of fx

[arctic jacinth]

so put 2 in that equation

[terse jacinth]

f(2)= 0

[arctic jacinth]

good

now, what happens

if we put

zero in that equation?

what's the resulting equation

[terse jacinth]

we can get the constant of the g(x) i mean if g(x)= ax^2 + bx +c then we can get the C

[arctic jacinth]

excellent

[terse jacinth]

and the C is 3

[arctic jacinth]

and what if i tell you to do the same for second equation?

the m(x) one

what do we get

put zero in it

[terse jacinth]

thats a problem if i put 0 for 2nd eq problem become complex dont you think

i mean in that way we have to find 6 known variables

[arctic jacinth]

f(x) = (x² + 1)m(x) + 6 - 8x

[arctic jacinth]

We just need to find f(x), why should we find g(x) ?

[arctic jacinth]

f(0) = m(0) + 6

[terse jacinth]

oh yah sure

[arctic jacinth]

m(0) = 6

[terse jacinth]

okey

[arctic jacinth]

f(2) = 5m(2) + 6 -8(2)

[terse jacinth]

okey

[arctic jacinth]

what is m(2) ?

[terse jacinth]

how can we know itz unknown one

[arctic jacinth]

you're missing something

we know the value of f(2)

[arctic jacinth]

here

[terse jacinth]

oh yah okey i miss that part thx go on

[arctic jacinth]

tell me what's f(2)

[terse jacinth]

0

[arctic jacinth]

find m(2) now

[arctic jacinth]

put f of 2 here

[terse jacinth]

m(2)= 2 right?

[arctic jacinth]

let me calculate

yes, excellent

m(x) = x² + (something goes here)x + 6

do you get this

[terse jacinth]

how can we say that x^2 why it cant be 2x^2 or something

[arctic jacinth]

we can divide the complete equation by coefficient of x²

[terse jacinth]

you mean f(x) divid by x^2?

[arctic jacinth]

another way to verify is, lets us say there is some coefficient to x²

very quadratic is of form

k(factorz)

so basically

m(x) = K(stuff goes here)

[terse jacinth]

nice i get it go on

[arctic jacinth]

m(0) = k(6) = 6

because i just proved you that constant term of m(x) is 6

[terse jacinth]

okey

[arctic jacinth]

hmmm, this doesn't feel right

[terse jacinth]

yes

[arctic jacinth]

but we can still cross check our answer if it is divisible by x -2

[terse jacinth]

sensi i found another way to fix it please look at this

[arctic jacinth]

go on

[terse jacinth]

wait im still writing

[arctic jacinth]

I think coefficient of x² is 2

[terse jacinth]

oh there was a mistake

[arctic jacinth]

you should try putting x=2 ad f(x) = 0

that way you can get a relation in A and B

[terse jacinth]

we can get 1 relation but we need 2 to find both variables

[arctic jacinth]

Product of roots is 12, we already know 2 roots

product of rest of the two roots is 3

sum of roots is

• (2A + B) = 2 + 2 + ( other two roots)

do you know the rest of the roots are roots of g(x)

[terse jacinth]

no i dont

[terse jacinth]

please look at this i mean we can find a , b and both lamda and Mu using this right?

[arctic jacinth]

yes

[terse jacinth]

that's allso a hella long way but i guess those are the only ways to fix this

[last parrot]

looks good

[terse jacinth]

haha thats crazy man

[arctic jacinth]

right

we can get answers by cmparing coefficients and equating them to solve for it

[terse jacinth]

let me solve them that way we can check the answers are right or not

[terse jacinth]

thx for the help haha that was fun

.close

[devout snow]

Channel closed

Closed by @terse jacinth

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[opaque ferry]

I require assistance with this question

[opaque ferry]

these are the values I managed to get but I am unsure to how you find OZ

[dull parrot]

you've gotten OS as 4.5b - 2a right?

[opaque ferry]

yes

[dull parrot]

they've given you a ratio of 1 : k

from OZ : OS

[opaque ferry]

Im pretty sure oz is like x(4.5b -2a)

[dull parrot]

$\frac{(4.5b-2a)}{1+k}$ actually

[woven radish]

MxRgD

[dull parrot]

now try to find a different path for OS and then OZ

[dull parrot]

then equate it with this so you can solve for k

[opaque ferry]

like OR + RS + SZ and OQ + QS +SZ

[dull parrot]

yeah something like that

[opaque ferry]

I end up getting 4.5b -2a / -2a + 4.5 b -SZ = 1+ k

I tried multiplying the 1+k by the denominator

but it gives me -2ka + 4.5 kb - kSZ = SZ

it gives me k(4.5b - 2a ) = SZ if I factorise

@dull parrot

[dull parrot]

Okay nice, so you now have OZ ans SZ

Use those two to relate them together from the ratio and solve for k

[opaque ferry]

how do I do that

[opaque ferry]

wdym

.close

[devout snow]

Channel closed

Closed by @opaque ferry

Use .reopen if this was a mistake.

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[kindred mauve]

how would we prove it is valid for all values of x

[faint gorge]

show convergence radius is oo

[kindred mauve]

and how do i do that

[faint gorge]

do you any tests for convergence

[kindred mauve]

no

[faint gorge]

ratio test?

[devout snow]

@kindred mauve Has your question been resolved?

[devout snow]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[karmic mesa]

im wondering between 9841 and 9842

i think they are both wrong instead

guysss

[deft tapir]

Is that supposed to be the 9th derivative of f?

[karmic mesa]

nah

[tepid stag]

f(f(f(f(...(x)))..) 9 times

[karmic mesa]

f(f(f(f(f(f(f(f(f(x)))))))))

[deft tapir]

Oh yeah

[deft tapir]

Do you happen to have the roots of f?

[karmic mesa]

nah it's not root

[tepid stag]

it can be factorised to x(x-3)(x-3)

[deft tapir]

It's pretty much that you want to find any value that leads to a root of f

For example 0

F(0) = 0, therefore f(f(0)) = 0

And so on

[karmic mesa]

can you elaborate

[deft tapir]

So if 3 is a root, we would look for f_k(x) = 3 such that k < 9

[karmic mesa]

why do we start with root and then with composite function?

[deft tapir]

You work it backwards, you start from f(x) and move all the way to f9(x)

[karmic mesa]

yeah but like why find the root?

[deft tapir]

Suppose f(x) = 0 for x = { 0 ; 3} (0 and 3 are roots of f)

[karmic mesa]

because x=0 is only one of the solutions for this equation

[deft tapir]

Then at any point of your function, if you achieve f(3), then that's a solution

[deft tapir]

0 and 3

[karmic mesa]

it's not unfortunately

you can try

im talking about the composite function

f9

[deft tapir]

x³ - 6x² + 9x = x(x²-6x+9) = x(x-3)²

I'm talking about the main f function

[karmic mesa]

oh yeah

i got it

[deft tapir]

We have that f(0) = 0 and f(3) = 0

We want f(f(x)) = 0 or 3

[karmic mesa]

yes

[deft tapir]

f(f(f(x))) = 0 or 3

And so on

[karmic mesa]

yeah
and we have to find how many x to sastify that "so on"

this is what im asking for

[deft tapir]

We know that 0 is one solution for all composite functions

So we check for 3

Solve for f(x) = 3

You get some value b
Which we know that f(f(b)) =0

Cuz f(b) = 3 and f(3) = 0

[karmic mesa]

and then f(f(f(f(f(x))))))) =3 as well

there are ton of solutions

[deft tapir]

And then we want to check for f(x) = b, we get some value c, then we check f(x) = c

[deft tapir]

Yup

[karmic mesa]

the problem is how many

[deft tapir]

It's pretty much that you want f8(x) = 0 or 3

And you work from everything past that

[karmic mesa]

well, finding the exact b and c isnt an easy job. I put it on my calculator and they are like 3.879385242

what is the exact algorithm to calculate f9(x)

also|
what if it's fn(x)

then we can't just calculate and find the exact solutions

[deft tapir]

Check for all values that achieve
f8(x) = 0, 3
f7(x) = b, 0 or 3, such that f(b) = 3
Then f6(x)= c, b, 0, 3 such that f(c) = 3
Then f5(x) = d, c, b, 0, 3
Then f4(x) = e, d, c, b, 0, 3
Then f3(x) = f, e, d, c, b, 0, 3
Then f2(x) = g, f, e, d, c, b, 0, 3
Then f(x) = h, g, f, e, d, c, b, 0, 3

The thing is, those values get repetitive

Cuz realistically, you only need
f(x) = h, g, f, e, d, c, b, 0, 3

9 solutions

Unless there are multiple solution to for example f(x) = 3

Then that gets tedious

Idk how you can potentially achieve a formula to summarize this

Actually, we do know how many solutions approximately

Which is 3⁹

Actually no

It's 2^3^...^3, 9 times

[karmic mesa]

i think we have 3^8 + 3^7 +...+3^0

[karmic mesa]

that would be so many

the problem is from my practice test

none of the given A,B,C or D go past 5 digits

[deft tapir]

Think of it like this
x³ generally has 3 solutions or for the sake of accuracy at max 3 solutions

We conclude that the number of solution is at max the exponent of the biggest term

f(f(x)) gives you (x³)³ = 3^3
By extension we get 3^3^...^3

But then again we have 0 which is a general solution for all composite functions, and 3 is a double solution