help-27

[abstract sleet]

thanks

.close

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[somber shore]

hi

[somber shore]

I dont understand something in this example

[woven radish]

NotDyatlov

[somber shore]

we can say that this is equal to

,tex $\lim_{x\to2}{\cos({\frac{x+2}{2}\pi})}$

and this is equal to

,tex $\cos({\frac{2+2}{2}\pi})$

there reason that we are allowed to do this is because cos(x) is continuous on its domain

but in the original functin 2 is not in the domain at all

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[dawn oar]

am i supposed to use this 2nd formula here?

[lofty niche]

yes, the second formula is the definition of the derivative f'(c)

[dawn oar]

so after i find the secant line i plug 2 in?

[lofty niche]

oh, the derivative at a specific point is not a secant but a tangent

[dawn oar]

so it is asking for the tangent when x=2?

[lofty niche]

im guessing your class just introduced the derivative, so you didnt do $f'(x)=nx^{n-1}$ if $f(x)=x^n$ yet ?

[woven radish]

ImToxiiq

[dawn oar]

yeah we did, but im allowed to use chain rule even thought we haven't learned ityet

it's a few units down but somebody asked if we can use it and the professor said yes

wait is that chain rule

[lofty niche]

no, its not

[dawn oar]

my bad. it looked similar

[lofty niche]

you can solve the derivative of h(x) with the rule above or with the definition of the derivative. both are valid

[lofty niche]

its called power rule btw

[dawn oar]

okay let me think

so would i do that above rule with the 7-4x^3?

[lofty niche]

i mean to do the derivative without the definition you need the sum rule too. i would advise against it for now if you havent covered all of that in class yet

[dawn oar]

ok

i'll try to set it up with the definition lmk if i do this right

and then i solve?

[lofty niche]

no

if you plug $c+h$ into $h(x)$ you have to cube all of it

[woven radish]

ImToxiiq

[lofty niche]

h(x) is a function that takes some x, which can be anything (in this case (c+h)) and does something to it (cubing it) then it multiplys by 1 and adds seven

[dawn oar]

so i would cube the h as well

up top

[lofty niche]

wait ill make an example to show you

[dawn oar]

ok

[lofty niche]

example $g(x)=x^2$, then the derivative is $g'(c)=\frac{(c+h)^2-c^2}{h}$ because plugging $(c+h)$ into $g(x)$ gives you $(c+h)^2$

[woven radish]

ImToxiiq

[dawn oar]

okay i think i get it

hold on

wait ill rotate it

[lofty niche]

,rotate

[lofty niche]

two key points:
1.you only replace all x with (c+h),not the whole term has to be cubed
2. you cannot plug in any specific number, like 2, yet. this is only allowed at the very end, if the derivative has been calculated

in my example above, if $g(x)=x^2+1$, you would have to plug in c+h again and would get $\frac{(c+h)^2+1-(c^2+1)}{h}$

[woven radish]

ImToxiiq

[dawn oar]

Ignore top

[lofty niche]

right, now you just have an extra +h in the middle that you dont need, and you forgot the minus sign before the second 4

[dawn oar]

i thought the 4 would be positive since it is originally -4x^3

i see the extra h error though

[lofty niche]

oh my bad

yes its +4

[dawn oar]

ok

[lofty niche]

ill brb

ok

[dawn oar]

i got h^2+14

[lofty niche]

After doing what exactly ?

[lofty niche]

Oh, please dont forget that $(a+b)^2=a^2+b^2+2ab$

[woven radish]

ImToxiiq

[dawn oar]

oh my god

im gonna go eat im to braindead to do math rn

sorry brother i dn't wanna waste anymore of your time

.close

[devout snow]

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[devout snow]

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[plucky drift]

How do i start this?

[cold bough]

do you know how to calculate the distance of r from origin?

[long fog]

do you know how to calculate the distance of r from (0,0,0)?

[devout snow]

@plucky drift Has your question been resolved?

[plucky drift]

let t = lambda

r = (7 + 2t, -1 - t, 2 + 3t)

is it that?

[cold bough]

this is a vector

not a positive real

the distances squared is $x_1^2+x_2^2+x_3^2$ where the vector is $(x_1,x_2,x_3)$

[plucky drift]

yh we just add the direction vector to coordinate no?

oh mb

[woven radish]

everg

[cold bough]

now just find the minimum of the function distance(r)

[plucky drift]

it's just $sqrt(2^2+1^2+3^2)$

[woven radish]

ether

[cold bough]

this is the distance of (2,1,3 ) not (7 + 2t, -1 - t, 2 + 3t)

[plucky drift]

ahhh

so we just solve that?

[cold bough]

depend on what you mean for solve...

this function has no zeros ... so you have to find his minimum

i would use the derivative maybe

[plucky drift]

,w expand sqrt((7+2t)^2+(-1-t)^2+(2+3t)^2)

[cold bough]

i just said that this function has no zeros.....

[plucky drift]

apologies

[woven radish]

Results provided by WolframAlpha

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

Requested by ether#2229

[devout snow]

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[oblique gale]

I have to find the highest and lowest value of the function in given domain

[oblique gale]

I'm very lost when it comes to graphing the derivative of the function

I will send my "solution"

[spare hollow]

does your teacher make you find the max and min by graphing?

[oblique gale]

Nah

[spare hollow]

ok good lol

[oblique gale]

We calculate like

Fmin(x)

[spare hollow]

ok show ur work lemme see lolz

[cold bough]

in (0,1) are both incrising function ... so have the min in x=0

[oblique gale]

Lemme write it on the whiteboard for better clarity

[spare hollow]

ok

ty btw I hate reading blurry papers lol

[cold bough]

in (-3,0) are both incrising function ...so the product is incrising right? so have the min in x=-3

[spare hollow]

everg go to the available channels!!

like literally the section "available channels" sorry that sounded rude

[oblique gale]

I'm too new to use latex in here

lol

[cold bough]

slapppoo ... i just answered to the question of this channel ...

i didn't ask any new question

I accept your apology

[oblique gale]

I could explain what steps I take

[spare hollow]

oh sorry everg

[oblique gale]

So basically from what I remember from class

We first calculate f(-3) and f(1) (not sure why even)

[spare hollow]

ok let's stop there

the reason you do that is in the case the endpoints of your interval are actually the lowest or highest part in the function

otherwise, as you know, they'll be at critical numbers

ok keep going

[cold bough]

because an incrising function f in the domain [a,b] has the maximum and minimum in a and b

[oblique gale]

Then we get the f'(x)

[spare hollow]

I'd distribute the x first btw easier to derive

[oblique gale]

If I did it right it would be f'(x) = 32 + 4x^3

[spare hollow]

yes

[cold bough]

now your function its everywhere increasing

[oblique gale]

Then we equal it to 0

And get the x's

[spare hollow]

yerp

those are ur critical numbers

[oblique gale]

So I got 0 and x^2 = -8 which is (idk the english word but not right)

[spare hollow]

you were close

[oblique gale]

Oh shit

RIGHT

It's fine then lmfao

So we have x=0 v x=-8

Then we draw the function on a graph

[spare hollow]

not quite

[oblique gale]

Oh

-2

sorry

[spare hollow]

yerp

lmao you just had an oopsie

[oblique gale]

Yeah my head hurts af

I can barely do it but I have an exam tomorrow

[spare hollow]

aw gl!!

[oblique gale]

So, now when we draw the thing

Lemme take a pic

[spare hollow]

ok

[oblique gale]

So I have something like this

The dots marking that the domain is closed on both ends

Now the -2 and 0 are in the domain so the graph will be a parabola

Going through -2 and 0

Upwards

And after that I have no clue what the fuck is going on

[spare hollow]

have you done 2nd derivatives/concavity

[oblique gale]

Apparently the function stops at the extreme points

[spare hollow]

that's how we do it

[oblique gale]

Lemme translate that real quick lmfao

This doesn't ring a bell

[spare hollow]

I think this might just be a language thing but I don't get your thought process with your graphing

but keep going

[oblique gale]

Yeah that's where it ends for me 😂

Maybe we had done 2nd derivates something in class but I just don't know without seeing

[spare hollow]

have you done increasing/decreasing using 1st derivative

[oblique gale]

Math language barrier much 🤣

[spare hollow]

ikr

[oblique gale]

Where are you from btw

[spare hollow]

united states

wbu

[oblique gale]

Poland

Yeah not gonna help either lmfao

[spare hollow]

oh wow

yeah I don't know polish 😮

what a shocker

[oblique gale]

Neither do I

(almost)

[spare hollow]

what is your native language

[oblique gale]

Polish

But I use it very rarely

Aight back to the question

What do you mean by increasing/decreasing using 1st derivative

[spare hollow]

do you know what critical numbers are

or do you use another name

[oblique gale]

We have a completely different name for that

It's called critical point I think?

[spare hollow]

but wherever the derivative = 0 or DNE

is a critical number (the x value)

[oblique gale]

Oh

[spare hollow]

dne is does not exist or undefined

[oblique gale]

Yea yea

[spare hollow]

so you can actually set up intervals using your critical numbers

like

in your case

(-3, -2) (-2, 1)

and then you pick two x values to test in those intervals

[oblique gale]

Oh wait is it related to this

With like a table

[spare hollow]

probably!!

[oblique gale]

Yeah then we did I think

[spare hollow]

that's super useful when you have to graph a function

[oblique gale]

It's like <-3, -2>. -2, <-2, 1> right?

[spare hollow]

whatever notation your teacher likes

we just use ( )

[oblique gale]

It would be an open thing no?

[spare hollow]

open yes

but even if it was included

you just don't pick endpoints idk

[oblique gale]

Aha

I see

Maybe I missed something in class lmfao

[spare hollow]

so have you done concavity?

with second derivatives?

I don't see how you avoided that one lmao

[oblique gale]

googles images

Oh

I think so?

We usually draw arrows

On the graph

Pointing if the graph is decreasing or increasing

[spare hollow]

that's not with second derivatives

[oblique gale]

And there are mins and maxes

hmmm

[spare hollow]

second derivatives is like

is the graph a smiley face or a frowny face

[oblique gale]

Here?

A smiley face

lmfao

[spare hollow]

do you need help with those topics or are they like

just the same thing but with different names

[oblique gale]

I need to know how to get the fmin and fmax

That's the hard part

[spare hollow]

the absolute or relative?

[oblique gale]

what

[spare hollow]

lmao

in your case there is just one minimum,

[oblique gale]

yeah and one maximum

We are looking for min and max in the domain

[spare hollow]

you're doing absolute then

[oblique gale]

We call it local I think 😂

[spare hollow]

local means relative

[oblique gale]

b r u h

The smiley face stops at -3 and 1

Is there like a proper math vocabulary book in english

So I can actually talk wiht people

[spare hollow]

hmm

[oblique gale]

If you have a spare minute could you draw the graph properly

[spare hollow]

are you comfortable just calling, I'll admit this is pretty visual so screenshare might be nice

[oblique gale]

Sure

[spare hollow]

ok give me 2 seconds I gotta hop on my ipad

[oblique gale]

Take your time

[devout snow]

@oblique gale Has your question been resolved?

[devout snow]

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[sage kernel]

For part a, I found theta, but how do i find r?

[devout snow]

@sage kernel Has your question been resolved?

[sage kernel]

.close

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[jade sleet]

is this right?

[jade sleet]

what do i need to fix?\

[pseudo basin]

going from y=g(x) to y=g(x/2) is a stretch by 2

in the horizontal direction obviously

also the peak should have the same height as it did pre transformation, which rn it doesnt

[jade sleet]

so like this?

[restive river]

you don’t half your y values

[jade sleet]

i just leave it right?

[restive river]

so the new graph should have the same height

but be narrower

for example, your highest point should be (1,4) not (1,2)

[jade sleet]

oh 1,4

.close

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[pseudo basin]

. @jade sleet you still got it wrong -- you compressed the graph by 2 when you should have stretched it

[jade sleet]

oh

[jade sleet]

wait i was told to make it more narrow

[jade sleet]

right here

[jade sleet]

so who is right

[pseudo basin]

me.

[restive river]

Nah im on crack

[pseudo basin]

try graphing something like sin(x) vs. sin(x/2) in desmos

you will see sin(x/2) is stretched

[jade sleet]

ok

so then this is right

[pseudo basin]

no

you stretched it by the wrong factor

2, not 1.5 as you did

[restive river]

a little more

stretxh

[jade sleet]

i dont understand

[restive river]

you stretched your x value by 1.5x, not 2x

2 times 2 is not 3

[jade sleet]

so this is the final then

[restive river]

your 3rd point is not stretched enough either

[jade sleet]

how

[pseudo basin]

(4,0) does not transform into (6,0)

[jade sleet]

oh its 8 my b

[pseudo basin]

2*4 isn't 6

[jade sleet]

i didnt look at it my b

ok so now im 100% good

[restive river]

Looks good

[jade sleet]

.cloes

.close

[devout snow]

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[restive river]

my bad for forgetting algebra 2 concepts lol

[devout snow]

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[mystic musk]

I watched a video of him proving this theorem and had a question about it

[mystic musk]

so it is only linear independent if c1 to ck = 0

[urban harbor]

well, what does orthogonal mean?

[stone stump]

linearly independent means that sum c_i v_i = 0 implies c_i=0

[mystic musk]

orthogonal means perpendicular

ye I understood that part

[urban harbor]

so is 0 vector orthogonal to 0 vector?

[mystic musk]

but he also said c1 to ck had to be 0

[mystic musk]

no

[urban harbor]

?

[mystic musk]

right?

[stone stump]

well yes he proved that

[urban harbor]

it says "nonzero" vectors

[vast rain]

yes it is

[stone stump]

he proved that c_i=0

so he proved that they are linearly independent

[mystic musk]

but where is the part he proved that c1 to ck except ci = 0?

[vast rain]

wdym except ci = 0?

he proved that c1 to ck are all 0

[stone stump]

he took sum c_iv_i=0

[mystic musk]

where

[stone stump]

and then multiplied both sides of that by v_j

on the left only c_j v_j*v_j is left

on the right 0 is left

[urban harbor]

im confused now on what your question is

[stone stump]

v_j*v_j is nonzero because v_j is nonzero

[urban harbor]

why are you talking about 0 vectors when the statement clearly says nonzero vectors

[stone stump]

so c_j*(nonzero) = 0

so c_j=0

[mystic musk]

okay wait

I understand that ci has to be 0

[stone stump]

you are talking about 0 vectors

[urban harbor]

a set that contains the 0 vector, even a set of a single 0 vector is not linearly independent

[mystic musk]

but why is c1 c2 c3 etc also zero?

or is ci

[stone stump]

well you do the same for all of them

[mystic musk]

or is i 1 to k?

[stone stump]

i runs from 1 to k

yes

[mystic musk]

but isn't i just 1 particular number?

[stone stump]

well for each number you can do it separately

[mystic musk]

oh

so i is basically saying it for all number that way

[stone stump]

yes

[mystic musk]

I think I then understand it

[urban harbor]

that part of the proof which i think you are showing is just setting a linear combination of vectors equal to the 0 vector and showing that if you dot product that with each sides v_i must automatically be the 0 vector

[mystic musk]

ye and vi times vi can't be zero

so ci has to be zero

and the i of ci implies 1 to k so all c are zero

[urban harbor]

aha

[urban harbor]

so yeah to answer your original question, the set is linearly independent if and only if the only representation of the zero vector is the trivial one (all c's = 0)

i think i was confused and misread at first, i thought you were asking if the v's were equal to 0, my bad

[mystic musk]

I was also wondering about this one

he is talking about standard basis vectors

does he mean vectors with only a 1 and 0 everywhere else?

so [1, 0 ,0 ]

[0,1,0] etc

[urban harbor]

well yes thats for R3 specifically, but this is a more general statement on Rn

[mystic musk]

ah but in other dimensions

[urban harbor]

so (1,0,0...,0), (0, 1, 0...,0) ... (0,0,0...,1) etc

[mystic musk]

it all just a 1 somewhere and a 0 everywhere else

no other ones right?

[urban harbor]

yes thats what is meant by standard basis

[mystic musk]

ah okay thx

[mystic musk]

any other basis which are not the standard one are called just basis right?

[urban harbor]

I suppose so

:p

[mystic musk]

do u by any chance know how he got this?

do I put in in a matirx?

ye I see it it I put in matrix then row reduce it

[urban harbor]

x = -y

and then just substitute that in the first

[mystic musk]

oh

that might be faster

[urban harbor]

2x + z = 0

x = -z/2

and since y = -x, y = z/2

[mystic musk]

ah

[devout snow]

@mystic musk Has your question been resolved?

[mystic musk]

can someone explains how the matrix becomes like that

so why is it q1 * q1

so acutally why is q1^T the same as q1

[mystic musk]

do u know this too?

[mystic musk]

I think this is because it is a vector therefore the transpose is itself

but now I am wondering it says it counts for all m x n matrix but then the they won't be a vector and therefore the transpose is not itself

<@&286206848099549185>

[devout snow]

@mystic musk Has your question been resolved?

[devout snow]

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[devout snow]

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[hushed hinge]

hey im not sure how to do this question: (the answer is (0,6))

[hushed hinge]

i got points of inflection as x=-1,1

but i dont know what to do next

[restive river]

find the tangent line equation at x = -1, 1

[hushed hinge]

i got 8x+1/4

for -1

-8x+1/4 for 1

[restive river]

you sure?

cuz i got 8x+6, -8x+6

[hushed hinge]

is -2 the value the you made it equal to?

thats what im getting

[restive river]

no just the tangent line at -1

[hushed hinge]

ya but using derivative would give you slope of 8

[restive river]

f(-1) = -2

[hushed hinge]

8x+b

and then i solve f(-1)=-2

[restive river]

8(x-(-1)) + (-2)

[hushed hinge]

oh wait im so stupid

[restive river]

-8(x-(1)) + (-2)

[hushed hinge]

im dividing*

[restive river]

and then intersect them

[hushed hinge]

ok

thank you

[delicate seal]

Yo

[devout snow]

@hushed hinge Has your question been resolved?

[devout snow]

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[violet matrix]

idk what I did wrong for e)? Does anyone see where I went wrong?

[devout snow]

@violet matrix Has your question been resolved?

[nova idol]

that is a nightmare to go through

just ask an integral calculator

[devout snow]

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[proud nimbus]

.close

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[forest hound]

just wanna make sure my answer is correct?

[hard sand]

the second equation has me messed up

if x = 0 y = 4

but no line goes thru (0,4)

[wooden wraith]

they all do

The axis scale counts by 2

[forest hound]

it’s kinda confusing

[wooden wraith]

oops lol

@forest hound Look at the second segment on the graph of C

What x-value does it start at?

[forest hound]

ohh i see

so it can’t be c

[wooden wraith]

yeah

in fact c isn't a function

It overlaps itself around -2 to -3

[forest hound]

hmmm

[wooden wraith]

what I mean is

C doesn't pass the vertical line test

[forest hound]

ohhh right right

my other option would be b?

[wooden wraith]

Yeah

Now that I look at these, B is the only graph that's even a function lol

It's the only one that passes the vertical line test everywhere

[forest hound]

😂i thought so

[wooden wraith]

From your equation too, we can see it's supposed to switch rules at x=-2 and x=2

which B does

[forest hound]

i def see it now

thank you for ur help!

🤞🏽🤭

[wooden wraith]

no problem 👍

[forest hound]

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[lavish canopy]

If there’s a - like in d and h

Like -3(pi)/4 for example

Does that mean the answer will always be negative?

[hybrid snow]

cosine is negative if and only if the angle terminates in Q2 or Q3

[lavish canopy]

Ok so it still depends on where it is

Right?

[hybrid snow]

Ofc

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[torpid roost]

Can someone please help?

<@&286206848099549185>

[devout snow]

@torpid roost Has your question been resolved?

[torpid roost]

Someone please help

[devout snow]

@torpid roost Has your question been resolved?

[devout snow]

@torpid roost Has your question been resolved?

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[proud nimbus]

i solved it and found $\frac{1}{2}$ \
But the answer is wrong.

[queen zephyr]

,w 17/36+1/2+2/8+13/18+9/27

[woven radish]

Bunnings

Results provided by WolframAlpha

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

Requested by bettim#9852

[proud nimbus]

how do you calculate median ?

[queen zephyr]

wait shit

[proud nimbus]

why you add all numbers ?

[queen zephyr]

sorry

lol

so

convert them all to same denominator

[proud nimbus]

i did

.205, .303, .5, .702, 2.10107

.5 should be median right ?

w, calculate median of 17/36, 1/2, 2/8, 13/18. 9/27

[queen zephyr]

$\frac{17}{36} , \frac{18}{36} , \frac{9}{36} , \frac{26}{36}, \frac{12}{36}$

[woven radish]

bettim

[queen zephyr]

its $\frac{17}{36}$ no?

[woven radish]

bettim

[proud nimbus]

yes but why ?

[queen zephyr]

so

median is the center element of the sequence

[proud nimbus]

yes

[queen zephyr]

you have arrange them first in ascending order then find the middle most elemnt

[proud nimbus]

but i did arrange them, convert all the fractions to decimals and then arranged them from low to high

[queen zephyr]

no need to convert to decimal

[proud nimbus]

what then ?

[queen zephyr]

convert them to same denominator

like this

[queen zephyr]

...

[proud nimbus]

okay

but how you got the answer ?

[queen zephyr]

arrange them in ascending order

the middle element will be the answer

[proud nimbus]

ok, i'll look into it

thanks

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[wet pagoda]

.reopen

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[odd elbow]

.

In the given circle, DC is a cord and BF is perp to EF and AE is perp to EF

[odd elbow]

In the given circle, DC is a cord and BF is perp to EF and AE is perp to EF

Prove that EF || DC

Any idea how to do it??

[violet wind]

often I think it's helpful to have a list of things you know

and maybe also a list of things that you want to find out

So we can start with AE || BF

<EBF = <AEB by alt. interior angles

hmm

[devout snow]

@odd elbow Has your question been resolved?

[violet wind]

Drawing out some less symmetric examples gives a bit of insight

Calling the unnamed intersection point M, we see that AMB and CMD are similar

AME and FMB also similar

From there try to prove EMF and DMC are similar

[odd elbow]

Well OK

I'll rry

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[umbral roost]

Are the calculations circled in red correct?

[umbral roost]

.close

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[somber shore]

hi

[somber shore]

can I have a veryyyy small hint for this question

[pseudo basin]

half angle identity on sin^2(x) might help some

...or maybe not, on second thought

triple angle identity has a better chance

[somber shore]

I have already tried that but lemme check again

[supple knot]

do you just look at it?

[quaint citrus]

Rare triple angle identities sighting

[supple knot]

no way the 2 in front of cos is the same absolute value as -2 on the right is a coincidence

[somber shore]

I tried that as well, I moved it to the rhs and then rewrite it as -2cos^2(3x/2)

[supple knot]

by this i mean, find an x value in the cos(3x) that gives the correct sign according to the -2 on the rhs. then what happens when you plug that x value into sin(x)?

[somber shore]

I did not get it.

btw the actual question asks for the number of answers between -pi and pi

[supple knot]

when is 2cos(3x) = -2?

[supple knot]

in this range for x

[somber shore]

yeah

[somber shore]

well x =pi/3

[supple knot]

keep going

[somber shore]

but 5sin^2(pi/3) is not equal to 0

so what?

[supple knot]

keep listing all the x

[somber shore]

no way man

there should be something 🥹

[supple knot]

is it too hard to solve?

[supple knot]

first divide by 2 on both sides

then substitute y=3x so you get cos(y) = -1

[somber shore]

I know what you mean but its not good enough 🙃
but works

thank you

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[supple knot]

why isn't it good enough?

.reopen

[devout snow]

✅

[somber shore]

I was looking for a trigonometrical way

I mean something like this: cosx=cos a or sinx = sina

[supple knot]

is this not trig?

there's a cos

[supple knot]

does it not get you all the answers?

[somber shore]

but by just plugin the numbers, I didnot find any answer

either it does not have any asnwer or I have understood something wrong

[supple knot]

that's cuz you gave up?

[supple knot]

and didn't do this?

[somber shore]

I did this but wherever cos3x = -1 , sinx is never equal to 0

[supple knot]

you didn't find all the x in [-pi, pi] then

[somber shore]

exepct for 6pi/3

[somber shore]

2kpi /3 are all of them but only at 6kpi/3, sin is equal to 0

[supple knot]

nope

[supple knot]

you missed this one

[devout snow]

@somber shore Has your question been resolved?

[somber shore]

I am really really sorry but could explain once again? I think I did not get it right

I did not get what should I do after pi/3

[supple knot]

after finding all y where this is true, solve for x using y=3x

because cos(y) = cos(3x)

[devout snow]

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[somber shore]

.reopen

[devout snow]

✅

[somber shore]

y = pi and -pi

x = pi/3 and -pi/3

[supple knot]

Only partly correct

[supple knot]

That's why this list is incomplete

[somber shore]

oh because x is between -pi and pi
y can be between -3pi and 3pi

so x=-pi, -pi/3, pi/3 and pi
got it
I am just stupid ty

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[dusk sand]

why is my answer incorrect

[dusk sand]

<@&286206848099549185>

here is how they did it for a similar problem

I followed similar steps and my answer came out wrong

<@&286206848099549185>

[young plover]

You used a decimal and not fractions

Definitely the first issue I notice

If you’re confident that your method is correct I’ll bet it’s just that, since the question specified that you need to give your answer with integers and fractions

I’d highly Recommend solving this type of question by hand

It will give you a much better intuition than just using a formula and plugging it into a calculator

[dusk sand]

so i got the right answer but i need to type ln2*(1/3) for k? the exponent? to get an exact value?

they never said to round to 4 decimals so i wasnt sure

[young plover]

They said to not use decimals

So they wouldn’t need to tell you what to round to

[dusk sand]

thanks

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[signal canyon]

when i try to solve this i keep getting the wrong answer

[signal canyon]

do i solve this by taking the <∂z/∂x, ∂z/∂y> * u ?

and then plugging in the points

[young plover]

no you have to use the limit definition

This is from wikipedia

f(x) is given in your problem statement

and v in this definition correspond to u in your problem

[signal canyon]

oh man i have to take the limit for this ??

[young plover]

so just plug everythjing in and solve that limit

yeah thats what the question says

if you need help with using this definition i can try to help

[signal canyon]

so would the limit just go to 0/0?

[young plover]

i havent done any work, so would you show me yours

if it is 0/0 you could use lhopital rule tho

[signal canyon]

i forgot how to do limits

so would i plug in f(x,y) + u for (f(x + hv)

or would u == 0 since h -> 0

[young plover]

no, just lemme show you, gimme 5

[signal canyon]

ok

[young plover]

I think you might have been misunderstanding the formula

you gotta remember that $f(\vec{x})=f(x,y)$

[woven radish]

llspacebarll

[young plover]

its a function that takes a vector as input so you have to put the different components in the right spots like i did

for $f(\vec{x}+h\vec{v})$, recall that $\vec{x}+h\vec{v}$ is a vector in itself: in your case $\vec{x}+h\vec{v}=(3+h\cos(\pi/4),4+h\sin(\pi/4))$

[woven radish]

llspacebarll

[young plover]

so then you plug those components into the function f like i did

once you get where i got, you just need to expand the squares and and try to simplify as much as you can, ideally the h's will eventually cancel out somehow and you can take the limit easily

[signal canyon]

ok im getting it now

i should be able to solve from here

thank you so much for your help

[young plover]

nw friend

[signal canyon]

.close

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[balmy bloom]

How would I find the domain and range from these functions

[balmy bloom]

@restive river

[devout snow]

@balmy bloom Has your question been resolved?

[balmy bloom]

<@&286206848099549185>

[tired grail]

@balmy bloom the domain of question 16 will be all real number. Because nothing can stop it

As for range

Conver f(x) into f(y) then find the domain of it. It would be the range of f(x)

Similar with question 1

y=2(x+5)²-1
It's domain will be all real numbers

For its range convert f(x) into f(y).

Thus. x=(√(y-1)/2) - 5

Now finds its domain

It will be the range of f(x)

[devout snow]

@balmy bloom Has your question been resolved?

[devout snow]

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[distant root]

hi, i need help with this problem; it was on my test today and i memorized it and wrote it down to solve later. i just didn’t really know where to start with it

[distant root]

and no the area was not given

[eternal mauve]

can anyone help me with this?

[nova idol]

@eternal mauve#❓how-to-get-help

no files

dont click yall

[winter patrol]

you're given sufficient info to determine the area

[distant root]

i dont really know since i dont know the height

[nova idol]

use pythagoras

[eternal mauve]

what type of image should i upload?

[nova idol]

thats my hint

an image not a file

[distant root]

wym hint

[eternal mauve]

okay

[nova idol]

also this channel is occupied

[nova idol]

wdym wym hint

[winter patrol]

rotate the page a bit

[distant root]

i tried using pyth on the test

like 90 degrees?

[nova idol]

label all the sides you know

[winter patrol]

until the side with 36 appears to be the base

[distant root]

holy shit

your a god

im an idiot

[nova idol]

neither is true

[distant root]

does this mean its 24???

or like

do i do something else

[nova idol]

ohyeah

[winter patrol]

wdym by "it"

[nova idol]

you can just do that

the height

[distant root]

the height

the base would be 36

[nova idol]

yep

[distant root]

and the height would be 24

dude omg

so just 36 by 24 for area

tysm i was clueless

what did you mean by use Pythagoras though

how would i use that?

im curious now

@nova idol

[nova idol]

I realise that it was unnecessary, ramonov’s answer was much better

[distant root]

thanks alright

also

rq

is there like a place where i can find good formulas

like a lot of them

[nova idol]

Google

[distant root]

fair enoigh

enough

I’ll cya then

[nova idol]

cya

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[floral turtle]

Just want to check, is this correct?

[floral turtle]

.close

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[restive river]

why???????????

and helllo

[wooden veldt]

abuse of notation

[restive river]

explain

please

🥺

[wooden veldt]

https://www.cantorsparadise.com/the-ramanujan-summation-1-2-3-1-12-a8cc23dea793

[restive river]

damn

.close

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[trail stratus]

How do I identify the sides of the square or an angle, when I dont have a parallel line to reference to?

[hybrid snow]

It says they're perpendicular to the x axis

The other other thing on the XY plane that's perpendicular to the x axis would be anything parallel to the y axis

[trail stratus]

I'm not sure what you mean by this?

[hybrid snow]

It says that "the indicated cross sections [are] taken perpendicular to the x-axis"

So they gotta be parallel to the y axis

Well technically parallel to the y and z axis but I wouldn't worry about the technicality

[trail stratus]

ok

makes sense so far

so how do I find the dimensions?

using that information

[hybrid snow]

If the cross sections are parallel to the y axis, then each cross section's length is gonna be the vertical distance of the region at any given instant

That is, upper function - lower function

[trail stratus]

oh its like the washer method

What if it was a rectangle?

How do I find the width

[hybrid snow]

Width is just the distance. Are you talking about height?

Like its height parallel to the z axis?

[trail stratus]

No the x axis

Are you sure its just the distance?

hm

ok right

its the distance

but how do I assume the distance?

I mean sorry, find the distance?

Is it a default 1?

[hybrid snow]

Oh the width

Like parallel to the x axis

It's a cross section

[trail stratus]

yes

[hybrid snow]

It's basically 0, but not quite

[trail stratus]

0?

[hybrid snow]

The cross section lives only on planes parallel to the YZ plane

If you add all those cross sections on those planes, you get the volume

Yeah no if you cared about volume cross sections, you're accidentally finding the 4D volume lol

[trail stratus]

lol

[hybrid snow]

But those planes have nothing to do with the x axis

Other than they're "perpendicular" to the x axis

You'll learn more about this if you take multivariable calc

[trail stratus]

But in this question, why did he say that the "width" of the rectangle is 1

[hybrid snow]

He means width as in the length

Like

His width is my length

[trail stratus]

I get that

but why 1?

OHHH

1 is parallel to the z axis

aha

I just got what you said to me lol

ChatGPT is fucking terrifying, this mf solved it all with details

fuck it made a mistake

.close

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[mild basin]

how would I solve for a?

[random temple]

just plug in 0 and 3

and then find slope

[mild basin]

so 3 = 3 + 0 + 3(0)^2 - (0)^3?

3 = 3

[random temple]

f(0)=3

what is f(3)

[mild basin]

oh

[random temple]

mb typo

ur right

[mild basin]

f(0) = 3
f(3) = 3 + 3 + 3(3)^2 - 3^3
f(3) = 6 + 27 - 27
f(3) = 6

for secant I use y - y1 = m(x-x1)?

[random temple]

yup

[mild basin]

OK so i find m using point slope form for a

how about for b?

find all points x = c (if any) on the interval (0,3) such that f'(c) = m

[dense jay]

differentiate f, then set it equal to m found in (a)
you will have a quadratic that you can check if it has roots or not, if it does then those are your solutions

[mild basin]

for b I'm trying to find roots?

roots are the answers?

or slopes are

[dense jay]

you are finding any x such that f'(x)= the gradient of the secant line in (a)

[mild basin]

that's a lot of words

trying to understand the question

[mild basin]

if it does (have roots) then those are your solutions

[dense jay]

yeah, because those will be the x values where f'(x)=m

the quadratic you are solving will be f'(x)-m=0

[mild basin]

oh and it just so happens using zero product property the solutions fall on the x-axis

so that will tell us the slope wherever y = 0

depending if there are roots are not

if there are no roots, no solutions?

and only between (but not including) x = 0 and x = 3

interval

[dense jay]

the gist is if f'(x)-m=0 has any solution on [0,3] then yeah those will be your 'c' values

[mild basin]

(0,3)

[dense jay]

true

[mild basin]

why f'(x) - m = 0?

like what formula are we using here?

[dense jay]

youre finding any points where f'(x)=m, if there are any

[mild basin]

oh

what a strange question to ask.. i wonder if we would ever use it in life..

but i guess math is not about practicality, it's about logical thinking and puzzle solving

[nova idol]

It’s def used in life

[vast rain]

well, not all questions have to be directly applicable to life; they might identify gaps in your understanding

and understanding calculus is definitely used in life

[vast rain]

some forms of math, maybe, but certainly not calculus

[mild basin]

example where i need to use this in life? find all points x = c (if any) on the interval (0,3) such that f'(c) = m

[nova idol]

For optimisation for example

[vast rain]

the very fact that you cannot figure it out immediately by yourself shows one useful application in life -- reinforcing your knowledge of calculus

[nova idol]

I mean learning calc is important for learning calc

[arctic field]

,w mean value theorem

[woven radish]

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[nova idol]

But I think that’s not really an application

[vast rain]

but uh yeah the mean value theorem is actually used in life

well, it's intuitive, but still used in life

[mild basin]

wait this is mean value theorem? find all points x = c (if any) on the interval (0,3) such that f'(c) = m

[arctic field]

it literally is MVT

[mild basin]

i thought it looked familiar..

[arctic field]

imagine caring about applications of math

[mild basin]

interval and roots

[vast rain]

it's not exactly the mean value theorem, because you're asked to exhibit the point

but the existence of the point is because of the mean value theorem

[mild basin]

ikr

https://tenor.com/view/you-have-no-value-ian-mcshane-mr-wednesday-american-gods-worthless-gif-18700225

[vast rain]

one of the funniest moments this month for me was one of my friends telling me that they were never going to need piecewise functions in their life

and then also telling me they spent money on a paid tax preparer

solid 20 minute roast session

[mild basin]

taxes are different tho, you need to know what forms to fill, maybe there are things you don't know

extra refunds

i don't see how it relates to piecewise functions lol

is not really gonna help at the tax office

[vast rain]

the amount of tax you pay against your taxable income is a piecewise function

[mild basin]

lol sure, but it's not quite that simple

[vast rain]

actually it is

[mild basin]

no, there are other forms you can fill out

income, working from home, spouse, etc. etc.

[vast rain]

it matters not much in the sense that you have to know how to evaluate a piecewise function, but in your decisionmaking with regards to tax avoidance

yeah that's why I said taxable income

[mild basin]

i guess it depends on how you look at it. piecewise function (math) or "tax bracket"

[vast rain]

no it doesn't

[mild basin]

i mean you don't need to know this math is what I am saying

[nova idol]

you need to know how it works

[vast rain]

yes you do, if you're going to make certain decisions before the tax year is over to minimize your tax liability over time

[mild basin]

sure but the notation is kinda loose

you can imagine it pretty easily

[vast rain]

for example, if you have a bunch of unrealized losses, there is a mathematical way to understand how much of those losses you should realize per year

uh no you can't

[lusty sapphire]

yo avid is up late

[mild basin]

no person on planet Earth can imagine what a tax bracket is without first visualizing this piecewise math function using mathematical notation of left curly bracket { to declare each piecewise function declaration?

[vast rain]

the mathematical notation is very easy to learn, but the underlying intuition about it is not

[mild basin]

12:17am here, hbu?

[vast rain]

and chances are if you can't see how piecewise functions apply to taxes in a very relevant way, you don't also get it

[lusty sapphire]

a different time

[mild basin]

i suppose you can just look at your bracket, if your income falls within it, follow that, ignore the rest

this feels a bit philosophical, how everybody must think, is a hard notion to force on the world

[vast rain]

are you sure you even know what a tax bracket is?

tell me how much tax someone with $60000 in taxable income would pay

single filer

[lusty sapphire]

not enough

[mild basin]

60% lol

[vast rain]

yikes

the government thanks you for your donation

[mild basin]

high earners get taxed a lot, believe me

[vast rain]

so I'm not even referring to the calculation of your tax liability, because you could conceivably outsource that

but you need to know how to do that at the bare minimum to actually make decisions to reduce it

[nova idol]

Why reduce it

[vast rain]

because it all gets wasted anyway

might as well go enjoy life with it

[mild basin]

meh, most people just take it to tax firm, or use tax software. all of this math is done for them.

[nova idol]

Depends on the country

And your opinion

[vast rain]

yeah the tax firm won't tell you what to do to reduce your liability before the tax year ends

it'll just calculate an amount you have to pay

and you pay that

[mild basin]

lol how is this related to piecewise functions and a 20 minute roasting session?

[vast rain]

not to mention you pay an exorbitant amount

[nova idol]

Tbh I didn’t even know people could reduce their liability

[nova idol]

It’s free

with intuit or smth

[vast rain]

because if you need to understand piecewise functions and the math behind them to optimally reduce your tax liability

[nova idol]

At least in the us

[vast rain]

only for returns that are sorta simple

[mild basin]

https://tenor.com/view/ronburgundy-agree-disagree-ron-burgundy-gif-5109282

[vast rain]

for example, if you have $200,000 in unrealized capital losses, and you make $150,000 in capital gains in year 1 and $100,000 in capital gains in year 2, as well as $50,000 in ordinary income in year 1 and year 2

[nova idol]

What do you consider “sorta simple”

[mild basin]

https://tenor.com/view/tax-doing-taxes-busy-typing-gif-16555503

[vast rain]

ones that don't involve certain partnerships, random capital gains, possibly AMT

[nova idol]

What percentage of normal people have that stuff

[vast rain]

I'm saying that most people can outsource the calculation of their tax liability

but they can't outsource the decisions that they make before the tax year is over to reduce it

there are reasons, for example, to sell your loser stocks before the end of the tax year to reduce the amount you pay

[mild basin]

it's all in SVB and FTX anyways. Easy! $0.