help-28

[echo merlin]

I didn't think I was wrong either but then when checking for derivative I made a slight error

[torn jolt]

differentiable bc the derivative of both functions approach to the same value as x approaches 3

not because it's continuous

[echo merlin]

Yeah

[torn jolt]

derivative of both functions approaching 3 is equivalent and so is the function value itself, therefore continuous and differentiable

continuous does not nexessarily imply differentiability

i have class now bye

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[serene sage]

i know volume around y axis is integral of pi * x^2 * dy

but im not really sure how to do this here

do I substitute x =4 in the equation or smth?

[spiral vigil]

we're revolving around the x axis

[serene sage]

find the volume ... when rotated completely about y axis\

[spiral vigil]

oh

i read the stuff on top

[serene sage]

wait on the top it does say x -axis 😭

[spiral vigil]

that's for problem 7 i think

[serene sage]

wait nvm thats other qs yeah

[spiral vigil]

anyway I'd probably use the cylinder method

aka the shell method

[serene sage]

is that integral of pi * r^2 dy?

thats the only one i have been taugt yet

[spiral vigil]

it's integral of 2π x h dx

where h is the top curve minus the bottom curve

[serene sage]

ah i haven't learnt that in school :/

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[woeful anvil]

How would I do problem 10? I’m kinda confused

[woeful anvil]

Can someone walk me through

Am sorry

[full forum]

@woeful anvil Has your question been resolved?

[leaden ermine]

What have you tried

[woeful anvil]

am cry

[leaden ermine]

this is what we wanna work

[woeful anvil]

Yes that’s not cool

[leaden ermine]

irrelevant what you think

(riemann way)

so

[woeful anvil]

I know as x goes to negative infinity it goes down towards -1 right

[leaden ermine]

yes

I would first plot f(3) =4

[woeful anvil]

Ok

[gritty rose]

can you not be a dick, thanks

[leaden ermine]

sori

[leaden ermine]

can you tell the vertical and horizontal asymptotes you have?

[woeful anvil]

Vertical asymptote at 0, 1, -1, 4

Right

?

[leaden ermine]

vertical asymptote is just at x=0

[woeful anvil]

Oh am sorry

[leaden ermine]

because there your function goes to infinity or -infintiy

[woeful anvil]

Oh okay I see I see

[leaden ermine]

and horizontal would be where x goes to -inf/inf which results to -1 and 1

so

the plan looks

we will take care of the limit as x->3 in abit

so we know as x goes to -inf it approaches -1 also as x approach 0 fromt he left it approaches +inf

[woeful anvil]

I’m gonna try to graph it

Wait a bit please

[woeful anvil]

Is this correct I’m not sure

[leaden ermine]

i got almost the same

it's abit unprecise too

[woeful anvil]

Yea I do not like this problem

It’s like the mental illness to the head

[woeful anvil]

Oh right

Open hold?

Hole

Right

[leaden ermine]

yes

and the other other piece could be a bit smoother

approaching the line y=1

ig something like that

but it's okay

[woeful anvil]

Thank you sir

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[woeful anvil]

.reopen

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✅

[woeful anvil]

Can someone check if I correctly implication differentiated the first problem?

And if I did the second one correct too

Sorry for bad handwriting

Second problem is ln(x+sqrr{x^2-1})

[leaden ermine]

product rule is fine

[woeful anvil]

Is it not minus though

Cause

-x

[torn jolt]

of its a minus ?

mb

thought it was +2xy

[woeful anvil]

Oh am sorry

Maybe my bad handwrite idk

[leaden ermine]

1. looks fine

[woeful anvil]

The first problem is x^4-x^2y+y^4=1

Ok thank u

[leaden ermine]

also pleas in the 3.

use brackets

at pre last step it's wrong

[glossy valve]

bacc (unhelpful)

[leaden ermine]

I hope you can finish from here properly

and btw (1+x)/x doesnt reduce to 2 but to 1/x + 1

idk how you thought that's 2

but it's anyway a consecutive mistake

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[woeful anvil]

Oh I see sorry for late delay I was in class probably should have waited until class ended skull

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[torn jolt]

oh nvm i think i got it

shouldnt have removed the n

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[umbral dome]

yes but you didn't put it as + 0, you kept it

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[dull heron]

Can someone help me please? Whenever I do gaussian elimination, I start off good but the ending always confuses me

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@dull heron Has your question been resolved?

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[midnight lotus]

hi

[midnight lotus]

why is the root of 2x-1 squared + 2x-1 and not also -2x-1

[midnight finch]

you mean like this -(2x-1)?

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@midnight lotus Has your question been resolved?

[midnight lotus]

ya sorry thats what i meant @midnight finch

or any other <@&286206848099549185> that is available. doesnt matter

[midnight finch]

it will be mod 2x-1

the root of 2x-1 squared

[midnight lotus]

wdym

?

and also how is the root of 1 plus minus 1 but the root of 2x-1 squared is plus 2x-1

[midnight finch]

its not minus 1

you cant get a negative value as a root

[midnight lotus]

but the root of 9 is plus minus 3

so u can

cant u

[midnight finch]

its not

it is only 3

[midnight lotus]

wait what

[midnight finch]

minus of root 9 is -3

[midnight finch]

hence we put the mod

[midnight lotus]

but when i do my math hw if its like 9 squared equals ... then i do plus minus equals ... and get the answer right

i have always been doing this

[midnight lotus]

whats a mod

[midnight finch]

what grade you in?

[midnight lotus]

12

[midnight finch]

its a function to make a number positive

you cant get negative value equal to a root

like mod -3 is 3

mod 3 is 3

[midnight lotus]

like when u do root 9 equals 3 -4x

the 9 tuirns to plus minus 3

i have been doing this for idk how many years

[midnight finch]

you dont do only root 9 you do plus minus root9

[midnight lotus]

and never had an issue

yes which is plus minus 3

[midnight finch]

the sqrt function can only retun positive values

it cant return negative values

[midnight lotus]

okay that makes sense but when i havr been doing my equations in the past if something is squafred i just do plus minus root of both sides

[midnight finch]

if you try to plot the graph of a square root x you will get only postive values no negative values

[midnight finch]

if its a equation you need to do both plus minus

cause you are unsure if you plug in x its gonna be negative or postive

[midnight lotus]

okay so then for this:

how do i do

[midnight finch]

hence we take mod

[midnight lotus]

what is a mod

i still unsure

[midnight finch]

to make sure whatever x we plug in we always get a positive value

[midnight finch]

its just a function which turns any negative number into a positive one

like mod of -3 is 3

mod of -2 is 2

mod of 3 is 3

[midnight lotus]

so for this i eventually get 1 = (2x-1) squared

then i square root both sides

so i put plus minus on both sides?

i should have plus minus on both sides right? (this is chat gbts work)

[midnight finch]

in this case

if you put +- on both sides

you will get the same answer regardless

i mean you can try it

but generally we take the mod of 2x-1 to be equal to 1

hence when we open a mod we get the plus minus sign on the other side and not on the number inside

[midnight lotus]

are u able to explain without mod

or no

wondering since i dont think supposed to know what a mod us

is

[midnight finch]

idk how to explain it without mod

[midnight lotus]

so its not wrong to put plus minus

on both sides

when something is tangent to a parabola does that mean it is paralell to it or can it be going in a different direction

[midnight finch]

what

[midnight lotus]

like does a tangent line have to be paralel

to the function

[lime ether]

it means it intersects at a single point

look up an illustration

of tangent line

[midnight lotus]

okay then how do i do 13

thas solution

for that part

we are saying slope = slope

so isnt that the same line

since it has to go through 2.-3

2,-3

like both of them have to go through that point

[lime ether]

well yes

[midnight lotus]

if its the same line then why does question say two lines

thas what i dont get

if two lines have same slope and pass through the same point then thas just one line

isnt it

[lime ether]

because there are two different lines that have that property

[lime ether]

what is the same line?

[midnight lotus]

how is that possible for two lines to have the same slope and go through the same point

[lime ether]

nono

[midnight lotus]

this is saying slope equals slope so thas the same line

[lime ether]

they are tangent to the parabola at different points, with different slopes

[midnight lotus]

but the equation is saying the slope is equal to slope

and what a value makes the slope equal to slope

[lime ether]

this is just setting the derivative equal to the slope of a line, which in fact yields two values of a

[lime ether]

yes and youll get two values of a, hence two different slopes

[midnight lotus]

but the derivative is the slope and the rise over run formula is too

[lime ether]

when did i say it wasnt

[midnight lotus]

isnt that true

derivative means slope at any given point

and so does the rise over run

[lime ether]

but the rise over run isnt for the tangent line

[midnight lotus]

oh i didnt read that right

[midnight lotus]

wdym

[lime ether]

well i guess it is technically

this would be much easier to show graphically

hold on

[midnight lotus]

okay appreciate it

[lime ether]

do you agree that two lines can have different slopes yet pass through the same point

[midnight lotus]

different slopes yes

but the equation is saying the same slope

even my teacher wrote someone in the lesson slope = slope

[lime ether]

right and by setting the slopes equal we get two different possible slopes

[lime ether]

this is true, but you dont get one unique slope becausae two lines can pass through the same point and yet have different slopes

notice they didnt say tangnet to the curve at that point

[midnight lotus]

im a bit confused what the two different x values mean though

[lime ether]

they said it just had to pass through the point

[lime ether]

the two values that the lines passing through the point are tangnet to the curve

[midnight lotus]

ok so basically we sent slope equal to slope to make it a quadratic formula

so if we get on answer that means the slope is the same at that point

(x coordinate)

and then the other x is when the slopes are also the same

[lime ether]

hopefully you see now

see where the green and blue intersect

thats at (2,-3)

[midnight lotus]

ya

[lime ether]

but they are tangent at different points

all we needed was for the lines to have the same slope as the curve at some point

hence why we set the slopes equal

which yielded two possible x values

with the added condition that they pass through the point of course

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@midnight lotus Has your question been resolved?

[midnight lotus]

how do u go from derivative graph to the corresponding function graph

[lime ether]

wdym

[midnight lotus]

Like how do u look at a derivative graph of a function and them draw the function

From just derivative graoh

[lime ether]

is this a separate question

unrelated to the first

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[hollow summit]

what

why

[hollow summit]

they have same force

[grim skiff]

Yes but case a has an upward force, from the block too

[hollow summit]

yeah i thought

of that

but

its

so

stupid

that

i

was like

rly no way

cuz like what can create smt that doesnt have an upward force

[grim skiff]

If you put a block, that was equal mass to the block A, then block A won't move, so the tenison needs to be less than 10 N for block A to move

[grim skiff]

Pulling on it would produce negligible upward force

[winter glen]

I don't quite understand how the rope can cause 10 N of tension in case b when it is massless

😔

[hollow summit]

no cuz its frictionless no?

even if mass is less than block A it would move im p sure

[winter glen]

This is quite confusing, actually. If the coefficient of friction is 0 then there is no friction force or in other words where does the upward force come from

pulley is also massless and frictionless

[buoyant sierra]

In case b, block A is accelerated across a frictionless table by a steady 10N tension in the string.

[winter glen]

Yeah. I am also wondering whether the block A is accelerated first or it is caused by gravity

[buoyant sierra]

A is accelerated first as given in question

Acceleration should have been the same though

In both cases, the tension in the rope will be the same, as the weight of the block and tension in the rope are of the same magnitude.

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@hollow summit Has your question been resolved?

[winter glen]

I am so confused. Suppose block A is accelerated at a constant velocity at t_0 then from the point of view of the rope, it is like the rope is pulled toward the ground (let's call it tension force). Then in case a the force is combined with both the tension force and weight of the 10N block

Then isn't block A is accelerated faster in case a? 😔

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[lime saffron]

How do I find the local min? I already found that the global max is at E, and the global min is at T, I found the local max's which are C,E,S

[buoyant sierra]

The net tension is 10N in A and the net tension is 10N in B. So their acceleration should be same

[lime saffron]

<@&286206848099549185>

[stable nest]

how do you find local max?

flip your head upside down and it's the same process

[lime saffron]

I already tried what I think are the local mins but it's incorrect each time I submit

[stable nest]

hmm what'd you get

[lime saffron]

T,R,B,D

[buoyant sierra]

Are you sure the global ones are included with the local ones

[lime saffron]

The global max was included with the local max so that should be the case

[stable nest]

not the same

end points do not count towards local min max

[lime saffron]

That's probably what I did wrong then I've been including the global minimum

Apparently it was B,C,D,R :0

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[supple crown]

can i have help?

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Please don't occupy multiple help channels.

[hallow vault]

@supple crown close one channel

[supple crown]

how do i do that?

[hallow vault]

.close

[supple crown]

k

.close

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[polar surge]

<@&286206848099549185> need help, mock test timo 2020 senior secondary

i have no coach so i have to study by myself T_T

[torn jolt]

90

[buoyant sierra]

@polar surge you know about vertically opposite angles ?

[elfin edge]

does it not vary?

[buoyant sierra]

Nope

Oh wait maybe it does

[elfin edge]

it could stay const

could

but idk

[polar surge]

angles opposite each other?

[buoyant sierra]

Nvm

It doesn't vary

[buoyant sierra]

Yes

[elfin edge]

geogebra?

lmao

[green merlin]

is the original question in chinese

内错角

[elfin edge]

ok maybe

[buoyant sierra]

Imagine this being your quadrilateral

[green merlin]

or vert. opp. angle

[polar surge]

yup, i think so.

[buoyant sierra]

So one angle is equal to another angle which is vertically opposite

[elfin edge]

i mean like

when you consider the length of the diagonal AC

that lenghth can vary

[buoyant sierra]

Length of the diagonal does not matter

[elfin edge]

from 8 to 22

[buoyant sierra]

Have to check

It varies

Obv it can't be that easy

Well the ans is not 90

But I don't know what it is then

No information about the diagonal length is given

[elfin edge]

so when the length of the diagonals vary

that angle also varies

maybe assume that AC=l

and then try to figure out the other diagonal

and the area

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[polar surge]

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[blazing violet]

I got a bit of confusion going on. I do understand that for a function to be injective f(a) must be different from f(b) for which a is not equal to b. But what function satisfy the opposite? That a = b => f(a) = f(b)

[blazing violet]

I mean, doesn't that sound useless? Or maybe I am not getting the use of it

[fast peak]

every function needs to satisfy a=b => f(a)=f(b)

if you put the same thing into the function you better get the same thing out

[rapid rain]

a function maps every input to a single output

if a = b, then f(a) = f(b) because both are f(a)

[blazing violet]

So basically, a = b => f(a) = f(b) is just another argument that resulted from the implicit opposition compared to a ≠ b => f(a) ≠ f(b) ?

As in, "if this exists then we have to create the exact opposite assumption"? Excuse my english, I'm romanian

[fast peak]

a=b => f(a)=f(b) is just a basic property that every function has

it has nothing to do with injective or any other properties

[blazing violet]

I did ask because I thought a ≠ b => f(a) ≠ f(b) did the job itself and the latter felt useless

[fast peak]

even if it looks similar

[blazing violet]

Yeah, overall it is a fundamental after all

Also just to check because I want to master the knowledge without skimming through the textbooks, if the derivative is positive, then the function is monotonous and thus injective?

[fast peak]

yes

[blazing violet]

Okay, closure and explanations are all I needed, have a good day or night

Peace!!

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[vocal sonnet]

why did this not include both y values but the second one does 🤔

[vocal sonnet]

$-x^{2}+\left(y^{1}+x^{\frac{2}{3}}\right)^{2}=1$

[glossy valve]

smeagol

[vocal sonnet]

original function

$y=\sqrt{1+x^{2}}-x^{\frac{2}{3}}$

[glossy valve]

smeagol

[vocal sonnet]

simple but not full

$y=\frac{\left(1-x^{\frac{4}{3}}+x^{2}\right)}{y+2x^{\frac{2}{3}}}$

still has everything

[glossy valve]

smeagol

[vocal sonnet]

Oh I found it

I need to +- the sqrt

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[cunning terrace]

Hello, I am in geometry, and I am not sure what I am doing wrong. Here is a picture of the question and my answers.

[cunning terrace]

.close

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[crude grove]

Can someone confirm if this is correct please

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[crude grove]

<@&286206848099549185>

[torn jolt]

yes

[crude grove]

is there a faster way of doing it?

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[dry pumice]

<@&286206848099549185>

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[subtle void]

.

F(x)=1/x-4 + 2

[subtle void]

a(4;2)

Prove that it’s center of cimetry

Symmetry *

Using f(a-x) + f (a+x) = 2b

[eternal dock]

is it 1/4-x+2 or 1/4*x+2

[subtle void]

1/x-4

Alone

Plus

2

[eternal dock]

that's different than what you wrote initially.

[subtle void]

I was wronf

[eternal dock]

so it's 1/x-4+2?

[subtle void]

Yes

The +2 is by itself

[eternal dock]

is that a fraction

okay

[subtle void]

.

The thing about this

Is that first u have to prove that
A-x € Df and a+x € Df

Which is i think impossible

Am i wrong ?

[eternal dock]

well what's Df

[subtle void]

Wdym

Oh

It’s
Df = R -{4}

[eternal dock]

and what's the equation for checking symmetry

[subtle void]

Using f(a-x) + f (a+x) = 2b

That’s not where my issue is

My issue is in proving that

A-x € Df and a+x € Df

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[wet wind]

?

[thick hedge]

I want my proof verified

[wet wind]

What's ur proof?

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[thick hedge]

Given that V is a finite dimensional vector space and that $U$ is a subspace of $V$ , If $dim(U) = dim(V)$ then $U=V$

[glossy valve]

A dense set

[thick hedge]

So we want to prove that if $U \neq V$ then $dim(U) \neq dim(V)$

[glossy valve]

A dense set

[thick hedge]

If the vector spaces aren't equal and one is a subspace of another, then their dimensions can't be the same , as all the basis of a given vector space have the same dimesniosn

is this fine

[topaz valley]

that doesn't seem like a correct argument

you've assumed that U and V are not the same vector space

so why should all bases of U having the same cardinality tell you anything about bases of V?

[untold lichen]

If U is a subspace of V and $U \neq V$ then there exists at least one vector in V that's not in U. This would mean that $dim(U) < dim(V)$. Therefore $dim(U) = dim(V)$ implies $U = V$.

[glossy valve]

LooseEthics

[topaz valley]

you are missing justification here

why should dim(U) < dim(V)

[untold lichen]

Any basis of U is extendable to a basis of V. If x is a vector in V and not in U, then it can't be created as a linear combination of the basis of U. Then the basis of U combined with x defines a vector space W such that $dim(U) + 1 = dim(W) \leq dim(V)$.

[glossy valve]

LooseEthics

[topaz valley]

i mean this is kinda skipping a lot of checks

the point is to cite theorem 2.38, which says that a LI list of the right length is a basis

if dim(U) = dim(V) then U is forced to be V

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[calm sandal]

I'm confused on how the left side of the function is supposed to be portrayed

particularly

between (-infinity, -4)

because in the information given, it does not say that it touches the horizontal asymptote

however, it is said to be positive fully through that interval

[torn jolt]

Bruh I can help

[calm sandal]

ok, go ahead

[torn jolt]

1. U can't cross a horizontal asymptote, only once tho, wich shouldn't happen tho on this graph

(still thinkin)

gimme 1 min to channel my inner sigma gyatt

[grave elm]

^ counterexample to this

[torn jolt]

That doesn't exist

Bruh using sus sine/cosine

[grave elm]

I graphed it, it clearly does exist, wdym?

[calm sandal]

that's actually impossible here

because x=1 at 3 locations

y*

[torn jolt]

one more min

im usin big brain right now...

[calm sandal]

can someone else help me

[torn jolt]

done

That should be the graph

[calm sandal]

yeah, that does not seem right

[grave elm]

does it have to be a rational function?

[calm sandal]

yes

[grave elm]

that's pretty strange

it tells you f(-2) = f(-4) = f(0) = 0

3 roots

[torn jolt]

Oh well, glad I could help

[calm sandal]

I don't have to find the equation

it's just a sketch

[torn jolt]

Bruh, i belive u got this, it aint rocket science

[grave elm]

yeah, the problem is that if it has 3 roots, the numerator must be a polynomial of at least 3rd degree

[torn jolt]

at least

[grave elm]

and the denominator is of 2nd degree

that doesnt look like it would have a horizontal asymptote

[torn jolt]

so then doesn't it have an oblique asymptote then?

Oh well, glad I could help!!

[calm sandal]

<@&286206848099549185>

[grave elm]

to me it jus seems impossible

[calm sandal]

I even tried searching it up

and there was a verified answer on chegg

I could not access it though

unfortunately

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[grave elm]

. https://www.freemathhelp.com/forum/threads/using-information-to-sketch-graphs-of-rational-functions.130693/

[teal basalt]

(x^i + y^j + z^k)^(n)
can I make the x + y + z be separated by just the +?

like
x^a + y^b + z^c
as you can see they are not inside bracket anymore

[grave elm]

not really

[teal basalt]

any way to force it?

[sudden condor]

a and b and c being i j k multiplied by n ?

[teal basalt]

no, it's just the form that I want

[grave elm]

in some special cases, there could be a way

[teal basalt]

like I don't the bracket

[sudden condor]

nope you can’t

[teal basalt]

I need it for general purpose

hmm...

[grave elm]

But (x^i + y^j + z^k)^(n) won't algebraically simplify to x^a + y^b + z^c

through trinomial theorem, you could expand it to a certain sum

the number of terms in this sum would depend on n

so it's not really any nicer

[grave elm]

Why do you need it btw? Is it part of some larger problem? Maybe it's not actually necessary to solve it like this

[teal basalt]

hmm... can't use that, too specific requirement

[teal basalt]

yeah it part of large problem. I will try to think another way

thx btw

[grave elm]

You could post the relevant parts of the problem here if you need help with it

[teal basalt]

I want to make a c++ struct. that can fit around 30 digits.

I want it to be able to support nth root and power.

currently I'm thinking of combining multiple interger to make the 30 digit. but thinking how to do the root and power calculation is hard

also I don't want to use any library

[grave elm]

if it supports multiplication, then you could probably do power by just multiplying them repeatedly

[teal basalt]

yeah, i could brute force it that way for power

but root is a whole other problem

[grave elm]

nth power could technically be computed in O(log(n)), assuming multiplication is O(1)

for the nth root, you could either just guess it bit by bit

or use sth like newton's method

[grave elm]

by binary searching, it could be also O(log^2(n)) if im not mistaken

[teal basalt]

i will look into this thx

[grave elm]

ChatGPT (surprisingly) wrote a decent code

[teal basalt]

Newton better. I will just use that

[grave elm]

okay nvm it doesnt work properly

the relevant algos for nth root and power are more or less correct tho

and they have decent time complexity as well

[teal basalt]

thx I will look into it

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[tawny sierra]

How do i find the mobius transformations that preserve the upper half-plane? I got that b/a is real and d/c is real, by plugging in some values, but I dont know how to proceed

[tawny sierra]

im working with the extended definition

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@tawny sierra Has your question been resolved?

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[gritty rose]

Theorem 5 here is pretty close to what you're asking:
https://johno.dk/mathematics/moebius.pdf

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[tawny sierra]

aight thank you ill check it out

[tawny sierra]

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[torpid perch]

1.- Let ( S ) and ( T ) be subspaces of ( \mathbb{R}^4 ) where
( S = \langle (1, 3, 2, 0), (4, 1, 0, -1) \rangle ),
( T = { x \in \mathbb{R}^4 \mid x_1 + x_3 + x_4 = 0 } ),
and ( H = { x \in \mathbb{R}^4 \mid 3x_1 + x_2 + x_4 = 0 } ).
Define, if possible, a linear transformation
( f : \mathbb{R}^4 \to \mathbb{R}^4 ) such that
( f(S) \subset T ) and
( \text{Ker}(f) + \text{Im}(f) = H ).

[glossy valve]

938c2cc0dcc05f2b68c4287040cfcf71

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<@&286206848099549185>

[torpid perch]

<@&286206848099549185>

[torpid perch]

<@&286206848099549185>

[eternal stone]

As far as I remember we already discussed a ton of linear algebra with you

Are you sure that you don't know how to solve this?

What are your main ideas at the moment?

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[storm tusk]

I have the exercise:
Which of the following statements about real functions with ID = IR are true and which
incorrect? Justify your decision carefully.
a) If a function is strictly monotonically decreasing, then it is differentiable.

My answer/thoughts:
Basically I'm currently wondering if I need a function that is strictly monotonically over the whole ID (= definition area) or if it's enough when it's only a certain area in ID

with f(x) = -|x| the statement would be wrong, but only if it's possible that we only take IR^+ for all x values in consideration

if we need to take all IR in consideration, then it's also strictly monotonically increasing (so here i'm wondering...)

otherwise we would take f(x) = -x but this isn't differentiable, then the statement would be correct

[rare dock]

strictly decreasing without any specification of being on a certain set means strictly decreasing on the domain

regardless your answer doesn’t make much sense to me

[storm tusk]

maybe for f(x) = -√x could be an example for strictly decreasing and it's not differentiable

but i'm not sure

[rare dock]

well you want the domain to be R

[storm tusk]

I feel like there is no function that would fullfill this maybe

[rare dock]

and that function is differentiable

fulfill what?

[storm tusk]

-x would be differentiable and strictly decreasing right?

[rare dock]

yes

[storm tusk]

but there is no function that is strictly decreasing and not differentiable?

[nocturne current]

-floor function

[rare dock]

why not?

[storm tusk]

if it's the whole domain then f(x) = -|x| wouldn't work

because it is strictly increasing for some x values and strictly decreasing

so it's not "only" decreasing

[rare dock]

yea. think of something else then

[storm tusk]

lool I think we have no function with abs lol

so far, I never saw sth like that

[rare dock]

that example was overkill

[minor crater]

true

[rare dock]

just take any decreasing function and break it into something piecewise, shifting one piece to make a discontinuity

[storm tusk]

ooh okay, maybe

-x for x <= 0
and -2x + 2 for x > 0

[rare dock]

not quite what i said but yes that works

[storm tusk]

if I add +2 for the 2nd function, then is it like you said with the shifting?

[minor crater]

why +2

maybe you mean -2

this isn't strictly decreasing

[storm tusk]

oh

I adjusted sth wrong lol

ok thank you

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[nocturne current]

https://en.wikipedia.org/wiki/Monotonic_function#Some_basic_applications_and_results for you information

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[fallen sierra]

why is this indeterminate

[fallen sierra]

0^0 i get

it logically cant be 1 because youre getting something from nothing

but a really big number ^ 0

is 1

1 ^ a really big number

is 1

whats indeterminate here

[nocturne current]

inf power 0 is not 1, only a very big number power 0 is 1, 1 power inf is tricky, it is not 1 either

[fallen sierra]

but that just doesnt make much sense

and the argument that infinity technically isnt a number isnt very convincing since it kind of has to be

especially in this context i think

[nocturne current]

if infinity is a number, then it can be calculated right? i.e. inf+1>inf, but no, inf+1=inf

[fallen sierra]

what is it if not representing a number

[nocturne current]

it is a concept, regarding the concept that nothing is bigger than it

[fallen sierra]

arent there infinities larger than others

[nocturne current]

yes, but then that is concept about cardinality, nothing related to numbers

or i clarify it, it is a concept that no number is bigger than it

[fallen sierra]

but logically how would those cases be indeterminate

‘anything’ raised to 0 is 1

[nocturne current]

on the other hand, why 1^inf is not 1, consider Euler constant e, the definition is (1+1/n)^n when n tends to inf, so when if 1^inf is 1, then e=1

[fallen sierra]

why would that not hold in a hypothetical

[nocturne current]

'any number'

u wont say a cloth rasied to 0 is 1

so similarly, when inf is not a number, it raised to 0 is not 1

[fallen sierra]

i dont think im following here

[nocturne current]

do u know 'e', the euler constant, 2.71828

[fallen sierra]

yes

[nocturne current]

great, then what is the definition of it, there are several, but the most obvious one should be

[fallen sierra]

yes

[nocturne current]

exactly, then when n tends to inf, 1/n=0 right?

[fallen sierra]

sure

[nocturne current]

so it becomes 1^n(non-rigorous but just to give u an insight)

[fallen sierra]

oh then the definition is 1^inf is e

[nocturne current]

yes

1^inf is not e tho

but if 1^inf is 1, it leads to contradiction

so it must not be 1

[fallen sierra]

ok that sort of makes sense

ty for your help

[nocturne current]

hope this help:)

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[unborn mica]

this makes no sense. i had multiple times to try because its just practice so i ended up going down the list till i got the right one to try and reverse engineer it but i dont understand
because there's no e to be using ln

[foggy trout]

Where are you stuck?

[unborn mica]

Where does ln come from? He didn't teach to use ln and this was lesson 1 on inverses

And logs

Together

Ln is log base e but there's no e

My answer was log base 12 of t+2

Lol

[foggy trout]

It's needed cuz the inverse function is x = -2(12^y)+4 and we need to get the y out of there

[unborn mica]

Yeah I got log base 12 of (t-4)/-2

Where does ln come from

[foggy trout]

U can use other logs but there are only ln in the answers

So u should use ln

[unborn mica]

And my question is how can you use ln without an e

Ln is log base e but there's no base e

It's base 12

[foggy trout]

ln is just used for to get the exponent out if you know what i mean

[unborn mica]

I don't know what you mean because ln is base e

There's no e

How can you use it

Without an e

[foggy trout]

We need to know what's y equals to

So we are using ln

[unborn mica]

Ok I understand that you flip y and x. That's not the problem. You have to use log base 12 not ln because ln is log base e

There's no e

I understand inverse

I don't understand how you can use log base e

If there's no base e

[foggy trout]

You can use log_12 but there r only ln in the answers

[unborn mica]

I need someone else to explain because we are going in circles. I don't think you understand my question

Lol

[foggy trout]

Idk why u should use ln only when there's e

[unborn mica]

Because ln is log base e

12 is not e

It's base 12

[violet bolt]

log base is arbitrary

[foggy trout]

U can use any base for this but the answers are in ln so you got no choices

[violet bolt]

$\log_a(x) = \frac{\ln(x)}{\ln(a)}$

[unborn mica]

But I don't understand how you use any base

[glossy valve]

kaue

[unborn mica]

Hm my teacher told me $\log_a(x) = \frac{\log_10(x)}{\log_10(a)}$

Log base 10

Not log base e

[violet bolt]

generally, $\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$

[glossy valve]

kaue

[violet bolt]

for any b you want

[unborn mica]

Oh

[foggy trout]

Log base anu number except 1 is possible

[violet bolt]

this is the change of base formula

[unborn mica]

Thank you. Can you explain why that works or not rlly

[foggy trout]

Explain what?

[unborn mica]

.

[violet bolt]

there are many proofs for this property on youtube, the term is "change of base formula for logarithms"

[unborn mica]

Tysm

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[smoky river]

so, i decided "why not just find a math discord server for this"

i'm struggling to understand the more advanced notation of integrals than the most basic stuff
i'm trying to recreate FFT in Desmos (the 3b1b way)
as shown in red, i've made an initial waveform like so: the fundamental frequency with a -45 degree phase shift and the 3rd overtone with regular phase but at 1/2 the amplitude (just like the formula depicts)
then i plot into polar coordinates 24 cycles of the waveform, shown in yellow
then i use the green and blue graphs to show myself the change in X and Y coordinates for the values of theta (offset upwards for clarity)
and afterwards i find the center of mass of the polar-coord shape (the purple dot) with the two integrals defining its X and Y position, respectively
but now i'm stuck
how do i plot the change in both coordinates of the dot while making the x axis represent the values of the "n" variable?

[smoky river]

(holeh moleh this took way too long to write)

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[smoky river]

nope, not even close

<@&286206848099549185> i guess

[smoky river]

<@&286206848099549185> are there even ppl with this role

[sacred lotus]

?

[smoky river]

no way

[smoky river]

and we keep waiting

i have a hypothesis that i need to transform the integral into something different

however idk how to integrate either so i guess i'l google it while waiting for someone to notice

whatever, i give up lol
might revisit this sometime later but not now

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[scarlet timber]

I am lost

[scarlet timber]

I did

$a^2+ai-1=(a^2-1)+ai$

[pearl trout]

+ai

[glossy valve]

yøung matr!x

[scarlet timber]

yes sorry

then

$\frac{a^3+i}{(a^2-1)+ai}*\frac{(a^2-1)-ai}{(a^2-1)-ai}$

[glossy valve]

yøung matr!x

[scarlet timber]

the problem is

when I multiply

I cant

idk why

I jus can't

<@&286206848099549185>

[proper leaf]

cross multiply

multiply both sides by ((a^2-1)+ai)*((a^2-1)-ai)

[scarlet timber]

here is the thing

I will show you what happens

[proper leaf]

sure

go ahead

[buoyant skiff]

The denom. should have strictly positive real terms in it

[scarlet timber]

yes

my problem is in the numer

[buoyant skiff]

The num is okay

[scarlet timber]

found it

[buoyant skiff]

Its fine if you get something complex in the numerator since you can just separate the numer. into two fractions

[scarlet timber]

the conjugate

it's

a+I

$$a+i$$

[glossy valve]

yøung matr!x

[scarlet timber]

I take the negative out then factorize

@buoyant skiff @proper leaf thx

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[proper leaf]

yw

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[fast flicker]

Can someone refresh my memory on this

why are these in distance and not forces

and why is ABx = -40m*i? Is it A to B so 40m backwards from A?

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[opaque locust]

find relative extrema using second derivative

[opaque locust]

can endpoints be a relative extrema???

cause in the answer the endpoints are included but

[azure burrow]

end points can be relative extrema

[opaque locust]

oh

is google wrong then 😭

[azure burrow]

but some schools teach it differently based on their definition

its based on your book definition

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[worldly cairn]

can someone help explain what i did wrong

[worldly cairn]

i tried submitting as x = 4 for absolute min and local min values x = 2, x = 5, x = 1

[lime ether]

the y values sir

[viral jasper]

First question is asking for maximum value

[lime ether]

not x values

[worldly cairn]

oh

im stupid

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[compact cipher]

guys for the a)

will the inners integrals bounds be from 4 to x^2 or from x^2 to 9

[umbral dome]

can you draw a sketch of the region?

[compact cipher]

from the looks its from 4 to x^2

i just want to make sure

[umbral dome]

so the question is, is your region of integration the green or orange region?

[compact cipher]

i guess green

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[crystal ivy]

Here he solved this question was solved using path analysis couldnt we use sandwich theorem like remove the y and e^y sandwich between 0 and 1 and solved when i solve like this the answer is 0 but here he stated the answer as DNE

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[slow flare]

hi I don't know if i should how to do a riedman sum for this graph

[stable nest]

what did you try?

[slow flare]

adding in the right points

[foggy trout]

Can u show ur work?

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[slow flare]

Ignore the answers i put in the website

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[torn jolt]

Help

[torn jolt]

I got this one wrong but is this how you would do it

6w+3x+4y-2z=60 if yall can't understand my beautiful handwriting

<@&286206848099549185>

[gusty summit]

Ok so if ur trying to find every variables value, then just isolate it

for example lets say you want to find z

then do 2z = 6w+3x+4y-60 then z = (6w+3x+4y-60)/2

@torn jolt

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[quaint terrace]

10 a. need to solve for x.

[quaint terrace]

not sure what to do after

[woeful pasture]

${(x^2 - 3)(x^2 + 3) = (x-\sqrt{3})(x + \sqrt{3})(x - \sqrt{3}i)(x + \sqrt{3}i)}$

[glossy valve]

k

[quaint terrace]

how do you do that?

[woeful pasture]

difference of square

[quaint terrace]

the (i) is for the x^2-3 right?

like it corresponds to that part of the equation?

[woeful pasture]

x^2 + 3

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[worldly surge]

is this good?

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[worldly surge]

<@&286206848099549185>

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[gusty summit]

use the quadratic formula

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[slender tundra]

lil help please

how do I even begin

[meager surge]

ummmm

i'm not the best at trig

but i think you could probably set similar triangles and go from there, no?

[slender tundra]

guess so?

[midnight dew]

draw a diagram of each triangle

[narrow path]

To be honest I forgot what secant and csc meant

[slender tundra]

it like just sin cos and tan but like flipped

[inland moth]

sec = 1/cos

csc = 1/sin

[narrow path]

Thanks

[slender tundra]

sorry but like I'm like lost

solving for the (pic) will give me the side for A

right?r

https://tenor.com/view/dm-crying-about-it-ub-ratio-gif-25077200

alright then

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[torn jolt]

How do I express the domain in interval notation?

[oak ruin]

well what is the domain first of all

[torn jolt]

How do I find it

I struggle with finding it so idk

[hoary ember]

do you see anything thst could limit the domain?

[torn jolt]

5?

[hoary ember]

?

[oak ruin]

Yes 5 makes you divide by 0 which is a problem

[oak ruin]

?

[torn jolt]

?

[torn jolt]

And what do I do with this info

[oak ruin]

this tells you 5 is not in the domain

because it gives you nonsense

What other numbers are not in the domain

[torn jolt]

0?

[oak ruin]

x=0 gives you 0, which works

Let's do a more general question, what's the domain of sqrt(x)?

[torn jolt]

0,∞

But I also don't really understand the concept behind the like brackets and parentheses

Its like [0,∞) or something

[oak ruin]

yes

and yes

[a,b] is inclusive, (a,b) isn't

[oak ruin]

So given that, you have a square root on the denominator here. So does this restrict your domain more?

[torn jolt]

Yes?

Bc it can't produce negatives??

[oak ruin]

Not exactly

You can't input values of x that make the denominator negative (or zero as we said earlier)

in other words, you need 5 - x > 0

And these are the only restrictions on domain

since the numerator is just 5x which is fine