help-42

[vocal summit]

integrate the function and take bounds from 0 to 60

[torpid summit]

i swear i did that but it gets you like 8000 smth liters

nvm im high

thanks lmao

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[verbal geyser]

Hey I need help with this badly

[verbal geyser]

My assignment almost due

6+384672818+3926572818x48583818495827184958538divided by 138582

Fast!

[drifting seal]

<@&268886789983436800>

he’s trolling in other channels too

#help-41 message

[unique jackal]

[clear delta]

don't troll in help channels please

or anywhere else really

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[opaque yoke]

this is the solution for a problem

trying to find k if one of the roots is the reciprocal of another

at the end it says use shortcut for reciprocal

im not really sure what this is

could somebody please explain this to me

[calm coral]

@opaque yoke Has your question been resolved?

[calm coral]

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[potent totem]

I am completely forgetting how to determine continuity and differentiability of intervals. For example:

[potent totem]

$f(x)=x^{4/5} \hspace{2cm}$

That did not work!

[potent lotus]

lifemath

[potent totem]

$-1 \leq x \leq 1$

[potent lotus]

lifemath

[wet urchin]

do u know what makes a function continuous

3 things

[potent totem]

Sorry, didn't see that someone had responded.

I would say that for a function to be continuous it needs to be defined for all of its domain, no holes/jumps, etc., that its left and right limit exists for all points.

I don't think this is precise, but I didn't want to just say "tell me."

Could you offer the three?

Or, that it's left and right limit are = each other for all x in its domain?

So, like, I could determine if a function is not continuous at a point by testing if it's left and right limits are equal to each other around that point.

[wet urchin]

No gaps or jumps:
A continuous function has a smooth, unbroken graph where you can move across the entire domain without encountering any sudden jumps or gaps.

Limit exists and equals function value:
For a function to be continuous at a point "c", the limit as x approaches "c" must exist and be equal to the function value at "c" (f(c)).

Defined at every point:
A continuous function must have a defined value for every point in its domain.

-google ai

[drifting seal]

!nogpt

[calm coral]

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

[wet urchin]

u r actually

like

u need help

[drifting seal]

no, you do

[wet urchin]

no you do

i know what makes a function continuous

i read it first bro

[drifting seal]

every help channel i’ve seen you in you’ve either used AI or can’t solve the problem yourself

[wet urchin]

😭

[wet urchin]

i do need help

why do u think im here

im tryna get good at math

🤯

[drifting seal]

open your own channel then

[potent totem]

Okay, so if I have my function, I just asking the questions:

"Is there any point x in my function's domain that would cause either a discontinuity or problem?"

[wet urchin]

erm actually !no gpt !!!! 👆 🤓

i could have just said

its from me

and u would have never known

but im not a plagirizer

[drifting seal]

no one would believe you

it’s so obvious

[wet urchin]

its not that deep bro

[drifting seal]

i was going to call it out before i even saw the "google AI"

how is using AI helping you get better at math

it’s making you worse

[wet urchin]

thats literally

a definition

[drifting seal]

you get better at math by doing it

[wet urchin]

im just not writjng it out

[drifting seal]

thinking for yourself

[potent totem]

.close

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[drifting seal]

you can’t even define continuity

[wet urchin]

and how would u know that

[drifting seal]

because i’ve seen you struggle with algebra 1 problems

[wet urchin]

that has absolutely

no

correlation

what so ever

[drifting seal]

it does

[wet urchin]

it doesnt

im in calc 3

[drifting seal]

and?

[wet urchin]

i know what makes a function continuous bruh

[wet urchin]

and?

and what 😭

[drifting seal]

"you can’t pick up your pen"

[drifting seal]

being in a specific math course doesn’t mean you have mastered everything before it

in my ap calc class kids couldn’t do rudimentary algebra

and hence why they struggled

[wet urchin]

i use very litte algebra

in my class

i know all the algebra i need

[drifting seal]

if you have a hard time with simple concepts then it’s a very good indication that you have no grasp of rigorous concepts

[wet urchin]

besides the wack shit

[drifting seal]

apparently not

[wet urchin]

show an example of what alegebra problem

[drifting seal]

this conversation is pointless

[wet urchin]

i struggled with

[drifting seal]

idgaf about your math ability

[wet urchin]

ok than stop talking dumb fuck

your wasting ur own time

[drifting seal]

<@&268886789983436800>

nice one

[wet urchin]

nice one what

😭

[drifting seal]

*you’re

smay this person uses ai frequently

and is just rude

[wet urchin]

bro says i cant do algebra 1 than says he doesnt care

[drifting seal]

^

[drifting seal]

*then

[wet urchin]

you the type of person who gets bullied for sure

[drifting seal]

you have no idea who i am

[wet urchin]

i dont

and you have no idea wh oi am

[drifting seal]

exactly

i don’t

i don’t care to

[wet urchin]

so u cant say i dont know what makes a functionm continuous 😭

[drifting seal]

if you did then you wouldn’t use ai

but again

[wet urchin]

ight lil bro

[drifting seal]

i don’t care what you know

[slate field]

stop posting in other peoples help channels when you don’t know the answer, we don’t condone the use of AI to help people in help channels.

please

[drifting seal]

"lil bro"

power move man

[slate field]

can we stop fighting now? the help channel is closed.

[wet urchin]

the objective was to make you feel belittled

[drifting seal]

my feelings are very hurt

[drifting seal]

smay is very nice

lol anyways

have a nice day

[wet urchin]

what is a smay

[drifting seal]

the mod in the chat

[wet urchin]

ic'

[calm coral]

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[final scarab]

crazy

[final scarab]

anyway

not sure how to do part B

[winter elbow]

Have you done part a yet?

[final scarab]

cus they dont provide the numbers and all the examples i see have the vectors start at the origin

ye

i moved U to the tail end of V

[winter elbow]

I see your doubt

[final scarab]

yeye

erm

!helpers

[calm coral]

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

[final scarab]

wat

someone help please im getting tired and ts is due tmr 😔 🙏

[tender spoke]

length is just pythogoreans a bunch, direction is usually just an angle? is there a answer box with more specifics?

[final scarab]

nop

thats all i had

which is why i think my professor just wants me to label the resultant as A rather than calculate a side? but idk cus it does say to get the direction as well so im stuck

[tender spoke]

ah i thought it was an online homework, but if youre turning some paper in then you can calculate the length (aka magnitude) of vectors just by doing pythogorean's thrm with the x and y "lengths" of the vector. like u in this case goes over 2 in x and up 1 in y, so sqrt(5)

[final scarab]

wait

but isnt that just for right triangles

[tender spoke]

ye but there are right triangles 🙂

[final scarab]

oh is it bc the grid?

ahh

[tender spoke]

yep !

[final scarab]

okok this makes a lot more sense

so then i use that, pythag the V side, and use those to get A?

[tender spoke]

well you have to add the vectors first and get A, then you can find the length by the pythag

[final scarab]

yeye

alr ty

that helped a ton

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[tiny magnet]

What steps do I take to begin proving divergence? By Adding sqrt(1) to the numerator and subtracting 3 from the denominator, I get a greater function... Which even though it diverges, can't be used to prove the original series diverges. How do I begin to get a function that is less than the original, while also simplifying it to be able to compare it?

[manic hawk]

To make your simpler function smaller, you can do things like divide by 10

[tiny magnet]

How does that help me progress in terms of simplifying the function to something I can compare to?

[manic hawk]

5n^3-1 > n^3,

If you didn't have the 5 there, you would need to divide by something

Here we can divide by 5 to just drop it

[tiny magnet]

thank you

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[hearty heart]

guys can you show me how to integrate this step by step?

[hearty heart]

dunno how to use the substitution here

i suppose it is similar to this rule

but what do i replace in my case?

u = x^2 +1

but then x gets weird

u - 1 = x^2 and i need to use the sqrt?

[manic hawk]

You should split the integral into two separate pieces first

[crisp portal]

since it's under modulus, split into 2. int from -inf to 0 -x/1+x^2 and int from 0 to inf x/1+x^2

its simple integration after that

[hearty heart]

huh where is the guy who said it diverges

it basically goes into infinity on both sides. I discussed this special case with someone else earlier ^^

[pseudo wedge]

that was me

I didn't realise it was the absolute value

[pseudo wedge]

what do you mean

[hearty heart]

i meant to show "divergent" integral on the graph

is that not the correct intepretation?

[pseudo wedge]

the graph doesn't tell us whether the integral converges or diverges

[hearty heart]

oh it can't be seen on the graph?

ah ok sec i found a method

$$ \frac{x}{1+x^2} = 0.5 \cdot \frac{2t}{1+t^2} = ln(1+t^2) $$

[potent lotus]

Jaeger

[hearty heart]

this is like a special rule

@crisp portal@manic hawkdid you have a similar idea or do it differently?

[manic hawk]

No special rule here.

0.5 ln(...)

And not equal. The last one is the integral

[hearty heart]

but there are 2 ways of getting here right?

can you show me the one with substitution

[manic hawk]

Do you mean u=1+t^2?

[hearty heart]

yeah

[crisp portal]

just substitute t = 1+x^2, which after integration is ln(t) = ln(1+x^2)

[hearty heart]

yeah but what do you do in the further steps

uff my bad i made a mistake

top should be x

[calm coral]

@hearty heart Has your question been resolved?

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[rain fossil]

why are they so close but not exactly the same?

[rain fossil]

can you also explain how the formula
dz = df = df/dx dx + df/dy dy
works?

cause it's like

if we cancel everything out

dz = df = df(1)+df(1)
dz = df = df + df
dz = df = 2df, which isn't true-

(Calculus 3)

[swift laurel]

that's why "canceling out" differentials does not work in a context of partial derivatives

they are not exactly the same because one is an approximation of the other

[rain fossil]

when look at (the partial derivatives) in this problem, I think of the wronskian and exact equations

is there any connection?

[rain fossil]

hm, which one is more accurate?
I'm guessing the deltaz as opposed to the dz because it uses a change in the function rather than its derivatives

[swift laurel]

an exact equation is in the form
total derivative = 0

the delta z is the actual change in z, the differential is an approximation to that

[rain fossil]

alr

[rain fossil]

so it would be T(x,y)=t(x,y)-E(x,y)

and we have 0.01 error

that's like what I saw

earlier

but yeah thank you

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[rain fossil]

it no close i guess

.reopen

[calm coral]

✅

[rain fossil]

why in the world is this difference so high

what causes it to not be like different by 0.1 or something but like an absurdly high number

why is it so innacuratwe

is it cause of the nature of e

and it only does that for weird functions like trig functions, e and ln or like

does it have to be a polynomial function to be off by a very small amount?

[frank shoal]

its because dz uses linear approximation whereas delta z is the actual difference between the points. since dz uses linear approximation, if the function's slope changes too fast over the interval, that can create inaccuracies in the approximation

[rain fossil]

ooooo

oooOOO

I SEEE

OK

[frank shoal]

👍

glad to help

[rain fossil]

So the delta z accounts for the entire function I'm guessing

and the dz only accounts for over that interval

which makes it inaccurate in general

[frank shoal]

yeah delta z is like i know the first point i know the second point

where dz is like i know the first point but im guessing the second point based on the data from the first point

[rain fossil]

ye

[frank shoal]

it approximates that the slope doesnt change

[rain fossil]

ye

[rain fossil]

[frank shoal]

yeah it assumes the slope doesnt change over the interval

so if the interval is too big, the actual value of the graph can run away quickly

[rain fossil]

that sucks

like really bad

lol

[frank shoal]

its useful for small intervals and for functions that are difficult to evaluate at every point

but yes, for the most part it does suck lol

[rain fossil]

by any chance do you have time to explain this

[frank shoal]

yeah its basically saying

you have a function f(x,y) right

[rain fossil]

ye

[frank shoal]

and theres a tangent plane at 0,0,0

its basically saying does there exist a value close to 0.0.0 such that the tangent plane approximation is within 1/5 of the actual function?

actually its saying

theres a region in which the distance is always less than 1/5

[rain fossil]

its a disk so there has to be

;-;

0_0*

right?

[frank shoal]

which is yes because when you create a disk, everything closer to the middle is going to be closer and closer to the original function, i.e. the difference is always smaller

so you just have to make sure the edge of the disk is less than 1/5

which always exists if you think about it

[rain fossil]

basically the radius of the disk is equal to the error function E(x,y)

so if the radius is less than 1/5

then it exists

[rain fossil]

ye

[frank shoal]

yeah basically lol

yeah

[rain fossil]

I wasn't really taught calc 3 right so I'm thinking practically a lot of the time

thanks for bearing with me

[frank shoal]

thats actually good, just memorizing equations without thinking about what they mean and how they come to be is really bad for when you're applying them later on

especially in unfamiliar situations

[frank shoal]

of course! im always glad to help

[rain fossil]

(true but I don't see why a tangent plant is really that important lol, or why the dot product is woven into like every definition in terms of how it makes it work)
I could go on forever cause I'm always open to learning new things but yeah, (if you can help me walk through some of these calc 3 problems that would be much appreciated. Ima keep going till I can't no more so I'm wondering if ur good with showing me some of the ropes)

[frank shoal]

tangent plane is just linear approximation but in 2 dimensions lol

[rain fossil]

so it's finite

[frank shoal]

i mean yeah im going to sleep soon but i'd be happy to help in the future

[rain fossil]

alr

ima be studying diff eqns this weekend but I also got calc 3 to do

so I think I might do a lot tomorrow night

[frank shoal]

its as big as you want it to be

just as it gets bigger i hets more innacurate

as it is with linear approximation

[frank shoal]

alr gl

i will be taking my leave now

[rain fossil]

night

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[weak rapids]

the definition of surjective function here is wrong, right?

[fleet verge]

It is wrong, yes

[weak rapids]

oh ok, weird because this was the very first site that showed up when i searched their definitions

thanks anyway

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[red locust]

so im working on this question rn

[red locust]

i just had a question

would 1.1 be my common ratio here?

like is it 1 + 0.1

i already know its geometric

[unkempt drift]

exactly!

[red locust]

okay got it thank you bro

[unkempt drift]

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[distant fog]

A cube of side lenght 8cm is immersed completely in a rectangular vessel containing water. If the base is 16 cm long and 10 cm wide, then, find the rise in water level in vessel

[distant fog]

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[red locust]

im doing Part A of this question and this is my work

[red locust]

does everything look good

<@&286206848099549185>

[south thorn]

yes, but instead of using: a(1-r^n)//(1-r), I would use a(r^n - 1)/(r-1)
It doesnt change the result, just makes both numbers positive

[calm coral]

@red locust Has your question been resolved?

[red locust]

okay thank you so much ill change that

[calm coral]

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[heady nebula]

Hello, I am doing the log unit, and my teacher said on my test, there will be a question about finding a point of intersection between an exponential function and a log function. He also specified that we could use the Liner equations method of substitution or elimination. How will this work out?

[floral vessel]

you have an example ques or something?

[heady nebula]

i wish i had, he just said this is from 9 grade and you guys should get it

[leaden thunder]

make up some values for the exponential: https://www.mathsisfun.com/sets/function-exponential.html and logarithm: https://www.mathsisfun.com/sets/function-logarithmic.html and practice

[tropic panther]

so like the intersection between 2^x and log(x)?

[heady nebula]

yep

[heady nebula]

thank you!

[tropic panther]

set them equal to each other and algebraically solve

[heady nebula]

i would set the two eq equal

[heady nebula]

exactly

[tropic panther]

well, in general you probably wont get such an intersection unless you have some offset, e.g

2^x = log(x) + 3

log(1) = 0
values less than 1 approach negative infinity

n^x only approaches 0, so it never reaches the negatives, and therefore only has a chance to intersect at x > 1

but if x > 1, log(x) is strictly less than n^x

[calm coral]

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[red locust]

am i right with B here?

[slow bane]

a

[red locust]

really?

wait why

[floral vessel]

seems like a

[gray smelt]

why

[red locust]

thats what im asking 😭

[gray smelt]

something to do with sqrt(x^2)

assuming x is positive sqrt(x^2) = x

but here its given x is negative

[slow bane]

oh i missed that part

yeah b

[gray smelt]

bro

[slow bane]

im so smart

[gray smelt]

@red locust anything else

[red locust]

okay lol i was scared

[red locust]

nah this was it i got more questions for different channels though

[calm coral]

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

[red locust]

.close

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[dense owl]

Can someone explain to me why the standard gravitational acceleration (9.81m/s²) is used in Tsiolkovsky rocket equation?
Δv=Isp×g0×ln(m0/mf)

I wondered about this for quite a while now as in space, especially in vacuum the gravitational pull of the earth should be basically negligible.

At first I thought it's because of density, but I managed to only confuse myself further

[calm coral]

@dense owl Has your question been resolved?

[dense owl]

Alright, I'm just stupid probably

.close

[calm coral]

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[small beacon]

I need to know if I'm right

[small beacon]

is it (3,-5)

[indigo grove]

Yea
But why is there a I don’t know option lol

[small beacon]

readiness check

@indigo grove

[indigo grove]

It’s not linear
the rate of change isn’t not constant

[indigo grove]

Simply if it’s a line it’s linear duh

[small beacon]

this is what i get confused on bruh

[viscid nymph]

Basically 'line'ar is a straight line and anything else is nonlinear

[small beacon]

alright

[indigo grove]

A line/linear function/graph always have a constant rate of change other than a line it’s no constant change

[small beacon]

oh

wait

so a vertical function is non linear

[remote mural]

hi

[indigo grove]

By a vertical you mean a vertical line ?

[small beacon]

yeah

[remote mural]

😭

[indigo grove]

A vertical is a line but it’s rate of change (gradient) is not defined

[remote mural]

Hi?

[indigo grove]

Hello

[remote mural]

Oh hello

[indigo grove]

[remote mural]

Oops, I'm Brazilian, so if it takes me a while to respond, it's because I'm translating lines.

[indigo grove]

It’s ok if you have a question try using available help channels

[small beacon]

@indigo grove so linear

=

no rate a change

it stays the same

[remote mural]

Oh yes of course I will use the channels but I came here on this server because I wanted to learn more about mathematics since I am very curious I also have personal goals and I need to become smarter

[indigo grove]

Can you show the question ?

[small beacon]

let me know if i got this right

this a linear function

[indigo grove]

Yep

[small beacon]

what to write down in my notes?

[indigo grove]

about linear functions/graph ?

[small beacon]

yeah

so i dont keep getting confused

[remote mural]

[indigo grove]

A linear function/graph is a line that has a constant rate of change if it’s a horizontal line then the rate of change is 0
if it’s a vertical line it is linear but it’s rate of change is not defined
if it’s slanted at an angle then it has a rate of change

[small beacon]

i need a visual representation of this right here

[remote mural]

This seems so complex compared to the math I'm currently learning considering I've started studying math in more depth now

[solemn herald]

search it up. qudrants and (x,y) values

[small beacon]

how old are u

[small beacon]

quadrant 3

[solemn herald]

yes

[sharp heath]

Yes

[small beacon]

ts so easy once i know

once i get something it get hella easy

wait now im confused

im guessing its 6

but i dont like guessing

[solid pollen]

Have you used functions before? They're written like f(x)=...

[remote mural]

14 years, however, at my school I still haven't even learned geometry and the teachers keep reminding me of subjects like first-grade equations, numerical expression, etc., and he didn't even have time to finish teaching algebra because I had surgery and had to take a leave of absence from school...☠️ ☠️ but next year I'll be back in the 9th grade

☠️

[small beacon]

yea f of x

[solid pollen]

How would you write f(x) that satisfies the description you have there?

What would be the explicit formula, I mean

"every y-value is 6 more than 3 times the corresponding x-value"

[small beacon]

its not giving me the x value

[solid pollen]

no, but let's turn this into an f(x)

what's the y corresponding to an x? if it satisfies the rule above

[solid pollen]

let's turn this into a formula

if x=1, how do you find y?

[remote mural]

sad school reality

[solid pollen]

figured how to find f(x)?

[small beacon]

uh no

😭

[solid pollen]

"y is 6 more than 3 times x"

How would we turn this into a formula?

y= ....

[small beacon]

uh

[potent lotus]

Wild123

[solid pollen]

no shaming, it's supposed to be very elementary xd. I don't want to give you the answer, I know you can find it.

[small beacon]

this is middle school

where are u from?

[solid pollen]

if "y is 6 more than 3 times x"

[remote mural]

But soon I'll be smart and then well... what am I going to do again? Oh yes I'm going to be a chemist hahahaah

[solid pollen]

how would we turn this into an equation

replace the words...with maths

[small beacon]

y = 6x + 3x

i think

[solid pollen]

Romania...it's supposed to be middleschool material here too. but the part where we transform "y is 6 more than 3 times x" is pretty much primary school.

[solid pollen]

close enough

y=6+3x

"6 more than 3 times x"

[small beacon]

ah alright

more = plus

[solid pollen]

so f(x)=?

[remote mural]

Não estou entendendo nada pois não estou traduzindo mas acho que não preciso

[solid pollen]

What's louis doing?

😄

[small beacon]

bro are you from portugal?

[small beacon]

now im confused again

[solid pollen]

if for a given function, 'every y-value is 6 more than 3 times the corresponding x-value'

we know y=6+3x

so f(x)=y means f(x)=6+3x

does this make sense?

[remote mural]

Ah, I'm Brazilian, I already told you, right?

[small beacon]

OH YEAH MY TEACHER DID SAY THAT

f of x just means y and vice versa

[solid pollen]

So you agree f(x)=6+3x?

[remote mural]

Quando for minha vez é só falar .

[solid pollen]

We have to find the 'y-intercept'

what could this mean?

[remote mural]

.

Estou apenas traduzindo as falas de vocês agora.

[small beacon]

yes

[solid pollen]

remember something about y-intercept?

[small beacon]

uh no i learned it but dont remember

[solid pollen]

y-intercept means it intersects the y axis, so the first coordinate is 0.

a point of the form (0, y)

But we look for the y-intercept of the function f(x) we described earlier

How could we find it?

[small beacon]

idk 😭

[solid pollen]

Maybe at some point the teacher mentioned the graphic of f is the set of points (x, f(x) )

[small beacon]

wait..

i asked ai

waittt

[remote mural]

Kamishi like your skull doesn't explode

[small beacon]

so basically if the y intercept intercepts 0

you just substitute it for x

[solid pollen]

Ai is often mistaken...but yes... this time it's correct.

[solid pollen]

the y intercept is the point (0, f(0))

[small beacon]

but how is it zero all the time

i got this right?

[solid pollen]

y-intercept means it's on the OY axis. Have you done XOY graphics?

Ys, like that XOY graphic.

[small beacon]

uh no

[solid pollen]

an y-intercept is a point on OY.

In the image you just sent...that's a system XOY. Maybe you called it something else?

a ...cartesian coordinate system?

an ortogonal system?

anyway, y-intercept is a point on the vertical line. The one with an y at top

as such, a point on this line has first coordinate 0.

[small beacon]

uh

we have NOT learned that bs

is it 0,2

[solid pollen]

absolutely

y-intercept: intersects vertical line

x-intercept: intersects horizonal line

[solid pollen]

what would be the x intercept here?

[small beacon]

0

[solid pollen]

every point is a pair ( , )

of 2 numbers

so...definitely not 0

🙂

[small beacon]

bro

its asking about the y intercept

[solid pollen]

yes

[small beacon]

i think it's 0,2

[solid pollen]

I am asking you a follow-up question

[solid pollen]

yes, you are right

I am trying to see if you understood

by asking you...the x intercept.

[solid pollen]

But...you did the y-intercept correct. it's (0, 2) here

Ok, let's try something else. say, you didn't have the drawing, but you had the formula of the function: x-4y=-8

How would you find the y intercept (that you know is (0, 2) )?

any idea?

[small beacon]

is this right?

[solid pollen]

...You're switching from 1 question to another

[small beacon]

cause i solved it

[solid pollen]

I cannot see the other axis of the graphic.

But it looks correct, if each rectangle horizontally is 1 week.

[small beacon]

she already has 30

[calm coral]

@small beacon Has your question been resolved?

[calm coral]

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[wheat wyvern]

derive

[wheat wyvern]

I'm not sure how to start
am I supposed to plugin 2x for t then derive?

[glad parrot]

Let F' = sin(t² + 3) iirc

And after it will be F(2x) - F(6)

[wheat wyvern]

then I need f'(x) ?

since the overall is 5. Find the derivative of each equation given below.

[glad parrot]

You need F

If you have g(x) = int between x and 2x of f(t) dt then if F is an antiderivative of f(t) it will be F(2x) - F(x)

[wheat wyvern]

,, d/dx ( sin((2x)^2) + 3) - sin(39) )

[potent lotus]

smeagol

[wheat wyvern]

like this?

f(x) = sin((2x)^2 + 3) - sin(39)
f'(x) = above?

sin(4x^2 + 3) - sin(39) --> cos(4x^2 + 3) * 8x

thank you

@glad parrot I don't think this is right

the answer key says it's 2 sin(4x^2+3)

<@&286206848099549185> i didn't get it right can you help please

I know that it should be 2 sin(4x^2 + 3) but I have no idea how

[untold drum]

your f(x) is this. so derive F(2X) - F(6) and youre done.

[wheat wyvern]

that's what I did though

[untold drum]

show.

[wheat wyvern]

F(2x) = sin((4x^2 + 3)
F(6) = sin(39)

f'(x) = cos(4x^2 +3) * 8x

[untold drum]

sorry, F(X) is not sin (...)

F'(X) is sin(..)

[untold drum]

this.

derive F(2X) - F(6) and youre done.

[wheat wyvern]

\int sin --> - cos so
F(2x) = -cos(4x^2 + 3)
F(6) = -cos(39)

[untold drum]

you dont need to know what F(X) is, you only need to know that F' is sin (....)

[untold drum]

do this.

[wheat wyvern]

F(2X) - F(6)
2 * F'(2x)

[untold drum]

well now use that you know F'

[wheat wyvern]

so then
2 sin(4x^2 + 3)

thank you so much!

.close

[calm coral]

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[calm coral]

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[glad sinew]

I just want someone to confirm my sol cause theres no ans in the textbook

[glad sinew]

is this right? I shifted index first.

for 3a)

i know this is like elementary calculus😓 , im just bad w series so i want someone to confirm👉 👈 🥺

[calm coral]

@glad sinew Has your question been resolved?

[calm coral]

@glad sinew Has your question been resolved?

[whole hinge]

it's been a while since I've used the ratio test, but looks good to me at least!

actually you didn't shift the indices right

it would be 2m-1 not 2m

just try it without shifting any indices and applying the ratio test directly

|(3(m+1)+1)(x-1)^(2(m+1)+1)) / (3m+1)(x-1)^(2m+1)|

[glad sinew]

oh right yes

omg yes okok

thanks

.close

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[glad sinew]

everything I get, until the highlighted part

because t=x+1

why is it x+2 now

[mortal orbit]

should be x+1

prob typo

[glad sinew]

ok

thank youuu

[calm coral]

@glad sinew Has your question been resolved?

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[tall tusk]

if im using trig equivelance's

[tall tusk]

and i have cos pi/4

and i want to make it negative sqrt2/2

does it turn into -cos3pi/4

or does the -cos cancel otu with the fact that 3pi/4 is already negative

or is it just cos 3pi/4

[torpid summit]

i mean pi - pi/4 is just 3pi over 4 lmao

[tall tusk]

yeah

but the image shows that its -cosx

so would it be

cos (4pi/4 - 3pi/4) = -cos pi/4

does the negative come into place to turn it into a equality

[torpid summit]

Oh i see what your question is

cos (4pi/4 - pi/4) = -cos pi/4

[tall tusk]

and the negative is on the side of my cos pi/4?

ah gotvcha

[torpid summit]

yep

[tall tusk]

and that simplifies to cos 3pi/4

i see

thanks you

thank you*

.close

[calm coral]

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[calm coral]

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[torpid summit]

hm

[torpid summit]

https://tenor.com/view/math-calculate-confusing-figure-out-gif-6237717

[leaden thunder]

Find the formula for c_n first

[torpid summit]

i get its like a repeating thing like

1 2 3 4 1 2 3 4

but how does the formula work

[calm coral]

@torpid summit Has your question been resolved?

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[hushed crater]

Why is (2x+10)² equal to 4x² + 40x + 100 and not 4x² + 100?

[potent igloo]

https://tenor.com/view/kitten-silly-derp-foil-gif-15720250

foil

[hushed crater]

Aren't exponents distributive, so (2x+10)² = (2x²+10²)

[potent igloo]

no

[marsh summit]

well take x = 1, is 12^2 equal to 104 or is it 144?

[hushed crater]

144

[viscid zenith]

,tex .freshman

[potent lotus]

kaue

[crystal forge]

think about simple examples \ counterexamples when you have a question like this

is $(1 + 2)^2 = 1^2 + 2^2$ ?

[potent lotus]

from math import sqrt

[crystal forge]

https://www.youtube.com/watch?v=yfGtbNgcrQ8&ab_channel=MathematicalVisualProofs

[blazing coyote]

$(a+b)(a+b)= (a+b)^2$

[potent lotus]

A dense set(Ping when reply)

[blazing coyote]

Try expanding that

[hushed crater]

I got it now thanks everyone 👍

.close

[calm coral]

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[remote mural]

For future reference, whenever I am given an equation in this form, the sloping asymptote is just the term that isn't part of the fraction?

[marsh valley]

If it's in that form, yes. The key point is that 3/(x-3) gets insignificantly small for large x, and so you're left with a dominating 5x term

[remote mural]

Gotcha thanks

.close

[calm coral]

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[calm coral]

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[sudden willow]

26. How to find circumference of this half circle?

I did

[sudden willow]

Pi*r2:2

.close

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[sudden willow]

Is this 19 cm to the whole side or just to the height?

[calm coral]

Please don't occupy multiple help channels.

[fickle tide]

just to the height

[sudden willow]

How’d you know?

[fickle tide]

because the arrow ends at the height

if the arrow stretched all the way to the end then it means that the whole side is 19cm

[sudden willow]

Ok makes sense

[fickle tide]

but because it ends at the height that means only that part is 19cm

[sudden willow]

I got 54,94 cm as circumference @fickle tide

can u check it for me

it’s to be graded assignment

[fickle tide]

you mean the perimeter?

[sudden willow]

Circumference what’s around the figure

[fickle tide]

are you trying to find this?

[sudden willow]

Yes

Also please find area and circumference of this trapeze.

I got a = 60 cm^2 and c = 34,78 cm.

[maiden path]

For the area you can use 1/2h(base 1 + base 2)

[sudden willow]

I found it out already

Can you see if I’m correct

[maiden path]

Yes sure

60 is right

Good job

And the perimeter is also right

Any thing else @sudden willow

[sudden willow]

But here?

[maiden path]

Do you not know how?

[sudden willow]

I know

[maiden path]

What did you get

[sudden willow]

P = 54,94 cm

[maiden path]

I got 62.68

Did you round your values before adding them?

[sudden willow]

Thank you. Can you also tell me if I got this right?

Area - 28,27 cm^2
Circumference - 18,85 cm

[maiden path]

We got different values do you not want to know what you did wrong?

[maiden path]

This is right

[sudden willow]

Look 3. @maiden path

[sudden willow]

For this -

[maiden path]

Ik got the same value

Your equations are right i think you might have gone wrong somewhere

I’ll check

Ok i see

When you did 19^2 and 12^2 they are supposed to be added but after you squared the values your next line is 361 - 144 it should be 361 + 144

@sudden willow

[sudden willow]

Ok

I’ll check that later

@maiden path

[maiden path]

Ok

[sudden willow]

I’m finding perimeter. @maiden path

I’m finding perimeter now of half circle

2pir(1/2)

Do I also have to subtract the diameter?

[maiden path]

It’s the same equation for the circumference but it’s half because it’s only half of the circle

[sudden willow]

I don’t count the diameter…

[maiden path]

Instead of doing a full rotation which is 2 pi it’s only half so it’s just pi

[sudden willow]

It’s one figure

[maiden path]

No you use the diameter to find the radius

[sudden willow]

The formula for circumference is

2 pi * r

[maiden path]

To find the circumference of the circle it’s usually 2 pi r but now that it’s half a circle it’s just pi r

[sudden willow]

And I need for half circle

So divide that by half

[maiden path]

Yes that’s what I’m explaining

[maiden path]

Yesss

[sudden willow]

Pi * 5 is 15,71

[maiden path]

Yesssss

[sudden willow]

2pi5(1/2) is is 15,71

Now do I subtract with 10?

[maiden path]

No

[sudden willow]

To find circumference of the ENTIRE figure

[maiden path]

We are finding the perimeter which is just the outside

Then you have to find the sides of the triangle part

You already calculated those

So just add them to the circumference you got for the half circle

[sudden willow]

Perimeter isn’t this

[maiden path]

No not the line through the middle

[sudden willow]

It’s this

[maiden path]

It’s whatever lies on the outside

Yessss

[sudden willow]

Exactly so I’m substracting the diameter

[maiden path]

No

You would add it if it was apart of it but it’s not

You don’t need to walk across the diameter to go around the shape

[sudden willow]

This is 15,71 cm

[maiden path]

Huh

[sudden willow]

Pi*r

[maiden path]

Yes

[sudden willow]

And I found this

[maiden path]

And add the sides you got for each of your triangles on top

[sudden willow]

I can’t do that

I think your wrong lady

<@&286206848099549185> can anyone check?

[maiden path]

To find the perimeter of the whole shape you add all of the sides together, you got 15.71 for the half circle and then each side of the triangle is 15.81 and there are two so you added them together like 15.71 + 15.81 x 2

[sudden willow]

But the HALF circle

Is the DIAMETER included

This is 15,71 right

We need to get rid of the base

[maiden path]

Ohh i see what you’re saying

Yea

[sudden willow]

Exactly !!

[maiden path]

I’m not sure tho

[sudden willow]

@fickle tide Thoughts?

[maiden path]

I calculated the whole circumference and it’s 31. 47 half of that is what you got

So the base isn’t included you would have to add that on if you wanted to find the perimeter of just the half circle

That just half the perimeter of the half circle doesn’t include the base

[sudden willow]

I’m getting 37,33 m

<@&286206848099549185>

[maiden path]

You should get 47.33

[sudden willow]

I did

2(15,81)+5,71

[maiden path]

Yes that’s the answer

The perimeter of the circle is 31.47 and half is 15.71, which doesn’t include the base

[maiden path]

See you have to add on the diameter separately if you want that

[sudden willow]

oop

ur right then

[maiden path]

Just half of the circumference is 15.71

The whole perimeter of the half circle would be 25.71

[sudden willow]

Oh yeah

Then the full Formula would be

[maiden path]

But we don’t need that

[sudden willow]

Pi*r+d

[maiden path]

We jsut need half the circumference

[sudden willow]

If we would seeking this

But we don’t need the base

[maiden path]

Yes so the answer we got before will do

Technically the diameter and circumference are two separate line segments so unless you’re specifically asked for the perimeter of the semi circle you don’t add those values together

[sudden willow]

Final ans 47,33 m

[maiden path]

Yessssss

Good job

[sudden willow]

Full formula of semi circumference circle is

pir+d

I get it now

[maiden path]

No

[sudden willow]

Semi

Circle

[maiden path]

Yea

[sudden willow]

But we don’t use perimeter

Ok

Let’s not complicate it

[maiden path]

Yes

[sudden willow]

I got area of 118,32 m^2

@maiden path

[maiden path]

for the same one?

for the half circle i got 78.54

for everything i got 153.54

the area of each triangle is 1/2 (15) (5) and there are two so you should get (15)(5)

@sudden willow

[sudden willow]

I got the triangle 79,05 m^2 @maiden path

Cause 10 * 15,81 * 1/2

[maiden path]

the area of the triasnge is 1/2 base x height

your base is 5 and height is 15

[sudden willow]

My base is 10

Oop I didnt do height i see

[maiden path]

no the base for one triangle is 5

they are just side by side

[sudden willow]

It’s 114,27 m^2

10* 15 * 1/2

[maiden path]

the area for one triangle is 1/2 (5) (15)

no 10

[sudden willow]

I don’t understand?

It’s a * h * 1/2

A is 10…

10 is the diameter of this circle

[maiden path]

the height is 15

[sudden willow]

As well as the base of the triangle

[maiden path]

you have it marked in

[sudden willow]

The height is 15

[maiden path]

yes

the base is the bottom

[sudden willow]

The base is 10

[maiden path]

together it would be 10 but they are side by side

there are two bases together

and the triangles are equal to eachother

[sudden willow]

It’s the same answer

75 m^2

@maiden path

[maiden path]

you you said 114

[sudden willow]

Because

[maiden path]

that is right

[sudden willow]

75 m^2 + 39,27 m^2

39,27 m^2 is the area of the semicircle

[maiden path]

where are you getting 39.27 from?

no

the area do the semi circle is (1/2) pi (5)^2

[sudden willow]

pi * r^2 * (1/2)

[maiden path]

yes

[sudden willow]

It’s giving me 39,27 m^2

Pi * 5^2 + (1/2)

Mhm

@maiden path for 3. I got now 62,28 cm

[maiden path]

its (1/2) pi (5)^2

[sudden willow]

Mhm

I did that

39,27 m^2

[maiden path]

oh sorry

yess

[sudden willow]

The perimeter is 62,28 cm?

[maiden path]

we did that one already?

yes

[sudden willow]

You did tell me to correct it

Cus I did - instead of +

[maiden path]

...

yea

[sudden willow]

Ok ty

Cus this is graded

And I wanted to be sure

[maiden path]

mhm

[sudden willow]

And this was just stupid mistake to do

.- instead of +

[maiden path]

yea its ok we all do, i do

[sudden willow]

I did mistake like this before

And he didn’t give me correct for that even tho my formulas were ok

Ok ty

.flose

.close

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[upbeat vigil]

V, W, U are finite dimensional vector spaces, $f: V \to W, g: W \to U$, how can I prove $\operatorname{rg} f + \operatorname{rg} g \leq \operatorname{rg} (g \circ f) + \operatorname{dim} W$?

[potent lotus]

hanno

[calm coral]

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[upbeat vigil]

.reopen

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✅

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[calm coral]

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[honest kite]

Whats the relation between continuity and differentiability? Are all functions that are differentiable are continuous?

[gleaming shuttle]

All differentiable functions are continuous, yes

But not all continuous functions are differentiable

take these functions

[honest kite]

And another thing, if there is a vertical tangent line at any point, is it still differentiable?

[gleaming shuttle]

These are continuous, in the sense that there are no holes or asymptote, but they are both not universally differentiable

[gleaming shuttle]

No.

[honest kite]

Ookay, I think I got it

[honest kite]

but why does the sharp corner not let the function be differentiable?

If I apply the limit on that specific point would it not be possible to calculate?

[gleaming shuttle]

The limit would be different if you do it from the left vs if you do it on the right

that means the limit does not exist

[honest kite]

Makes sense, thankss!

.close

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[west ermine]

how would i put this problem in a matrix

[west ermine]

.close

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[spare void]

On what interval is the graph of f(x) increasing if f'(x) = -3x^3+21x^2-30x

[spare void]

So I worked out the math and got
(-inf,0) u (2,5)

And apparently

it's supposed to be inclusive

But I don't see why

if the graph of f(x) is changing directions at that point

Because it can't be increasing or decreasing

and it's not like it said find the limit from the right or left

[spark stratus]

inclusive is sometimes done if youre using a separate definition of increasing which means:
"a < b must mean that f(a) < f(b)"

[spare void]

Didn't mention anything about that though

[spark stratus]

thats the best I can say

otherwise it wouldnt be correct if using the derivative > 0 definition

[spare void]

Infact in a previous problem it said since a function can't technically be increasing at a point take an extremely tiny range from in front and behind

[spare void]

Oh ok