help-0

[hoary nimbus]

Nah

I had to do the inductive hypothesis and Pk —> Pk+1 bs

It’s aight i figured it out

[west rampart]

Just replace n by k and continue, it's the same

[hoary nimbus]

Yeah i just had to assume true for n=k
Then f(k+1)-f(k)=24p where p is an integer
Then f(k+1)=24(p+r)

And thus proved

.close

[lone heart]

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[thin zinc]

how can i solve this functional equation?

switching x and y doesnt seem helpful

[lone heart]

@thin zinc Has your question been resolved?

[thin zinc]

<@&286206848099549185>

[desert raptor]

f(1) = 0

why is the derivative given

[thin zinc]

how can you say that?

[desert raptor]

put x = y = 1

[thin zinc]

i have 0 idea

okay but still thats just f(1)

[bleak heath]

if a function's output is 0, doesnt always mean that its derivative is zero

[desert raptor]

i know

[thin zinc]

so how can i use the derivative?

differentiating this would be a pain i feel

[thin zinc]

i get the transformation

[bleak heath]

looking at this, it feels like a log function

[thin zinc]

im not sure if we can guess anything by looking at it

its not a general case i feel

[bleak heath]

put x=1

we'll get $f(y)=1/y^y\cdot f(y^y)$

[desert raptor]

try this

f(1) = 0 here

you may also try f(x) = log(x^x)

actually lemme do the 2nd one

check the derivatives at 1

[thin zinc]

how can you guess the function?

[desert raptor]

cause i can

[ocean seal]

Aria

[thin zinc]

now? differentiate it?

[bleak heath]

uhh no substitute $f(x)=a\cdot lnx$

[ocean seal]

Aria

[desert raptor]

this actually satisfies the derivative

might worjk

na it doesn't work

[thin zinc]

how do you get an idea of what to put?

and what do i do of f'(1) 😭

[bleak heath]

you have to look at the equation and think on what would a function be to produce this type of result

[thin zinc]

what type of a result are you talking about?

[desert raptor]

this type of result

[bleak heath]

i think f(x) would logx, that works

not sure

[thin zinc]

i feel its hinting towards differentiation yet not too sure

[desert raptor]

i've tried

didn't work

[true verge]

hi

[bleak heath]

f'(1)=1/x=1 and f(1)=lnx=0

[desert raptor]

you don't want to differentiate that

[desert raptor]

ok make it satisfy that functional relation

this one

you'd get 1/y log y - 1/x log x = (log y - log x) * x/y

adding constants won't help

[bleak heath]

if i put it in this, i think it works

we can write $x^x =e^{xlnx}$

[thin zinc]

are you talking about xlnx?

[bleak heath]

only lnx

[thin zinc]

okai

[desert raptor]

woah woah woah HOLD ON

[thin zinc]

use {}

[bleak heath]

ok thank you!!

[ocean seal]

Aria

[thin zinc]

yes

[bleak heath]

yup there we go

[desert raptor]

i dont see how that helps

[bleak heath]

this would make the equation: $lny-lnx= e^{xlnx-ylny}\cdot ln{e^{ylny-xlnx}$

[thin zinc]

you forgot a $

[ocean seal]

Aria
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[desert raptor]

,w d(lnx)/dx

[ocean seal]

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Requested by _nofluxgiven

[desert raptor]

am i dumb or is desmos fucking with me

desmos is fucking with me

[bleak heath]

why are you differentiating lnx rn

[thin zinc]

why is this problem such a mess 😭

im used to solving functional equations not by assuming but by transformations and rarely calculus

assumptions are when its general linear/ exponential/ log functions but i dont see that form here

[bleak heath]

simplifying this $ln(y/x)= e^{xlnx-ylny}\cdot (ylny-xlnx)$

[ocean seal]

Aria

[bleak heath]

it is lmao or maybe we are doing something wrong

[thin zinc]

probably

[bleak heath]

this will need assumptions that's fs

[thin zinc]

and whats worse is i feel more lost than anyone here 😭

[desert raptor]

not me trying to brute force

[thin zinc]

i cant do that cuz we are not allowed calculators for graphing and values

[bleak heath]

lmaoo

[thin zinc]

yea... 😞

[bleak heath]

is this a jee question by any chance??

[thin zinc]

not sure but i am preparing for advance

[desert raptor]

,w int (x^ln(x))

[bleak heath]

ahh now it makes sense lmao

[ocean seal]

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Requested by _nofluxgiven

[desert raptor]

i think it's this

[bleak heath]

tf

[desert raptor]

the function

not kidding

[thin zinc]

brother, im sure such stuff isnt a part of my syllabus

[bleak heath]

we have to calculate f((2025)^2) nah it cant be this

[thin zinc]

yeaa

[desert raptor]

notice

45^2 = 2025

do smth with that

like

put y = x^2

honestly

[bleak heath]

integration is a part of jee advance

[desert raptor]

i have no fucking idea

[bleak heath]

me neither lol

[thin zinc]

it is, but such functions cannot be integrated by basic ways, so its not a part of the syllabus

[bleak heath]

yeah this aint

[echo spire]

Hi

Soo

[desert raptor]

we're stuck

[bleak heath]

that's why we have to guess the form of the function

[desert raptor]

have fun with this problem

[bleak heath]

lol

[thin zinc]

💔

[echo spire]

On what are we stuck

[desert raptor]

uh the first step

[bleak heath]

uhhh everything

from the beginning

[echo spire]

Give me the exercise

Again xD

[thin zinc]

we're still at the start 😭

[thin zinc]

.

[desert raptor]

you know f(1) = 0

and that f'(1) = 1

find f(x^2)/f(x)

[thin zinc]

im sure this cannot be it cuz the answer is integer type.

[desert raptor]

YO WE DONT NEED TO FIND F(x)

[thin zinc]

????

[desert raptor]

WE NEED TO FIND THIS

[bleak heath]

oh also i noticed you two have similar usernames...like flux and the gauss's formula

[desert raptor]

aria i promise we're not alts

[thin zinc]

i dont know this person 😭

[bleak heath]

lmaoo yeah yeah its just a nice coincidence lol

[thin zinc]

okay ig this is the new goal. right?

[desert raptor]

yep

[bleak heath]

how will we do that...

[desert raptor]

yo

[thin zinc]

we still got x in exponent so idk how we get rid of that

[desert raptor]

check the answer key is it 2

[bleak heath]

where did george go??

[desert raptor]

@thin zinc

[thin zinc]

i dont have the answer key

[bleak heath]

OHH YEAHHH IT WOULD BE

[thin zinc]

it was sent to me

[desert raptor]

ok ask

ask the person who sent u

for the answer

[thin zinc]

w8

[desert raptor]

i have a very strong feeling it's 2

[thin zinc]

the person said its 2*2025=4050

💔

[thin zinc]

what did u do?

[bleak heath]

are they sure about that?

[thin zinc]

yes

[bleak heath]

well uh

we are doomed

[thin zinc]

certainly

[desert raptor]

it

is

if f(x^2)/f(x) = 2x

then f(x^2) = 2x f(x)

it's giving e

[thin zinc]

e?

[bleak heath]

yeah that doesnt make sense

lemme ask my friend, if she can help

[thin zinc]

probably

how did u get 2 tho?

[desert raptor]

f(x^2) = (f(x^2))'

find this function

let's reverse engineer and learn

[thin zinc]

e^x

[desert raptor]

nope

[thin zinc]

right?

[desert raptor]

e^x^2 =/= 2x e^x^2

[thin zinc]

function being same as its derivative is e^x

[desert raptor]

nuh uh

here u have

[thin zinc]

oh

crap

[desert raptor]

f(x^2)

not f(x)

[thin zinc]

yeah i got it

$f(x^2)=\frac{d}{dx}f(x^2)$

[ocean seal]

∮Ē.dĀ = Qₑₙ꜀/ε₀

[desert raptor]

,w f(x^2) = d/dx f(x^2)

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by _nofluxgiven

[desert raptor]

brat

[bleak heath]

,w d/dxf(x^2)

[desert raptor]

f(x) = e^√x

solved

[ocean seal]

Results provided by WolframAlpha

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Requested by ariaa_26

[desert raptor]

but nah

[thin zinc]

😭

[bleak heath]

it has to be a ln function of some type

[desert raptor]

,w d/dx (e^(x^1/2))

[ocean seal]

Results provided by WolframAlpha

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Requested by _nofluxgiven

[desert raptor]

nope, doesn't work

[thin zinc]

but how are so so sure about this? where did this come from?

[desert raptor]

our hypothesis is INCORRECT

and OVERRULED

[bleak heath]

only then can we get f(1)=0 and f'(1)=1

[desert raptor]

cause ur friend said that f(2025^2)/f(2025) = 2 * 2025

[thin zinc]

oh

[bleak heath]

i think that's incorrect

[thin zinc]

thats the given answer tho

[desert raptor]

ykw

[thin zinc]

4050

[desert raptor]

skip this problem move on the next one

!!

[bleak heath]

fr bro

[thin zinc]

😭

might need mental help after not being able to solve this

[desert raptor]

wdym

[thin zinc]

brain damage is real

[bleak heath]

it might be incorrect, books give wrong answers sometime

[desert raptor]

anyways i have a suggested integral

which u might want to try

OH FUCK NO WHY AM I ACTIVE AGAIN

FUCK THIS BLUE ROLE

[bleak heath]

lmaoo

[thin zinc]

xd

it better be in my syllabus

[desert raptor]

it's a very beautiful integral

[thin zinc]

yeah.... very

can the limit be taken inside?

idk when we can and when we can not

oh no nvm

i cant

[desert raptor]

actually nvm im not supposed to give you a problem

u go on with ur problems

[bleak heath]

log(a+x)-log(x)

...

[thin zinc]

no thats okay

but now im curious

i wanna solve this

[desert raptor]

it took me hours

[thin zinc]

but i have 0 idea where to start

[bleak heath]

can you dm me the question please??

[thin zinc]

okay nevermind i got an exam tomorrow 🙏

yes me too

i will try it later

[thin zinc]

@desert raptor can u dm me it pls

[desert raptor]

already did

[thin zinc]

oh got it

thanks

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[spark lodge]

Tg^2x+1 = 1/cos^2x?

[sly mantle]

yes

[spark lodge]

Ok ty

Thats all

[sly mantle]

np

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[lone heart]

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[pliant moon]

Is this the correct approach to the question:

For minimum cost I just let the edge be 1 and then did Kruskal's algorithm.

For maximum cost, when normally doing Kruskal's algorithm the greatest weighing edge is 9 so you can remove one of the 9 edges and let it be the question mark edge.

[vale wigeon]

hmm...

wait but you're not maximizing the cost at any point are you

or like

ok we are still looking for MSTs but you essentially got a maximin problem on your hands...

[pliant moon]

Its still an MST

just the minmum and maximum possible cost for the MST

[vale wigeon]

yeah

[pliant moon]

Which u obtain by setting ? to a value

[vale wigeon]

seems like quite the complicated decision problem

im not sure maxing out the ?-edge is gonna lead to the biggest mst

[pliant moon]

I think ur right cause now thinking about it again Im pretty sure u can make the ? edge a value greater than 9 and u still have to include it in the MST

[vale wigeon]

the greatest weight among all the other edges is 18

[pliant moon]

Doesnt the ?-edge have to be less than 9 actually

If u want it to be in the MST

[lone heart]

@pliant moon Has your question been resolved?

[lone heart]

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[coral steeple]

$\int \frac{t^2 \cdot e^t}{(t + 2)^2}$ dt

[ocean seal]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[coral steeple]

should we suppose: du = (t/(t+2))² ?

[slim kite]

i think taking v = 1/(t+2)² and taking du = t²e^x would be better

no, i mean the reverse

v = t² e^x and du = 1/(t+2)² dt

[coral steeple]

Can you tell me how you analyzed it to come to this conclusion?

[slim kite]

integrating this would be a pain in the ass

i would like to simplify the powers of both the numerator and the denominator

the denominator, integration does the job

and for the numerator, differentiation

integrating just 1/(t+2)² would be much easier than t²/(t+2)²

[slim kite]

hence, i selected that

and it appears that in the term $\int u\ dv$, (t+2) would cancel out (this ofc is found out after calculation)

[ocean seal]

Suika

[coral steeple]

I had a similar idea but didn't know how to decide what to choose as du

$[-\frac{t^2 \cdot e^t}{t + 2} + t \cdot e^t - e^t]$

[ocean seal]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[coral steeple]

That's the answer

[slim kite]

yes

[coral steeple]

||I don't want to see someone who reminds me of +C ||

[coral steeple]

Ok ty

[slim kite]

Oh, and also, u forgot the +c

[coral steeple]

It's acceptable from u

[slim kite]

ok lol

[coral steeple]

Ty

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[kind pivot]

Can someone explain how III works

[kind pivot]

wait nvm my dumb brain found out how it works

[lavish cave]

so the change in x for AB is 16 - 0 = 16
and the change in y for AB is 9 - 5 = 4

[kind pivot]

but wait i rmb the teacher asking us to not add up to get the cords

is it allowed because its parallel?

[kind pivot]

ya i realised

[lavish cave]

yes that's the really important part

[kind pivot]

so if its a regular quadrilateral cannot addup?

[lavish cave]

there'd be no way of knowing what C is, mhm

you'd instead have 2 + 8 cos theta and -3 + 2 sin theta, where theta is unknown

[kind pivot]

oh ok thnx

[lavish cave]

what I mean by that is that C could be any point on the circle with radius sqrt(8^2 + 2^2) and centre at point D

distance fixed but no direction

[kind pivot]

are there any other exceptions where you can like add stuff to find cords

[lavish cave]

adding stuff is like

[kind pivot]

like the thing done in this problem

[lavish cave]

well that's an application of (initial point) + (direction vector) = (final point)

[kind pivot]

ya that thing

when is it applicable

[lavish cave]

literally all the time in coord geo

the more you practice the more you'll see it applied

also it's more than coord geo, vector geo too

[kind pivot]

oh ok

tysm

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[lavish cave]

npnp!

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[woeful scroll]

why did they write $\sin(\pi x)$ as $e^{i\pi z}$ ?

[ocean seal]

jandro0103

jandro0103

[woeful scroll]

this is the graph

Hi

<@&268886789983436800>

[lone heart]

@woeful scroll Has your question been resolved?

[woeful scroll]

<@&286206848099549185>

[scarlet thunder]

:(.

[woeful scroll]

?

[scarlet thunder]

Doesn’t seem like they do? The integral which contains $e^{i\pi z}$ (i.e the integral around gamma) goes to 0 as R goes to infinity.

Leaving only the integral with the $e^{i \pi x}$ term, which they split up using the identity $e^{ikt} = cos(kt) + isin(kt)$.

Not sure if this answers your question, or if I’ve misunderstood it?

[ocean seal]

Spuerst

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[severe horizon]

hi

[coral steeple]

!original

[lone heart]

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

[severe horizon]

hi

[severe horizon]

yes

[coral steeple]

Hello

What's ur question?

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@severe horizon Has your question been resolved?

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@severe horizon Has your question been resolved?

[severe horizon]

no

[lone heart]

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[woeful cloak]

Can anyone help me with trigo?

[tulip bone]

yuh

wsp

[woeful cloak]

I need to find the mesures

I found CB but idk how to find AC and AD

[pine garnet]

Do you know how to find angle ABC?

By trigonometry

[woeful cloak]

No

Is it the sin cos tan formulas?

[pine garnet]

yes

[woeful cloak]

Idk how to use them

[patent vale]

is ACB a right triangle?

[pine garnet]

True

[woeful cloak]

Im not sure

[tulip bone]

wot

[patent vale]

I think it must be right angled or else the problem is not defined well enough

@woeful cloak are you still here

[pine garnet]

No it's fine

But you need cosine law

[tulip bone]

broda

😭

[pine garnet]

@woeful cloak

[tulip bone]

he dont even know sin cos tan

fuck cosine law

[pine garnet]

yeah

But that's literally the only way I can think of to solve this-

[patent vale]

sqrt(xy)=h

[patent vale]

have you heard gm

the geometric mean

assuming its a right angled triangle you can use this

[pine garnet]

Yes

I know

But we don't know if it's right-angled or not

Which is the problem

But if you use cosine law, it doesn't matter if it's right-angled or not?

[patent vale]

yeah but im 99% sure if its not right angled there are infinite triangles that fit the conditions

[pine garnet]

The other problem is that the guy does not know how to use trigonometry

[patent vale]

basically a bazillion triangles

[patent vale]

??

[woeful cloak]

Oops my bad

lets say its a right triangle

How do i find the angle of B?

I found CB : 13.42

Tan=6/12=0.5

Tan-1(0.5)=26.57?

[blissful spoke]

in triangle CDB tan<DCB=DB/CD=12/6=2

since ABC is a right triangle (<C = 90°) <BAC=90° - <ABC

in triangle CBD <DBC = 90° - <BCD

therefore, <BAC = 90° - (90° - <BCD) = 90° - 90° + <BCD = <BCD

therefore, tan<BAC=tan<BCD=2

in triangle ACD, tan<DAC=DC/AD

therefore, AD = DC / tan<DAC

AD = 6 / 2 = 3

from that, we get AB = AD + BD = 15

in triangle CDB you can use the Pythagoras theorem to find BC

and when you find BC, you can again apply the Pythagoras theorem in ABC to find AB

and this is how you can find all of the sides

[lone heart]

@woeful cloak Has your question been resolved?

[lone heart]

@woeful cloak Has your question been resolved?

[patent vale]

bro😭😭😭

[lone heart]

@woeful cloak Has your question been resolved?

[patent vale]

@woeful cloak

are you even olline

[lone heart]

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[gloomy vigil]

can anyone explain to me how to approach this problem?

i literally watched all the required lessons on KA, yet it does not explain how to solve this problem still

if anyone can help out, would be appreciated.

please advise,

thanks

[tacit arch]

,tex .shift trig

[ocean seal]

riemann

[tacit arch]

these can be derived using addition formulas for sin/cos/tan

[gloomy vigil]

@tacit arch dude are you on here 24/7?

[vale wigeon]

this + the tan one can also be derived from the cos ones

the ones for adding pi can be seen relatively directly by going halfway around the circle -- and i believe i recall giving you something like that from my own practice...\

[tacit arch]

yes the first thing i do when someone helps me is annoy them with something irrelevant

[gloomy vigil]

@patent vale ok thanks

@vale wigeon did you help me before? I don't recall

I only recognize riemann, cause this guy literally on here all day everyday

[void nymph]

as am i

as is ann

[hazy breach]

so im on acellus and how do i put the plus sign where it makes it correct

[void nymph]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hazy breach]

cause on the frist part i put +8 but is not letting me answer it

oh sorry

[buoyant saddle]

you have a strange way of thanking people bro

[gloomy vigil]

how tf is this the answer?

[gloomy vigil]

cause he's not actually helping...and he is also has a tendency to just abandon you for no apparent reason

he likes to pretend that he's helping

but anyway, i dont want to focus on this person

[patent vale]

a little incomprehensible but uhhhhhhhhhh

[gloomy vigil]

dude what am i even looking at?

[patent vale]

Essentially the period of tangent is pi so adding pi to your angle doesnt change the output

[vale wigeon]

bruh riemann actually gave you a thing that was 1cm away from solving the entire problem for you

this alone already answers why tan(pi + theta) = -9.9

@gloomy vigil

[gloomy vigil]

@vale wigeon i apologize if i was disrespectful to you before

[vale wigeon]

i do not recall you being disrespectful

it must have been more of an annoyance

[gloomy vigil]

ok i apologize if i was an annoyance to you before

[lone heart]

@gloomy vigil Has your question been resolved?

[gloomy vigil]

negative

[lone heart]

@gloomy vigil Has your question been resolved?

[flat barn]

@gloomy vigil hi

[gloomy vigil]

sup

[flat barn]

Whats the problem?

[gloomy vigil]

trying to figure out how to approach this problem #help-0 message

[flat barn]

You mean solve ?

[gloomy vigil]

basically

i already know the answr but unsure how it got to there

[flat barn]

Ok

I think i got this

[gloomy vigil]

cool

[flat barn]

The key idea is that the tangent function is periodic with a period of pi.

Ok so far?

@gloomy vigil

It means that:

tan(theta + pi) = tan(theta)

tan(theta + 2pi) = tan(theta)

Hello???????

[gloomy vigil]

im here

[flat barn]

?

[gloomy vigil]

ok

[flat barn]

Yes?

In the problem, we are told that tan(theta) = -9.9. So, using the property above:

tan(pi + theta) = -9.9

tan(2pi + theta) = -9.9

Both values are the same as tan(theta) because of the periodic nature of the tangent function.

That was all....

[gloomy vigil]

ok got it...thanks

[lone heart]

@gloomy vigil Has your question been resolved?

[lone heart]

@gloomy vigil Has your question been resolved?

[lone heart]

@gloomy vigil Has your question been resolved?

[tacit arch]

.close

[lone heart]

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[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[torpid tinsel]

where did the numbers circled in red come from

[torpid tinsel]

like why did -square root 8 turn into 0

and where is the 2 from

[austere granite]

the 2 comes from the fact that its symmetric so instead of evaluating

[vale wigeon]

even function integral symmetry

specifically

[austere granite]

-sqrt8 to sqrt 8 you can just evaluate 0 to sqrt 8 and multiply by 2

[torpid tinsel]

i’ve never heard of that

[vale wigeon]

for an even function $g(x)$ integrated over an interval of the form $[-a,a]$ you always have $$\int_{-a}^a g(x)\dd{x} = 2 \int_{0}^a g(x)\dd{x}$$

[ocean seal]

Ann

[vale wigeon]

it needs to be an even function for this trick to work

[torpid tinsel]

is it ok to just leave it like this and solve

[austere granite]

depends on ur prof loll

[vale wigeon]

it is, but it is gonna be fairly laborious.

[torpid tinsel]

oh ok i haven’t been taught that even symmetry rule

how do you use it

[austere granite]

bro tbh i think they just gloss over it

in calc b

this is calc b right

[torpid tinsel]

i’m in ap calc ab

[shell agate]

Even function is symmetric about y axis

[shell agate]

So basically the area to the left of y axis will be equal to area to right of y axis

So take area of left and multiply by 2

[austere granite]

damn

[shell agate]

Did u understand that

[austere granite]

yoo cr lol

[shell agate]

What yes

[torpid tinsel]

yes so you use this rule whenever the graph is symmetrical to the axis?

[shell agate]

If it's an even function

And even functions are symmetric about y axis

Do you know what an even function is?

[torpid tinsel]

yea

like even powers?

[shell agate]

Uh

No

[torpid tinsel]

oh

[shell agate]

f(-x)=f(x)

[austere granite]

i think it means it has to be the same at x and -x

yeah

[shell agate]

Just put -x and see if you get the same

[austere granite]

thats a neat way to put it lol

[shell agate]

Like y=|x| is an even function

[torpid tinsel]

i vaguely remember this…

[shell agate]

Because y=|-x| will give us same as y=|x|

That's it

It's a property of definite integrals

[torpid tinsel]

sooo x and -x give the same output

[shell agate]

yes

[torpid tinsel]

that’s what makes it an even function

[shell agate]

Another example is y=x^2

[austere granite]

is it not useless to mentally rotate graphs and compute the integrals that way?

[torpid tinsel]

ok i think i understand more now

[austere granite]

i always thought it was stupid they made us do this in calc b

cuz in calc c you can do the exact same thing way easier in a 3d space

[torpid tinsel]

thank you so much both of you

.close

[lone heart]

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Use .reopen if this was a mistake.

[torpid tinsel]

.reopen

[lone heart]

✅

[shell agate]

What?

[torpid tinsel]

i need help with another question

why is it bottom - top in this integral?

shouldn’t it be the other way around

i’m talking about the last step

someone please help it’s 4 am and i have a test tmrw 😓

nvm

.close

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[strong lintel]

Good morning, can i have someone verify my graph

[strong lintel]

My inflection point is dne so im a bit confused what it does

<@&286206848099549185> anybody here this morning?

[shell agate]

What even is the question

[strong lintel]

if i drew the graph correctly

[shell agate]

For what equation

You can always check using desmos

[strong lintel]

oki let me go look with desmos too

humm

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[dusky pasture]

Guys please

Its the exam from the other class

I need a better grade

Bless me and my friend pls

[devout ermine]

this is beyond my scope unfortunately

[dusky pasture]

How

[void nymph]

i cant read french handwriting

which part

can you type it out

[dusky pasture]

You dont need to read the question

I can translate

[glacial patrol]

This is somehow both very neat handwriting and very messy handwriting

[void nymph]

i can understand french xD

thats not the issue

[dusky pasture]

1. Calculate the next limites:

[void nymph]

which part

also can i PLEASE get a top down screenshot

[dusky pasture]

2. Be f(x)
   Study the devaribilite of f in 1 and interpret

[strong lintel]

J’aime le mix de lettre moulé et attaché lol

[dusky pasture]

Bro i paid a guy from another school to send me this

I can

[void nymph]

dommage

alright

so do you wanna start with the limits

[strong lintel]

Essaies tu de dérivés fx/gx

[dusky pasture]

Calculate f'(x) in each case

[wheat isle]

||i think helping someone with their exam is against the helper law ||

[shell agate]

Merb speaks french

[shell agate]

It's not their exam

Read carefully

[void nymph]

is this exam

[dusky pasture]

Ex4: 5: draw the table of variation of f

[strong lintel]

Ya but im still new to calc 1 lol

[shell agate]

rip

[wheat isle]

he just said he paid someone to get this exam paper and needs a better grade Lol

[dusky pasture]

Bro..

[strong lintel]

And that is barely legible

[shell agate]

Uh doesn't that mean like

His exam is like in a few days

[dusky pasture]

Yes

[shell agate]

That's what

[dusky pasture]

But in a few hours

Its 1 pm and the exam is in 4 30 pm

[strong lintel]

The 3x+wtv/wtv+2. You need to find top and bottom derivative then you need to do the derivative of fx/gx

Which is

The f(x)/g(x) one

[shell agate]

So which question are you asking about

[shell agate]

Which question

[dusky pasture]

All

[strong lintel]

Hes asking help for all of it i think

[shell agate]

..

[strong lintel]

Lol

As tu étés a ton cours lol

[shell agate]

Yea I cannot see and understand

Merb got french keyboard nice

bonjour

[strong lintel]

Canada type shit

I do math in english and french in my brain its funny

Well bro try the one that i helped you with

Do the top and then the bottom and then the derivative i sent

[void nymph]

imagine being quebecois

[shell agate]

If you can type all the questions maybe we can

[strong lintel]

Best of both worlds frl

Hannah montana type shit

[lone heart]

@dusky pasture Has your question been resolved?

[lone heart]

@dusky pasture Has your question been resolved?

[grave matrix]

@dusky pasture c'est quoi exactement ta question / what exactly is your question

tsais évaluer les limites ?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[tawdry urchin]

Let $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_n,b_n)$ be the ordered pairs $(a,b)$ of real numbers such that the polynomial
[p(x) = (x^2 + ax + b)^2 +a(x^2 + ax + b) - b]has exactly one distinct real root and no nonreal complex roots. Find $a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.$

[ocean seal]

Dork9399

[tawdry urchin]

so assuming f(x) = x^2 + ax - b, g(x) = x^2 + ax + b

p(x) = f(g(x))

idk what to do from here 😭

<@&286206848099549185>

[void nymph]

what does 'one distinct no non-real complex' imply?

[tawdry urchin]

there is exactly one real root?

implying that all 4 roots coincide

@void nymph

[void nymph]

that doesn't make them distinct though

[tawdry urchin]

how else would this make sense though

[void nymph]

which order polynomial has only one distinct real and no nonreal complex roots?

[tawdry urchin]

linear

but thats impossible

[void nymph]

should be possible

[tawdry urchin]

but the x^4 term has no coefficient

the polynomial has to be fourth degree

[void nymph]

Hmmmmmmm

ugh is this question even valid

[tawdry urchin]

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[marble portal]

can someone walk me throigh the steps of what i need to do here 🥲 i dont know what im supposed to be doing here

[naive valley]

it's asking if there is a solution to Ax=b

[glacial patrol]

You could do row reduction

[marble portal]

So does it just want me to put it into rref form and see from there

[glacial patrol]

Yeee

[pallid scarab]

Column reduction seems more appropriate? The rref form, while having the same rank, won't span the same column space

[marble portal]

Column reduction?

[pallid scarab]

It's like row reduction

But you do stuff on the columns instead

[marble portal]

Ohh

[pallid scarab]

Like, an easy example

Take matrix $\begin{pmatrix}1&0\1&0\end{pmatrix}$

[ocean seal]

rafilou is not not born in 2003

[pallid scarab]

Its RREF form is $\begin{pmatrix}1&0\0&0\end{pmatrix}$

[ocean seal]

rafilou is not not born in 2003

[pallid scarab]

Yet this one has in its column space (1 1)

[pallid scarab]

Which is not found here

[marble portal]

Okay i think im getting this 🥲🥲

Thank you :p!!

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[shrewd saffron]

Can someone explain to me how they’re combing the terms?

[shrewd saffron]

I see it says distribute and collect terms by degree

[vale wigeon]

and indeed that is all that's done.

[shrewd saffron]

But like I still don’t really get it

[naive valley]

try doing it one degree at a time

[vale wigeon]

ok like

^

and also imagine the ... were not there

[shrewd saffron]

So like if I want degree of 2 I just multiply the terms from each series that get me x^2?

[vale wigeon]

....yes

[shrewd saffron]

Wow I tried lookin at another example and I’m even more confused now ngl

Hold on

[shrewd saffron]

Ok yeah I get it now this visualization made it clear

Thanks

.close

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[fossil sundial]

I'm confused in how to do the question. I started off using formula for geometric series

The sum

Then I got Sn = (1+x)^n -1 / x

[vale wigeon]

parentheses

or better, LaTeX

anyway

[fossil sundial]

Yeah Idk how to use them so I'll take a picture of my page

[vale wigeon]

$S_{25} = \frac{(1+x)^{25} - 1}{x}$ yes?

[ocean seal]

Ann

[vale wigeon]

the coefficient of $x^2$ in $S_{25}$ is equal to the coefficient of $x^3$ in $(1+x)^{25} - 1$.

[ocean seal]

Ann

[fossil sundial]

I got that without the 25 in it?

[vale wigeon]

you got it in terms of n

i put n=25 for you

[fossil sundial]

How do u learn latex

[fossil sundial]

Oh, thanks

[vale wigeon]

#latex-help has a cheat sheet for basic stuff

i learned it way back

[fossil sundial]

Oh god, a bad picture

[vale wigeon]

,rccw

[vale wigeon]

but ok, yes, this is correct

point uno:

you got it in terms of n
i put n=25 for you

[fossil sundial]

I know now I gotta simplify the (1+x)^n

[vale wigeon]

point dos:

the coefficient of $x^2$ in $S_{25}$ is equal to the coefficient of $x^3$ in $(1+x)^{25} - 1$.

[ocean seal]

Ann

[fossil sundial]

Where's the 25 even from

Oh it's a numerical example

[fossil sundial]

I don't understand that part

[vale wigeon]

$(1+x)^{25} - 1 = S_{25} \cdot x$

[ocean seal]

Ann

[vale wigeon]

do you agree or disagree

[fossil sundial]

I presume the dot is multiply?

And s25 is sum of 25 terms

[fossil sundial]

I don't have a clue

Is there background on why that is

[vale wigeon]

yes of course it is

[vale wigeon]

yes there is, it's called basic properties of division or something

you are overthinking it severely

[fossil sundial]

😭😭

[vale wigeon]

$\frac{a}{b} = c \implies a = c \cdot b$

[ocean seal]

Ann

[vale wigeon]

it is literally just this

[fossil sundial]

Oh, I understand that

[vale wigeon]

but with more complicated shit in lieu of a, b and c

$S_{25} = \frac{(1+x)^{25} - 1}{x}$

[ocean seal]

Ann

[vale wigeon]

you understand this, yes?

[fossil sundial]

Can I see how the denominator cancels out to get x?

[vale wigeon]

1 + x - 1 = x

the 1 and -1 cancel out...

[vale wigeon]

you even had it here

[fossil sundial]

Omg💀

I'm actually stupid

I just didn't read the brackets

[fossil sundial]

Oh yeah

Alright, now we should be ready

[fossil sundial]

Yeah I understand that

[vale wigeon]

$(1+x)^{25} - 1 = S_{25} \cdot x$

[ocean seal]

Ann

[vale wigeon]

do you understand this

now that i have primed you for it and dragged the concept of division back to the front of your memory

[fossil sundial]

Yeah

I just didn't realise you used the s25 equation and thought you used 2 separate things

[vale wigeon]

ok right

now

[fossil sundial]

I get this now

[vale wigeon]

multiplying S_25 by x means taking each term in the fully-expanded form of S_25 and raising its degree by 1

[fossil sundial]

Why are we using 25 first? Isn't there parts before it

[vale wigeon]

oh, i guess i thought you were already past showing that the coefficient of x^2 in S_n equals that sum of binomial coeffs

that one is not hard either tho

[fossil sundial]

That's a relief

[fossil sundial]

I got up to this part with an n instead of the 25 for part 1

[vale wigeon]

ok right so

the thing is actually

you only needed the geometric series sum formula for the second half of the question

which ig is what threw me off

anyway

here's something you'll need to recall for both parts of the question anyway: the binomial theorem.

do you know what that is?

[fossil sundial]

Yeah

[vale wigeon]

ok

so then, you understand that each bracket of the form $(1+x)^k$ (for $k$ going from $2$ to $n-1$ inclusive) contributes the term $\binom{k}{2}x^2$ to the sum (if we are looking at exclusively the $x^2$ terms, that is)

[ocean seal]

Ann

[vale wigeon]

yes?

[fossil sundial]

No

That's the formula sheet they give

The only uses of binomial I had prior to this question was expanding terms like (1+x)^5 etc

[vale wigeon]

ok do you at least understand sigma notation

[vale wigeon]

ok so you have that same thing here but many of it.\

im saying that if you look at $(1+x)^2$ and its $x^2$ term you will find it's $\binom{2}{2}x^2$

and if you look at $(1+x)^3$ and \textit{its} $x^2$ term you will find $\binom{3}{2}x^2$

and if you look at $(1+x)^4$ and \textit{its} $x^2$ term you will find $\binom{4}{2}x^2$

and so on and so forth

[fossil sundial]

Kind of, I know it means the sum of

[ocean seal]

Ann

[vale wigeon]

do you understand it when it is phrased this way

[fossil sundial]

Yeah, I understand that way of phrasing

[vale wigeon]

ok

i am just saying this for all of these brackets being added up all at once

[fossil sundial]

Oh so is the entire term (1+x)^n-1?

[vale wigeon]

each $(1+x)^k$ yields $\binom{k}{2}x^2$ (where $k$ ranges from 2 to $n-1$)

[ocean seal]

Ann

[fossil sundial]

Why are we using k then

[vale wigeon]

no, (1+x)^(n-1) is just the last one in the sum

[vale wigeon]

because i want to talk about all the brackets at once and not only the last one

[fossil sundial]

Oh

[fossil sundial]

I understand this part now to get the x² term

[vale wigeon]

so the point now

is that when you collect all of those x^2 terms you get from each bracket

you add up the coefficients

and that is why the coefficient of x^2 in the entire S_n is given by that summation printed in the question

which ig means i did this specific part of the question for you kinda but there was also no way i could have conveyed it without

[fossil sundial]

Oh wow, that solution is elegant

Do I manually add them all up now?

[vale wigeon]

idk how much can be said about it being "manual"

[fossil sundial]

The x² terms

[vale wigeon]

when you collect all of those x^2 terms you get from each bracket
you add up the coefficients

this is basically already it

[fossil sundial]

And by adding them up, I'll get the summation that it wants?

[vale wigeon]

yes

[fossil sundial]

Thank you! That part should be fine now

Now for part 2....

[fossil sundial]

So the s25 part can I just use this

And then I can use the x² summation part 1 and shove in 25

[vale wigeon]

mmm

well yes and no

• multiplying S_25 by x means taking each term in the fully-expanded form of S_25 and raising its degree by 1
• therefore the coefficient of x^2 in S_25 is the same as that of x^3 in xS_25
• but since xS_25 = (1+x)^25 - 1, its x^3 coefficient can be computed on its own merits

[lone heart]

@fossil sundial Has your question been resolved?

[fossil sundial]

I'm back*

Part 1 got defeated! Idk how I found it difficult now😭

[fossil sundial]

Is the 4 choose 2 just from another part they added

(1+x)^4

I'm stuck on part 2 now

[vale wigeon]

mmm

ive already said everything i could say about this

and i do not know of any other reformulation

[fossil sundial]

I just need to know as well, is x³ relevant for this question

[vale wigeon]

i...

well, yes, it is

[fossil sundial]

I came up with a tactic

I manually added up all of the terms and got 2288

And I let that equal to p choose q

So I could say p is 2288 and q is 1?

Oh, it gets me 2300

And then I can say 2300 is the same as 2300 choose 1

p is 2300 and q is 1?

I'm sure that method isn't allowed

[fossil sundial]

I googled something and hockey stick identity comes up. Is that good?

[vale wigeon]

identity*

... and i guess?

[fossil sundial]

Yeah

Identity

[vale wigeon]

no actually i am completely stumped as to what i could say, like anything i could say now would just make your confusion worse without recovery

[fossil sundial]

Is this method different to yours

[vale wigeon]

... that is gpt

[fossil sundial]

Oh💀

[lone heart]

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).

[fossil sundial]

Oh

[vale wigeon]

but also i am out

[fossil sundial]

I think we're almost there

.close

[lone heart]

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[lone heart]

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[wraith marlin]

would anyone be free to hop on a call to help me with calc 2?

[solemn juniper]

https://tenor.com/view/we-dont-do-that-here-black-panther-tchalla-bruce-gif-16558003

[patent vale]

snakes and ladders bro good luck

[north rover]

Post your questions here instead! We’ll love to help.

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[tawdry gate]

Substitution method pls

[naive valley]

"we find and equal to" ??
what is the problem asking for?

oh probably "find y" not "find and"

[lone heart]

@tawdry gate Has your question been resolved?

[north rover]

Have you tried using Gaussian Elimination? Also, if you’re more comfortable with Spanish, that’s fine.

Oh, subsitution.

Hmm.

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[lofty ibex]

Um I know the double angle identity but I do not know how to actually apply it beside plugging stuff in

[lofty ibex]

actually i dont know what identity to apply here

[tacit arch]

$\tan^2 + 1 = \sec^2$

[ocean seal]

riemann

[tacit arch]

then uhhhh

,tex .quadratic formula

[ocean seal]

riemann

[lofty ibex]

set the equation to equal zero first?

[tacit arch]

yea try it

[lofty ibex]

okay, i used variable substitution and then factored with the quadratic formula, got pi/3 and 5pi/3

check answers real quick

okay right, thank you

[lofty ibex]

so is this another form of pythagorean identity?

[tawdry gate]

Yes

[tacit arch]

$\sin^2 + \cos^2 = 1$ and divide both sides by $\cos^2$

yes

[ocean seal]

riemann

[daring lotus]

can someone explain how he got the ( x^2 + 4 )^2 at the second part

[patent vale]

good question i also cant see where that is on the page also this is someone elses channel

[daring lotus]

Oh sorry

[lofty ibex]

aaaaah i see, ok thanks alot

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[tacit jewel]

hi

[tacit jewel]

can anyone explain if this can be intuitive / how i should think about this:

[tacit arch]

might be easier to think of the permutation formula first

[tacit jewel]

my book says "is read “n choose r” and represents the number of subsets of size r that can be chosen
from a set with n elements."

do you recommend the wiki page

[tacit arch]

yea just read as much as you need

[tacit jewel]

ok

.close

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[coarse elm]

Gr 12 calc

So I know a) i got right

for b) the time when its 50% decayed is at 0.14

so to plug that into the derivative i get -248

the answerkey is -2.5

so thats why im a little confused

[oak chasm]

What did you get for a?

[coarse elm]

-500e^-5t

same as the answerkey

[oak chasm]

OK, so at which t do we have 50% of the original sample left?

[coarse elm]

Ok so I plugged P as 50 for the original equation

50 = 100e^-5t

and t = 0.14

then i plug t as 0.14 for the 1st derivative

(i think lol idk why my answer is different)

[oak chasm]

,calc log(2)/5

[ocean seal]

Result:

0.13862943611199

[oak chasm]

OK, so let's just leave it as log(2)/5.

[coarse elm]

oh😭

okok

[oak chasm]

[P'(t) = -500 e^{-5\qty(\frac{\log(2)}5)}]

[ocean seal]

Chai T. Rex