help-0

[nocturne dove]

arcsin(fx)

If fx is between -1 to 1

[north adder]

but x gives us the domain

[nocturne dove]

For all x belongs R

[north adder]

OH

ok

[nocturne dove]

I'm sorry if I wasn't able to convey it properly, but I'm trying xd

[north adder]

okay to summerise what youre saying is they should show the fraction in case of abs(x)

nono I really appreciate your effort

[nocturne dove]

Oh ok

I get it now

@north adder

[north adder]

also also sorry to go back on this but how is this relevant

[nocturne dove]

They have written |x|≤1 because the function is not bijective otherwise

[north adder]

why is it required to be bijective at this stage

[nocturne dove]

I think if you apply the formula of arctana - arctanb it should all cancel out nicely

[nocturne dove]

Again arcsinfx is only defined when sinfx is bijective

[north adder]

okay yea

it

makes sense by a thin line

im surprised you sitll remember all of this stuff

even though its been a year

[nocturne dove]

Hehe I'm preparing for jee

That's why I remember all this

[north adder]

I feel like the 2x/(1+x^2)

luckily coincides with the -1 to 1

it wouldnt apply if for example it was 3x

[nocturne dove]

Yep bijective in -1 to 1

No it wouldn't

[north adder]

ahh good luck with that 😬

[nocturne dove]

Thanks man.

What grade u in btw?

[north adder]

finished 12th

but didnt do cbse

and have to do cbse for cuet

[nocturne dove]

Ohh

Good luck with that

[north adder]

oh also

another thing i noticed while learning these ridiculous formulas was

the tan ntheta formula

is like the binomial theorem?

[nocturne dove]

Yess

[north adder]

ohhh thats cool :')

[nocturne dove]

Its

[north adder]

how long have you been preparing for jee btw?

[nocturne dove]

(1 at a time - 3 at a time and so on)/ (1-sum of 2 at a time+(4 at a time)-....)

[nocturne dove]

Just this year

[north adder]

did you take a gap year or do uni with it

[north adder]

yeahhhh, but do you know the proof for it?

[nocturne dove]

Gap uesr

Year*

[north adder]

interesting

youre smart tho, I think it will work out to your favour

[nocturne dove]

I suppose you can, tan(@+(n-1)@) then expand

Unsure about it tho

[nocturne dove]

Hehe wish I was but thanks for the kind words

[north adder]

yea i'll try that out later

either ways, staying on task, so for this question you said tan^-1 x - tan^-1 y?

but wouldnt that only work if denom was like 1 + xy

[nocturne dove]

I was talking about considering x/y as a and (x-y)/(x+y) as b

[north adder]

how do you think of this stuff.

alright will do that

[nocturne dove]

Hardwired in my brain practised a lot of trigno

[north adder]

initially i tried tan addition formula

lol its the same thing

okay im breaking

thanks Teek

appreciate it

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[low drift]

How do I do fixed point iteration on a TI-84 calculator?

[north adder]

you mean a stationary point?

pretty sure you cant

[low drift]

Like x=f(x) into a TI84 and just spamming = sign is what I was told

Apparently you can, I just don't know how

And then it should converge

[north adder]

what

wait

are you talking about stationary points?

[low drift]

I think so?

I havent heard that term used before but probably

[north adder]

nvm im dumb you can do 2nd trace max or min right?

if you want a stationary point

[low drift]

No idea

Not very adept with teh ti84

[north adder]

lol nvm I think youre talking about advanced math

[low drift]

0.2-((2x^2+.0562x)/(x^2+.0562x+.00305)*.1)

That's f(x)

Solving for x by the fixed point iteration but idk how to do it on the ti84

I know you can solve with the graphs or wolfram alpha, etc, but I'm trying to use fixed point iteration

[north adder]

sorry, yea idk how to do that on the ti84

[low drift]

All good I can wait if anybody happens to know

[lone heart]

@low drift Has your question been resolved?

[lone heart]

@low drift Has your question been resolved?

[simple turtle]

This is for 83, but it is about the same. I hope it helps. https://www.math.colostate.edu/~spriggs/M155/calculator.html

[low drift]

wait it's that simple???

lol

[low drift]

tysm!

[lone heart]

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[lone heart]

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[cunning trout]

So where am I wrong here?

[gray isle]

they want the equation of the normal

(not tangent)

[cunning trout]

Ok I see

What did I do now?

[gray isle]

-1/e^3 isn't equal to e^-3

[cunning trout]

But isn’t it negative reciprocal of gradient?

Which would result in a positive sign

And then a negative power

[gray isle]

the values themselves weren't equal which is one issue
so you should be writing any equations saying that

and they're not negative reciprocals of each other which is another

[cunning trout]

Then what would the gradient be?

[gray isle]

take the negative reciprocal properly

[cunning trout]

Ok

[gray isle]

it looks like you did the negative power stuff in addition to taking the reciprocal

which just undoes what you did

[cunning trout]

I see

[gray isle]

so overall you just did the negative here

[cunning trout]

So would m=e^3 ?

[gray isle]

where m represents the gradient of your normal line, yes

[cunning trout]

Ok

And are my points correct?

[gray isle]

you should write something like
$$m_{norm}$$
to be clear in your work

[ocean seal]

ℝamonov

[cunning trout]

Mm ok sure

[gray isle]

your point is correct

[cunning trout]

Ok

Can you tell me where I went wrong

8. the ans says something else

Ramonov?

[pliant wave]

textbook is wrong

ignore the weird slant, i have weird axis numbers

[cunning trout]

Ok right I see

Thanks

.close

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[tidal zealot]

may someone identify what i did wrong

bcs the answers are suspoed to be 63 and 39

<@&286206848099549185>

[wide raven]

a negative sign missing

[nimble fern]

Does the question mean this?

[gray isle]

they too the negs of everything before applying qf

the values seem alright

,w solve 35=22tcos(x) and 8 = -4.9t^2 + 22t*sin(x) + 2 and 0<x<pi/2

[ocean seal]

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Requested by ramonov#0921

[gray isle]

,calc 0.609918 * 180 / pi

[ocean seal]

Result:

34.94572724906

[gray isle]

,calc 1.13066 * 180 / pi

[ocean seal]

Result:

64.782046064262

[nimble fern]

Then maybe I was right

[wide raven]

wait what's happening?

ohh damm i thought you were asking a question

i'm sorry😅

[nimble fern]

Since Ramonov confirmed about the numbers,
@tidal zealot
must have misunderstand the question about "35 m from where the ball was thrown"

[gray isle]

the wording is open to interpretation

[tidal zealot]

hmm

wait so

am i wrong

[nimble fern]

The words are unclear, but if the answer need to be 63°, 39°, then yea, you're wrong.

[tidal zealot]

so wht did i do wrong

in my equation

[nimble fern]

This

35 is not the horizontal distance

[tidal zealot]

hmm

so would i have to use pytag to get the horizontal

wait

then

what is 22

oh shit

wait

22 is the speed

not veloctiy

[nimble fern]

22 is the speed, that part you're correct imo

[tidal zealot]

how would i get the velocity

[nimble fern]

You did used sine and cosine to get the horizontal and vertical speed using 22

So, for those two equations that you've constructed, the only part that is wrong is the 35.

[tidal zealot]

hm

im confused

wht do i put instead of 35 then

[nimble fern]

Which you did correct

Replace the 35 with
sqrt( 35²-6² )

[tidal zealot]

im not getting the right answer still @nimble fern

far outt

idk what im doing wrong

[lone heart]

@tidal zealot Has your question been resolved?

[tidal zealot]

wht do i do

would you asssume that these two questions are somewhat similar? <@&286206848099549185>

[north adder]

yes, but dont instaping

.close

[lone heart]

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[tidal zealot]

i had this opennd for ages @north adder

but anyways

[lone heart]

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[digital spoke]

Can anyone give me a hint on why the last equation is true?

[lone heart]

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[remote kettle]

If |sinx + cosx| = |sinx| + |cosx|, where sin x /= 0, cosx /= 0, then in which quadrant does x lie ?

[remote heron]

in general where does |x+y| = |x| + |y|?

[remote kettle]

idk

sed

[remote heron]

you can split this out into every possible case and even then its only what like 9?

x can be negative, 0, or positive

same with y

your problem removes 0

so you only need to check positive and negative

thats 4 cases

[remote kettle]

hmm

ye

[remote heron]

you should check where |x+y|=|x|+|y|

do the 4 cases

[remote kettle]

how to do ?

the 4 cases

[remote kettle]

how did u get thid

this*

[remote heron]

cogwheels is around

why even try

[remote kettle]

im doing inequalities and got this question

so i don't even completely understand what you r trying to say

sed

[oak perch]

I just thought maybe he can draw some diagrams😂

[remote heron]

idk if drawing diagrams like

[oak perch]

Thought he knew what |x|+|y|=k looks like

[remote kettle]

sed

idk

[remote heron]

think about it like this

[remote kettle]

yes ?

[remote heron]

|x+y| where both are negative

so just rename them if u need to

say theyre -a and -b

[remote kettle]

the absolute val will be (+)

[remote heron]

where a and b are positive numbers

so we have |(-a)+(-b)|

[remote kettle]

ye

[remote heron]

|(-1)(a+b)|

|(-1)||(a+b)|

|(a+b)|

[remote kettle]

oh

[remote heron]

they are strictly positive

so (a+b)

[remote kettle]

is it modulus

[remote heron]

it is not modulus

[remote kettle]

?

then ?

what is | |

[remote heron]

[remote kettle]

they mean the absolute values

ryt ?

[remote heron]

yea

[remote kettle]

like

[remote heron]

its just distance right

[remote kettle]

|-x| = x

[remote heron]

distance from zero

[remote kettle]

oh

OHHHH

[remote heron]

if you drive a mile from your house

it doesnt matter if you go east

or west

or north

[remote kettle]

like magnitude ?

[remote heron]

youre still a mile from your house

[remote kettle]

kinda

[remote heron]

yea

same idea

[remote kettle]

ok got it

so

[remote heron]

thats why |-x|=|x|

[remote kettle]

sinx + cosx is strictly positive

[remote heron]

dont even worry about sin and cos

solve the x+y problem first

[remote kettle]

oh

[remote heron]

heres what i would suggest

pick one of the four cases

[remote kettle]

we have to do every possibility ?

[remote heron]

then like i just did, represent x and y in terms of some strictly positive variable

[remote kettle]

hmm

then

[remote heron]

then see if you can make the equation true

[remote kettle]

hmm

ok

so

[remote heron]

try the positive positive case

is is true then?

[remote kettle]

i shud pick every possibility for both the sides

[remote kettle]

ok

wait a sec

[remote heron]

you are just trying 4 possibilities

theyre both positive, both negative

you could even reduce it to three

both positive, both negative, or one of each

[remote kettle]

i think both positive case satisfies the equations

equation*

oh

i got it

[remote heron]

how about negative negative

[remote kettle]

it also satisfies

ig

[remote heron]

positive negative?

[remote kettle]

no

[remote heron]

its that lefthand side, right

[remote kettle]

ye

[remote heron]

because |x+y| = |-(x+y)|

[remote kettle]

ye

[remote heron]

but theres no fixing |x-y|=|y-x|

so ye

you have solved the easier problem

[remote kettle]

Oh

[remote heron]

|x+y|=|x|+|y| is true where ....

how can you translate this back into cos and sin?

[remote kettle]

so in this case no need to worry about sinx and cosx

nvm

sed

[remote heron]

there is a need, since the problem is asking

but

its a harder problem

you said its true where both are negative

or both are positive

[remote kettle]

ye

[remote heron]

so theres your answer

but where is it satisfied with sin and cos

,w plot cosx and sinx

[ocean seal]

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Requested by jan Niku#2119

[remote heron]

or you could maybe use a unit circle

[remote kettle]

unit circle ?

[remote heron]

dwai

[remote kettle]

dwai ?

[remote heron]

dont worry about it

[remote kettle]

oh

[remote heron]

just use whatever method is comfortable for figuring it out

you are on the final step of the problem

[remote kettle]

how to figure it out ?

[remote heron]

👀

[remote kettle]

i don't know to

find

the value of

sinx

where x is an integer

sed

[remote heron]

can you restate like

okay whats the problem now, whats the next step?

what are you trying to do at this point

[remote kettle]

hmm

trying to balance the equation ?

smthing lik that

[remote heron]

what was the solution to where |x+y|=|x|+|y|?

what conditions did we need for x and y?

[remote kettle]

+,+

-,-

[remote heron]

yea

[remote kettle]

so for sin and cos how does it differ ?

[remote heron]

so what conditions are on |sinx+cosx|=|sinx|+|cosx|

what makes you think it will differ?

[remote kettle]

sinx is not equal to 0

neither is cosx

[remote kettle]

hmm

thinking

the value

ig

[remote heron]

you dont need to calculate sinx or cosx

[remote kettle]

then ?

[remote heron]

you just need to extend your reasoning on the |x+y|=|x|+|y| problem

[remote kettle]

oh

Sad

[remote heron]

to this

[remote kettle]

how.....

[remote heron]

i dont want to spell it out explicitly

[remote kettle]

ok

[remote heron]

you know where the x y problem is satisfied

im telling you

identical conditions will make it true in the cos/sin case

[remote kettle]

so

[remote heron]

+,+ and -,- as u say

[remote kettle]

+,+ & -,-

is it correct ?

[remote heron]

where is this satisfied for sin and cos

where are they the same sign?

[remote kettle]

RHS

[remote heron]

[remote kettle]

why ?

in rhs only

[remote heron]

.

idk what you mean right hand side

[remote kettle]

no matter what the sign it becomes positive

so

even if it is +,-

it becomes +,+

[remote heron]

you are misinterpreting what i am asking

[remote kettle]

oh

[remote kettle]

quadrant 1 m

[remote heron]

i dont mean in your uhh

sure quadrant 1

what about 2 3 and 4

[remote kettle]

ye

oh

so the anser is

quadrant 1 and 4

😅

[remote heron]

are you sure?

[remote kettle]

YEs

is it ryt ?

😭

[remote kettle]

wwaut

i dint know this

NANI

i don't know this table

[remote heron]

you can use this graphic to correct your mistake

[remote kettle]

😭

[remote heron]

its pretty minor

lol dont give up so easily

youre almost done

[remote kettle]

i still need to learn more

so quadrant 1 and 3

[remote heron]

yea

[remote kettle]

not giving up

[remote heron]

and not 2 and 4?

[remote kettle]

NO

[remote heron]

yea

[remote kettle]

cuz different sign

[remote heron]

so

[remote kettle]

so unbalanced equation

[remote heron]

just depends on how your questions wants the answer

but

you have the answer now

its where sin and cos have the same sign

[remote kettle]

hmm

[remote heron]

quadrant 1 and 3

[remote kettle]

yea

[remote kettle]

wdym ?

[remote heron]

well do they want degrees or what

[remote kettle]

no

[remote heron]

or what form to write it

[remote kettle]

lol

[remote heron]

oh it just says quadrant

[remote kettle]

just quadrants

[remote heron]

then youre done

nice

[remote kettle]

if they ask degrees ?

is it 180 degrees ?

[remote kettle]

?

[remote heron]

dwai

just use quadrants

[remote kettle]

hmm

quadrants ?

[remote heron]

👀

like you just said

1 and 3

[remote kettle]

ok

so

quadrant 1

90 degrees

and quadrant 3 90 degrees

so

totally 180 degrees

am i correct ?

[stone glen]

:/ you lack theoretical knowledge@remote kettle

[remote kettle]

theoretical ?

[remote heron]

dont listen to this person

[remote kettle]

its ok

[remote heron]

i wouldnt worry about degrees right now

[remote kettle]

ok

[remote heron]

it just makes it more complicated

[remote kettle]

oh

[remote heron]

you can do that later

[remote kettle]

ok

thank you for ur time

[remote heron]

no prob

[remote kettle]

✌️

.close

[lone heart]

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[fallow cradle]

What kind of transformation does a matrix product like this represent, geometrically?

[fallow cradle]

If we have a certain vector and a (2x2) matrix, then we can conclude that it’s a certain transformation, for example a rotation, but what does matrix vector multiplication of this type represent exactly?

[vale wigeon]

well you could view [2, -1] as a linear functional on R^2

ie a linear map from R^2 to R

[fallow cradle]

And this is because we only have one basis vector?

I’m really struggling to visualise this

We have one basis vector with two coordinates and it collapses onto one point

How

[vale wigeon]

???

idk what you're talking about sorry

[fallow cradle]

How a (2x2) matrix takes a certain vector and makes it another vector

How does this collapse onto one point

While if we inversed the order of the matrixes we would get a (2x2)

[vale wigeon]

(2x2) multiplied by (2x1) yields (2x1)

[fallow cradle]

Yes

[vale wigeon]

(1x2) multiplied by (2x1) yields (1x1), i.e. a single number

[jagged trout]

https://www.youtube.com/watch?v=LNoQ_Q5JQMY&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=7

[fallow cradle]

I’m not interested in the math but what the geometric interpretation is

[fallow cradle]

This looks like what I am looking for thank you. It’s going to take me a while to get through the video though so before you go, the inverse question: what if we switch the order, what does the (2x2) matrix represent? I skipped through the video but didn’t find an answer looking at briefly

Also the person who was typing, whatever you were typing for a while please feel free to post I would be happy to hear everything

I mean the thing in blue

[jagged trout]

That's a Tensor-/Matrixproduct

[fallow cradle]

A tensor and a matrix product at the same time you mean?

[jagged trout]

https://www.youtube.com/watch?v=YK2zVcWpROA&list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG&index=14

[fallow cradle]

I have no idea what tensors are aside from vaguely hearing about them so forgive my noobie questions

Okay nice thank you

Appreciate it a lot

[jagged trout]

Maybe you should look the playlist from the beginning

[fallow cradle]

Yea I will

Thank you

Appreciate it a bunch

.close

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[desert fractal]

Post questions

[tight locust]

No

[lone heart]

@toxic lake Has your question been resolved?

[sly mantle]

.close

[lone heart]

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[weary shard]

How do we got from
$$x+x^2F(x)+xF(x)$$
to
$$F(x)=\frac{x}{1-x-x^2}$$

[ocean seal]

redve

[weary shard]

I read about generating functions

[mortal trellis]

\begin{align*}F(x) &= x+x^2F(x)+xF(x) \
F(x)-x^2F(x)-xF(x) &= x \
F(x) (1-x^2-x) &= x \
F(x) &= \frac{x}{1-x^2-x} \end{align*}

[ocean seal]

Denascite

[weary shard]

Oooh

Ok, thanks

.close

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[dawn quail]

I am very confused what the correct answer should be here

If the left version does not work, can someone help explain why?

[worn fox]

The second line of the left version

You have (h+1)h^2 on top

Expand that, see if it is equal to what is on the line before

[dawn quail]

Oohhh

Ty, that took me down the wrong road!

Good eyes

[worn fox]

No worries!

[dawn quail]

What is the cube formula called again? For the right side

It’s like saying 1 cubed

I didn’t bother to expand on that

[worn fox]

Uh it's sum of two cubes formula

[dawn quail]

Thanks

That one is hard to remember

I can remember difference of two squares

This will take more practice

[worn fox]

If you remember the formula for geometric sum then you can remember it easier

Divide both sides by h+1

And its a geometric sum formula with common ratio -h

[dawn quail]

😆

Haven’t learned that one yet either

Good to know!

[worn fox]

Oh lol, something to look forward to haha

[dawn quail]

Are you taking math in university?

[worn fox]

Just finished my integrated masters

[dawn quail]

Wow 🤩 Congrats!

[worn fox]

Thanks😄

[dawn quail]

What do you plan on doing after university?

[worn fox]

Got a PhD lined up in September

Basically avoiding the real world for as long as possible😅

[dawn quail]

Awesome! But after all the school you wanna get into a field with computer science or teaching or?

Nothing wrong with PhD 😄

Only the select few make it that far

[worn fox]

Will have to see, my opinion might change alot I 4 years hahaha, I wanna teach and do research but it involves a lot of moving around on temporary contracts

Will have to see if I'm up for that

Otherwise will go into industry

[dawn quail]

Yeah

Big money to make the 4nm SoaC at Apple 😉

But too small and get into quantum limits where electrons pass through logic gates

What Apple did with M1 is pretty remarkable

Anyways I will let you go

Thanks again!

[worn fox]

See you around:)

[dawn quail]

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[quaint orbit]

Hi just like to confirm,

My own answer to the question is: The nullspace of C contains vectors that lie in both the nullspace of A and the nullspace of B

that's the same as what the solution is saying right

[mortal trellis]

yes

[quaint orbit]

ok thank you 🙂

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[dawn wraith]

how do i go about doing question b?

[lone heart]

@dawn wraith Has your question been resolved?

[winter tangle]

do you know what the standard deviation means?

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@dawn wraith Has your question been resolved?

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[brazen copper]

Anyone know how to get the answer to this? I tried a few times but only end up with impossible answers where z is a real number.

[gray isle]

can you show your attempts

[brazen copper]

well it was mentally but I can write it and then send

[oak perch]

This is quadratic in terms of 7^z

[brazen copper]

yes

[gray isle]

well it was mentally but I can write it and then send
yeh, don't do that mentally

[alpine sable]

Always write

[gray isle]

trying to do something that involves several lines of work mentally will most likely lead to mistakes

[alpine sable]

Hmm

There're no real roots I assume

[median oar]

no there isnt

[brazen copper]

i kinda gave up after that

bc 7^z = 0,-2 makes no sense

[gray isle]

are you sure you're being asked for real solutions?

[median oar]

well there is solution(s) if u know complex numbers

[alpine sable]

Yea you got it right

[brazen copper]

it doesn't specify

[median oar]

and that too, usually z indicates complex numbers

[alpine sable]

I assume they asked you to find all roots in complex range

[gray isle]

if z is being used then its possible that complex numbers are involved

[brazen copper]

school sent it for summer break practice (and I'm doing it on the last day) but I haven't been taught imaginary numbers

[alpine sable]

well

Then no roots

Since you hasn't been taught complex numbers

[gray isle]

then yeh, write no real solutions

[brazen copper]

so just z is not a real number?

[alpine sable]

Yea, you can write in both way, no roots or no real roots

[brazen copper]

why roots

like why write roots

just real number should be fine

[alpine sable]

To be precise

[brazen copper]

right

ty for your help

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[mild solstice]

I know this is wrong, I know the silly mistake, but i just don't know how to get on with it the correct way

[mild solstice]

This is the working out

I just can't understand how to inverse this

[cobalt remnant]

this one is easy

[mild solstice]

it's my first time doing inverse functions so uh yh

i mean functions in general

but u get the idea

[cobalt remnant]

i am joking i dont understand this one too, i am trying to do it but i cant

[mild solstice]

oh rip

[stone glen]

Which one does thou wants?

[mild solstice]

b)

the h(x) is fg inverse

[stone glen]

Is ur answer not correct?

[mild solstice]

i reached till here

but i don't understand how to inverse it

[stone glen]

Fg means means multiplication right?

[mild solstice]

no, its one function in another

i think

[stone glen]

Is that not fog(x)

[stone glen]

How sure are u on the scale from 1 to 10

Ask ur teacher

[mild solstice]

compound function

so id say 90% sure

[stone glen]

Okay

[stone glen]

Ur working seems to be wrong then

@mild solstice

Nice name btw , i support it

[lone heart]

@mild solstice Has your question been resolved?

[mild solstice]

So this?

Thanks

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[stone glen]

U closed , but yeah

[lone heart]

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[ancient pecan]

is this possible ?

[oak perch]

It converges

[alpine sable]

$\lim_{n \to \infty} \frac{3^n*n^3}{8^n}$

[ocean seal]

π^2=g

[ancient pecan]

what does that even mean

😭

[oak perch]

What?

[alpine sable]

have u understood the concept of limits?

[ancient pecan]

basically

no

[oak perch]

Just Prove it is zero

[ancient pecan]

howww

[stone glen]

Zewo

[median oar]

that is very advanced for someone who hasn't even learned the basics about limits

[oak perch]

Wait why are you asking this without even knowing the definition of limit?

[alpine sable]

look into what are limits first

and understand them

[ancient pecan]

no I know but not in english.

[alpine sable]

uk $\epsilon ion and \delta$

[oak perch]

Does language really matter in math?😂😂

[ancient pecan]

well you see 😭

[ocean seal]

π^2=g

[stone glen]

Even so , which language have u learnt in?

[ancient pecan]

arabic

and hebrew

[alpine sable]

oh man my man why does my latex sucks

,w convergence of limit in arabic

[ocean seal]

Wolfram Alpha doesn't understand your query!
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Requested by pi=e#5213

[stone glen]

My latex is awfull

[oak perch]

My language from English is almost same as how far your language from English though…😂

[stone glen]

Which

[oak perch]

Mandarin

[median oar]

exponentials beat x^3

[alpine sable]

هل تعرف حدود متقاربة؟

[median oar]

so ignore it

[stone glen]

LMAK WHAT

[alpine sable]

thanks to google translate

[ancient pecan]

oh wait

[median oar]

3^x loses to 8^x

so the bottom grows fasters

so it tends to 0

does that help XD

[ancient pecan]

yea it does but like Idk how much the n is

does that matter

[stone glen]

Epik lojik, (but it actually works)

[median oar]

n is going to infinity

[ancient pecan]

like what if

OH WAIT

[median oar]

it's asking what the thing would equal

if n is very big

very very very big

[ancient pecan]

yea yea

okay okay

don't mind me guys i'm in high school

still learning limits

[median oar]

all good have fun

[stone glen]

By big he means VEEEEERRYYYY BIG

[alpine sable]

equal?

[ancient pecan]

😭

[median oar]

TEND TO

[alpine sable]

perhaps what the thing is approaching as n becomes very very very .... big

[median oar]

sorry i slipped D:

[stone glen]

You saved him, he was gonna die there

[alpine sable]

ya then its good

[alpine sable]

[oak perch]

Not sure he can solve this just by definition … I used Hopital…

[stone glen]

What crime m8

Honestly

[ancient pecan]

yea about Hopital

I still didn't learn about it or whatever

[alpine sable]

ya infinity/infinity use lhoptal

[ancient pecan]

or maybe we did and i missed classes

i'm doomed

😭

[stone glen]

L^🏥

[oak perch]

Then you better catch up..

[alpine sable]

💀 so you only know factoring methods?

[ancient pecan]

yea

[stone glen]

What else would you use but Lhoptial, I'm actually lost here

BRUH

Dude

[alpine sable]

wait what

[ancient pecan]

well basically, we learn calc in high school but it's so basic, but since i'm " good " at math, a teacher took me and a couple of students and started teaching me college stuff

or whatever

[alpine sable]

is symbolab saying

[ancient pecan]

so yea 🙂

[worn fox]

They put it in wrong

[alpine sable]

,w limit as n goes to infinity (3^n*n^3)/8^n

[ocean seal]

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[stone glen]

Why do you think i said bruh

[alpine sable]

oh ok

[alpine sable]

coz some people like the word bruh

[median oar]

i dont think this is "college" level math yet

[stone glen]

Bruh , not me

[ancient pecan]

I'M STILL

IN BASICS

don't kill me

🙂

I suck at limits

[median oar]

no im just saying this is like high school level advance stream type topic

[ancient pecan]

https://tenor.com/view/skull-gif-23663947

[ancient pecan]

🙂

[median oar]

https://math.stackexchange.com/questions/55468/how-to-prove-that-exponential-grows-faster-than-polynomial

[stone glen]

@ancient pecan focus more on math than league

[ancient pecan]

i'm happy anyways with how far I came 🏃

[ancient pecan]

HEY

we don't talk about league

[stone glen]

League <<<

[median oar]

you can read up on how he does the proof for how exponentials grow faster than polynomials

[ancient pecan]

ty

[median oar]

then u can factor the x from 3 and 8

then put (8/3)^x on the bottom

[stone glen]

I actually didn't know this , thank you :3

[median oar]

so you have a polynomial on the top

and exponential on the bottom

[ancient pecan]

well anyways

thank you for helping

am I supposed to close this ?

.close

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[civic ferry]

how could you solve this by factoring?

[gray isle]

start by rearranging the equation into general form

[civic ferry]

15c^2-8c-12=0?

@gray isle

[gray isle]

yes

[civic ferry]

where do i go from there>

?

[gray isle]

for non-monic quadratics consider stuff like ac-method and grouping

i.e. consider the value of ac, in this case 15 * -12
find a pair of values that multiply to that and sum to b=-8

and use that to split the -8c term

[civic ferry]

would it be wrong to solve it with quadratic formula?

[gray isle]

depends on what you're being asked to do

if there are no explicit instructions, you can use whatever valid method you want

[civic ferry]

it says "solve by factoring"

and that's it

[gray isle]

then yeh, it'd be wrong to use the QF

as that isn't solving by factoring

[civic ferry]

oh okay

i missed the lesson on solving by factoring so idrk

[gray isle]

for non-monic quadratics consider stuff like ac-method and grouping
i.e. consider the value of ac, in this case 15 * -12
find a pair of values that multiply to that and sum to b=-8
and use that to split the -8c term

i gave you a brief intro to the method i prefer

[civic ferry]

ok thanks

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[toxic fox]

this question do be confusing me

[toxic fox]

the answers say this

where did the 11 and 6 come from and can someone explain this to me

[drifting hull]

For a=11, b=6 you know that 82896=(a+b)^4-(a-b)^4. You can now simplify these as polynomials: (a+b)^4-(a-b)^4=8ab(a^2+b^2) for general a,b. So you get 82896=8 * 11 * 6 * (11^2+6^2)

I would guess that in part a) of the same exercise a similar thing was done...

[toxic fox]

part a was this but i didn't realise they were related

[drifting hull]

🙂

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[obsidian wagon]

For part b are they asking me to just integrate normally?

[obsidian wagon]

First time coming across a question like this for areas under a curve

<@&286206848099549185> 😭

[lime bobcat]

Yes

The first part is to calculate numerica integration. The second part is for exact symbolic integration

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@obsidian wagon Has your question been resolved?

[obsidian wagon]

Sorry what’s numerica integration?
I’ve only pretty much done reverse chain rule, parts and u sub

[last ether]

Numerical

Prob a typo

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[iron tree]

how do you find the LCM of an expression and then two numbers for example:
2/x + 2 - 1/3 = 1/15

[slender gull]

First take LCM for 2 - 1/3 for ease.

Then, with x in the denominator for the first term, you have to multiply x with the other denominator. Since you don't actually know the value of x, the product of x and the other denominator should actually be their LCM as of now.

Then repeat that with 15 if you wish to.

@iron tree

[iron tree]

Ok

so what's the real LCM

what do we multiply the 2, 1 and 1 with ??

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@iron tree Has your question been resolved?

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[lone skiff]

.close

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[visual stag]

how could i integrate that

i used reverse chain rule aand got x/3(Inx)^3

but the markscheme used integration by parts and got something completely different

[mortal trellis]

try differentiating x/3 ln(x)^3

I don't know what you mean with "reverse chain rule". the tool to "undo" the chain rule of differentiation is a u-sub

but I don't know what you u-subbed here

[visual stag]

if i differentiate that using chain rule i do get the original

[mortal trellis]

chain rule and product rule?

[visual stag]

ahhh i see what u mean now

i cant use chain rule with 2 terms

tyy

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[night pumice]

pls help

[high rapids]

what have you tried maam

[alpine sable]

Eh

You know how y=x^3 looks like

Right

[night pumice]

EVERYTHING MAN 😭😭

I’ve learned nothing from my teacher

[alpine sable]

,w plot y=x^3

[ocean seal]

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[alpine sable]

See

[obtuse valve]

anyone have chegg
i really need help here.

[alpine sable]

Just plug in the biggest number in the set

[alpine sable]

Not here sir

[obtuse valve]

sry

[alpine sable]

#❓how-to-get-help

[stone glen]

I don't think she will understand like this , she may get intimidated by the graphs

[night pumice]

yea-

[alpine sable]

or simple way:

just plug all three values and compare

[night pumice]

is there like a video I can watch for me to catch up?

[alpine sable]

I have no idea what year are you in now

[stone glen]

I'd say grade 8

Not sure tho

[alpine sable]

uk or america?

[night pumice]

America, 7th grade 💀

[stone glen]

Yeah, there is alot of content in the internet just search for it

I found alot of it in my native language, I'm sure u will find alot in English

[alpine sable]

just search year 7 maths recap in youtube

[night pumice]

What do I search up

ok

[stone glen]

What chapter u wanna learnm

[stone glen]

No don't search like that

[stone glen]

Not the right approach

[night pumice]

idk I’m failing every mp

[high rapids]

Can you see the relationship between y and x here?

[night pumice]

no

[high rapids]

It's written at the top

Can you spot it?

[night pumice]

Oh ok

[stone glen]

I'm pretty sure she saw it?

[night pumice]

yes

[high rapids]

Can you write it here?

[high rapids]

Yes

y=x^3 right?

[night pumice]

ye

[high rapids]

What can x be?

[night pumice]

idk

[high rapids]

It's written

[night pumice]

oh

-1/3, 1/2, 1/3

[high rapids]

It's either x = -1/3, 1/2 or 1/3

Yes

Suppose x is -1/3

What is y then?

[night pumice]

-1/3^3 ?

[high rapids]

Exactly

[night pumice]

yas

[high rapids]

Can you simplify more?

[night pumice]

no

idk

[high rapids]

Well you can write -1/(3x3x3)

[night pumice]

oh

[high rapids]

Which is -1/27

Right ?

[night pumice]

yea

[high rapids]

Now what is y when x = 1/2?

[night pumice]

.125?

[high rapids]

Well yeah

Or you could write as 1/8

[night pumice]

yea

[high rapids]

Now what s y when x = 1/3

[night pumice]

1/27

[high rapids]

Yes

[night pumice]

yas

[high rapids]

Now compare the results you got

-1/27, 1/8 and 1/27

[night pumice]

1/8

[high rapids]

Which one is the biggest number?

[stone glen]

-1/27

[night pumice]

wat

but that’s negative

[high rapids]

Vanilla answer

[night pumice]

1/8?

[stone glen]

She did

[high rapids]

Yes

So 1/8 is the maximum value of y

[night pumice]

oh

yay thank you so much

[high rapids]

You and @alpine sable both are quite similar

[night pumice]

really

how old is

[high rapids]

I mean just look at his profile

He's like 13

[night pumice]

OMGG so cute dogggoo

mines rats kissing

[high rapids]

Yuck

🤢🤮

[night pumice]

maybe

ok tysm!

[high rapids]

I will kill those rats