precalculus

[winter comet]

no its impossible

[charred stirrup]

I'll find a way

Just wait

[winter comet]

re-define the entirety of math and normalize it and then its possible maybe

[charred stirrup]

Nah just wait u just keep laughing I've spent all of today on this

[winter comet]

what does solving 3x+1 mean

[safe basin]

i think he means the collatz problem

so consider the function $f(x) = \begin{cases} x/2 & \text{if x is even} \ 3x + 1 & \text{if x is odd} \end{cases}$

the conjecture states that if you recursively apply this to any positive integer it will eventually reach 1

so like for instance if we take x=1, then 3(1)+1 = 4, then 4/2 = 2, then 2/2 = 1

or x=2, then 2/2 = 1

and so on

the reason it's kind of a meme is that like

somehow this problem has eluded us but it's really simple to state, so it's kind of a sinkhole to start working on it

i mean there are other things that are like easy to state but unsolved but those usually have some broader relevance to other things and afaik collatz doesn't

[obsidian monolith]

FEIN FEIN FEIN FEIN FEIN FEIN FE

[safe basin]

forgot to @ you

[winter comet]

oh yeah that thing 💀

wouldn't say thats 'solving' 3x+1...

[safe basin]

yeah 3x+1 is just a nickname for the problem

[charred stirrup]

Then what is it

[winter comet]

oh

[safe basin]

explained above

it's not like solving the equation 3x+1 on its own or something

[charred stirrup]

I'm asking what he calls it

[safe basin]

some people just call the problem i described the 3x+1 problem

whos he

[heady brook]

do not spend time on the collatz conjecture bro💀 correct me if I'm wrong but I thought it was made by Nazis to distract Allied powers mathematicians. you are much better off trying to solve a different hard problem😭 also you are still pre-uni math you are still developing crucial math skills

[winter comet]

me? i'd call it the collatz problem or at least be more specific LOL

[safe basin]

yeah

[winter comet]

LOL imagine if this was true that would be hilarious

[charred stirrup]

I'm in highschool I got enough time

[heady brook]

I thought it was a theory or something I might be wrong

[safe basin]

there have been partial results on it so far though

[charred stirrup]

Honestly if u multiply something infinitely by 2 you would have solved it

[safe basin]

what

[charred stirrup]

Because it decides by two if it's even

[heady brook]

there is literally no point in working on it rn as it stands. especially given your level of education. phd scholars work on this and are stumped even with their level of education

[safe basin]

idk what you mean by the infinite part but for all powers of 2 it would be trivial i guess cause for 2^k you just apply the function k times to get to 1

[charred stirrup]

Ya but you can't multiply something infinitely so that can't be the answer

So the answer is not a multiple of two and an even number

[safe basin]

the answer isn't a number though

it would be yes or no

or like yes with some conditions

or something like that

[charred stirrup]

So that means it doesn't exist?

[safe basin]

means that what doesn't exist

[charred stirrup]

The number that answers the equation

[safe basin]

idk what "answers the equation" is supposed to mean here, the conjecture is that if you take some positive integer and then recursively apply the function to it it will eventually reach one

[charred stirrup]

Yes the goal is for it not to reach one

[safe basin]

so then idk what your question is cause if we knew of a counterexample that means we wouldve proven it false

but its still open

[charred stirrup]

My question is do you think a number exists out there that if you use these rules on it it won't ever reach one

[safe basin]

it could go either way, if i HAD to guess i would say no because of heuristic evidence

by heuristic evidence i mean like

we've brute force checked it all the way up to 2^68

and everything weve tested so far converges to 1

but that doesn't necessarily mean there's not some random massive number out there that doesn't ever reach 1, just that if i had a gun to my head i would probably say there isn't

[unborn brook]

why can't I convert f(x) into g(x) and then find wath the domain is?

[willow skiff]

hold on

you probably did the domain wrong from there

the problem is the form of g(x) is not very useful

[unborn brook]

Graph the two functions, they are not the same according to the graphing utility

[willow skiff]

ah yeah cause of the domain

I see now

[willow skiff]

yeah $\sqrt{a} \sqrt{b} = \sqrt{ab}$ is only true for $a, b \ge 0$

otherwise the LHS isn't even defined

[obsidian monolith]

south's secret twin brother

[unborn brook]

I used to wonder why there's a "nonnegative" restriction in the definition of that property of the square roots.

Is this true for all even indexes except zero?

[unborn brook]

Why aren't negative real numbers included in the domain of this one?

-1, for example, does yield in a real number.

[willow skiff]

you can show that -1 = 1 this way

https://math.stackexchange.com/questions/2047349/when-does-sqrta-b-sqrta-sqrtb

[unborn brook]

But I've already paid attention to not use the product rule of square roots that way. -1 still yields in a real number, why isn't it included in the domain?

(a & b are positive real numbers)

[willow skiff]

well in the complex numbers you can have two square roots

$-i \sqrt{a}$ is a perfectly good square root of $-a$ as well

[obsidian monolith]

south's secret twin brother

[willow skiff]

the convention is that $\sqrt{x}$ is nonnegative in the real numbers, to make $y = \sqrt{x}$ a function (which passes the vertical line test)

[obsidian monolith]

south's secret twin brother

[willow skiff]

in the complex numbers, $f(z) = \sqrt{z}$ is by definition a multivalued function

[obsidian monolith]

south's secret twin brother

[unborn brook]

Sorry but I can't see how that negates this operation

[willow skiff]

Well you could choose -i sqrt2

Or -i sqrt4

[uneven nexus]

solved

[serene elbow]

hii

@distant hound

[daring tapir]

#calculus or idk maybe the analysis channel, def not precalc tho

[fading monolith]

Property of sqrt(a)sqrt(b)=sqrt(ab) doesnt hold in general in complex numbers. The square root of a complex number z is multivalued, since the definition is sqrt(z)=e^(1/2 ln(z)) where ln(z) is also multivalued and need to choose a brach to make it single valued. Most common is take the argument of z restricted to [-π,π)

[arctic meteor]

$$\frac{1}{n}*\left[(a+\frac{1}{n})^{2}+(a+\frac{2}{n})^{2}+...+(a+\frac{n}{n})^{2}\right]$$

[obsidian monolith]

wolly5114

[arctic meteor]

Can this be a series?

I found it in my textbook.

[willow skiff]

wdym, this is a series

as in summation

[arctic meteor]

yes summation there was a limit to infinity exercise in my textbook and I thought that the limit of a function can be a summation.Is this true?

@willow skiff ??

[willow skiff]

yeah you know what Riemann sums are right

this is a Riemann sum

so it's the integral of some function from 0 to 1

[daring tapir]

Hmmmm

[exotic barn]

bruh

[terse aspen]

Can someone walk me through this

Like where does the 35 minutes come from next to the 45 degrees

[unborn brook]

So it's not in the domain because it also yields in some non-real complex numbers as well?

[willow skiff]

it's part of the problem

by definition that's 46 + 35/60 + 0/3600 degrees

1 arcminute = 1/60 degree

1 arcsecond = 1/60 arcminute = 1/3600 degree

[willow skiff]

yes your domain would be the complex numbers cause of this

and square roots in complex numbers work differently

[novel spindle]

can someone tell me what I did wrong for 83 and 91?

[willow skiff]

tan(0) = 0 and hence by periodicity tan(pi) = 0 and so on for 83

for 91 you should fully factor

(2 sin x - 1)(cos x - 1) = 0

as (2 sin x)(cos x - 1) + (-1)(cos x - 1) = 0

so you are missing the solution to cos x = 1

or solutions, depends if 2pi is included in the domain or not

[willow skiff]

or when you divide check the case where cos x - 1 = 0 separately

dividing by something that can be 0 is very sus

[novel spindle]

im not sure what you mean by this

[willow skiff]

why are you using pi/2 and 3pi/2

when those are the x-values such that tan(x) is undefined

[novel spindle]

oh

ur right

ok thanks

[unborn brook]

Is the proof of the fundamental theorem of algebra out of the scope of precalculus?

[willow skiff]

yes

you learn the techniques to prove FTA at uni, through various proof-based courses

https://www.youtube.com/watch?v=RBRVL6nP2Dk

there are good explainers online, just not full proofs

[fading monolith]

Even with analysis you need some advanced results

[formal bronze]

Btw I’m not covering anything

[formal bronze]

OMFG I thought it was gx i- 😭TYSM SAVED

Also I wanted to ask when I know it’s 90/ or 99 cuz I saw it in some examples

I think if it’s Immediately times 100 then it’s 99 but if it’s 10, 90

[winter comet]

doesn't really matter

you just want to eliminate the repeating decimals lol

you could subtract x = 0.28888888... if you want

it would still work

[formal bronze]

Thank you so much

[jagged patrol]

How do you pronounce these functions

1. f(x)
2. f
   3.f^-1(x)
3. f^-1
   My best guess is
4. f as a function of x or f of x
5. function f
6. f inverse as function of x or f inverse of x
7. function f inverse

These seem kinda wordy and idk if they are even correct. If possible id like to know a more consise way to say them.

[summer ruin]

the inverse function

[unborn brook]

I've just attempted to justify the statement "The graph of a polynomial function of degree n (where n is at least 1) can intersect any straight line in at most n points," with the fundamental theorem of algebra (Which implies that f(x)=0 can have at most n real roots,) was I right?

An unrelated question: how do we know for sure when a graph increases or decreases without bound? This is a bit like "How do we know Pi doesn't come to an end?"

[willow skiff]

Any polynomial does this

There are a couple of ways to justify this but there can be at maximum n - 1 turning points for instance

The idea is that x^n goes to infinity for n positive integer

Or -infinity

[willow skiff]

Yes this is correct

[jagged patrol]

You have to be more specific it really depends on the graph

[unborn brook]

Take the graphs of polynomial functions with n≥2

[jagged patrol]

well there are a couple ways.
lets consider the function f(x)=x^2
we know that the maximum amount of turning points is n-1 or 1 so the increasing/decreasing behavior of the function will be the same on the interval (0,infinity) or (-infinity,0). lets use the former. we can verify quite a few ways algebraically or visually that for example on the interval [3,4] f(x) is increasing. so this means that for all values of x that are greater than 0 f(x) will be decreasing, in other words: the function is increasing on the interval (0,infinity). since we now know that the function will be increasing as x approaches infinity this means f(x) will increase infinity as well.

im pretty sure this isnt what you intended to ask for, but it is worth noting that negative leading coefficient polynomails will decrease on the right endbehavior as x approaches infinity. and in even degree polynomials both end behaviors will be the same, while odd degrees they will be opposite

basicially this ^

the reason we know this though is more based on the turning points because we know it can never swap direction once the turning point limit is reached

how we figured out the turning point maximum i have no clue but im sure theres a logical reason

mathematics is just complicated logic after all

[viscid thistle]

wait guys

sincere question

what happnes when i differentiate on both sides

when there is a $$\frac{dx}{dt}$$

[obsidian monolith]

Professor Uchiha

[viscid thistle]

wrt

dx

something like

$$x^n = \frac{dx}{dt}$$

[obsidian monolith]

Professor Uchiha

[viscid thistle]

this is not the exact thing

but

say i differnetiate both side wrt dx

[willow skiff]

if $y = x^n$, then $\frac{dy}{dt} = nx^{n - 1} \frac{dx}{dt}$ by the chain rule

[obsidian monolith]

south's secret twin brother

[viscid thistle]

i dont understand

like i cna understand this

but how does it apply to what i said?

[arctic meteor]

How does $$\left[(a+\frac{1}{n})^{2}+(a+\frac{2}{n})^{2}+...+(a+\frac{n}{n})^{2}\right]$$ = $$ (n-1)a^{2}+2*a\left(\frac{1}{n}+\frac{2}{n}+...+\frac{n-1}{n}\right)+\frac{1^{2}}{n^{2}}+\frac{2^2}{n^{2}}+...+\frac{(n-1)^{2}}{n^{2}}$$?

[obsidian monolith]

wolly5114

[arctic meteor]

I tried something but I don't know if this is correct and it's not the same with the upper image

!

$$\frac{(an+1)^{2}}{n^{2}}+\frac{(an+2)^{2}}{n^{2}}+\frac{(an+3)^{2}}{n^{2}}+...+\frac{(an+n-1)^{2}}{n^{2}}+\frac{(an+n)^{2}}{n^{2}}$$ = $$ \frac{1}{n^{2}}\left((a^{2}n^{2}+2an+1)+(a^{2}n^{2}+4an+4)+(a^{2}n^{2}+6an+9)+...+(a^{2}n^{2}+2an*(n-1)+(n-1)^{2}+(a^{2}n^{2}+2ann+n^{2})\right)$$

[obsidian monolith]

wolly5114

[arctic meteor]

$$\frac{(an+1)^{2}}{n^{2}}+\frac{(an+2)^{2}}{n^{2}}+\frac{(an+3)^{2}}{n^{2}}+...+\frac{(an+n-1)^{2}}{n^{2}}+\frac{(an+n)^{2}}{n^{2}}$$

[obsidian monolith]

wolly5114

[arctic meteor]

=====

$$ \frac{1}{n^{2}}\left((a^{2}n^{2}+2an+1)+(a^{2}n^{2}+4an+4)+(a^{2}n^{2}+6an+9)+...+(a^{2}n^{2}+2an(n-1)+(n-1)^{2}+(a^{2}n^{2}+2an*n+n^{2})\right)$$

[obsidian monolith]

wolly5114

[arctic meteor]

$$+((a^{2}n^{2}+2an(n-1)+(n-1)^{2})+(a^{2}n^{2}+2an*n+n^{2}))$$

Is it correct what I wrote??

[obsidian monolith]

wolly5114

[misty zenith]

anyone need help

?

[arctic meteor]

Anyone?

[winged peak]

Could anyone please help me I don't understand in general

[ember hamlet]

he wants you to write the wave function that describes this graph, like a sine or a cosine one. To do that, you need to see the amplitude and the period of the wave, and put that on the function you are writing...

[charred stirrup]

Guys I couldn't solve 3x+1 even after 2 days

[tame crystal]

We draw a 2024 × 2024 grid of unit squares. We call the vertices of the unit squares in the
grid lattice points; there are 2025^2 of these in our grid. Someone chose 10 of these lattice
points, and drew all the line segments that connect any two of them. Show that at least
one of these drawn line segments will contain at least two more lattice points besides its end
points.

pls help me

[charred stirrup]

Bro I didn't understand any of that

[zealous patio]

Can someone check if these are right?

[winged peak]

Hey man, could you help me out? I think I figured this out but IDK IF I GOT IT CORRECT

ANYONE?

Omg omg, help mae

wait, why is it 3/4 can anyone explain to me how to calculate an amplitude when it's a fraction

[winter comet]

The amplitude is half the distance between the lowest and highest y values

[merry widget]

3x+1 =0

3x=-1

x=-1/3

ahahaha

[charred stirrup]

It's a conjecture

It's not a function

[merry widget]

oh..

show

[stable sierra]

Ohhhhh

HIIIII

[arctic meteor]

$$\sum_{k=1}^{n} \frac{1}{(k-1)!+k!}$$

[obsidian monolith]

wolly5114

[arctic meteor]

$$= \sum_{k=1}^{n} \frac{k}{(k+1)!}$$ ?????

[obsidian monolith]

wolly5114

[heavy surge]

isn’t this a proof

[sacred aspen]

why do you keep convicing urself you dont?

lock in

[dense urchin]

How do you solve submission sin x²

[daring tapir]

what

[dense urchin]

Can someone explain if possible and thanks

[daring tapir]

thats very famously unsolvable in elementary functions

,w sin(x^2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by enderdoesntmind

[dense urchin]

Wow thank you so much

[dense urchin]

Here in Egypt we study it before university

[daring tapir]

so do we

[charred stirrup]

Guys I found the answer to 3x+1

I think I might have solved collatz conjecture

[scenic dome]

Holy

[charred stirrup]

Check the math discussion tab

I explained it there

[scenic dome]

Kk

Which one 1 or 2?

Nevermind

[kind iron]

Could anyone explain to me fraction derivatives and natural log derivatives?

do they also work the same when doing 2nd derivatives or are there more things to it

[hoary meadow]

Wait what

[charred stirrup]

It's over we're done with the discussion

I'm still right tho that's the good thing

[hoary meadow]

Im always curious how can you prove some integral cant be written in elementary functions

[fading monolith]

No, its not

[primal comet]

Hello! Can anyone see what I did wrong?

[pale nebula]

Hi Adrian! I have been at this problem for quite a bit and obtained the answer of 64 (when rounded) would you like an image of how I got there?

If 64 isn't right, then OOF

[primal comet]

Hey! @pale nebula Id appreciate that!

[pale nebula]

Was it right? Or are there no retrys for the question given?

[primal comet]

Sorry to say but it was right 😔

Wast

[pale nebula]

DARN!

[primal comet]

Was not lol..

[pale nebula]

sorry Adrian

[primal comet]

This one was tricky!
No sweat! I strongly appreciate you trying!

[pale nebula]

of course! Yes, it seems to be quite a tricky one

I noticed an error within my process, another answer will be here shortly!

[primal comet]

Thank you!

[pale nebula]

okay

[pale nebula]

Now I got 150 feet

if THAT doesn't work, it's ogre

[pale nebula]

it rounds up from 149.7618914

[primal comet]

No that was my last try. The answer is 193 🤷🏻‍♂️

[pale nebula]

!

I am so sorry

[primal comet]

It's okay! I still would like to know what went wrong so I can try this question again 😎

[indigo valley]

yo, i had a question

so we use limits to define the derivative, and that is quite intuitive, and then you can do the same for definite integrals, basically write down the sum if areas of the rectangles and take the limit as the width goes to 0. But then how would you define the indefinite integral? We were just taught its the antiderivative, but is there any actual limit definition?

[winter comet]

if f'(x) = lim dx->0 [f(x + dx) - f(x)]/dx, then f(x) is the inverse of this. I don't think theres an easy great way to describe indefinite integrals other than just saying its the opposite of taking a derivative. 🤷‍♂️

[fading monolith]

No, there is not. Indefinite integrals are just that, family of functions F(x)+C (due +C) such that its derivative coincide with f(x)

For definite integrals you have some definitions as Riemann sum or Darboux sums

[serene elbow]

hi any tips for learning about differentiation and integration?????????

[merry widget]

study it first

[serene elbow]

yeeahh about that

any book/yt suggestions??

[quartz pagoda]

How does it become - 2x+3-x-2=4x-1

[willow skiff]

in case 1 both moduluses are negative

-(2x - 3) - (x + 2) = 4x - 1

[quartz pagoda]

Ooooooh it's that simple thank youu

In the next it would be - (2x-3)+(x+2)?

[willow skiff]

yep
and then (2x - 3) + (x + 2) finally

no worries!

[quartz pagoda]

Do you maybe know why do we need conditions, I dont know the logic behind them

[night herald]

there can't be a negative quantity under the radical sign

[willow skiff]

without going into complex numbers, yes

[night herald]

also, a square root with the symbol gives +ve answer

[night herald]

yeah surely

[quartz pagoda]

Aah got it thanks

[merry widget]

plusve?

[zinc compass]

Can anybody help me determine what I need to catch up on math? I never learned x^2 inequalities properly, and don't know much about polynomials (factoring and common polynomials).

I need to catch up to derivatives and functions analysis for my uni exam. What do you suggest me to do? Where should I study?

I have a few books, Khan Academy and some resources from the uni (video lectures and stuff like that, but they assume you already know lots of stuff that comes before)

[simple scroll]

hey, can someone help me solve this?

4 / p + 1 = 5/p2 + p + 1/p

and when i say p2, i mean p squared

[fading monolith]

Multiply both sides by p^2

[simple scroll]

Is that the LCD? P^2 by itself? If so, why not the + p as well?

[slender rover]

is it
$$ \frac{4}{p+1}$$
or
$$ \frac{4}{p} + 1 $$

[obsidian monolith]

reaver

[simple scroll]

The first one

[slender rover]

oh ok

then in that case you have to multiply by the LCM of the 3 denominators

[simple scroll]

I was told it was p^2

Is that all or is there more?

[slender rover]

i think they assumed the + 1 was not in the denom

[simple scroll]

Ohh

[slender rover]

you need to cancel
$$ p + 1, p, p^2 $$
so find the LCM

[obsidian monolith]

reaver

[simple scroll]

P?

[slender rover]

LCM not GCD

[simple scroll]

Oh okay

[slender rover]

the smallest number that p + 1, p, and p^2 go into

[simple scroll]

P^2? Is it not?

[slender rover]

what about p+1?

does p+1 go into p^2?

[simple scroll]

Why would that fit?

[slender rover]

it doesn't, so p^2 doesnt work

[simple scroll]

I was about to say…

[slender rover]

so p^2 works to cancel the denom of p and p^2 right

so that leaves p+1 still in the denominator on the LHS

so what do we need to multiply both sides by to get rid of the denom?

[simple scroll]

Sure, but how would that cancel out p + 1? Doesn’t it need to cancel everything?

Oh okay

Well I don’t see why 1 would work it never does

[slender rover]

1?

ok so first we multiply by $$p^2$$
$$ \frac{4}{p+1} = \frac{5}{p^2} + p + \frac{1}{p} $$
and we get
$$ \frac{4p^2}{p+1} = 5 + p^3 + p $$

[simple scroll]

Wouldn’t you only cancel out one p?

[slender rover]

no because we multiply both side by p^2

[obsidian monolith]

reaver

[simple scroll]

The p^2 and p we’re in the same denominator

[slender rover]

oh what?

[simple scroll]

Yeah no +p by itself

[slender rover]

oh nvm im tweaking mb

[simple scroll]

Here let me get a picture just a second

[slender rover]

ah ok

makes more sense now

ok so i see you've factored the denominator already

[simple scroll]

Kinda yeah

[slender rover]

what can we multiply both sides to get rid of all the denominators?

[simple scroll]

Is not p now? 😭

[slender rover]

ah but that leaves p+1

we have denominators p+1, p(p+1), and p

[simple scroll]

Yeah

[simple scroll]

Right, but they both have a singular p

I can’t add + 1 to the remaining p

I’m sorry I’m genuinely confused

Ik I shouldn’t be

[slender rover]

no, but you can multiply twice
if multiplying by p cancels p
we end up with p+1 and p+1 in the denoms
so what do we multiply this by

if you have, for instance, an equation
$$ \frac{1}{p+1} = \frac{2}{p+1} $$
what would you multiply both sides by

[obsidian monolith]

reaver

[simple scroll]

P + 1

Both sides cross multiply

[slender rover]

yes

so combining our multiples of p and p+1,
we multiply both sides by p(p+1)

to cancel out all the denominators

[simple scroll]

But it’s already like that without the additional p?

Why not add the other p instead of multiplying it?

Cause it’s already factored

[simple scroll]

Seriously though

[slender rover]

ok let me do latex of it

[simple scroll]

5/ p^2+p = 5/p(p + 1)

But you still have 1/p

[slender rover]

we multiply first by p:
$$ p(\frac{4}{p+1}) &= p(\frac{5}{p(p+1)}) + p(\frac{1}{p})$$
$$\frac{4p}{p+1} &= \frac{5p}{p(p+1)} + \frac{p}{p}$$
then its obvious that the p's cancel on the right-hand side, giving us:
$$ \frac{4p}{p+1} = \frac{5}{p+1} + 1 $$

[obsidian monolith]

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

[simple scroll]

Oh I see

Cause I forget you usually only change the numerators

[slender rover]

yes

so then to do it in one operation, we mulltiply by p(p + 1)

[simple scroll]

So P was the LCD, right?

Or GCF I mean

[slender rover]

no, p(p+1) should be the LCD

[simple scroll]

I’m sorry idk why it’s not clicking still

[slender rover]

then we multiply both sides by p+1 as well, giving us
$$ 4p = 5 + 1(p+1) $$

[obsidian monolith]

reaver

[slender rover]

and then
$$ 4p = 5 + p + 1 $$
$$ 4p = p + 6 $$
$$ 3p = 6$$
$$ p = 2$$

[obsidian monolith]

reaver

[slender rover]

ok so we want to get rid of the denominators of all the fractions - so we have to multiply by the LCM of each of these, which i believe is also the LCD?
LCM(p(p+1), p, p+1) is p(p+1)
and then we multiply both sides by p(p+1) and end up with an equation with no fractions

srry if it doesnt make sense

[simple scroll]

I think what’s getting to me is that p is not greater than p + 1

[slender rover]

p < p + 1 of course, otherwise if p = p + 1 then 0 = 1, or p > p + 1, then 0 > 1

im not really sure what you're confused about, is it because you're multiplying by two things?

[little glade]

P(theta)=1/2cot(1/2(theta+pi/6))-2

Is this right?

I messed up the asymptote

But just look at the dots

[surreal summit]

just taking a quick look, did you translate it down 2 on the graph? I might be misreading it but

[little glade]

Ya

I forgot to translate horizontally by pi/6

[surreal summit]

your period is also off, it should be 2pi not pi, at least that's what i'm seeing from the graph

since normal period of cot is pi, and period is pi/(.5) = 2pi

[little glade]

Ya

I stretched it by 2 then shifted it pi/6

[surreal summit]

and remember when you translate it downwards that means the shift between concave up and concave down happens at y=-2 and i don't see that on the graph

when you shift it left pi/6 the asymptotes are right if your period is 2pi

[little glade]

Midline would be at -2?

[surreal summit]

inflection point should be, yes so yeah midline too

[little glade]

I put it into desmos and its not like that

[surreal summit]

am i looking at the wrong graph? lemme just double check

wrong equation*

this is your equation right

[little glade]

Yea

P(theta)

[surreal summit]

well, yeah but that shouldn't make a difference. desmos is showing the midline at -2 for me

[little glade]

How do you set that?

[surreal summit]

i wrote the equation on one line and set y=-2 for a horizontal line to double check

also have asymptotes too

[little glade]

Oh yeah

I see it but idk why i didnt think of that

Ok thank you

[surreal summit]

np i hope i helped somewhat? Sorry for being confusing lol

[little glade]

Its fine

I just needed to double check really

Bruh i needa memorize the 4 new filler point sets

Or i put them on a post it in my calculator

😛

[brazen cargo]

@atomic ridge

[atomic ridge]

alright

[brazen cargo]

so quadratic equation is when you have something like x^2-12x+8=0 right?

[atomic ridge]

exactly

they look like this on a graph(generally)

this shape is called a parabola

do you mind defining what a normal equations is/looks like?

[brazen cargo]

like 8x+19=20 and then you solve x

[atomic ridge]

so that's basically going to be a straight line

[brazen cargo]

it doesnt look like our math is teaching us graphs for this, at least not in the moment

[atomic ridge]

Hmm ok

Well your normal equations are basically going to be a straight line going down if you use x
or going horizontal if you're using y

if you use both x, and y the graph is slanted or linear

and if you square x you get a quadratic

I'm sorry im absolutely ass at math, I'm not sure if this helped a lot

[brazen cargo]

nw yeah i dont think we work with lines and graphs

we're just doing numbers

i'm trying to understand quadratic equation

[atomic ridge]

Oh ok

I found that looking at it graphically helped me learn a lot

[brazen cargo]

like, why cant we just solve x like regular equations for quadratic equations
x^2-12x+8=0
x^2-12x=-8
etc...

[summer ruin]

well what's the next step

[atomic ridge]

well you can try doing that

do you want to try doing that right now?

fuck itI'll open logseq

[brazen cargo]

divide 12

then square root

[summer ruin]

so you get $\sqrt{\frac{x^2}{12} - x} = \sqrt{\frac{-8}{12}}$

[obsidian monolith]

Transparent Elemental

[brazen cargo]

what

[atomic ridge]

so uh dude

this is basically what you're trying to do

[summer ruin]

that's what you said

[atomic ridge]

we're trying to solve for x like a normal equation right?

get x all alone

[brazen cargo]

oh yeah exactly

[atomic ridge]

see that isnt
exactly solveable

[atomic ridge]

because there is a negative root right there

and you cant take the negative root(normally)

[summer ruin]

the negative root isn't even problem, just divide by -12 instead of 12

[brazen cargo]

so i really gotta memorize like 20 steps of the pq formula to solve this equation

[summer ruin]

you didn't do anything useful to left hand side

[atomic ridge]

so you kinda just have to memorize it

because it becomes kinda super mega important in calc and precalc

[summer ruin]

there's only 2 steps to quadratic formula

[atomic ridge]

yeah
you do the basic equation
and then you do the + or -

[brazen cargo]

wdym 2 steps

[summer ruin]

where are you getting 20 steps from

[brazen cargo]

x^2-12x+8=0
x=-(-12/2)+-V(12/2)^2-8
and then it continues till you solve the right hand, thats like 10 steps right there

and then you gotta calculate x1 and x2 too right? so add about 10 steps there too

[atomic ridge]

woah

dude

what do you think the quadratic equation exactly is

[brazen cargo]

i dont know

lol

[summer ruin]

just google quadratic formula

[brazen cargo]

oh

thats not the formula

[atomic ridge]

not even close

[brazen cargo]

im talking about this one

[atomic ridge]

that

[brazen cargo]

?

[summer ruin]

that's the same thing

[atomic ridge]

its just a different way of showing it

i think

but uh we use another formula

its a lot easier to remember

[summer ruin]

I mean if you consider simplifying an expression as something that's hard to do that requires tons of work, maybe you should learn that first

[brazen cargo]

ok, well i need to study this one

[atomic ridge]

I mean your perogative but you might wanna use the simpler one

quadratic equations are supposed to be souls-like bosses 😭

[brazen cargo]

i dont really see the point of studying something that isnt in our book and wont come up in our exam next week 🤷‍♂️

im just trying to understand why i need this formula to begin with

is it because x^2 is unsolveable in regular equations?

[atomic ridge]

ok so

i want you to try and solve a problem

x^2+x=100

solve for x

[brazen cargo]

with or without the formula?

[atomic ridge]

i mean solve it normally

[brazen cargo]

with the formula i know how to do it, its just many steps

[atomic ridge]

i realize now i gave you a pretty shitty question

it'll give you a decimal answer

[summer ruin]

you're saying it as if there isn't a formula for a linear equation - there is

[atomic ridge]

but you need to use the equation to solve it because solving it normally just isnt possible

[brazen cargo]

maybe there are, i just dont know of em

[summer ruin]

and moreover there's a process that lets you solve any quadratic equaton without quadratic formula

it's just that you end up using quadratic formula anyway

[brazen cargo]

is the zero product something something

[brazen cargo]

so it is because ox the x^2 or is it because of the +x?

[atomic ridge]

both

[summer ruin]

ax+b = 0 is solved by x = -b/a, that's the formula for linear equation

[atomic ridge]

you can sovle x^2 = 100

but you cant solve x^2+x=100

[summer ruin]

yet you used it for every linear equation

without knowing it

[brazen cargo]

only if i did quadratic formula it will get solved yes?

[summer ruin]

if you learn the proof for quadratic formula you'll see why it is the way it is, there's nothing special about it

[atomic ridge]

yeah

[brazen cargo]

which one?

[atomic ridge]

^

[summer ruin]

this

[brazen cargo]

i've never done this in my life

[summer ruin]

you just didn't notice that you actually used it

[brazen cargo]

can you show me an example in practice?

[summer ruin]

try making one yourself

[brazen cargo]

2x + 8
x = -8 /2
x = -4

?

[summer ruin]

try solving 5x+3 = 15

[brazen cargo]

how does that work

if 15 is neither b or a

oh nvm

5x+3 = 15
5x+18 = 0
x = -18 / 5
x = -3,6
?

[summer ruin]

that's x = 12/5

[brazen cargo]

ok is that correct?

wait i did the move wrong

5x+3 = 15
5x-12= 0
x = -(-12) / 5
x = 2,4
?

[summer ruin]

yes

[brazen cargo]

yeah i've never done this

i do
5x+3 = 15
5x = 12
x = 2,4

[summer ruin]

you just did the same thing

[brazen cargo]

i dont see how that's the same but i'll take your word for it

so why do we have to wait with solving square root of a number if the result is a decimal? is it theoretically incorrect to do early rounding?

[summer ruin]

what?

[brazen cargo]

?

[summer ruin]

I have no clue what you're asking

[brazen cargo]

say in the end

you have x = -9 +- V37

why not calculate the result from the square root right there

instead of trying to save it to last

[summer ruin]

I don't see the problem

[brazen cargo]

what?

[summer ruin]

there's no problem in what you're describing

[brazen cargo]

what problem, im not describing a problem

[proven comet]

omg....

He just said that there is nothing wrong with this whole thing :

This is a correct way of doing it

[formal bronze]

Where did the 16 go I’m begging .. and how did the xy change

Wait is did the 16 turn into 2? Bc 8 x 2 is 16 ?

[summer ruin]

yes

[formal bronze]

Why did the x and y lose a square root?

Girl not a square root I mean

The number on top of them idk how to say it in English

Tysm also

[summer ruin]

because (x^3)^(1/3) = x

[formal bronze]

I’m sorry

I talking about the first part where x^5 and y^4 was removed

But Ty I was wondering the last part too

[summer ruin]

you just factor out x^3 and y^3

[formal bronze]

Thank you so much 🤍

[brazen cargo]

which is correct?

im confused

[proven comet]

I think both are correct. It's not like every maths problem has only one path to the correct answer. Most of the time, you will find more than one way to get to a satisfying conclusion.

Either way, you'll get the right answer, so it doesn't really matter "which is correct". Every path that leads to the same answer is a correct path.

[viscid thistle]

Hii, I don’t know if this is the right channel to ask this but I wanna study precalc and calc on my own, unfortunately I don’t have any books
Can anyone recommend me youtube channels or pdfs if possible? 😭

[winter comet]

Paul's online math notes, I don't know if it has precalculus but it probably does

it def has calculus tho

and is decent

[viscid thistle]

That’s perfect

Thank you

[shell ibex]

Try 3Blue1Brown on Youtube for an intro to concepts. Look up the "Essence of Calculus" playlist

[winter comet]

yea 3b1b has good videos for understanding things conceptually/intuitively

[true vessel]

are limits, derivatives, differentiability considered pre calc or calculus

[river drift]

that is all calculus

[true vessel]

bro i've been learning calculus since last year?

this school education sucks

[viscid thistle]

Noted! thank youu

[viscid thistle]

From what I know theyre an intro to calculus

[true vessel]

so basically cancer

[viscid thistle]

😭😭😭😭😭

I don’t like math but I unfortunately have to do it 😔

[south pecan]

Are you in a STEM strand?

[drowsy hemlock]

is the "precalc curriculum" an American thing? I'm trying to find where to talk about differential equations for an integration paper I have

[winter comet]

"precalc" is an american thing yes.
if you have a question on ordinary/partial differential equations, try #odes-and-pdes
idk what an integration paper is

[drowsy hemlock]

its an exam paper with questions solely around the integration part of calculus

ty

[winter comet]

and it has differential equations

[drowsy hemlock]

yes, you just don't need to differentiate much or at all

its weird, but I swear it makes sense to us

[winter comet]

wdym?

you mean in order to solve?

it depends but its not just soley integrating XD

unless its seperable and then it pretty much is i guess but 💀

[drowsy hemlock]

Ignore the workings I'm still figuring it out

[winter comet]

lol yea thats seperable

[drowsy hemlock]

and would you say that thats "precalc"

[winter comet]

no

its probably better in #calculus or #odes-and-pdes

did you have a question about it tho?

[drowsy hemlock]

I think I will soon, still puzzling it out tho

idek what seperable means in this context

[winter comet]

a seperable differential equation is just when you can write it in the form dy/dx = g(x) * h(y)

[drowsy hemlock]

wouldn't you guys cover it in like grade 12 tho?

[winter comet]

depends

[drowsy hemlock]

ah right, just a guess but is every state different?

[winter comet]

i mean
this is something that would appear in calculus or a basic differential equations class. calculus is commonly taught in high school or early college but it depends on the person lol. also its mostly more common for people in like stem

i'm not sure if its enough to say its 'normal' or 'standard' but its the case for a lotta ppl

[true vessel]

No idea what that is

[winter comet]

...got a question?

[true vessel]

I just looked it up

No im in high school rn

We started calc last year (11th) grade

[drowsy hemlock]

👍

[winter comet]

what is it?

[true vessel]

Im in the 12th grade this year, which is the last year of high school

[true vessel]

Science technology engineering snd mathematics

[winter comet]

thats just STEM

[true vessel]

Yes no shit

[winter comet]

but what about the 'strand' part and what does that have to do with high school

[true vessel]

A person asked me if im in a stem strand

I said no

Im in highschool

[winter comet]

whats a stem strand

[true vessel]

I dont take engineering or technology

[winter comet]

STEM is just science technology engineering and mathematics, which you can study in high school or college or heck kindergarten

[winter comet]

oh i don't think you need to take all of them to be considered do you?

[true vessel]

I dont know

[winter comet]

💀

[thorn pecan]

Wait where to study stem

[dire aspen]

in highschool or college or kindergarten like vicious viper said

[merry widget]

philippines shits lmao

so for context at grade 11 and 12 the 2 years before college students can choose strand basically lets just say its like ap

choices are stem, humanities, and business/accountancy

and what strand someone chooses is what they gonna focus at for 2 years

[wanton ginkgo]

does anyone have calculus 1 notes?

[viscid thistle]

pauls notes is gooooood

[fresh birch]

Hey

When finding the ciritical point sin rational inequalities should I first cancel outcommon terms form the numerator and denominator?

[willow skiff]

yes

[uneven nexus]

Any ideas of this?

[daring tapir]

you know about reimann sums right?

also

!status

[tender quest]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[uneven nexus]

1

[daring tapir]

how about reimann sums?

[uneven nexus]

Not sure if it can apply here

[fresh birch]

What if there was a hole where the sign changes though?

[agile moat]

guys

im having trouble with converting the sfe of a parabola to the gfe in the factoring part

so currently i have 16(x^2-64x +32) -25(y^2 -50y +625) =361 + 32 + 625 i already did the completing squares part and grouping

ok wait nvm

turns out i had to factor something

;-;

ok but how did this happen

[willow skiff]

by a hole, you mean a pointwise discontinuity right

then if you fill in the hole, the function will have a root at the hole

so it doesn't matter: when you cancel out like terms in the numerator and denominator, the function will equal zero there

[willow skiff]

try expanding to convince yourself this is true

$-25 \cdot y^2 + (-25) \cdot 2y$

[obsidian monolith]

south's secret twin brother

[agile moat]

Sorry sorry

I got it :3

Thanks man

[viscid thistle]

[willow skiff]

what are you confused about

[fresh birch]

Thx

[viscid thistle]

nvm

[viscid thistle]

Does anyone know how to solve this? I keep getting it wrong (if u could show the solving that would be better)

[viscid thistle]

Show your work

[glossy heath]

its just the derivative?????

[echo sinew]

Yeah it is

[winter comet]

they showed their work...theres just nothing there 😭

[main glacier]

$0=2x^2+12x+19$. Find the vertex.

[obsidian monolith]

zhph

[winter comet]

the vertex of f(x) = 2x^2 + 12x + 19? why did you set it equal to 0

[main glacier]

oh oops-

mb

i forgot

[viscid thistle]

Good point lol

[echo sinew]

Do you know the formula for the x-coordinate of the vertex?

[main glacier]

i just factored 2 then completed the square

2(x^2+6x+19/2)

2(x^2+6x+9+1/2)

2(x+3)^2+1

oh

ok so i did it wrong in the competition

because i just got the right answer

$(b/2a, (c/2-(b/2a)^2)a)$

[obsidian monolith]

zhph

[main glacier]

lemme use fractions

$(\frac{b}{2a}, a(\frac{c}{2}-(\frac{b}{2a})^2))$

[obsidian monolith]

zhph

[main glacier]

it should be -b/2a now that i think abt it

$(-\frac{b}{2a}, a(\frac{c}{2}-(\frac{b}{2a})^2))$

[obsidian monolith]

zhph

[main glacier]

2(19/2-(12/4)^2)

19-18

1

yeah

isnt that cool

[echo sinew]

I usually don't do it like that but if you don't remember the formula yours is a good way 👍

[main glacier]

shrug

thanks

[unborn brook]

Are there any flaws in my proof?

[willow skiff]

your proof doesn't work when p = 0

ah wait didn't you use what you wanted to prove

if you want to show $\log_b (m^p) = p \log_b m$

[obsidian monolith]

south's secret twin brother

[willow skiff]

you've used what you wanted to prove in the third line

[unborn brook]

I just multiplied both sides with p

[willow skiff]

how did you get $\log_b (M) = x/p$ in the first plcace

[obsidian monolith]

south's secret twin brother

[unborn brook]

Converting from exponential form to logarithmic form

[willow skiff]

wait right yeah it follows from b^(x/p) = m

ahhhh I see so it does work

[willow skiff]

I mean I just haven't seen anyone do it like that before

usually you'd just show $b^{\log_b (m^p)}$ and $b^{p \log_b (m)}$ are equal

[obsidian monolith]

south's secret twin brother

[unborn brook]

Well it can't be 0 in the first place anyway. Assume I've specified that.

[willow skiff]

well you'd just check 0 separately then

LHS is just 0
RHS is log_b (1) = 0

[stray ingot]

hh

[merry widget]

log(a) • b is same as blog(a), no?

[willow skiff]

yeah

[terse aspen]

Hey

Can someone explain why sin theta is less than tan theta in quadrant 1?

[cloud steeple]

Idk if im right, because im also studying pre calc

But sin is most of the times a decimal number

And cos is also a decimal numbers

Sin/cos=tan

So, the division of those two numbers should be less than the numbers right?

But idk

[winter comet]

tan(theta) = sin(theta)/cos(theta)
since 0< cos(theta) < 1 in quadrant 1
sin(theta)/cos(theta) > sin(theta)

[winter comet]

basically yeah, since you divide sin by a number less than 1 and greater than 0 (cosine) you know sin/that number will be greater than sin

[cloud steeple]

Yeah i've been studying precalc but i've just started

[terse aspen]

Ok you just gotta know that? And sin has to be greater than 1 i assume as a rule

[winter comet]

sin isn't greater than 1

you gotta know what happens if you divide by a fraction

like

[terse aspen]

…

[winter comet]

you know if you divide by a fraction your number will get bigger right?

1/(1/5) = 5

[viscid thistle]

Does pi/2 come under first quadrant or second quadratic ?🤔

[cloud steeple]

(a/b)/(c/d)=(a/b)(d/c)

[terse aspen]

Ye

[winter comet]

a fraction less than 1 and greater than 0

😔

[terse aspen]

Ohhhhhhhhhhhhh

🤯😲

[winter comet]

its not in any quadrant, its just the divider

[viscid thistle]

okay ty

[somber holly]

Can someone please help me remember trig identities? I'm trying to understand them but they don't follow any rules that I know.

[unborn brook]

Why doesn't Descartes's Rule if Signs apply to this function?

Two real zeros: 0 & ln3

[river drift]

that is not a polynomial

[unborn brook]

There should be 2 or 0 according to the rule

[unborn brook]

Oh wait

Sorry Descartes you can keep resting

What am I missing in this line of reasoning? What's the relation between being a function and the latter statement?

[river drift]

a function has only one output for any given input

so if two inputs are equal, then the outputs when passed into a particular function are equal

[agile moat]

so guys

im kinda confused about the signs in factoring

16(x^2-32x+256) - (-25)(y^2 - 2y + 1) in this right

(x plus or minus? 16) ^2

and (y plus or minus 1)^2 and why did the sign become that

hol on

nvm guys

the computation iswrong

;-;

[viscid thistle]

What should i do once ive reached here?

[hoary pulsar]

in the same question put x=3 in f(x) u'll get one more equation
now u have two equations

solve and get the answer

[viscid thistle]

I dont get, if its ok could u like show me? Like on a photo or something. I dont understand math in words 😅 english isnt my first language

[viscid thistle]

Im confused now, some people are telling me its -10 and others say its 6 and im getting 10 through chatgpt

[terse aspen]

Hey how do I do sin(theta-90)?

[unborn brook]

How can I find the inverse of this function?

[willow skiff]

$\frac{y + 6}{3} = |\ln x|$

[obsidian monolith]

south's secret twin brother

[willow skiff]

ah you'd need to split into cases, so for 0 < x < 1 and 1 < x

so that you can have -ln x or ln x on the RHS

[hard harness]

Is this channel for people who are learning cubic equations

Idk what class it's in I just know it's ahead of me

[willow skiff]

sure

standard precalc topic those are

[hard harness]

Well I'm making a calculator on scratch to solve cubics, using Cardanos method, but I can only get it to work when b=0. Is there a different, possibly easier method I could use for if b/=0

[willow skiff]

what do you mean by b?

[hard harness]

Like ax³+bx²+cx+d

[willow skiff]

well you've surely heard of depressing the cubic

to make b = 0

[hard harness]

I'm in geometry so not really

So I can make b=0 and still get the same answer as before b was 0?

[willow skiff]

https://en.wikipedia.org/wiki/Cubic_equation#Depressed_cubic

you can sub x = t - b/(3a)

and then the t^2 term in this new cubic after the substitution will become 0

[willow skiff]

so no that's not what I meant

https://www.youtube.com/watch?v=N-KXStupwsc

also this video is terrific

[hard harness]

Tyvm, I'll check this out once I'm home

I really appreciate it :D

[willow skiff]

no worries!

[jagged patrol]

Just use cubic formula

If it's done by a computer might as well

[hard harness]

I tried cardanos and couldn't get it to work
I'm coding it all by hand with scratch tools so it's very limited

[unborn brook]

This doesn't really seem right on the calculator

Plus I want to know how to do that, answer alone doesn't really help

[uncut mantle]

You need to switch x and y (f(x) is y) in the equation, and then solve for y.

I think the other person forgot to switch x and y

[unborn brook]

Yes, due to the domain-range relation between inverse functions. What boggles my mind is the absolute value in there. I tried the switch-and-solve you're mentioning but I ultimately got two functions, neither of which is the inverse of the original function (they were partial inverses)

That's why I posted the question here

[uncut mantle]

Oh it's because the inverse isn't a function

Sorry I just realized that

[merry widget]

damn thats a pain to derive to find x

u gotta do sqrt twice??

[hard harness]

Wym?

[merry widget]

quadratic equation is so easy to derive to find x

but cubic equation looks painful to deal with

[polar halo]

If you want to extend to all polynomials later, check these out: https://en.wikipedia.org/wiki/Durand–Kerner_method https://en.wikipedia.org/wiki/Jenkins–Traub_algorithm

[hard harness]

Yeah, the cubic formula had been a MAJOR headache

[polar halo]

Newtons is probably easiest but you need good initial guesses

[hard harness]

Can I send link for the calculator in its current state?

https://scratch.mit.edu/projects/1053228736

[polar halo]

why on scratch

really cool though, great job

[hard harness]

Why not

[hard harness]

Ty, been working on it since like June off and on

[hard harness]

I love the math and variable engines of scratch, also I don't have to learn a new language just for a calculator since I learned scratch in middle school

[polar halo]

fair enough

[hard harness]

I FIXEX IT

HAHA

[quartz pagoda]

Probably a dumb question but how do we know from what number do we make an interval

[echo axle]

When solving an inequality, it remains an inequality. So x>=5, not just equal.
As for where you start the interval, start from the constant (number) and then go the way the inequality tells you

[quartz pagoda]

Aa thanks mate

[versed jolt]

Does anyone have a shortcut on how to do matrices?

[hoary iris]

like how?

[tribal heart]

Hello Mathematicians all over the round earth,
Myself AK here. I am preparing for the second toughest exam in the world JEE, I have maths going really tough. I love calculus, but allergic to the complex language of LIMITS, Continuity and Differentiability, I am somewhere able to do differentiationa n integration easily, but okok it is. I have my first attempt on 22.01.2025
I also have problems in algebra, geometry, specially trigo, coordinate geometry, conics and other topics. PNC is the most easier, but its quite dicy for me, as my thoughts are always flopping on me.
I need help seriously. Please advice, give me some medicines professors.

[jagged patrol]

#competition-math or #calculus

[cloud steeple]

Can anyone help me with some function topics?

I have a few questions

[dull raven]

yes

[cloud steeple]

Ok, so i need help with horizontal stretch and horizontal compression

[dull raven]

oki post the question

[cloud steeple]

No question

I just can't understand

How to

[dull raven]

give me an example of what u mean

[cloud steeple]

f(x-h) means a shift h units on the x axis

[viscid thistle]

h shift to the right

[cloud steeple]

Yeah

But

If i have the shifted function

To get the original function, how should i do?

[viscid thistle]

Then do the opposite

[cloud steeple]

Lets say

f(x-h)=3x+2

[viscid thistle]

So let's say I have a function f(x-2)

Oh nevermind

[cloud steeple]

How can i find the original function?

[viscid thistle]

Adding h to the function

It's usually for graphs

[cloud steeple]

So f(x)=3x+2+h?

[viscid thistle]

No

That's just adding h to the output

[cloud steeple]

oh

Yeah

[viscid thistle]

It's a horizontal shift

[cloud steeple]

That would be the same od f(x)+h=3x+2+h

[cloud steeple]

Ok

[viscid thistle]

This is a list of the rules

I don't think you would encounter questions where they would just say

Let f(x)= some function

Find f(x+2)

You could find it but you wouldn't have a value unless there is a value for x

So usually they will ask questions like that with providing a graph

[cloud steeple]

mhm

[viscid thistle]

That's actually a kind of question they would ask on the SAT

[cloud steeple]

Ok, so i'll read it again and try to do some exercises

[viscid thistle]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec2f6f830c9fb89:shift/e/shift-functions

You can do exercises here

[cloud steeple]

Sorry for the dumbness and thanks for the patience ⭐

[viscid thistle]

No worries

Let me know if you have any other questions and I'll try to help

[cloud steeple]

Ok so, on 25 i said: the graph h(x) is a vertical shift of 3 units on the y axis compared to f(x)

f(x)=(2^x)
h(x)=(2^x)-3

[viscid thistle]

Would it not be

If f(x)=x^3+2x

[cloud steeple]

Nono

That's other problem

[viscid thistle]

Oh okay

[cloud steeple]

Im talking about the one below the number 25

[viscid thistle]

3 units up or down

[cloud steeple]

Down

[viscid thistle]

Good then

[cloud steeple]

Ok thank youuu

[hard harness]

I pretty much finished the cubic section, what should I do next?

[merry tide]

@viscid thistle you like math?

[tame pike]

I need help w/2 & 3

[viscid thistle]

what have you tried?

[uncut mantle]

not sure where this goes, but im having trouble with understanding why the bottom experission isnt equivalent to the top one

i understand logically kinda

like it has to do with how you cant do things like sqrt(1)=sqrt(-1*-1)=sqrt(-1)*sqrt(-1)=i*i

but not sure how you'd get the right answer

which is factoring out -i rather than i

[versed jolt]

An easier concept for the topic

[viscid thistle]

I like to think so

[cloud steeple]

lol

[willow skiff]

seems to do with the fact that $i^2 = -1$ doesn't imply $i = \sqrt{-1}$

$i = -\sqrt{-1}$ is also possible

,w 1/sqrt(x^2+4) - 1/(-i * sqrt(-x^2-4))

[obsidian monolith]

south, just south

Results provided by WolframAlpha

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

Requested by sooouth.

[safe basin]

yeah youre right

you can't do those manipulations there cause you start making non well defined choices

[shadow summit]

sqrt(ab)=sqrt(a)•sqrt(b) only when a and b are positive and real.

[willow skiff]

yes there's a 'proof' that 1 = sqrt(-1 * -1) = sqrt(-1) sqrt(-1) = -1

[safe basin]

Could be 0 as well

so nonnegative

[shadow summit]

sqrt of 0 is 0, and 0*0=0

[safe basin]

Yeah

so a and b can be zero as well

Not necessarily only positive

[shadow summit]

but its a bit redundant

[safe basin]

Well it’s not like the biggest mistake in the world or anything but still important to note lmao

Also i guess it’s sufficient but “only” won’t be true cause you could weaken that condition to say at most one is nonnegative without running into any issues

without loss of generality let $a<0$ and $b \geq 0$, then $\sqrt{a} \sqrt{b} = i \sqrt{|a|} \sqrt{b} = i \sqrt{|a| b} = \sqrt{(-1)|a|b} = \sqrt{ab}$

That should track

[obsidian monolith]

FEIN FEIN FEIN FEIN FEIN FEIN FE

[weary fjord]

Pre calc is this hard?😭

[willow skiff]

no

working with complex numbers properly is this hard

[willow skiff]

but yeah many things could be precalc that are not often covered

such as sketching the graph of y = -sqrt(-x)

function transformations btw

[weary fjord]

I never seem complex number in calc 1, is that in calc2?

[safe basin]

category theory

[weary fjord]

This is fine

[weary fjord]

What is preorder

[safe basin]

I mean you might see it somewhere before calc or during just to mention it but doing calculus with complex valued functions needs a proper calc background to make sense of in the first place

[willow skiff]

#help-32 message

yeah we only properly defined Ln z in the combined multivar and complex functions course

[safe basin]

Combined multivariable and complex functions sounds nice

I haven’t heard of a course like that here in the US

It makes total sense to put them together though obviously

[willow skiff]

Australia progressive

8 weeks multivar 4 weeks complex

[safe basin]

Guessing you switch over around when you talk about green’s theorem

[willow skiff]

I can send you those course notes!

I'll DM

[safe basin]

Ooh okay

Yeah id be interested

[distant pagoda]

This is art

Helped me so much in my pre cal class last year

So glad my teacher had me memorize the whole thing.

[willow skiff]

that is ridiculous

you just need the values in the first quadrant

then the rest follows by symmetry

in fact the entire thing is just based on two triangles

30-60-90 and 45-45-90

so like you can always convert cos(60) = sin(30) for example

[distant pagoda]

Yeah I know

Regardless however it helped me when it came to my tests.

Also helped me in my Ap exam

It’s as hard to memorize as it looks either

Once you know the main points it’s easy.

45 degree angles for example will always have (x/2) (x/2) coordinates

Well

Sq2/2 I should say

[willow skiff]

okay thank god

you had me worried there

[distant pagoda]

💀