precalculus

[silk dew]

yeezzzzzzzzzzzzzz

[viscid thistle]

No

[remote cove]

Ok

[remote cove]

@silk dew

[remote cove]

Ok

[silk dew]

I have to do all this ?

[remote cove]

U can

If u want to

They are easy right ?

[silk dew]

Yess

They are

But why u asking calculus in precalculus group ?

#calculus go to this

[tender mist]

Yeahh, bring that to calc

[upbeat yarrow]

which ones

[remote cove]

Q4

[remote cove]

I asked but no body helped

[silk dew]

okkk

i will help u

q4 ?

[remote cove]

Yes

[silk dew]

okkk

is the answer e

?

[silk dew]

is the answr = e

[remote cove]

I actually don't have answers

[silk dew]

this is actually not an integral question

[remote cove]

Did u used Limits?

[silk dew]

it is more like of a limit

[silk dew]

yes

if dx goes to zeroo

it will be equal to e

[remote cove]

Ok

Are u Indian ?

[silk dew]

yes

why ?

[remote cove]

No reason

[silk dew]

u are too

?

[remote cove]

Yes

[silk dew]

ohhh buddy welcome

i love to talk to indian

[remote cove]

I have some more questions would u like to try out urself

[silk dew]

people here

[silk dew]

yes buddy i will help u

dm me

[remote cove]

Oh

[silk dew]

u which class ?

[quasi elbow]

i do not think i am doing the right thing here

[dry nest]

Should I give u a hint?

I proved it though

[quasi elbow]

sure

[dry nest]

First convert them into sin and cos

Then take the common term 1/(sinA-cosA).

I'll leave u from here

[quasi elbow]

i got it, thank you

[winged meteor]

guys can someone give me an equation of a hyperbola

[viscid thistle]

(x^2 / a^2) - (y^2/b^2) = 1

[viscid thistle]

xy=c also comes under a hyperbola

rectangular hyperbola

[quasi elbow]

how do we solve question 24? i am getting cos(A)/[1+sin(A)] = [1-sin(A)]/cos(A) but i do not know how to proceed further

[dry nest]

Here's a hint, start from RHS

Separate the terms

And try to use the formula a² - b² in a way.

[quasi elbow]

in LHS?

[dry nest]

No

In the RHS after separating

[quasi elbow]

but does not it just become secA-tanA

[dry nest]

It becomes secA - TanA after separating right?

[quasi elbow]

yeah

[dry nest]

Now multiply SecA + TanA both in numerator and denominator and try to remember a relation between sec and tan

[quasi elbow]

do i square both sides and use the identity?

ah

i am still not getting the answer

[dry nest]

Should I tell u the solution?

[quasi elbow]

no

let me try again

[dry nest]

Ok tell me what are you getting after multiplying secA + tanA?

[quasi elbow]

1/(secA+tanA)

[dry nest]

Cool but look at the LHS

It's in terms of cos and cot

So get it?

[quasi elbow]

oh

makes sense

[dry nest]

There u go

[quasi elbow]

thank you

[dry nest]

Welcome

SL loney's a great choice for trigonometry

[quasi elbow]

of what level is it, though?

[dry nest]

I don't know I have never done it lol. I have seen it's questions but

I tell u it's better for the practice

[quasi elbow]

fair enough

what does versin(A) mean?

[river drift]

https://mathworld.wolfram.com/Versine.html

,w define versine

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by cloudedhorizons

[river drift]

one of many historical "special functions" that were used before the advent of calculators, because it was useful to be able to read them out from tables

[quasi elbow]

that's interesting

thank you

[quasi elbow]

how do i do this one?

it seems super complicated to me

[elfin cargo]

covers, vers

[quasi elbow]

ancient trigonometry

[unborn brook]

How do we prove that polynomial functions of degree 2 or higher don't have "sharp corners?"

Additionally, why aren't polynomial functions of degree 0 and 1 considered as "smooth," unlike those of degree 2 or higher?

Oh wait, by "smooth" we mean a function whose graph only contains rounded curves

Ignore the second question

[unique parrot]

pray

its probably some trig identities mixed with partial fractions or something idk

[hybrid spruce]

why is r=3

[winter comet]

what is r

[quasi elbow]

great advice, thank you

[quasi elbow]

we do not see an r

[quasi elbow]

how do I proceed further? got it

[quasi elbow]

if we are given that perpendicular + base = hypotenuse in a triangle, what can we interpret from it?

if that is even possible

i cannot think of values that satisfy that

[worldly crater]

Question. With Horizontal Asympotes, why're you able to cross the HA in some cases?

[summer ruin]

why do you think it shouldn't be possible?

the definition of horizontal asymptote isn't that it's a line that the graph of a function approaches and never crosses

[dry nest]

It can only be possible if all the three vertices lie on the same line, i.e, they are basically collinear points.

The sum of any two sides of a triangle is always greater than the third side.

[quasi elbow]

right

[cloud spruce]

I am in confusion that what should I do first calculus or stats / prob

[willow skiff]

why are you confused?

both are perfectly valid options

depending on what you want to do

[uncut mulch]

calc

[formal bronze]

Would yall say this is easy/ easy to study ?

I have an exam on this entire portion, do yall think a week is enough to ace it?

[willow skiff]

yes but depends on your level of algebra

[formal bronze]

Idk what that means but we can’t use calculators 😭and the way they teach math here is terrible in high school

This is college btw,

[willow skiff]

like, what algebra have you learned so far?

but thanks for telling me that info

I bet Khan Academy can help you with most of these topics if you want to practice

[timber blade]

easy peasy chingling cheesy

[formal bronze]

I don’t really know their names but I’d say maybe a very small amount, idk what algebra really means if I’m being honest they straight up never explained mathematical branches it was just “math”

But I’d assume I know a tiny

[willow skiff]

so then these chapters would be new to you in some way

either you don't know them at all

or you've forgotten how to do certain things

hmmm there's a lot online and in various secondary school curriculums

Khan Academy as I said

[uneven nexus]

Why is this limit equal to 0?

[willow skiff]

maybe try LH on ln(e + 1/x) / (1/x)

[formal bronze]

Tysm this is great help 🤍

[willow skiff]

no worries!

[willow skiff]

also I can't send this here, but James Stewart's Precalculus

you can get an older edition like the 7th edition online

[formal bronze]

THANK YOUU OMG

I’m aceing this for sure.

[sick roost]

Stewart’s Algebra and Trigonometry is basically the same book as his precalculus. Buy used. But these are like big books. I have Stewart - brilliant. But Sheldon Axler’s Precalculus is shorter and better, I think. Cuts to the chase.

Oh, and Axler book includes the complete solutions manual!

[snow sleet]

Wordle 1,220 2/6

🟨⬛🟨⬛🟨
🟩🟩🟩🟩🟩

[shut willow]

this becomes x ln(ex+1) - xlnx
the 2nd part is just zero

focus on xln(ex+1)
plug zero in

0 * ln(1) = 0^2 = 0

[merry tide]

My brother, what is a "chingling cheesy"

[winter comet]

you dont know chingling cheesy??? :O

[merry tide]

I dont bro

I know i am ashamed

[winter comet]

hOw CoUlD YoU

[timber blade]

he is the greatest mathematician ever lived

[green jay]

tbh ye it is

[shut willow]

Checking in, how much progress have you made?

[formal bronze]

None

It’s in 2 weeks

And a lil more

so it’s not 1 week left planning to start soon

[shut willow]

You better start right now

[formal bronze]

I’m hella tired today might start tmrw

[shut willow]

fair enough

[formal bronze]

Also lowkey I’m scared of studying math for some reason

[shut willow]

it's very easy

[formal bronze]

Should I just solve examples non stop?

[shut willow]

no need to be scared

You are not to solve examples

Read em

understand them

[upbeat yarrow]

ur cooked

[formal bronze]

My issue is I solve a few examples a few days before the exam

[upbeat yarrow]

personally i would give up

[shut willow]

bro 💀

[formal bronze]

Wtf?

[shut willow]

dont listen to him

[formal bronze]

Bro this is hella short material

[upbeat yarrow]

u should give up

[formal bronze]

And I have 2 weeks and a half

[upbeat yarrow]

and sleep

[shut willow]

anyways @upbeat yarrow for DEs what year PYQs should I solve?

[upbeat yarrow]

des 2022 and 2023 mains some exact differential questions were pretty annoying

iirc

[shut willow]

what abt 2021 and 2020

[upbeat yarrow]

i dont remeber

[formal bronze]

Sakura pfp

[upbeat yarrow]

bad memory

[formal bronze]

Why did she lowkey carry Naruto

[shut willow]

okay im gonna go and solve 2020-23

[upbeat yarrow]

yes

[formal bronze]

FRR

[shut willow]

oh i thought that was sukuna or someone

💀

[formal bronze]

.

[shut willow]

didn't watch naruto ever

[upbeat yarrow]

L

[formal bronze]

Makes sense

I remember binging entire shipuden in middle school, was cozy and fun tbh

[upbeat yarrow]

i rewatched naruto part 1 very recently

didnt continue because i wasnt studying

[unborn brook]

In the derivation of the remainder theorem, we are setting the divisor (x-c) equal to 0 (c-c). How can this be working considering that the divisor is in the denominator before we manipulate the equation to get the division algorithm?

[terse aspen]

Hey why is this not x=ln-2/3

[terse aspen]

I dont got paper near me

But i ln everything that undid the left side so i have now 10x-7x=ln-2
Than 3x/3-> ln-2/3

[safe basin]

real valued log is only defined for positive numbers

I know what you did but you can’t do it directly that way cause it gives you something undefined

Get it in thr form of a quadratic and then factor it

[rocky whale]

I feel like this wiuld be rlly easy but idk how to do it

[west jungle]

you want to split it into two separate rectangles and then add the area of both

[rocky whale]

can you give me the equation im confused

[west jungle]

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

[rocky whale]

the answer key is 5x2+10x+4 idk how u get 5x^2

[safe basin]

What are you getting?

[rocky whale]

im getting brain damage

[safe basin]

Do you understand this image @rocky whale

[rocky whale]

yea but idk what the equation is saying

[safe basin]

[west jungle]

ah, the first part of the equation is calculating the area of the left rectangle

so that's the (3x+4)-(x+1)) (2x+1) part

and the second half is adding on the area of the right rectangle

which is the + (x+1) (x+1) part

does that make more sense?

[rocky whale]

yea

[west jungle]

not sure if you need this anymore but this is essentially you’d do that, i just skipped straight to imputing variables into the last part instead of breaking it down

[rocky whale]

thanks mane

ur carrying me

w

my friend says i love you

👍

[vague goblet]

guys

[odd agate]

Cant tell if you got an answer or not?

[proven night]

Hello, guys

Are there any "smart" ways of solving it without considering all the cases?

[winter comet]

guessing

[river drift]

think about which combinations of cases are possible. that narrows down the amount of cases you have to consider

[weak berry]

Hmm, whenever I see modulus, I do combinations type things

First case all modulus positive

Secondcase first two positive third negative

Third case first positive second negative third positive

Fourth case first positive rest negative

Etc

Ul get 8 cases

Solve em find the common intersection

[echo sinew]

I believe you can reduce it to just 4 (=3 + 1) cases:

1. x ≤ -2
2. -2 < x ≤ 0
3. 0 < x ≤ 2
4. x > 2

[terse aspen]

Oh ok thank you

[shut willow]

plot it

[stoic hollow]

I understand how to factor everything in magenta, but how do I determine the cyan part?

Like where does it come from

I know why it’s there, it allows you to fully factor the thing, but how did they determine that +4x^2 and -4x^2 was needed specifically?

[weak berry]

It's experience

The more u solve, the better ul get at it

[stoic hollow]

wait so like

There’s no rule??

Because I can use the diamond solver trick thing to find -4x and -15x easily

But I have to guess for the 4s?

[weak berry]

Hmm

Yep

[stoic hollow]

how irritating

oh well

[uneven nexus]

how can we divide x^3-3x^2+3x-1 by x^n?

[daring tapir]

n>3?

[uneven nexus]

it's not given

[daring tapir]

You cant do that without a remainder

[daring tapir]

Youre dividing x^n by x^3-3x^2+3x-1 not the other way around

And uh im not sure if you know the trick for the f(x) part

But its like let it = ax^2+bx+c

And sub x =1 on both sides

Repeat

After differentiating

[uneven nexus]

why?

[daring tapir]

And repeat again after differentiating

Then you get the values of a,b,c

Tho im not sure how you would get the g(x)

[daring tapir]

Because the degree of remainder of any polynomial is always less than the degree of division

[uneven nexus]

why diff?

[daring tapir]

What else can you think of?

That was what i was taught

So yea

Thoo if you have another method id really like to hear it

Cuz this one quite frankly is a pain

[uneven nexus]

Does this trick have a name? I'm not doubting you, I just want to know the reason behind this

[daring tapir]

I mean when i was taught it this just came under an example to the remainder theorem

Maybe it does have a name

Im not sure

[uneven nexus]

I mean like, why diff it suddenly?

[daring tapir]

Gotta do what you gotta do

Sure it was counterintuitive to me too

But well

If nothing else works

[remote heart]

hello

specifically b

i have a quiz today and i don’t understand this

it wont send nvm

[slender vault]

✨

[viscid thistle]

Guys

Can someone solve this

I tried it for 15 minutes and then gave up

[summer ruin]

the hins is sin(3x) = sin(x+2x)

[viscid thistle]

Man thanks

Got the answer

[hasty jackal]

wait so to factor it ill tell. (4x^2 - 15) ( x - 1)

[plain osprey]

trying to help someone with precalc, it gave them this sequence, and i said that the sequence could be represented as
$a_n = 2^{-2 + 5 floor(\frac{n}{6})}$, but the values in the screenshot (correct answer) make no sense to either of us

[obsidian monolith]

Alrighty

[daring tapir]

The floor thing doesnt work

It clearly says the func is of the form a* b^x

And not a * b^(g(x))

So that just implies the que has some error

[stiff sluice]

how to find the roots of x^(-2)

?

[errant bramble]

There's none

[stiff sluice]

elaborate

[errant bramble]

No x satisfies 1/(x^2) = 0

[stiff sluice]

,w roots of x^(-2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[errant bramble]

See

[stiff sluice]

why

like I was hoping at least a complex root is available

[merry widget]

cuz ur dividing 1

the lowest u can get is 0.000000000......1

infinity zeroes but theres 1 at the end

but still > 0

[errant bramble]

For a graphical demonstration

[merry widget]

What shape is that

[errant bramble]

Graph of 1/x^2

At x = 0, y would be infinity but for some reason infinity is undefined so yea no solution, real or complex

[plain osprey]

Look at the values given in the function’s correct solutions though, how do they remotely make sense

[old lark]

is this the final answer or can i rewrite it as

4 sec(4x) tan(4x) ?

[uncut mulch]

numerical coefficients are better written at the start

[plain osprey]

Are derivatives considered precalc?

[plain osprey]

Commutative and assosciative property of multiplication, you can put that 4 in the middle, in front, or at the end. Coefficients usually go in front though

[merry widget]

i believe its basic calc

[plain osprey]

Yeah but trig derivatives usually aren’t intoduced in pre calculus

In my precalc we got the formal definition of a derivative

And that was it

[merry widget]

lmao in mine we wrapped things up with hyperbola

wait no we went over unit circle

[daring tapir]

They dont

[plain osprey]

That’s what I’m saying

[daring tapir]

So the question is wrong?

(Also ping when replying)

[merry widget]

are conic sections taught in the us curriculum?

cuz it appears that in us they go straight to trigo and functions for precal..?

[elfin cargo]

That is weird. In precalc, they usually teach only trig stuff

[merry widget]

really

in my country precal was only conic sections then only do we slowly get introduced to trigo by the end of it

[elfin cargo]

I replied to the person above. And yes, I think conic sections are also taught in the US

[merry widget]

which makes me wonder that if u go straight to trig in precal, when do they teach conics?

damn so that could only mean

my country is far behind in math

[elfin cargo]

I just realized my sentence was misleading there. I meant that they teach you trig and its properties, not trig derivative

And there is no standard for precalc curriculum either. It depends on your school I think. They might teach trig, conic sections, complex numbers, matrix, probability, ... there

[merry widget]

its so interesting that people of the same age from different parts of the world could have very different levels of knowledge

[elfin cargo]

Well, you will learn all of this more in-depth in college anyway

[merry widget]

yeah thats good to know

im kinda scared for college cuz rn my only strong area is math

im so stupid at high school subjects other than math subjects like precal, stats and physics which are my strong forte lmao

[elfin cargo]

Umm but precalc is math

[merry widget]

yeah i would love to have math in college

[elfin cargo]

Ok I misunderstood it 😂

[merry widget]

im kinda leaning towards applied math or algebra but the dudes at #math-discussion got me rethinking it

i dont understand a single thing they talking about other than sigma symbol lmao

[elfin cargo]

Then go for math major

[merry widget]

yeah i would love to go for math major but it seems to limit my career to be a teacher

which aint bad at all but teachers dont get paid what they deserve

[elfin cargo]

Yeah. Can't argue with that. Becoming a math professor at a university is the only thing I know if I am a math major

[upbeat yarrow]

ur cooked

[merry widget]

i know

[arctic meteor]

Hi what does $x_{n+1}$ mean in $$x_{n+1} \leq x_{n}$$ and $$x_{n+1} \geq x_{n}$$?

[obsidian monolith]

wolly5114

[summer ruin]

the n+1'th term in a sequence

[arctic meteor]

i have found this in a textbook about series not sequence

@summer ruin

[summer ruin]

same thing

[plain osprey]

Yeah probably

[jagged patrol]

When generating exponental regressions and using y^=ab^(x) do I have to also have a ^ over x (y^=ab^(x^))

[summer ruin]

what does that even mean

[elfin cargo]

I think not because with regression you are trying to fit some curve over your datasets that is why you have y^ because it is just an approximation. But x is your input (not predicted x)

This is just a notation you can totally write y = ab^x but to distinguish between true y and predicted y, they usually write y and y^

[jagged patrol]

Idk my teacher just taught it today and I have hw on it

[jagged patrol]

Thanks

Can I use something like this to show that I want to find the y^ value for x=29. I'm 99.9% sure it's wrong but dont know how else I would write it

[elfin cargo]

This looks fine to me. Why is it wrong?

[jagged patrol]

Because it's not really a function just a equation for y^

My equation wasn't like y^(x)=. it was just y^=

[elfin cargo]

It is a function, tho

[jagged patrol]

Well yes it can be written as one I guess

[elfin cargo]

You are expressing y^ as a function of x

[jagged patrol]

Ok I see

I mean technically it's a function but I haven't been using function notation

Thats probably the cause of the confusion

[elfin cargo]

You can just set y^ = g(x) = ...

Like you would with y = f(x)

[jagged patrol]

Yes that makes sense but I'm not sure my teacher would want that

I'll ask him

Thanks for help

[merry widget]

math is vast

you can have different perceptions and solutions

but the final goal is to arrive at the correct answer

[winter comet]

not always 😄

[terse aspen]

For horizontal aymptote

If the denominator has a bigger degree than the numerator than horizontal to is zero, but if the denominator is a smaller degree than the numerator than the horizontal is undef and if numerator and denominator are the same degree, then it’s a coefficient of the numerator over the coefficient of the denominator of the highest degree?

[daring stream]

yea uve got the right idea, in general if the degree of the denominator is greater than the degree of the numerator then u get a horizontal asymptote at $y = 0$ bc as $x \to \pm \infty$, respectively the function will approach zero. if the degree of the denominator is less than that of the numerator then u dont get a horizontal asymptote as it is undefined, bc the function will continue to grow without a bound wether that be positively or negatively, as $x \to \pm \infty$, then our final case is if the denominator and numerator are equal then we get a situation where the horizontal asymptote it at $ y = \frac{C_{Num}}{C_{Den}}$ where $C_{Num}$ is the leading coefficient of the numerator and $C_{Den}$ is the leading coefficient of the denominator therefore we see that the horizontal asymptote is basicly the ratio of the coefficients, does that make sense?

[obsidian monolith]

emma

[rich fox]

hi, does anyone know how to derive the formula sin(A+B) from cos(A-B) = cosAcosB+sinAsinB?

[terse aspen]

Yes thank you

[terse aspen]

For a logistic growth graph the denominator number to the right of the 1 is always just 1 below the carrying capacity limit factory (the numerator?

[half star]

yes, it is whenever the initial value of y (at t=0) is 1

more generally you have this formula https://en.wikipedia.org/wiki/Logistic_function#In_ecology:_modeling_population_growth

[storm lodge]

did i just see sigmoid curve

https://tenor.com/view/mewing-cute-cat-meme-cat-cats-gif-10805439624456023806

[half star]

in your case K is 5000 and P_0 is 1. The growth rate r is 0.8

[willow dagger]

https://tenor.com/view/terrible-meme-bad-memes-meme-club-penguin-club-penguin-gif-gif-24873547

[terse aspen]

I see thank you and is t a time value set in days?

[half star]

depends on what your model describes; could be any unit of time

[terse aspen]

So it would needed to be multiplied or divided for hours or months

[terse aspen]

Oh ok

[half star]

if it's some kind of word problem I'd check what it says, it should mention the time unit used

[still laurel]

Guys help..

[willow skiff]

what have you tried so far?

it's in the form $y = k \frac{x - 3}{(x + 2)(x - 4}$ for some real $k$ btw

[obsidian monolith]

south's secret twin brother

[pseudo plover]

Why do we integrate to find arc length

If integration gives us the area under the graph?

[exotic barn]

Try to read some of this
https://tutorial.math.lamar.edu/classes/calcii/arclength.aspx

[broken pecan]

Does anyone have practice problems for graphing polar functions on both rectangular and polar axes

[willow skiff]

if integration was only useful for finding areas we'd be doomed

the correct statement is integration is a general method for coming up with exact answers by summing infinitesimal quantities

[winter comet]

☠️

[winter comet]

i like to think of it as a continuous sum :>

[willow skiff]

if we add up the areas of very thin rectangles, we can get the area under a curve

[willow skiff]

nice analogy

similarly, if we add up very short line segments, we can find the arc length

[willow skiff]

https://tutorial.math.lamar.edu/problems/calcii/polarcoordinates.aspx

try this

[quasi elbow]

can we always separate the terms like this?

[summer ruin]

C + C + C + C = C(1+1+1+1)

[quasi elbow]

ah

makes sense, thank you

[fresh vigil]

how is that precalc 💀

[quasi elbow]

I was studying that under height and distance

[elfin cargo]

It is a sum. Look precalc enough

[quasi elbow]

but I later realised it's just pre-requisites

my bad

[winter comet]

everything is precalc 😁

[fresh vigil]

💀

[safe basin]

what else would it be lmfao

theres no calc in that

[echo cedar]

Really

Is everything in algebra 1, 2, and geometry used in calc

And am I doomed if idk proofs

[winter comet]

no

[winter comet]

actual proofs or just geometry proofs?

[echo cedar]

I am not sure what actual proofs look like..

Like those

Like

Geometry

[winter comet]

like these?

nah

[echo cedar]

What’s the most important one used for pre calc?

[winter comet]

you dont need to know those

[winter comet]

most important what?

[echo cedar]

Yes

[echo cedar]

Out of the 3 subjects

[winter comet]

those are kinda bull imo 😂

[echo cedar]

What is bull

Like easy?

Sigh

[winter comet]

algebra 1 and 2 are mixed together for me, but more of those

[echo cedar]

Thanks!

[winter comet]

no like pointless

lol

[echo cedar]

Oh

I think so too

[winter comet]

they hand it to you on a silver platter to memorize

unlike actual proofs

lol

[echo cedar]

What are actual proofs like

[winter comet]

[echo cedar]

..

[winter comet]

horrible 🤣

[echo cedar]

Oh

[winter comet]

naw im just bad it lol XD

[echo cedar]

Wait let me search online

Oh

Looks so hard

[winter comet]

real analysis is literally calculus but proofy

[echo cedar]

When is it taught

actual proofs

[winter comet]

you usually get like a proofs class and i think maybe a little experience in some linear algebra classes? and a LITTLE experience in calculus class

but real analysis is like very proofy calculus

[echo cedar]

Ohh😭 I see

[winter comet]

calculus is fine but i would be so screwed if/when i would take real analysis ☠️

[echo cedar]

Is that its own Seperate subject

[winter comet]

I mean....

what would you consider a seperate subject 💀

real analysis proves concepts from calculus

I assume they use concepts that aren't in calculus so theres that...

[echo cedar]

Like a course you take at school for a year

[winter comet]

yes real analysis is its own course

[echo cedar]

Ohh okay

Do you think the best way to study math is to just do a lot of questions

[winter comet]

I think learning new concepts and being able to apply them in different ways is key ngl

and also reviewing so you dont forget

idk why emojis go first when i put them after :l

[echo cedar]

How long do u need to review

Like

After you learn it

And then u move on to another thing

[winter comet]

well the goal of reviewing is so you dont forget it XD

[echo cedar]

I mean like

Every few months? Weeks?

[winter comet]

so you gotta think about what you know and be like "oh i kinda forgot that thing" and then go back to it

[winter comet]

as long as it takes for you to not remember well, i don't have a set time 😂

it also probably depends on the topics

id say probably every few weeks, maybe a month idk its hard to generalize like that

of course if you know it you know it and you may remember it for like months or years without having to review lol

after a certain point it be like that

[echo cedar]

Okay

Thank u

Sigh

Oh math

[winter comet]

XD

[echo cedar]

Do you like math

[winter comet]

yus

[echo cedar]

Do you like it even when you don’t understand it

And is ur brain ever too tired for math

[winter comet]

uh

I like tryna understand it i guess?

[winter comet]

i mean sometimes i make dumb mistakes so yeah

[echo cedar]

Oh wow

[echo cedar]

Doesn’t your brain hurt tho

Like when you’re confused

And it feels like there’s a brick

And ur brain is glued

[winter comet]

maybe if i was pressured to do it but i haven't been for a long time cuz i usually learn ahead n stuff

if i need a break i take one lol

i feel like im not getting ENOUGH time to do math ngl

english sucks 💀

[echo cedar]

Usually learn ahead, like u learn before ur class

But isn’t that more confusing

I think my brain would hurt more

Good idea tho

I’ve been trying to do this for physics

[winter comet]

no why would it be more confusing

[echo cedar]

Or else in class I’ll be so confused

[echo cedar]

Bc ur reading it without a teacher telling u

Idk

[winter comet]

if i get it i get it

if i find something that makes sense 😂

[echo cedar]

O

I don’t ever

I always get things slower than my peers

But after I get it I think I get better than them

[echo cedar]

I love English

Jk I don’t

But I like writing

I never get tired of writing like I get tired of mathing

I’m so bad at analyzing work

[winter comet]

i don't love or hate it, its just not my thing

hours and hours of not my thing

[echo cedar]

Mhm

[winter comet]

rather than math, and the physics/cs i wanna learn 😭

[echo cedar]

But is hours and hours of math your thing

Physics is so painful

I can’t wait for chem

[winter comet]

tis a gun

a rifle

[viscid thistle]

No

[lavish cave]

hey

any one has the book:
pre -calculus, by art of problem solving?
and can share the PDF for it?

[daring tapir]

Piracy isnt really allowed in here

But i hear someone named anna has an archive somewhere

[polar halo]

I heard theres a library somewhere, think it was called genesis or something like that

[lavish cave]

Do you know How can i get to her?

[cursive ocean]

Hello 👋🏼
I found the pdf of that book online !
If you want , I can send it to you via direct message !

[fresh vigil]

its fein math

🤦🏻‍♂️

[oak kiln]

@hallow laurel can you help me with this please?

the big angles are putting me off

[hallow laurel]

no, dont ping me

[oak kiln]

ok

[quiet obsidian]

Hi could could use some urgent help… anyone active ?

[winter comet]

whats the question

[quiet obsidian]

How do I write the equation for this graph?

Like I know (x-2)(x-4) will be in the numerator and (x+3)(x-4) in the numerator but what I don’t understand is how to find the a value. Do I just assume that the y intercept is -1.5??

[winter comet]

if you multiply by a factor of 2 you should be good 💀

idk what the 'a' value is but

the limit approaching infinity of it has to be 2 because theres an asymptote at y=2

so it should have another factor of 2 in numerator

[echo cedar]

Read

Also depends on what ur writing

Ofc

[cloud steeple]

what do i need to start precalc

[winter comet]

algebra i guess?

[cloud steeple]

what part of algebra specifically

[winter comet]

half of precalculus is just a repeat of algebra so just knowing algebra in general is recommended

[cloud steeple]

oh ok

then i think i have what it gets

[winter comet]

probably :>

its not that bad lol i wouldnt worry too much and just start :D

[cloud steeple]

ok ill bolt trough it and finish this month

lol

[winter comet]

lol

[quasi elbow]

how do we interpret this question

[quasi elbow]

why have we taken angle QAP = theta and angle QBC = phi and not vice-versa? i get that tan(phi) is greater than tan(theta) but according to the first part of the question, should not it be the other way around?

because when i calculated it like that my answer was not matching

and like what if the question is in general form?

[quasi elbow]

in second figure, how can we say that pq is the perpendicular?

[quasi elbow]

this is the original problem

[quasi elbow]

what am I doing wrong

BP is d

[strong hedge]

yeah the diagram is wrong

should be the other way around

[strong hedge]

take the distance b/w the points as 100 ig

wait its given 1

hm

QAB should be 30 and QBP should be 60

cause 60 is greater than 30 so it should be closer to P

also what have you done in the top right?

[strong hedge]

this is 3d

gotta visualise it

practice 10-20 questions and youll get an idea

[strong hedge]

this also 3d

draw the figure out

[quasi elbow]

it's a formula

for that particular type of question, H = asin(alpha)sin(beta).cosec(beta-alpha); beta > alpha

[quasi elbow]

i am still not getting an answer

it's [2]

[quasi elbow]

meh

[quasi elbow]

i am running on two hours of sleep

[quasi elbow]

i know

i am just pretty scared lmao

my goal was to complete trigonometry by the end of october and i am two topics behind

[quasi elbow]

practice questions of height and distance and inverse trigonometric functions

[daring tapir]

Doable enough

[quasi elbow]

bro

you guys make it sound so easy lmao

[stiff sluice]

how do I get to understand trigonometric substitutions

[winter comet]

still #calculus lol

if u mean trig sub for integrals

[stiff sluice]

ok thank u

[simple scroll]

Hey can someone help me with this factoring?

[strong hedge]

cancel (x-7) and (x+2) out

[strong hedge]

practice

[quasi elbow]

we have to calculate the value of n

i don't know what have I done but can someone please check my work

[arctic meteor]

How did that partial fraction ended up as the bottom fraction?

where did that second fraction from the bottom come from?

[quasi elbow]

how do I proceed further

i tried applying cot(a) - cot(b) = sin(b-a)/sin(a).sin(b)

but it is not really taking me anywhere

i also tried equating (2) and (3)

but don't know where to proceed to from there too

[quasi elbow]

what am I doing wrong

[willow skiff]

$\frac{60 (\sqrt{3}+ 1)}{3 - 1} = 30(\sqrt{3} + 1)$

[obsidian monolith]

south's secret twin brother

[willow skiff]

does that match with the answer?

[quasi elbow]

oh

yeah, thank you

[willow skiff]

no worries!

[quasi elbow]

anyone?

please

[willow skiff]

$-\frac{1}{2} \frac{1}{n + 1}$ is remaining in the second bracket

[obsidian monolith]

south's secret twin brother

[willow skiff]

so -1 in -1/(n + 1) got split into -1/2 and -1/2

[viscid thistle]

they are splitting the denominator right?

the 3 linear factors into respective partial fractions?

[arctic meteor]

@viscid thistle yes the denominator

[viscid thistle]

ur asking

why

they are splitting it

?

[arctic meteor]

yes how did 1/2 and and the other 1/2 got there

did he repeated partial fractions again?

[willow skiff]

no

[viscid thistle]

bro

like

he assumed

that the fraction

with

n denominator

as

A

like the numberator

of that as A

ukw

lemme give a video linl

https://youtu.be/QKkdYW77xNI?si=JtUxSxcdf8KgzqCQ

[arctic meteor]

i know how to use partial fractions and this doesn't explain how the first ended up as another fraction in the 2nd

i found this on another video but it doesn't explain how from the 1st picture got to the 2nd picture

[viscid thistle]

umm bro

like

what they are doing is

they are taking 1/2(k+2)

as

1/(k+2)

-1/2(k+2)\

x-(x/2) =

+x/2

after then

they just took

2 common

from 1/2k

and

-1/2(k+2)

and -1 common from

1/(k+1) and 1/(k+2)

@arctic meteor

[arctic meteor]

ok i figured it

[viscid thistle]

nice

[long rapids]

I am in 9th grade taking foundations in maths -_- Who can teach me precalculus so I can skip my classes.

[viscid thistle]

lol

precalculus

involves what concepts?

also which country are u from

cuz

sylabbus varies

[long rapids]

America

[viscid thistle]

damn

so im guessing

ukw

since u understand

english

i presume

why dont you try out yt videos

the organic tutor

organinc chemistry tutor

i find him ver yhelpful

he has a series

for pre calc'

[long rapids]

Ok I want to learn harder maths because I hate my classmates in this class.

[viscid thistle]

damn

harder math?

sure

same here bro

so

like

what do you expect

from pre calc

im guesisng

basic interpretations of function

s

and stuff like those

basic algebra

log functions

and stuff?

[long rapids]

Is precalc hard?

[viscid thistle]

IDK LMAO

cuz

for me they dont take pre calc and all

they only have calculus

directly

Integral Calculus

they didnt teach me yet

[long rapids]

Ok is calc hard?

[viscid thistle]

i taught myself

[viscid thistle]

uhh depends

not actually

its basically algebra

but on steroids

u need to know the identities and stuff

and high pattern recognition

[long rapids]

If I don’t even know algebra 1 is it hard? How long it will take to learn all of this?

[viscid thistle]

bro

dont worry about time

the thing is

u have to allow ur mind to think and stuff

like

explore

and grasp

appreciate

the methods

and comprehend the beauty

like

caluclus

feels

like

literally cheating

the universe

[long rapids]

Oh ok

[viscid thistle]

calculus

is basically

calculating slope and area under the function

respectively

differential and integral

[long rapids]

Sorry I didn’t understand?

[viscid thistle]

um

basically

uk whats a slope?

[long rapids]

Yep

[viscid thistle]

yeah

so its basically

how y changes wrt x

does y change very fast

or does y decrease

or does it remain constant

if the slope is 2

that means

for every unit change in x

y changes by 2

or

y changes by one unit

for every 2 unit chasnge

in x

[long rapids]

Ok

[viscid thistle]

to get a better grasp

like

derivate of a function

is basically

calculating this slope

but for quadratic equation and stuff

the slope isnt constant

so it is denoted by

d(f(x)/dx

basically

for very small

infinitisemal changes in x

how y changes

[long rapids]

Umm I didn’t get can you simplify?

[viscid thistle]

umm

this might look very complex

but try to understand first

what individual terms in the graph mean

once ur done tell me

[long rapids]

Y means front and X means under

[viscid thistle]

x means front

y means under

[long rapids]

Oh ok

[viscid thistle]

yeah can u understand?

the individual terms?

ignore alpha and beta

those denote angles

but we dont need them now

so basically

when i take

the interval of x

for some value

i dont get the actual

slope

lemme show you

[jagged patrol]

Not at all

[tender mist]

Depends from person to person. But putting enough effort in, and making sure there's no holes in your knowledge, no, precalc isn't too hard

[jagged patrol]

https://youtu.be/4EMbtrRj0Vk?si=9BMd7pWlvhKg78kc

https://youtu.be/2wrPGtP61fo?si=_-2fA4Wj8--XNhqZ

https://youtube.com/playlist?list=PLE88E3C9C7791BD2D&si=VyAwqIvUKjcuxpee

Watch these in order then you'll be good to go

[surreal crescent]

Khan Academy

Best Education out there, and it’s free

Sal is my Hero

[zinc compass]

Anybody studied the whole precalc on Khan Academy? Do you think Khan covers everything?

[jagged patrol]

You can cross reference with the topic list in AP precalc if you feel like it missing something. GL if u gonna do it

[jagged patrol]

Is it not just [-7,4] [8,infinity)?

Have u already tried that

If it's not then [8,9] or [8,9), no?

[idle bridge]

it did not work

[jagged patrol]

What did it say the solution was

[idle bridge]

mb im on the next one

[jagged patrol]

Alr

[idle bridge]

this the new one

[jagged patrol]

Can you show the hint it gives you

Like the example

[idle bridge]

ok

this another one

[jagged patrol]

Try x<=-3 3<=x>=0 x>=7

[idle bridge]

it said this

[jagged patrol]

Hm

[jagged patrol]

Can you try and use the actual symbol for => and <= instead of the rough one

The one with the line through it

[idle bridge]

ok

it skip it i say you was right but it just did not work

nvm ty tho

[quasi elbow]

can someone please explain how we can say if the inverse of a function exists

like what exactly is "bijective" and how can we know by just seeing its domain and range

[daring tapir]

In short for every value in range theres exactly one value of x in the domain

That is mapped to it

[daring tapir]

We dont know that by just the domain and range

We judged it by seeing the graph and stuff

,w graph cosx

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by enderdoesntmind

[daring tapir]

See so in here for 0 to pi

[quasi elbow]

but

is not it 0 to pi for sin to

too

then why did we take another function

[daring tapir]

For sin its -pi/2 to pi/2

,w graph sin(x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by enderdoesntmind

[daring tapir]

See so in here for 0 to pi
You get two values of x for any values of sin(x)

Except 1

For -pi/2 to pi/2 theres a unique value

[quasi elbow]

two values?

ah

so

normal cos function

its domain is 0 to pi, right?

[daring tapir]

For that one value of sin(x)

[quasi elbow]

yeah i got that

[daring tapir]

There are two xs

[quasi elbow]

yes

[daring tapir]

For cos its principal domain is 0 to pi yea

[quasi elbow]

question

what is principal domain

[daring tapir]

But you can really just input any value from -inf to inf

[daring tapir]

Like every value of cosx that can ever be reached by subbing any value of x can be reached by subbing [0,pi]

Idk the rigorous definition

But this is the essence

[quasi elbow]

okay

so

the summary is

if a function has only one value at a point

its inverse exists?

oh

because

[daring tapir]

Uh can you word it better

Kinda confusing

[quasi elbow]

if a function is bijective

[daring tapir]

Ye

[quasi elbow]

and the reason is that

if there's two values, you'd be confused

where to go back to?

[daring tapir]

Yeps

[quasi elbow]

got it! thank you so much

oh also

[daring tapir]

More like both will be an answer

But by the definition of function for f(x) to be a function for every x there can be at most one value of f(x)

[quasi elbow]

do we learn the graph of each trigonometric function? because the place i am learning from is just like since we can see the domain of the function is this and this, we can say its inverse exists

[quasi elbow]

but then why is it not that for sin(x)

[daring tapir]

It will be better if you learn it yea

[quasi elbow]

okay

[daring tapir]

It is

[quasi elbow]

bro

[daring tapir]

So they changed the domain

[quasi elbow]

yeah but

after they changed it

[daring tapir]

To [-pi/2,pi/2]

[quasi elbow]

not before

yeah

[daring tapir]

Yra

They had to change it

[quasi elbow]

oh wait

is that the definition for inverse trigonometric function?

[daring tapir]

What is?

[quasi elbow]

.

[daring tapir]

Nope

Its just the definition of a function

,w define function

,w define a function

[obsidian monolith]

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

Requested by enderdoesntmind

[quasi elbow]

,w function

[daring tapir]

....

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by lemonadewithice

[quasi elbow]

okay so

[daring tapir]

Just google it lmao wolfram is dumb

[quasi elbow]

this may sound dumb but

my question is

when we were not studying itf

like, only trigonometric functions

we did not change the domain, right?

[daring tapir]

Ye

[quasi elbow]

then does that not defy the definition of a function?

[daring tapir]

Nope? For every value of x theres only one value of that function

So like sin(pi/2) is 1 there are not multiple values that satisfy it

[quasi elbow]

okay, got it

thank you

[daring tapir]

Google the definition of function btw it feels like i didnt explain properly i may have missed some shit

[quasi elbow]

the thing is

i get what you mean

by "function"

i just do not get

some stuff

[daring tapir]

Ask away

[quasi elbow]

which i will rather google because it sounds pretty stupid lmao

but thank you for your help

i got it

@daring tapir

so