#precalculus

1 messages · Page 74 of 1

whole void
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At what level?

velvet meadow
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like the basics, without the use of derivative

void charm
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wait isn't L'Hospital only work well with any limits of some exponents like 0^0 or 1 power infinity???

whole void
void charm
#

apply that on basic function would only make it harder for student I think

whole void
knotty summit
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It is simpler to multiply by the conjugate here

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I think L'Hopitals would make things a bit more messy with the square roots

whole void
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not rlly. The denominator goes away, the square root of 2 goes away

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either works

knotty summit
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sure

velvet meadow
whole void
willow skiff
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there's no AB or BC in precalc

smoky helm
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My school added it

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It depends on if you do unit 4 or not

willow skiff
smoky helm
#

Idk

whole void
burnt vapor
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hey everyone

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someone can help

modest bolt
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!da2a

tender questBOT
#

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

solemn olive
#

Suggestions please?

image.png
digital sage
solemn olive
digital sage
#

wait

true geode
#

Case by case

digital sage
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check if it's true with m = -2/3

solemn olive
digital sage
#

then divide both sides by 3m+2

true geode
#

So you want to consider when THIS is either positive, negative or zero

digital sage
true geode
solemn olive
digital sage
#

hmm

true geode
#

Yes: whether it's positive or negative will affect how the inequality flips

solemn olive
#

Aight, thanks.

true geode
#

And whether it's positive or negative is dependent on whether m is greater than or less than -2/3

shut rampart
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hello, are they any books or courses online from udemy/youtube people would recommend for precal to calculus 1-2 ?

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i’m at cal 2 learning integrations for the summer for next year but i find i need to brush up on the old concepts

willow skiff
soft plover
magic remnant
#

Okay

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I just want to know

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one thing

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where did sal khan

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get the 3 from

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This sounds dumb or idk if I'm slow

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But the 3 is messing me up

winter comet
novel girder
#

can i have help on this 🙏

image.png
digital sage
#

you can take the concentration of hydrogen ions in eggs divide by concentration of hydrogen ions in baking soda

azure jay
#

hey guys i can t figure out the convexity inequality

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m trynna use it to demonstrate the holder s inequality

jolly swan
#

so its 8.3/7.8

knotty summit
#

you have to use the logarithms

strong inlet
#

Lowk hate trigonometry 💅

main crystal
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Hi

winged wigeon
#

Hopefully it’s fun

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Managed to learn trig before the precalc book gets here

hardy willow
# magic remnant

What are "energy points" for? Is there a final boss made of tensors you must defeat?

hardy willow
#

I hope it has at least 1000 pages of value.

willow skiff
winged wigeon
#

And so that was the only thing I found

hardy willow
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I'm sorry to hear that.

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Knowledge should NOT cost that much.

winged wigeon
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Finally got it

winged wigeon
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Glad I didn’t have to pay $200

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For a new one

hardy willow
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I suppose.

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Still, saddens my heart.

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I have so many books to buy and can't afford to because of crazy prices. It's not paper costing, it's publishers. 😟

winged wigeon
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True

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If only James Stewart published this for free

hardy willow
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I bet it's Saleem Watson's fault.

winged wigeon
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😭

winged wigeon
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Holy shit

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There is so much exercise

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🥹

valid verge
hardy willow
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Thanks nature for the support.

valid verge
#

Anytime

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Pope

whole void
rigid dagger
rigid dagger
#

if you build this machine, you can fill it up with a liquid and it will calculate the square root of the volume of liquid poured into it

near quartz
hardy willow
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Haha I paid mine 45, checkmate.

near quartz
#

Wait until you have to purchase spivak and his solution manuel 🗿

hardy willow
#

Haha jokes on you I am not from the US and A.

whole void
half oasis
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Any high school student?

near quartz
#

Or books in general

echo stone
limpid nest
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how do i start learning precalc?

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do i have to know other forms of math b efore this?

near quartz
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Just basic algebra

limpid nest
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oh thats it? so like algebra 1 is good enough right?

near quartz
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I'm not familiar with american courses but if you know how to solve basic equations and manipulate graphs of functions it should be okay

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Look at axler precalc book and see if the beginning of the book looks familiar to you

limpid nest
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most of thes seem easy enough

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thanks

near quartz
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👍

echo stone
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I did precalculus after algebra 2 and geo

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but if that works for you, go ahead

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precalc is meant for ppl who finished alg 2 and a basic knowledge of trig, so I'd say u should at least make sure u know that

limpid nest
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alright so i have to learn alg 2 and trig correct?

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if thats the case ill start with those and continue

whole void
limpid nest
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and I do want to learn, just stuck on where to start

whole void
limpid nest
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i gotta get ahead

whole void
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In my opinion, precalc is kinda a waste of a course. This might be frowned upon, but I would actually recommend doing geometry and algebra in great detail and then going kinda straight to calculus

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but if u want u can also touch on discrete math or other things first

noble lava
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precalc is just a bunching of random topics

limpid nest
noble lava
#

do alg trig etc individually

limpid nest
#

whats the most optimal way of learning these?

noble lava
#

khan academy if u like learning online

whole void
noble lava
winged wigeon
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I literally just went to trig

whole void
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Precalc is basically just parametric/polar, conics (which are arguably algebra 2), sometimes more on complex numbers, and also vectors/matrices

noble lava
#

if you know of a reputable crash course thats in your budget you should consider enrolling

limpid nest
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crash course?

noble lava
#

like a course that introduces you to these topics in a way that will lead up to calc

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or just a course that covers these in general

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i would go for the second one since these chapters have a wide range of applications outside of calc as well

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how much time do you have before uni begins?

winged wigeon
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“Incoming freshmen”

limpid nest
noble lava
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yes i read that, does freshman not mean 1st yr undergrad

echo stone
noble lava
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ah

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well then you shouldnt be in a hurry to be finishing these topics then, you presumably have time, so a crash course wouldnt be suited for your needs

winged wigeon
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I am in the same situation as this guy I also am a incoming freshman (I took algebra 1 in 8th grade now I’m learning Precalcsmokingbread )

limpid nest
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well my main goal is to take the highest level of math I can and do it asap, im already skipping a level of math

limpid nest
echo stone
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don't be too much in a hurry

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or else you might not understand what comes later

noble lava
winged wigeon
# limpid nest HOW?

Well I took a geometry and algebra 2 course over the summer which I managed to finish it really quick as I have a good understanding in math.

noble lava
#

these chapters shouldnt be considered as a lead up to calc, but as chapters that have their own essence

echo stone
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if u skipped alg 2, I suggest u take precalc and not go directly to calc

winged wigeon
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I agree

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Precalc is just review of algebra 2 (at start)

limpid nest
winged wigeon
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But I have seen difference with other courses

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They teach the same content but sometimes in a different order

limpid nest
winged wigeon
#

I’m assuming you’re in the US but there should be a curriculum your school teaches from the state. Like how I am from Texas here and we learned from the TEKS curriculum. There are multiple textbooks that follow TEKS and I didn’t learned from them but I did review them as they were at a thrift bookstore and they followed the curriculum exactly.

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You should probably get a textbook that teaches your state curriculum

limpid nest
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thats a good idea

winged wigeon
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You’ll have knowledge of majority (if not all) that a average junior has been taught from your school

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Overall my recommendation is you follow a course/textbook from your states curriculum

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I no longer go off this branch anymore

limpid nest
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what do you do now?

winged wigeon
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I wanted to learn precalc by James Stewart as I heard his calculus book is good and well it is overall really good imo

limpid nest
#

wait so the person who creates the book will have different methods?

winged wigeon
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Sometimes

limpid nest
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what makes his so intriguing?

winged wigeon
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The amount of exercise and examples this guy has put on the book is incredible

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His teaching in text is really good

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Another main reason

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Is because most US colleges uses his textbook

noble lava
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it's pretty vast though

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it covers everything from calc 1-3

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so you might get overwhelmed

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but if you feel like u wont its good

winged wigeon
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That’s what I’m worried when I go to Calc

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But eh I think I’ll manage

noble lava
#

well the topics in the book are sequential though

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theres no mixing in that aspect

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just dont skip ahead and get scared

winged wigeon
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Yeah I understand

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I’m going to be really careful with calc book

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Like it’s my own child😭

limpid nest
#

wait so in school what level of math are you planning to take?

winged wigeon
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Well

noble lava
winged wigeon
#

I haven’t told my counselor I took algebra 2 so I have to tell her that soon so algebra 2 atm but once I tell them I will be learning precalc as I can’t prove my credit from a guy who made a house based off integral😭 (unless I take a test for it though which maybe)

limpid nest
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im so far behind

winged wigeon
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No you’ll be fine

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I am only doing it because I like math I didn’t care too much of being ahead

limpid nest
#

you are miles ahead of me

winged wigeon
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If it makes you feel better😭

limpid nest
winged wigeon
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I learned algebra 2 in like a week😭

noble lava
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no matter how far ahead u will be

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u ll always be behind someone else

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learn it cause u like it not to beat others at it

limpid nest
noble lava
#

dont rush tho

limpid nest
winged wigeon
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I literally got a full 100 on that course😭

noble lava
#

You learnt this part in a week?

image.png
winged wigeon
#

Sequence in my algebra 1 class

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Matrices and vectors not really🤷

hushed sphinx
#

Hmm, I vaguely thought "algebra 2" was a portion of high-school math, but matrices sound not particularly high-school to me.

noble lava
#

guess it's google messing up again

winged wigeon
#

AI overview😭

noble lava
#

no, other sites also tell me the same

winged wigeon
#

But also tbf many places teach by a different curriculum

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My state in algebra 2 did not cover trigonometry at all

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I learned it while my book was getting shipped to me ( through khan academy (I love sal))

noble lava
winged wigeon
#

also curious can you post trig here

noble lava
winged wigeon
#

Why have a trig Channel aswell😭

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lol

left sail
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what do we think about openstax for precalculus ?

noble lava
#

remove the precalc channel i say

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but that would get shot down so im not gonna suggest it

winged wigeon
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😭

winged wigeon
left sail
whole void
#

In some schools

neat wave
#

sequences and series is rlly easy

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so is prob and stats

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id say maybe vectors and matrices takes some time

noble lava
#

All of that cannot be done in a week

neat wave
#

except for sleep

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and eating

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or its like a diff type of schedule

noble lava
#

Still not possible to do it all well

neat wave
#

like if its me and u

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barely possible

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no offense to u

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but like if it was a genius

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then possible

red storm
#

they teach you their applications in solving systems of equations

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finding determinants, inverses and elementary row operations

quasi fog
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Yeah, row operations w matrices are usually in Algebra 2. But nothing too crazy

winged wigeon
#

For me matrices were only taught to solve system of equations

red storm
#

you can also solve for coefficients with them

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you can just fit a curve onto a set of points but it will require the r x c to get bigger

noble lava
versed ledge
bold inlet
heavy pewter
barren elbow
#

Anyone one wana do matrices group study with me in depth?

hardy willow
barren elbow
hardy willow
#

Answer is no.

modest bolt
#

If you are deeply studying matrices and get many doubts, you can create a thread for it(probably by asking mods to create one) and ask your doubts in thread, whoever is interested will help/join.

coral wedge
#

are trig identities and solving trig functions difficult?

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like will I need to memorize the identities or something like that?

modest bolt
#

trig functions are harder than others, so many manipulations and formulas needed flonshed

hardy willow
#

Sin/cos of sums, sums of sin/cos, a few things about dissected angles and doubled angles and you're pretty much good to go.

coral wedge
#

hopefully it’s not that bad

hardy willow
coral wedge
hardy willow
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Unjust.

coral wedge
#

which is the whole reason I took summer class

hardy willow
#

You're being forbidden from taking that class?

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That's not cool.

coral wedge
hardy willow
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Asking because I'm not familiar with that system.

coral wedge
#

which is dumb because no other school does it like dumb

coral wedge
#

if I don’t have a 93% they don’t allow me to take it as I’m not ready

hardy willow
#

Monsters.

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They deserve to be crucified.

coral wedge
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facts

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I have a 90% rn, maybe i can make it a 93 but im losing hope

hardy willow
#

You're almost there.

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The step is small.

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0.9/0.93 of the work has been done.

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Ask whatever you got trouble with and much good luck to ya.

coral wedge
hardy willow
#

What's up with them?

coral wedge
#

I got a 79 on that test because I had no clue what to do 💀💀

hardy willow
#

Dayum.

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You should really try and keep up with those.

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Have you tried using YT or Khan Academy (I personally never used this last one).

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Or asking here for help.

winged wigeon
regal oar
#

where have i messed up

echo stone
tender questBOT
regal oar
echo stone
regal oar
#

isnt this calclulus channel?

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like basic calculus

echo stone
#

see channel description

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for precalc: "anything in the us precalc curriculum goes here, examples include: trigonometry, logarithmic and exponential functions, function sketching, etc."

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for calc: "differential and integral calculus (of a single variable), sequences and series"

regal oar
#

ohh

winged wigeon
#

Should I skip this since section: modeling harmonic motion since this is mainly for calculus? I’m using James Stewart’s precalc book

IMG_1672.png
tough quail
#

Someone can you teach me differentiation 😭

willow skiff
tough quail
#

got it!

eternal basin
hushed sphinx
#

Don't crosspost between several different channels. It's wasteful because people risk using time on typing answers that have already been posted elsewhere.

viscid thistle
#

precalc is so much harder than calc

viscid thistle
#

different name

willow skiff
viscid thistle
willow skiff
#

You get energy points for watching videos

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But mastery points for doing quizzes

whole void
viscid thistle
viscid thistle
whole void
#

but yeah it definitely depends on how it’s taught

plucky mirage
#

bro precalc is so weird at our school

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american education system is horrible

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wish it was like india or china instead

whole void
slim steppe
# whole void why?

Pressumebly because U.S' system deprives the people of critical thinking. A kid growing up in the U.S will very likely be destined for having a career in content creations or in some situations, finance and buisness because there's no appeal there that motivates an ordinary child to go into stem, and the majority of the perception in schools is that "math is boring". That mentality is what is killing and will kill the deprived people there of any success. If you look at China-Hong Kong, Shanghai, Beijing, Hangzhou, but particuarly Shenzhen-it's a city that is completely technologized that generations to come will have the privelge of been raised in an environment that promotes technology, innovation, science, and what have you.

#

I'm not entirely sure about how it is in India given their infrastructure but I do see investments being made into IT and they're very patriotic people for chess but also in their success in the Moon Chandrayaan-3 mission

slim steppe
undone pasture
#

and also the critical thinking shi is not true at all

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in countries like india or china, they force u to memorize math for 8 hours a day

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which is not at all encouraging u to develop your critical thinking skills

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and all the tech in the cities like shanghai, beijing and blah blah blah is all on the surface level, it is very different from chinese people daily life

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i live in the us and my scjool is 90% asian and im telling u from their experience

stark tree
#

but they hate applications of derivative

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and also derivative of Trigonometries....

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those kind of stuff is kinda scary

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Since im business and commerce class, our math course is rather eassier than Science stream...

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like we just touched cal 1, right now our science stream in our grade is like in cal 2 or something

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oh im talking about grade 12 in our country btw

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if you confused

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idk if you guys know this but Asian countries mostly after grade 10 usually is complusory to learn AT LEAST Cal 1

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china is like grade 10, for us Science: grade 11, Business: Grade 12

slim steppe
#

I see that for a nation nearly 30 - 40 years ago what was once like India in some regard in terms of underdevelopment, then industralized itself to the level that the nation has its own credible space station, space programs, phones, vehicles, high speed rail, internet, ship building, and their enormous scale of manufacturing within their country and outside isn't something you base it off the basis that they "memorize math for 8 hours". They clearly work hard and they're motivated. What's interesting to me is the incredible achievements they will achieve within the next century as the generations will grow accustomed to that environment

stark tree
#

nowadays like 2-3 years

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you see those like indians TEACHING YOU How to solve MATH like calculus and integration

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YT Shorts those

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My friend even heard of 9yo indians solving calculus problems

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like you can see the point here

slim steppe
plucky mirage
#

Nah what I am saying is that the math taught in the american education system is barely sufficient

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Until AP calculus

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then it is okay

whole void
whole void
undone pasture
undone pasture
#

same with china

noble lava
#

precaldiscussy

mighty wind
stark tree
#

We just said cal for short

stark tree
plucky mirage
#

or calc for short

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nah man I was on call tutoring a 7th grader who could barely multiply fractions and simplify them

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and i know a 6th grader in india (my cousin) doing pre calculus

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wild

undone pasture
#

im taking calc next yr

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in 11th grade

slim steppe
mighty wind
noble lava
#

Not really a country thing

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Anybody could do it if they wanted to

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It's not like people here are told to study precal in 6th

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(I mean they might be by parents and coaching and whatnot, but it's not in syllabus)

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I think a difference between here and the US is that some people start learning adv stuff too early through coaching institutes, to prepare for boards and/or competitive exams, sometimes that has a positive effect and sometimes it doesnt

magic remnant
#

I solved this question right using the weird formula but I tried to solve it using sigma notation

image.png
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for some reason chatgpt said it would be this

image.png
#

why are we raising 3/4 to x-1 instead of multiplying it

hushed sphinx
#

Try writing out expressions for a_2, a_3, a_4, ... and see how they look.

magic remnant
#

oh wait I think I get it

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for a_2 it would be 8 * 3/4

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which is 6

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for a_3 it'd have to a_3-1 * 3/4 which is just 6 * 3/4

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which is the same as 8 * (3/4)^2

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Okay tysm!

hushed sphinx
#

Exactly.

winter comet
#

<@&268886789983436800>

fervent moat
#

Vro what is calculus

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Just got told to find the gradient on a curved line

noble lava
#

Or limits

stray dew
#

FR!?
this type of stuff is discussed here?

ripe halo
#

The struggle has only begun

#

It appears

charred jewel
#

am i ahead or behind if i take pre calc in 10th grade

opaque cobalt
charred jewel
echo stone
#

but as @opaque cobalt said, you're likely ahead

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welcome to the mathcord btw happy

charred jewel
#

tyyyy

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im planning to take amc

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10 and 12

torn pivot
winter comet
whole void
torn pivot
magic remnant
#

Throughout heaven and earth

image.png
#

Idk

charred jewel
#

why is bro doing this

torn pivot
hexed bison
magic remnant
magic remnant
hexed bison
#

Oh ok thx

charred jewel
tribal flare
#

@viscid thistle dm

steel moon
#

Does anyone happen to know maths here

winter comet
steel moon
#

Aww

#

mann

#

i though someone here might know some math

versed ledge
steel moon
#

ah alr goot u

delicate kernel
#

can I just skip factoring quadratics by grouping since the quadratic formula just does that a lot easier

charred jewel
#

youll rarely use quad formular

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quaf formula takes a long time and u can make more mistakes

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every other factoring method is wayyyy more effient

delicate kernel
#

so the quad formula really just odes 1 thing and it's just to factor quadratics?

#

I've learned by grouping now

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I appreciate all the help

charred jewel
#

it should be ur last resort

delicate kernel
#

Okay, I'll keep that in mind

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thanks!

charred jewel
#

but ig u can skip factoring if u want to go for speed

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if ur self studying alg 2or pre clac

delicate kernel
#

Yeah, I'm planning on resuming my engineering degree this fall and I started from the ground since it's been 15 years since I was at uni and I forgot a lot. I'm currently just finishing up algebra 1 and still have a lot to go so I'm not necessarily wanting to rush but I also don't have a ton of time to familiarize myself

#

algebra 1 on khan academy that is

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but they sprinkle in a lot of stuff

charred jewel
#

oh i see

delicate kernel
#

like I already understand refreshed exponential functions and arithmetic and geometric sequences etc

charred jewel
#

yeah factoring isnt gonna like kill you but like if would be beneficial

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special cases are more important

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esp for alg 2 or just all of math tbf

delicate kernel
#

honeslty I'm mostly worried about algebra and making sure I know it well

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calc is not so bad if algebra is okay

charred jewel
#

you should be fine if you know all the functions

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how to solve, graph , do the inequality version

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stuff like that

delicate kernel
#

Yeah I know basic inequalities and understand them well enough for now

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The main problem is that I also need to brush up on phyisics and chem but I'm certain I've went over a lot of non important material wasting my time with the math so far... I don't want a bad foundation which would be horrible but it would be nice to know exactly what I need to know so I can focus on that

charred jewel
delicate kernel
#

well I didn't finish my first year so it's just a basic start covering calc, physics, chem etc

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I haven't majored in anything yet

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hadn't*

charred jewel
#

oh do u plan on taking a specfiic field

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of engineering?

delicate kernel
#

I'm in ontario and I'm not sure what I would pick second year but probably mechanical or maybe electrical

charred jewel
#

oh alr

delicate kernel
#

If I do fine my first year

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or rather all I'm worried about atm is just doing well my first year

charred jewel
#

you should be okay if u have the basics down

delicate kernel
#

Thanks for your help! It's too bad I'm pressed for time because it's actually a lot of fun learning this stuff

#

not just wrote memorization but actually understanding it makes it soo much easier to piece it all together

north pecan
alpine rapids
torn pivot
ripe lake
#

Anyone mind helping

IMG_0789.png
tame lily
#

Reconstructing row 3 by subtracting row 1 from it

willow skiff
#

1 - 1 = 0
3 - (-2a) = 3 + 2a
(a^2 + 2a + 4) - 2 = a^2 + 2a + 2

willow skiff
#

curious on the source of this question

ripe lake
willow skiff
ripe lake
ripe lake
ripe lake
willow skiff
ripe lake
willow skiff
ripe lake
willow skiff
#

so expanding along the first column, you get:
1 * some determinant + 0 * some determinant + 0 * some determinant

ripe lake
#

AHHHH

willow skiff
#

only the 1st determinant survives

ripe lake
#

YEAH ur right

willow skiff
#

so what we want is to have a row or column with as many zeroes as possible

#

the more zeroes the better

ripe lake
#

ahhhh

#

but how about this

willow skiff
#

so in the line before the "=0"

ripe lake
#

Yeah

willow skiff
#

notice how (third column) = 2 cos(2) * (second column)

ripe lake
#

Yeah common factor of 2 cos2

willow skiff
#

so you can just multiply everything in the 2nd column by 2 cos 2

ripe lake
#

??!

willow skiff
#

then you get 2 cos 2 sin 2, 2 cos 2 sin 2
2 cos 2 sin 8, 2 cos 2 sin 8 etc

ripe lake
willow skiff
#

it doesn't matter that the determinant got multiplied by 2 cos 2 when you do that

willow skiff
ripe lake
#

Ahhh

willow skiff
#

just subtract the 2nd and 3rd columns and you get a column all 0s

ripe lake
#

Ah when a column or a row has the common factor non zero, the det is 0?

willow skiff
#

you're actually looking for one of the columns to be a linear combination of the other

#

like, 3rd column = 1 * 1st column + (-2) * 2nd column

#

cause then you can apply the column operations to make two columns the exact same

#

the exact same thing applies for rows

ripe lake
#

thanks mate

willow skiff
#

no worries mate

ripe lake
#

how does this work?

IMG_0791.png
willow skiff
#

multiply the 1st row by x and the determinant gets multiplied by x

#

multiply the 2nd row by x and the determinant gets multiplied by x

#

so if you multiply every single number in the matrix by x, the determinant gets increased by x^3

#

now we're multiplying every single number by x^(-1) instead, so the determinant gets changed by x^(-3), and hence we need to multiply back by x^3 to not change the expression

#

similarly the last equality comes from (-1)^3 = -1

#

well, 1 / (-1)^3

ripe lake
willow skiff
#

yeah so for a 4 by 4 matrix you'd have det(kA) = k^4 * det(A)
with the k^4

limpid socket
#

hi

#

im new

zinc herald
#

hi new

granite wolf
#

yo chat

#

can someboy explain me descartes theorem

#

used in circles

inner crag
#

hi guys

#

how do i read linear algebra properly

red storm
#

lin-ear algebra

drowsy wolf
#

whats the sin equatoin and the cos equation from this graph?

proud raven
drowsy wolf
#

oh i got them i think

#

y = 4sin(3x) + 2

#

and y = 4cos(3x+pi/2) + 2

proud raven
#

seems reasonable

drowsy wolf
#

dyk if theyre correct

proud raven
#

just plot them?

#

although it looks reasonable

#

,w plot 4sin(3x)+2

obsidian monolithBOT
proud raven
#

,calc 5*pi/3

obsidian monolithBOT
#

Result:

5.235987755983
proud raven
#

yea seems right

drowsy wolf
#

okok thanks

#

,w plot 2sin(1/2(x+pi/3))+1

obsidian monolithBOT
drowsy wolf
#

how do i make it from -2pi to 2pi

woeful egret
#

Adjust the plotting interval

#

If your using a graphing calc set the domain to about -6.28 to 6.28

trim salmon
#

,w plot 2sin(1/2(x+pi/3))+1 from -2 pi to 2 pi

obsidian monolithBOT
trim salmon
#

@drowsy wolf

tame lily
#

Hi, I’m Aditya — a high schooler exploring a symbolic system for prime numbers. I’m building a small informal group (3–5 people) to discuss, refine, and generalize this structure. Interested?

woeful egret
#

Sure

tame lily
#

U can dm me

storm halo
#

hi

#

someone please explain this to me. I think it is A but im not sure

#

i plugged in the numbers (-1, 0, 1) and it seems to be decreasing to a certain number but it doesnt seem to be either 0, 3/5 or 9/4

#

and when i plugged in 0 and 1, the output was a negative number which means the more positive x gets, the more negative y value i get

#

so it cant be either B, C, or D

#

so im convinced its A but can someone smarter than me confirm

willow skiff
obsidian monolithBOT
willow skiff
#

if you want to investigate the behaviour of this function for yourself, you should instead be substituting x = 10, 100, 1000 etc

storm halo
#

this was a past AP college board question on the actual AP Precalc test

#

it must have a solution, either A, B, C or D.

willow skiff
storm halo
#

there isnt x to infinity solution

uncut mulch
#

the question itself is asking for behaviour as x→inf

#

but you're considering stuff around x=0 which is irrelevant

storm halo
uncut mulch
#

yes

storm halo
#

so its hillarious that he would say the answer is x to infinity

uncut mulch
#

noone is saying that

storm halo
#

he literally said that problem is x --> infinity positive

uncut mulch
#

he's saying that's what the question is asking for

storm halo
#

im saying that the answer is A,B,C or D

#

right... so you plug in numbers which I am doing

uncut mulch
#

but you're plugging in the wrong numbers

storm halo
#

is there a quick way to solve it

#

without plugging in numbers

uncut mulch
#

there's the mega shortcut way of just considering the leading coefficients for this type of question

#

since the degree is the same and the limit is to infinity

storm halo
#

what is it

uncut mulch
#

or there's the justification behind that where you divide the numerator and denominator based on the degree of the denominator,
in this case start with dividing the numerator and denominator by x^2

storm halo
#

it clearly doesn't factor

uncut mulch
#

are you even reading what i'm saying

storm halo
#

and i don't need to divide it via polynomial division bc thats not supposed to be what i do in the question

#

ur just a bad tutor

uncut mulch
#

ok

willow skiff
# storm halo what is it

take the highest-degree terms and divide them when you have the limit of x to infinity

so just $\lim_{x \to \infty} \frac{3x^2}{5x^2} = \frac{3}{5}$

obsidian monolithBOT
willow skiff
#

be careful though, cause if you had something like $\frac{3x^2}{5x} = \frac{3x}{5}$

obsidian monolithBOT
willow skiff
#

the limit as $x \to \infty$ would be $\infty$ instead

obsidian monolithBOT
storm halo
#

ok so its 3/5

#

wow, thanks for being so helpful. I really appreciate it

void ruin
#

hi

#

i lately started studying precalculus

#

im 13

noble lava
#

Do you have a question

north pecan
#

(4th hand of the challenge of making the question harder and more complex after solving it)

good morning, lets
point P (1, -1) and point Q (5, 3) are points of the curve y=x²-5x+3
normals to the curve at P and Q intersect at point R.
point R extend to point S and point T, which are the x intercepts of the curve, and forms a triangle.
circle U can be represented by the function, x^2 - 6x + y^2 + 6y - 7 = 0
find the area of the intersection between circle U and triangle RST

versed ledge
#

oh it works

#

especially on social media

gilded hedge
#

What resources should I use to learn pre calculus in a month? I’m trying to Clep out of pre calculus but I also really want to learn/understand it. I study for around 5 hours a day

zinc herald
#

Khan Acedemy

#

search up Practice problems

winged wigeon
#

Has a lot of practice questions

gilded hedge
sudden stirrup
#

hello

sonic haven
#

What does this corollary mean?

image.png
heavy scroll
#

guys where shall I start with calculus

graceful delta
nova veldt
sonic haven
#

i don't understand what it says

nova veldt
#

A function can be continuous and fail to be differentiable somewhere

graceful delta
nova veldt
#

for the function f(x)=|x|, the limit does not exist at 0, it is not differentiable at 0, but it is continuous

graceful delta
#

the opposite, however, is not true

nova veldt
#

if a function has a derivative at that point, then it must also be continuous at that point
a function can be perfectly continuous and still fail to have a derivative somewhere
(right?)

graceful delta
#

yup

sonic haven
#

Oh, so a differentiable function is continuous, but it's not necessary for a continuous function to be differentiable!

nova veldt
#

Yeah the converse is not true

graceful delta
#

yeah that's it

sonic haven
#

Thank you guys

willow skiff
#

continuous everywhere

#

differentiable everywhere but x = 0

#

(take the limits of (f(x + h) - f(x))/h from the left and right of x = 0: they disagree)

storm relic
#

Guys need help with graphing sine and cosine functions rn

#

☺️🙏

sonic haven
storm relic
#

Oh okay

#

It's not really a question but

willow skiff
#

go ask it there anyways

viscid thistle
#

i’m a high school sophomore, and i’m taking ap pre calc this year, but my algebra 2 teacher was not good and i didn’t exactly learn much from her, how much will that play into pre calc?

regal tree
#

algebra is decently imp in pre calc

#

idk what they teach in algebra 2 though

#

do you have a topics list or smth

viscid thistle
#

it was a lot of quadratic functions and polynomials as well as some exponential and logarithmic equations, we also did like an hour of probability stuff

lethal perch
#

Im relatively good with math but this year i'll be taking pre-calculus & calculus so idk how i'll fair:/

ivory fractal
#

you can take both? precalc and calc at the same time?

willow skiff
#

usually it's precalc and algebra 2 that can be taken at the same time

ivory fractal
#

ohh alright

obtuse magnet
#

can someone reply to my question in

#

the thread that says "can someone check this for me"

lethal perch
ivory fractal
#

oh alright

#

i just didnt know you could do both in one year

merry tide
heavy pewter
#

mathematics as a package of topics like precalc, algebra 1-2, etc. is kinda strange to me eeveethink

#

where i'm from, they're more like units of a subject rather than its own standalone thing so you can't opt out of what would be equivalent to precalc and stuff

#

maybe i'm being silly and not understanding stuff, could be both sully

versed ledge
#

i see

nova veldt
sonic haven
#

Someone please differentiate this function with respect to x

image.png
hidden birch
sonic haven
#

the answer

image.png
hidden birch
#

Sir Wolfram

sonic haven
willow bear
#

and the chain rule in particular?

sonic haven
willow bear
#

ok then do it lol

hidden birch
#

let's see if it's the same

#

,w differentiate 2√(cot(x²)) wrt x

sonic haven
#

but this one is just confusing me

obsidian monolithBOT
sonic haven
#

,w differentiate 2√(cot(x²)) with respect to x

hidden birch
#

how did u get your answer

sonic haven
hidden birch
#

let's try graphing if their graphs match

#

,w plot (-2√2 x)/(sin(x²)√(sin(2x²)))

obsidian monolithBOT
hidden birch
#

,w plot -(2x csc(x²))/√(cot(x²))

obsidian monolithBOT
sonic haven
#

what?

hidden birch
#

not the same. is your book wrong

sonic haven
#

idk, it's the national council of education's book

hidden birch
#

lemme compare them

sonic haven
#

my teacher is confused too

hidden birch
#

worst case, you might be trolling and u made that up lolz

sonic haven
#

no, never

#

i can send you my book's PDF

hidden birch
#

no it's ok i was jk

# 
\begin{align*}
-\frac{2x\csc(x^2)}{\sqrt{\cot(x^2)}} &= -\frac{2\sqrt2}{\sin(x^2)\sqrt{\sin(2x^2)}} \\
-\frac{x\csc(x^2)}{\sqrt{\cot(x^2)}} &= -\frac{\sqrt2}{\sin(x^2)\sqrt{\sin(2x^2)}} \\
-\frac x{\sqrt{\cot(x^2)}} &= -\frac{\sqrt2}{\sqrt{\sin(2x^2)}} \\
-\frac{x\sqrt{\sin(x^2)}}{\sqrt{\cos(x^2)}} &= -\frac{\sqrt2}{\sqrt{2\sin(x^2)\cos(x^2)}}
\end{align*}
#

imma try simplify it

sonic haven
#

Google Gemini got it

hidden birch
#

so what u got

sonic haven
#

I'll send an image

obsidian monolithBOT
hidden birch
# 
\begin{align*}
-\frac{2x\csc(x^2)}{\sqrt{\cot(x^2)}} &= -\frac{2\sqrt2}{\sin(x^2)\sqrt{\sin(2x^2)}} \\
-\frac{x\csc(x^2)}{\sqrt{\cot(x^2)}} &= -\frac{\sqrt2}{\sin(x^2)\sqrt{\sin(2x^2)}} \\
-\frac x{\sqrt{\cot(x^2)}} &= -\frac{\sqrt2}{\sqrt{\sin(2x^2)}} \\
-\frac{x\sqrt{\sin(x^2)}}{\sqrt{\cos(x^2)}} &= -\frac{\sqrt2}{\sqrt{2\sin(x^2)\cos(x^2)}} \\
-x\sqrt{\sin(x^2)} &= -\frac1{\sqrt{\sin(x^2)}}
\end{align*}
obsidian monolithBOT
sonic haven
hidden birch
#

that's not an image

sonic haven
#

sorry, was too big to fit into an image

hidden birch
#

also, AI's are unreliable for maths

sonic haven
#

and Wolfram is an AI too...

#

solution looks good to me

hidden birch
#

didn't know wolfram is AI

#

yea i just checked

hidden birch
sonic haven
sonic haven
hidden birch
sonic haven
#

i can't understand your logic

hidden birch
#

not all prrograms are AI

sonic haven
#

whatever

#

i got my question solved and that's what matters for now

hidden birch
#

but would u know if it answered right?

#

i had to read the pdf to check that it did it right

hidden birch
#

i can't

#

ah i made a mistake. it should be csc^2

#

yep they're equal

versed ledge
#

but at this level certain ai can solve it with ease

pliant sedge
#

i have a doubt

#

why is 0.9 bar 1?

regal tree
#

let x=0.999...
then 10x=9.999...
10x-x=9x=9.999...-0.999...
9x=9
x=1
0.999....=1

pliant sedge
#

wow

#

thats is good

#

thank you

regal tree
#

np!

hushed sphinx
#

Wow.

versed ledge
#

wow

#

thats good !

#

i would say its even great

sinful mantle
fresh geode
#

May be a dumb question

This function is undefined at x=2 , still i can see the continues graph in desmos ? can anyone explain

image.png
keen garden
#

It’s not actually continuous, if you click on the graph of the function at x=2 it should say (2, undefined)

fresh geode
#

Thank you

image.png
willow bear
#

it'll say (2, undefined)

soft plover
zinc herald
#

the first method doesn't seem to work

#

you could use it to prove ...9999 = -1

soft plover
hidden birch
#

one method i know is using the geometric series

#

,,\frac1{1-x^2}=1+x+x^2+\dots

obsidian monolithBOT
hidden birch
#

then subtract 1 on both sides and replace x with 9•(1/10)

#

so you'll get 0.999… on the RHS

#

wait

#

wrong wait

soft plover
hidden birch
#

u have to factor out 9

#

yeah

soft plover
#

I have 2 other proofs

soft plover
hidden birch
zinc herald
#

assumes ..999 is a valid number

soft plover
#

for example if:

999 = x
then
9990 = 10x
so
999-9990 = -9x

#

and 999-9990 is not 9

#

regardless of the 9s are finite or not

zinc herald
#

uhh

#

sorry

#

when you subtract the 2nd line from the first

#

all 9s digits cancel out besides the ones place

zinc herald
#

b/c it "goes out forever" all the digits would cancel out

#

here is a simpler to understand method (maybe)

#

the issue with all this is that it assumes ...999 exists and can be manipulated like a normal real number

soft plover
#

yea I think it's not a really good method

drifting oyster
#

Is this rage bait

#

Im geniuenly confused

dapper depot
#

and of course, this yields ridiculous results like 999999999..... = -1

digital sage
#

10-adic has entered the chat:

hushed sphinx
#

I understood the point to be that one shouldn't expect the formal shift-and-subtract argument to be convincing for 0.999...=1 because the very similar argument for ...999=-1 concludes something that's not actually true about the real numbers.
In other words, TimesZeroed seems to be implicitly arguing that an acceptable argument for 0.999....=1 needs to go into details about what real numbers mean and how their decimal expansions work, instead of just assuming as given/known that infinite decimal expansions are meaningful and that school arithmetic algorithms work for them.

drifting oyster
#

And also 9 repeating (assuming thats a thing) thats not a finite number

#

It doesn't exist in R

#

I was just wondering if it was rage bait or not...

true geode
#

I wonder how many more people it will take before someone introduces p-adic numbe- oh wait it's me isn't it

drifting oyster
#

Ok but he clearly meant in R

#

I don't know why we are discussing that

heavy orbit
# soft plover regardless of the 9s are finite or not

A theorem of arithmetic says that there exists infinite numbers between any two distinct numbers.

Like 0.99999999 and 1 are diatinct as there is 0.999999991,0.9999999901... between them.

I challenge you to find me to find a number between 0.99999...∞ and 1. There aint any

heavy orbit
# drifting oyster Is this rage bait

This is one of the most confusing areas of maths dw.

Long time ago a person zeno was wondering that to travel to A and B one must travel half the distance and then a fourth the distance then an eighth a distance then 16th a distance..... And so on
So one can never reach the point B. But this is clearly not the case as i can clearly reach it

But now modern mathematicians agree that 1/2+1/4+1/8+.... Is exactly equal to 1.

#

And thereby explaining physical motion

#

You can look upto zenos paradoxes and once u start studying calculus i hope the idea gets more crisp

drifting oyster
#

dawg Im doing complex analysis right now

#

The need to mansplain is crazy

#

😭

willow bear
drifting oyster
#

I meant they're mansplaining Ann...

willow bear
#

oh the unununnium guy lol

drifting oyster
#

yea

nova veldt
heavy orbit
willow bear
#

enterlessguy was pointing the finger at you as the mansplainer

heavy orbit
#

Ok ig

#

Blud thinks he is skibidi level 10 gyatt rizzler in ohio probably

heavy orbit
#

Me no understand

hushed sphinx
#

... just because he expressed doubt at the sincerity of a calculation with an infinite sequence of nines to the left of the decimal point.

heavy orbit
#

And the other ppl had gave the other explanation

hushed sphinx
#

And people think it's a bit pretentious of you to assume Enterlessguy needed to be told that.

#

Since he's not the one who asked about 0.9999....=1.

heavy orbit
#

So i told him

#

The other guy was satisfied with the proof

#

Ig

hushed sphinx
#

Enterlessguy expressed skepticism about TimesZerored posts that were about ...99999 rather than 0.99999...

heavy orbit
#

Oh skill issue on my part then probably

#

Lmao

zinc herald
#

albeit really badly
it caused this chaos so ig it may have worked

hushed sphinx
#

Aw, and here I managed to extract a meaningful point from it.

sonic haven
#

,w differentiate cos(x)cos(2x)cos(3x) w.r.t x using Logarithmic differentiation.

obsidian monolithBOT
hidden birch
#

just type wrt no dots

sly prawn
#

hllo

willow bear
noble cave
#

y=px+3√(a^2p^2+b^2) and dy/dx=p

#

can someone help me with this problem?

#

i'm confused and i need someone to help me unconfused myself

regal tree
#

what do you need to find here?

#

like prove that dy/dx is p?

covert skiff
covert skiff
drifting oyster
#

what

heavy pewter
#

what

#

because if you integrate the thing you get y=px+C which is the same thing so eh eeveethink

hollow scaffold
#

I'm taking it next yr

north monolith
#

to all who took precalc, did precalc help you with actual calculus?

uncut mulch
#

the topics covered are essential
the course/class may come come under a different name or be delivered differently

sonic haven
regal tree
sonic haven
regal tree
#

you can change it to undergraduate math in #info

sonic haven
regal tree
#

not sure

#

im in 12th myself but i chose undergraduate since i wanted access to calc channel

#

there are lots of other channels too that you gain access to but i never use them

#

basically only use the ones in pre university and calc

hushed sphinx
sonic haven
nimble wolf
#

I'm about to take the AoPS Precalculus Course and I'm so scared 😟

viscid thistle
#

What is the best platform to learn about precalculus

#

Sorry

barren jewel
#

I have no idea

#

I never took precalc really. It feels like algebra 2 to me

edgy haven
#

I'm going into 9th grade this year, and I want to skip algebra 2 and go to pre cal. What should I do?

winged wigeon
winged wigeon
turbid canyon
astral harness
#

fr

smoky canopy
#

Help guys am I just stupid or is calculus hard

nimble wolf
#

It's hard when you think of it

#

But not actually. It's pretty easy than you think 😄

hidden birch
#

time will tell

hearty crow
willow bear
heavy orbit
# hearty crow

Bruh have u just considered the possibility u are annoying and wierd?

Who tf spams a physics jee question in a maths server and in channels like calculus and precalc?

hearty crow
#

bro be respectfulllll

crystal owl
hearty crow
#

fine

#

sorrry

#

i didnt mean to hurt anyone i am new to discord

echo sinew
#

If one can't help because they don't want or are not able, don't worry, there's plenty of other helpers

chrome acorn
#

hi sir

chrome acorn
spark flame
#

How do I get into the calculus channel

winged wigeon
ivory fractal
#

is it possible to go from pre-calculus to statistics?

willow skiff
#

You just need some basic knowledge for alg 1

#

There might be a few proofs or techniques that use algebraic manipulating

ivory fractal
#

Oh alright

torn pivot
viscid thistle
#

so how to determine this?

images_16.png
velvet sequoia
#
  • odd / even?
  • period?
  • amplitude?
viscid thistle
#

How to know that?

velvet sequoia
#

You can infer from the graph

viscid thistle
#

So, the function is even if what?

velvet sequoia
#

The function is even if for any x, we have f(x) = f(-x)

#

i.e. the y-axis is a line of symmetry

viscid thistle
#

mhm.

velvet sequoia
#

The function is odd if for any x, we have f(x) = -f(-x)
i.e. the origin is a rotational point of symmetry

viscid thistle
#

So that means this graph is even?

velvet sequoia
#

It's odd

viscid thistle
#

So, what i get is that, if a function is a rotational point of symmetry (And i don't know what that is), than the function is f(x)=f(-x)

velvet sequoia
viscid thistle
viscid thistle
velvet sequoia
#

This is showing what you get if you reflect the left side to the right side

#

It doesn't match up

#

So it's not even

viscid thistle
#

I see, i see.

velvet sequoia
viscid thistle
#

And do you have the proof that if a function is f(x)=-f(-x), than it is odd?

velvet sequoia
# velvet sequoia

If you rotate the left side 180° around the origin (brown), it becomes the green part

viscid thistle
velvet sequoia
#

Yeea

torn pivot
viscid thistle
torn pivot
#

im shaking

viscid thistle
velvet sequoia
torn pivot
viscid thistle
velvet sequoia
torn pivot
#

Physics 👾

torn pivot
#

even -- f(x) = f(-x)

viscid thistle
velvet sequoia
#

There are other functions that can be odd or even too

torn pivot
#

odd -- π rotation along y axis

torn pivot
viscid thistle
torn pivot
velvet sequoia
#

Yea

torn pivot
#

All functions are either odd, even or neither (non symmetric graphs)

viscid thistle
#

so that's first step.

#

Now how to know the period?

torn pivot
#

By analyzing the graph?

velvet sequoia
#

The period means how much you have to shift the graph left/right for it to match itself

viscid thistle
torn pivot
#

Lol

viscid thistle
#

Is that correct?

velvet sequoia
#

It doesn't match when shifted by π

#

It's upside down

torn pivot
viscid thistle
#

so 2π?

velvet sequoia
#

Yup

viscid thistle
#

Wait... it could be 4π too