precalculus

[grand sedge]

I can study 10 hours a day

straight

[hushed sphinx]

That's probably too much; you should give yourself some time for what you're learning to solidify.

[grand sedge]

I never give myself time

I am at my senior year

and next year I have to go college

I need to improve

[hushed sphinx]

Studying in an unproductive way (such as "10 hours straight") might be something you need to change in order to improve.

[grand sedge]

I have no choice

ACT is very competitive test

[hushed sphinx]

You "have no choice" but to deliberately act in a way that will sabotage your learning? Strange.

[grand sedge]

I just want that scholarship nothing else

[hushed sphinx]

You're not really giving any information that could inform personalized advice, but a generic suggestion would be to concentrate your effort on understanding the topics rather than drilling procedures for answering particular problems. That's what most students appear to be doing wrong.

[grand sedge]

During my last ACT on December 9th, my nose started to bleed. I stayed until 2 a.m. studying the whole month.

[hushed sphinx]

So you're actively sabotaging yourself by burning yourself out and not getting enough sleep to be able to learn anything, and you're dead set on continuing to sabotage yourself? I'm sorry, then there's no possible tip that can help you.

[grand sedge]

In addition, my parents put pressure on me, making fun of me by saying that if someone else can obtain 36, why can't you?

I have strict parent's

Plus they are indian so you already know

[hushed sphinx]

Why can't you? Because you refuse to act in a way that would make it possible for you to learn.

[grand sedge]

How can I obtain 36 on the ACT, in your opinion?

[hushed sphinx]

A necessary first step would be to stop frying your brain by "studying for 10 hour straight" and staying up to 2am.

[grand sedge]

Okay, next?

[hushed sphinx]

This is the best I can say for "next step" on the available backgroun.

[grand sedge]

Well, I'll start studying for three to four hours a day, with a break, and we'll see what happens.

If I don't get 36, I am blaming you.

[shadow summit]

Go over old ACT questions

You can access them

[grand sedge]

Isn't SAT and ACT Math different?

[hushed sphinx]

Also, you will find this server is much more useful if you use it to ask questions about concepts that are not clear to you, than just asking for generalized "tips".

[shadow summit]

I mistyped

[grand sedge]

Okay

[shadow summit]

Still you can access older questions

I don’t have to check them though cuz I ain’t from the US.

[soft hemlock]

x(2x^2 - k/x)^7
Constant is 20142
Find k

how do i solve this

[astral bronze]

Which one is the constant

[shadow summit]

Responded in your help channel

[vital palm]

take the test in a test format meaning structure your practice tests as a real test with the proper breaks. don’t get too wrapped up in one subject. practice everything, even the easiest things. before the test don’t study for 2 days. end on a good note though with a high score practice test for the right frame of mind. wear comfy clothes.

[viscid thistle]

exams ... 1. read problem, what does it want? 2. read problem again, what's given? 3. devise method to get from (2) to (1). 4. read problem, read answer, does it make sense to you?

can't count how many assignments I graded over 15 yrs where students answered a problem that was different than the one they had.

[leaden plume]

how is this incorrect??

<@&268886789983436800> please help

[rotund jewel]

Do not ping moderators for math help

[leaden plume]

o ma bad

[rotund jewel]

Either wait for someone to help, or open a help channel

[ebon sorrel]

the negative numbers in question:

[ocean fulcrum]

im so confused because the graphs equation IS the inverse of the original equation

[shadow summit]

f(x)=x^3

[hushed sphinx]

Looks like your graph shows a function with e.g. f(1)=6.
Does the purported inverse satisfy L(6)=1?

[ocean fulcrum]

wait so the orignal equation is y=sqrt(x-2) + 3. The inverse of that equation (as shown on the graph) is y=(x-3)^2 +2. However it says that the graphed equation is NOT the inverse. It satifies all of the points aswell. Does it have something to do with the fact that the square root graph is basically half of a parabola but the inverse of it is a full parabola?

[hushed sphinx]

Yes, there are points on the given graph that should not be in the graph of an inverse function.

The inverse function of L should have a domain that is exactly the range of L.

[viscid thistle]

can anyone give me difficult questions on logs, trig, rational equations, sequences, and radicals

pls

[fallen kettle]

How do i get this value? I just guess and check for now

[willow bear]

what are these lines supposed to be...?

[placid cave]

when it says function sketching, does it mean just drawing functions?

cus i need a bit of help

[elfin loom]

what is the question

[placid cave]

why are the old x values ignored if i said + (x-30)+2-0.01 (30-1)

oh wait

maybes its cus i forgot the parenthases

[stark current]

For option 5 f'(x)=2x, that means for anything below x=0 the function is decreasing. For option 4 f'(x)=-1, which means it is always decreasing. For option 1 f'(x)=-sin(x), meaning it is not always decreasing. For option 2 f'(x)=cos(x), also meaning it's not always decreasing. That leaves us with option 3, f(x)=x³. I am not sure, but by my definition it is not always increasing, it's just never decreasing. f'(x)=3x², so f'(0)=0. And it staying at 0 is not increasing, at least by my definition.

[smoky pendant]

how do i figure out the equations of these lines
i know the first one is a f(x)=-cos something, and the second one is f(x)= -sin something

[hushed sphinx]

That looks right.

[smoky pendant]

oh, wait i didn't realize that's all it was. thanks

how do i find the c value on this graph

[hushed sphinx]

You want a c such that the input to the sine becomes 0 or 2pi (or 4pi, etc) when x is about 1.35.

Since you're being promised that c is either pi or a small integer, there's only one of those options that's near the solution of pi·1.35 + c = 2pi.

[smoky pendant]

i tried 1.35, but it does not work

did i do the rest of the equation right

[hushed sphinx]

Do you mean you tried c=1.35? That's not what I said.

[smoky pendant]

yes

i don't understand

wait

[hushed sphinx]

1.35 is what I got by estimating the x-coordinate where the graph crosses the x-axis on the way up.

So you'll need ax+c to be one of the points where the raw sine crosses the x-axis on the way up -- that is 0 or 2pi or 4pi ... -- when x is 1.35.

[smoky pendant]

i think i get it now. so c would be -4.241150082?

[hushed sphinx]

That works for creating the graph, but unfortunately is neither pi nor a small integer. Try adding 2pi to that (obviously that would not change the graph).

[smoky pendant]

ahh, so 2.042035225?

[hushed sphinx]

Yes, and that rounds to 2.

The 1.35 I started was not very precisely read off the graph anyway. I just thought, "more than halfway from 1.2 to 1.4". If we had taken 1.37 instead, the same calculation would have given c = 1.98.

[smoky pendant]

got it. thank you

one last question. wouldn't tan(u+pi/2) be undefined

[hushed sphinx]

Why would it be? The value of tan(u+pi/2) is sin(u+pi/2)/cos(u+pi/2), and both the numerator and denominator there are nice nonzero rationals.

[smoky pendant]

oh wait im dumb

it's 4/3

[elfin meadow]

$\sqrt{5\sqrt{5\sqrt{5}}}=125^{k}$

[obsidian monolith]

Loyis

[elfin meadow]

Here's a neat puzzle

You just have to know your exponent rules and it's pretty straight forward

Solution: ||125^k=(5^3)^k=5^3k, then multiply the exponent by 2 to square it and subtract one to divide by 5||

[glad widget]

||k = 7/24 I think||

[storm violet]

x^4-x^3-7x^2-7x-4

$\x^4-x^3-7x^2-7x-4

[bronze stirrup]

anyone got anymore puzzles ???

[granite quiver]

This might be a dumb question but what is the difference between ln x and log x? I cant seem to understand this without a graph

[kind urchin]

log x, might be equal to ln x, however some people use log x to denote base 10

[glad widget]

ln(x) is just log base e of x and log(x) can have any base (if it doesn’t have a base that generally means as the other person said base 10 or base e)

[hushed sphinx]

Sometimes log is base 2, in particular in areas with connection to computer science.

[granite quiver]

I think I got it. This makes a lot more sense now

[wary plume]

part c anyone pleasse help

[elfin meadow]

#calculus probably

[uneven dew]

Ok, so question about derivation. We know that}
f(x)' = f(x+dx) - f(x)

if dx is 1 and: ```f(x) =x^2 + 3x - 5

f(x)' = ((x+1)^2 + 3(x+1) - 5) - (x^2 + 3x - 5)
f(x)' = x^2 + 2x+1 + 3x + 3 - 5 - x^2 - 3x - 5
f(x)' = 2x + 4 - 10
f(x)' = 2x - 6.```

Would this mean that the closer f(x+dx) is to f(x). The more accurate this derivative would be?

[river drift]

probably better suited for #calculus

[uneven dew]

f(x) = x
f(x)' = f(x + (x_2-x)) - f(x)
f(x)' = x + x_2 - x - x
f(x)' = x + x_2 - 2x
f(x)' = x_2 - x

[river drift]

but your definition if the derivative is incomplete

[uneven dew]

You talking about the /h part?

[river drift]

yes, or dx in this case

[uneven dew]

But this is also a valid definition, i think

[river drift]

remember that the derivative models the slope (rise/run) of a function. you can get the 'rise' by finding f(x + dx) - f(x), but you also have to divide by the 'run' dx. your example kind of works (although you made a sign error) only because dividing by 1 wouldn't change anything: if you took dx less than 1, it would become less accurate

[uneven dew]

f(x)' = f(x+dx) - f(x)

if dx is 0.3: ```f(x) =x^2 + 3x - 5

f(x)' = ((x+0.3)^2 + 3(x+0.3) - 5) - (x^2 + 3x - 5)
f(x)' = x^2 + 0.6x + 0.09 + 3x + 0.9 - 5 - x^2 - 3x + 5
f(x)' = 0.6x + 0.09 + 0.9 - 5 + 5
f(x)' = 0.6x + 0.99 ```

Might have done something wrong there, feel free to point it out.

f(x)' = 2x + 1.1

Why does c get affected soo much @river drift

[shadow summit]

Assuming you mean “-5” is the c value, think of what happens when you take the derivative using the power rule. It vanishes. So what happens when you take the derivative using your method? Is it getting smaller? Is it almost disappearing? Well it should be because the derivative would drop C.

Although I’m not familiar with this method of taking derivatives.

[uneven dew]

.

Its supposed to go to + 3, but it isnt, edited the msg to fix errors. Now it goes to + 1.1

nvm

So if dx < 0.3, c will be > 1.1?

But wont that change b since dx is linked to both "b" and "c"

So which value, approximately gives the correct derivative

[granite quiver]

What are things I have to learn and memorize in trig in my Precalc class?

[shadow summit]

Depends what your precalc course is. You can check your schools syllabus on its website most likely. But in general, knowing how to move a cos/sin/tan graph around and generally manipulate it is very important. Furthermore, knowing how to take the inverse function is pretty useful. This assumes you know about radians and how to solve trig functions to begin with.

As well as being familiar with which quadrant each function is positive and negative.

[granite quiver]

AP Precalculus

Right triangle trig wasn’t a problem in geometry but when I got to algebra 2, things started to get tricky

[shadow summit]

Idk what algebra 2 does, I’m assuming you did the cosine law? c^2=a^2+b^2-2abcos(C)?

Or did you do trig identities?

[granite quiver]

I think so

Graphing trig functions

Unit circle

We did not do trig inverses

[shadow summit]

When I say trig identities I mean like cos^2 + sin^2 = 1

[granite quiver]

Yeah we did that

But we didn’t do cosine law

And I don’t remember much of trig so I need a refresher

[shadow summit]

Dang, haven’t done cosine law? That’s weird.

Cosine law is pretty easy, watch a video or two on it.

[granite quiver]

Will do

I use khan academy for math help

[shadow summit]

arccos, arcsin, arctan

[granite quiver]

Yeah we didn’t cover that

Maybe in Precalc

[shadow summit]

You may have seen it in the form cos^-1(x)

$\cos^{-1}(x)$

[obsidian monolith]

TheLord26

[granite quiver]

We finished unit 1 which was polynomial functions. Now unit 2 logarithms and exponential functions. Next unit is trig which is when we get back from vacation

[granite quiver]

I see

Yeah I’ve seen it

At first I thought it was an exponent

[shadow summit]

That’s the only case when it isn’t an exponent lol

[granite quiver]

Until the lesson on inverse functions

[shadow summit]

sin^2 = sin*sin, sin^-1 =/= 1/sin

Knowing exact values is gonna be crucial

But yeah, most trig is in calc.

But algebra is 90% of calc

[granite quiver]

I need to refine my algebra skills

Calc is not algebra but many algebra concepts carry over to calculus

That’s the way I see it

[granite quiver]

Oh boy that sounds wonderful

Anything else I should know besides trig?

[viscid thistle]

I’m going into cal 2 and all I can tell you, is learn trig like the back of your hand. Because calculus is just more trig and if you don’t have a good grasp on it, you’re going to struggle

[lethal thorn]

would it be A?

my thought is that it is the inverse

[hushed sphinx]

Yes.

[pastel mason]

hi, any idea how to solve number 28?

[summer ruin]

find inverse function of g

[pastel mason]

I did it, but it gives me two solutions and I don't know which one to choose.

[granite quiver]

I guess I better get to studying

[summer ruin]

you're given that x >= -2

[gentle geode]

given that f is a one to one it limits your answers to only some 70 thousand possibilties

im talking completely out of my ass rn

came here for nerding out in vc.. no vc exists

introverts disperse!

[shadow summit]

theres a domain, x>=-2. so if you value has a x<-2, you know its wrong, therefor the other answer is correct.

[rugged wedge]

I need help here

f(x) = x² + 1
g(x) = 1/x

Find domain and range of (g • f)(x)

If we compute g • f, we get 1/(x² + 1). Its range is:

1/(x² + 1) = y
1/y = x² + 1
1/y - 1 = x² ≥ 0
1/y ≥ 1

y ≤ 1

[willow bear]

does the dot mean composition?

[rugged wedge]

Yep

But, if we look at the range of f(x)

y = x² + 1
y - 1 = x² ≥ 0
y ≥ 1???

[willow bear]

you made a mistake in your last thing for g o f

from 1/y >= 1 you would get 0 < y <= 1

[rugged wedge]

Oh right

How can we show that negative numbers are excluded?

1/y ≥ 1, of course y can't be negative, but how do we show that algebraically?

[willow bear]

(1-y)/y >= 0

sign change points are 0 and 1

[still folio]

Yall who can help me with math

[glad widget]

X^2 is always positive

For all real numbers

[willow bear]

lots of people potentially, but also:

!da2a

[tender quest]

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/

[near bluff]

Not really questioning about a question but this question that was given by a friend was insane to do genuinely

The (hardest/tooken the longest time) part would have to be the (b) subquestion

[faint pivot]

is calc not done in us high school

or is there just not a channel for it here

[summer ruin]

not the way it should be done

[river drift]

if calculus is done in high school in the US, it's usually as an AP class, which is supposedly college-level. any high schoolers taking calculus may discuss in #calculus regardless; the categories are mostly guidelines about when a student is most likely to learn a given topic

[viscid thistle]

Hello! How can I find the limit of f(x) = 1:x, as x approaches infinity (I know this is pretty basic, but I sometimes forget…)

[sacred light]

why is it only if x = 0, wouldn't the statement be true if x<0 or x>0 or x = 0?

[viscid thistle]

Thank you! I’m usually very good at mathematics.

[river drift]

it's equal if x = 0 and strictly greater otherwise

[vagrant pumice]

Halo

[dark igloo]

I hate maths GG KIDDOS

I hate maths GG KIDDOS

I hate maths GG KIDDOS

I hate maths GG KIDDOS

I hate maths GG KIDDOS

I hate maths GG KIDDOS

[fair pine]

Huh?

Why yall kicked him?

He can hate Maths..

[fair pine]

dot? you mean in er lc?

like mechanic

[fair pine]

Yeah ik the pokemon

[shadow summit]

Nonono, your getting confused with Arcanine, Arctibax and Archeops.

[fair pine]

Oh srry

[willow bear]

idk what "in er lc" is supposed to mean.

[hushed sphinx]

He started posting slurs instead of just posting "hate math".

[faint pivot]

thanks

[naive girder]

Without tracing paper how to find point of rotation

[shadow summit]

Like a point rotated around (0,0)?

[naive girder]

Can i direct msg you a question

[shadow summit]

No, I’ll just use your help channel.

[shadow summit]

Can’t help rn, doing some Christmas Eve stuff, I’ll help later, or someone else can help.

[hushed sphinx]

If so, please answer the copy of the question in the help forum: #1188312218769571942 message

[night surge]

can someone suggest some good book for differential and integral calculus from the very basics to advanced please?

[sleek laurel]

halo

hola

[warped cipher]

#book-recommendations

[lyric meadow]

bruh

[granite quiver]

Anyone know number 42?

[shadow summit]

Rearrange in the form y=mx+c

$2x=5y-4 \newline y=\frac{2}{5}x+\frac{4}{5} \newline \text{now identify the c value and replace it with ‘C’} \newline y= \frac{4}{5}x+C \newline \text{substitute the point (7,-6) into the equation and solve for C} \newline -6= \frac{4}{5}\cdot7+C$

[obsidian monolith]

TheLord26

[granite quiver]

How did you do that?

[shadow summit]

Wdym?

[granite quiver]

With the bot

[shadow summit]

uhhh, too complicated to explain. Plus I’m pretty shaken up rn, someone tried breaking into my house just now.

||yes I will use the attempted burglary as an excuse to not explain stuff||

[granite quiver]

You okay?

[shadow summit]

Yeah, luckily someone in my house got up and yelled at them to go away

They didn’t manage to break in, but they did burn a hole through the fly screen.

It happened at ~2:45am

It’s 3:30am rn

[granite quiver]

Oof that sucks

[granite quiver]

Get some sleep

[shadow summit]

I already don’t sleep much, I’ll probably end up pulling an all-nighter

[granite quiver]

You gonna call the cops?

[shadow summit]

Cops don’t do shit

Youth crime is massive in Australia

Second time kids have come into our yard. First time they stole a key to our car (didn’t steal the car though).

But that was a year ago

I don’t even live in a bad area

[granite quiver]

Have a cheap camera around

[shadow summit]

Just got a lot of youth crime

We do, they had masks on

One of them had a hand towel or something around their face with a cap on lol

They stole a hammer though.

[granite quiver]

If I had the math skills and materials, I would home alone the entire house

[granite quiver]

That’s…interesting

[shadow summit]

Bro if I had been the one to find them I would have made the most ungodly insults at them.

[granite quiver]

You gonna make the burglars cry

[shadow summit]

It was one of the only things they could really steal. I mean, we have boxes of stuff outside but there’s nothing really valuable in them.

[shadow summit]

I wish bro

[granite quiver]

Is this common in your neighborhood?

[shadow summit]

Not really. but that’s not that bad. Unless you live in really rich neighbourhoods it happens too often.

It’s honestly really bad how much youth crime there is in Australia

A bunch of people want to lower the minimum age of incarceration because of it.

Anyways should probably stop because this is off topic now

[granite quiver]

Yeah but this should stop. There has to be a better way to deal with these break ins

[viscid thistle]

eh

i dont see the issue

u can get it done in half the time if im honest

as long as u learn it all properly there really isnt an issue

js take it at ur own pace

theres no rush

[granite quiver]

Yes I completely agree with this

However

I don’t think 4 weeks is enough to simply carve all the material into your brain

[viscid thistle]

It is

trust me

[granite quiver]

You will need a couple more weeks to strengthen and build on this

You can learn this content sure

[viscid thistle]

You can lay the foundations for all the content in 4 weeks

[granite quiver]

But to me 4 weeks is a bit short, and I would use a few more weeks doing practice problems

[viscid thistle]

Strengthening it just happens over time

[granite quiver]

Yes

But can be sped up

[viscid thistle]

But honestly id just wait to do precalc until you cover it in school

[granite quiver]

I’m taking AP Precalc rn the course is fine

[viscid thistle]

If somethings in your syllabus just wait to do it

[granite quiver]

But we’re going kinda slow

I’m scared when we get to trig

[viscid thistle]

Theres no point on learning easier topics beforehand

[viscid thistle]

trigs easy

its just remembering identities n shit

[granite quiver]

There’s much to memorize

I sucked doing that in algebra 2

[viscid thistle]

I would recommend looking into the proofs/derivations for the identities in ur own time

[granite quiver]

We’re finished Unit 1:polynomial and ration functions

[viscid thistle]

It will help u massively if u understand how the identity came about

[granite quiver]

I hated doing proofs before

But I will try

[viscid thistle]

alot of the trig proofs just use the unit circle

if i remember correctly

[granite quiver]

I saw someone doing this hack for memorizing trig

Forgot how it went

They made a table instead of memorizing the circle

Once I memorize trig

Going straight to calculus

[river drift]

the full unit circle basically consists of the same angles (adding 90°,180°,270°), but with different signs depending on the quadrant

another useful trick is to memorize the special triangles these come from rather than the angles themselves

[granite quiver]

How is the khan academy trig course?

[river drift]

can't speak to that specific course but khan academy is a good resource in general so it's a good place to start

[granite quiver]

Got it

How long should it take

To learn trig

[viscid thistle]

memorise the triangles and the graph shapes

10x easier than anything else

forgot the values? just work it out w the triangles

[granite quiver]

Like right triangles?

[viscid thistle]

yep

the isosceles one for 45°

half equilateral for 30/60

[granite quiver]

Only thing I remember about graphs: sin graphs start at the midline while cosine graphs start at the amplitude (min/max)

[viscid thistle]

then remember the shape of graphs to figure out the alternate values

Yep

[granite quiver]

I had to do a project for algebra 2

[viscid thistle]

And u can use that to see sin 90 is 1 whereas cos0 is 1

[granite quiver]

Something about the way a Ferris wheel revolves on a graph

[viscid thistle]

u dont really need the unit circle

[granite quiver]

One look and I was shaking

[viscid thistle]

The unit circle is only useful for trig proofs + transformations on graphs

Its not even good for remembering trig values

[granite quiver]

Do we need to memorize proofs for trig?

[viscid thistle]

nope

i dont think so

Its just nice to know them

Solidifies your knowledge on the identities

Like the angle sum/subtraction identities are a bit random when u first see them but their proofs are simple

its nice to know them so you know how the identity works

[granite quiver]

Yeah

Math gets annoying when you don’t know why it even works

Is it possible to review the entire right triangle trig in one or two days?

[thorn kestrel]

I wouldn't really tell anyone not to use it... if it's slow for you it doesn't mean it's a bad pace for everyone

[lyric meadow]

this is the worst advice I have ever heard

[thorn kestrel]

Same... khan academy is like, such a fantastic resource idk how anyone could call it bad considering the lack of strictly better alternatives

[lyric meadow]

I'm sorry you are offended, it's just not good advice

[ivory mango]

I personally don't use khan academy

Deltamath is my goat fr fr

[valid shell]

the fuck is calculus

[gaunt carbon]

its when you use a value approaching another value to do a bunch of cool stuff

[ornate flame]

yeah lol

Grade 12 has calculus for me

so idk what this si

is*

[gaunt carbon]

it really isnt that bad tbh
if you wanna start looking into it i recommend learning limits

probably via khan academy or something adjacent

[ornate flame]

ik the basics of calculus

ik how to find the area under a curve

just saying, calculus should be included in pre university

[granite quiver]

What would you recommend then?

[slim steppe]

When arithmetic isn't enough

[fiery ocean]

Just read Stewart's early trascendentals, best begginner book

[granite quiver]

What about thomas' calculus?

[fiery ocean]

I prefer Stewart

[granite quiver]

I couldnt find a cheap stewart book but I heard great things

[fiery ocean]

You could borrow it, most libraries has it

[viscid thistle]

u could probably review it in 1 or 2 hours if im honest

[shadow summit]

You aren’t going to memorise all of trig using that table. And while you don’t have the learn about the points on the unit circle, learning it is very useful. But most importantly learn the exact value triangles.

[scenic coral]

Khan's fine, but kinda sucks as a stand-alone resource if you're only using khan, good intro to a subject but lacks depth and difficult practice questions imo

start with khan then go read a textbook is my opinion

[granite quiver]

I could but I’m worried if I review so much in one day I won’t recall it the next day

[granite quiver]

Got it

[viscid thistle]

Do challenge questions every week or so and u will remember 👍

[opal vault]

i agree with someone1010

i used larson single variable calc

it has a shit ton of questions which if thats what u need is good

tho tbh i feel like all calc books are the same

they all teach the same shit and there migthe be like 1 or more

different strats they teach ig

u can tell if u like thebook or not within a chap

[granite quiver]

Is trig going to be my worst enemy in Precalc?

[granite quiver]

Wow now that I hear this, I’m going to review all of trig in a single week. All my friends will call me nuts but Idc

Thank you for the encouraging advice

[granite quiver]

I just ordered 2 calc study books and 1 work book. Calc all in one for dummies and Thomas calculus. The workbook is some yellow calc book

[shadow summit]

trig is easy as long as you learn it. idk how indepth into trig your course will do into, but it shows up in calculus, algebra and linear algebra pretty often, so getting very good at it is a must.

[granite quiver]

Whats the difference between algebra and linear algebra

[shadow summit]

Algebra uses stuff like plus, minus, multiplication, division, exponentiation, logarithms, ect. While linear algebra uses vectors and matrices.

[tender mist]

I'm not really sure where to begin with answering this question. I don't really officially know how to solve these types of questions, as I usually just "guess", but this one is stumping me

[wispy pawn]

I think g(x) should be the inverse function of f(x), since their composite function just results in x again.

[shadow summit]

Note $f(g(x))=x \newline \text{And } f(x)=\frac{x}{x-2} \newline g(x)=y \newline \text{So } x=\frac{y}{y-2} \newline y=x(y-2) \newline y=xy-2x \newline y-xy=-2x \newline y(1-x)=-2x \newline y=\frac{-2x}{1-x} \newline \therefore g(x)= \frac{-2x}{1-x}$

[obsidian monolith]

TheLord26

[tender mist]

Ahhh okay, gotcha. Thanks!

[granite quiver]

How do people learn calculus without going through Precalculus?

[hushed sphinx]

They learn the same material under other names.

[ivory mango]

Yeah

My school has a course called "Algebra 3" which essentially is precalculus

[ivory mango]

Real

I love binomial expansion and Pascals triangle

[shadow summit]

They come in so clutch

[patent swan]

hi

[lofty dock]

offtopic

[granite quiver]

Pascals triangle is an interesting concept

Have you learned combinatorics?

[ivory mango]

not yet

[lyric shell]

I did basic stuff of this in Algebra 2 lol
Binomial Expansion

[granite quiver]

I do not like combinatorics

I prefer just using Pascal’s triangle

[hushed sphinx]

If Pascal's triangle is not combinatorics, then what is it?

[uncut mantle]

a triangle

[shadow summit]

magic

[elder sequoia]

Yeah magic

[hushed sphinx]

No. They're useful facts to know, but by no means exhaustive of anything.

[steady turret]

Not entirely, and also sin(x)/x is reducable using l'hopital

right yes

[hushed sphinx]

There's no circular reasoning involved with applying L'Hospital to sin(x)/x. It turns out not to lead anywhere if you don't already know the derivative of the sine, but the conclusion is perfectly valid.

But that's not specific to sin(x)/x -- it holds in general that L'Hospital will not be helpful unless you know derivatives of the numerator and denominator.

[kind valley]

Anyone have good question set for precalc

Like IB stuff

[cunning kindle]

But the proof of d(cosx) uses sinx/x

Also, im currently a high school student. Wanna learn university calculus early on. What textbook would you guys recommend?

[granite quiver]

Magic math

[old isle]

yeah

im doing iB rn

[kind valley]

nice

i found it though

[robust wedge]

guys is the aops precalc as good as the stewart precalc? cuz it has half the number of pages as the stewart precalc

[rocky wind]

since your question involves limits, that's a #calculus question

[zinc fulcrum]

idk what that even has to do with what troposphere said but there is no ‘the’ proof for that (i.e. there are more ways to go about it than the one you’ve seen, which probably doesn’t use a very rigorous definition for sin and cos to boot)

[cunning kindle]

I meant sinx

Idk why I wrote cosx

Let me paraphrase then

One of the methods to find the derivative of sinx uses sinx/x = 1 as x approaches 0

It would be circular reasoning if we applied Lhopitals rule on sinx/x as x approaches zero

[distant ledge]

Here is the technique to solve on YouTube: https://youtu.be/Ma877iQfVZY

[hushed sphinx]

No it wouldn't. L'Hospital's rule tells you that if the limit of sin'(x)/1 exists as x->0, then that limit is also the limit of sin(x)/x. This is completely true, and it is true no matter whether you know yet how to calculate the derivative of sine.
What you do with this information (and whether it is helpful to whatever you're doing) is not L'Hospital's problem.

[rain carbon]

Is precalculus hard if you have A’s in geometry and algebra 2

[granite quiver]

Precalculus shouldn’t be too hard if you’re good with manipulating numbers and you’ve done well with your prerequisite classes

Besides, there shouldn’t be any reason why no one can do well in Precalculus. Math is for everyone

[rain carbon]

Good to hear my

Guy

[granite quiver]

Are you learning Precalc rn?

[rain carbon]

I’m doing it next year

But I’m thinking about studying it through khan through the summer

So I can go straight to Ap calc about

Ab*

[shadow summit]

what exactly do you want to know, also we cant just teach you an entire topic, that is a teachers job.

[viscid thistle]

$(a_1-x)^2+(a_2-x)^2+(a_3-x)^2+\ldots+(a_n-x)^2$
find x that minimizes the expression

[obsidian monolith]

Mathemainia

[viscid thistle]

well we can expand the expression

as follows:-

$v=\sum a_i^2+nx^2-2x\sum a_i $

$v=\sum a_i^2+nx^2-2x\sum a_i$

[obsidian monolith]

Mathemainia

[viscid thistle]

then we find the derivative to find $\min(x)$

[obsidian monolith]

Mathemainia

[viscid thistle]

$v'=2nx-2\sum a_i \rightarrow x=\frac{\sum a_i}{n}$

[obsidian monolith]

Mathemainia

[viscid thistle]

i.e the mean of set $a$

[obsidian monolith]

Mathemainia

[azure inlet]

Can anyone help find the roots of this function?
I want to know why x = 4.965 and not x = 5.
I'm finding it after all ln(x) = ln(5)

[shadow summit]

"It’s not a root because this isn’t a function. And even if it were, it wouldn’t have a root." - 🤓

[dim peak]

@shadow summit is correct @azure inlet because the function does not represent ant root

[shadow summit]

this feels like im going to need the lamber W function, im gonna check with wolframalpha, and if it does im not doing it.

[summer ruin]

because e^(-5) + 5/5 = e^(-5) + 1 is not equal to 1

[shadow summit]

you have learnt the extent of logarithms, new achievement: lambert W function is difficult

just let x=0, simple, easy, solved.

[azure inlet]

Oh no, but you can show that x = 4.965 ?

[shadow summit]

thats not a function so im not sure how you are graphing it.

also even if i assume you meant either e^-x + x/5 = y (find x when y=1) or e^-x + x/5 -1 = y (find x when y=0), the graph doesnt look like that.

[summer ruin]

with w function, yes

[shadow summit]

you have to use the lambert W function, and im not paid enough to learn it. (im not being paid for this)

[azure inlet]

I don't know what that function is. 😢

[raven tinsel]

How does one do this

[viscid thistle]

Have u tried plugging in -5?

If it gives u an indeterminate form, then we can factor to cancel out some things and then plug -5 back in

[shadow summit]

If it’s indeterminate try using l’hopitals rule

[viscid thistle]

We could. But since this is precalc, I assume that the poster hasn’t done derivatives yet. But yes lhopital absolutely works too!!

[raven tinsel]

Wtf I thought it was 5 lol

I was plugging that in the whole time

[viscid thistle]

Nah it said -5 lmao

[ivory mango]

W(X times e to the x)= x or something like that

[ivory mango]

my precalc class hasnt even gone past algebra review, weve been doing rational functions for the past month

[viscid thistle]

Dang that sucks

[ivory mango]

Real

[viscid thistle]

Do u do extra math outside of school

[ivory mango]

Not really

I just watch calculus videos and trig videos on yt

[viscid thistle]

Ya I did that in freshman year. I stated watching bunch of math videos, and finished school math curriculum. And now I’m just self studying calc 3

[ivory mango]

nice

[viscid thistle]

I suggest just to do more math out of school cuz u r gonna learn sm more

[ivory mango]

yeah I plan on ordering books over spring break to study for the SAT next year

[ivory mango]

wassup

[viscid thistle]

Hii

[gaunt sand]

? There are many tools available online that can graph stuff that aren't functions, like relations. Desmos literally can.

[shadow summit]

Well no. That’s literally not how that works.

Go into desmos and type what their “graph” was

[gaunt sand]

Ah I see, cause it was set equal to 1, my mistake there for misinterpreting what the eq was

[shadow summit]

dw about it

[glossy fable]

hi

[arctic sundial]

What is the order I should perform during transformations concerning logs

Because during other transformations shift comes first and then reflection, but with logs reflection comes first and then shift? I am a little confused

[ivory mango]

like log base functions?

[arctic sundial]

yep

like log(x)

[ivory mango]

so

log a(x) is a parent function

and each parent function is the x value to a power

like x^0 is always one so your first value is one

and then your 2nd x value is the log base number

and then after that its just the log base number to the 2nd power, then 3rd, the 4th and so on

and then the powers to get to those numbers are the y values

[arctic sundial]

ye i understand what a log function is but i dont understand the order of how you should perform transformations

so for

log(-(x-1))

Should you reflect first or shift

[ivory mango]

is the original -(x-1)?

[arctic sundial]

Acttualy, if you have 2log(-(x+1)) + 3, what is the order of how you should perform the transformations

if the original is log(x)

[ivory mango]

your y value from the parent function will be 2y+3

[summer ruin]

you can do in any order you feel like doing

[ivory mango]

oh thats what you were asking

my bad

[arctic sundial]

its alright

[arctic sundial]

I tried doing different orders but got different results

[summer ruin]

then you did something wrong

[arctic sundial]

It depends whether you do reflections or shifts first

[ivory mango]

-(x+1) becomes -x-1

wait actually i shouldnt say anything im not helping

[arctic sundial]

This isnt a reflection across x-axis

[summer ruin]

it isn't

[arctic sundial]

im so confused

so what does the negative do then

Is it a reflection over the asymptote?

[summer ruin]

depends on where you use it

[arctic sundial]

or there is an order

[summer ruin]

cos(-x) = cos(x) so it does nothing

sin(-x) = -sin(x) is a reflection across x-axis

log, as you noticed, is reflected across y axis

[arctic sundial]

yes, but after it is moved it is reflected over the vertical symptote

[summer ruin]

yes

[arctic sundial]

so that is what the negative does?

[summer ruin]

that's the same as reflecting across x=0 and then shifting it to -1

[arctic sundial]

Yes, but not the same as shifting to -1 and reflection across y axis

[summer ruin]

again it depends on where you use it

[arctic sundial]

so there is an order

i think

[arctic sundial]

where else could i use it

[summer ruin]

no think about it again and look at what you observed earlier

if you're not convinced play both orders of transformation in your head

why should shift to -1 and reflection across -1 be different from reflection across y-axis and then shifting it to -1

[summer ruin]

I provided 3 examples earlier

[arctic sundial]

This is a reflection across y axis

is it because you distrivute the negative

[summer ruin]

no it isn't

these two curves are symmetric across vertical line at x=0, i. e. they're symmetric with respect to y-axis

ln(x) and -ln(x) are symmetric with respect to x-axis

[arctic sundial]

so symetric is not the same as reflection?

[summer ruin]

well depends on what you mean precisely

[arctic sundial]

As reflection over y axis i mean where the x values are multiplied by -1

[summer ruin]

no reflection has very specific meaning and it has nothing to do with multiplication

this is just wrong way to think about transformations because you won't get anywhere with this

[summer ruin]

see these 3 examples

they're not conistent as far as transformations are concerned

[arctic sundial]

So what does the negative in log functions do

im sorry im being stupid

[summer ruin]

you explained it yourself

[arctic sundial]

oh

so thats it?

[summer ruin]

in the case of log, yes

[arctic sundial]

Thank you so much

so the order of transformations doesn't matter

for log functions

[summer ruin]

for any function

[arctic sundial]

thank you so much lol

[ivory mango]

I've put something on the help forum if anyone is available

[dawn estuary]

hi

can someone help me

this is supposed to be easy but i slept in class

so i need someone to explain it to me

MY SAVIOR

SUB

[lone quiver]

https://tenor.com/view/e-there-is-nothing-we-can-do-gif-1915861908606230748

[broken hare]

Clueless

[dawn estuary]

oh

who is smart here

[broken hare]

As someone who just finished learning trigonometric functions of an angle through a unit circle, I do not understand the concept of a sinusoidal function.

[dawn estuary]

ok

:((

im supposed to be good at graphing them too

but no

some monkey speeds up time when im sleeping

so that i get tired at school

HELP ME

AND STOP REACTING

alr

just d

explain how i graph number d

[broken hare]

Not sure how it works, but this is what it looks like in Desmos...

We never learned how to graph trigonometric functions yet.

[velvet anchor]

cmon snow you got this

[paper tiger]

ok wait lol

we just did these in ap precalc lmaoo

first find ur period the number in from of the variable (x) in the pantheress in this case it’s 1 so you would do 1 times Pi (standard Period of all cotangent and tangent functions) So now we know our period is just pi

NOW

WAIT ITS COMING BAXK OMG

YOU NEED TO KNOW THAT THE VERTICAL ASYMPTOTES OF COTX ARE 0 AND PI. Take X plus pi/4 and set it equal to 0 in order to find your first asmyptote which is -pi/4 and then add that to your period which is 1 to get ur second asymptote which would be 3pi/4

Wait lol everything i just said is laid out in these very similar examples

The same process and everything

@dawn estuary

For csc/sec graphs it’s dif so here’s that

[turbid epoch]

#help-18 message

[ivory mango]

why does AP precalc even exist

[vocal cargo]

omfg wth is any of this

LOL

[ivory mango]

Uh

Are you not in precalc yet?

[river drift]

most universities offer precalculus courses, and ap courses exist theoretically to give college credit for equivalent courses

[granite quiver]

College course

tbh its not a very good cirriculum

high school precalc is probably harder than this

hopefully it gets harder when we get to unit 3 trig functions

[ivory mango]

I know what an AP class is lol but thanks

My precalc class is going over exponential/log functions

[terse thicket]

My school offers something called "Double Dual" where you take a College Semester of College Algebra immediately followed by a Semester of Precalculus. It's uh... abuse?

[tight mortar]

guys

can someone plz tell the the exact and actual meaning of integration

[shadow summit]

algebra is fun, precalc is easy.

[shadow summit]

integration is just the area under a curve

[tight mortar]

hmm

but i want to understand it more

[shadow summit]

say you want to calculate the area between x=0 and x=5 of the function f(x)=x/5 + 3

[tight mortar]

hmm

[shadow summit]

now do you know what a derivative is?

[tight mortar]

yea

to find the slope right??

and the opp of integration

[shadow summit]

opp?

[tight mortar]

opposite

[shadow summit]

ahh yes

derivative is rate of change

now, if you take the antiderivative

you can find the area

[tight mortar]

hmm

[shadow summit]

hold on while i draw some stuff on paint

screw this drawing is for nerds

[tight mortar]

lol

[shadow summit]

the antideritive for a function f(x) is F(x)+C

[tight mortar]

yea

[shadow summit]

such that the derivative of F(x)+C is f(x).

so the antiderivative for $f(x)=\frac{1}{5}x+3$ is $\newline \newline F(x)=\frac{1}{10}x^{2}+3x+C$

[obsidian monolith]

TheLord26

[tight mortar]

yea

[shadow summit]

And if you want to find $\int^{5}_{0} f(x)dx$

[obsidian monolith]

TheLord26

[tight mortar]

u take limits right??

[shadow summit]

You need to do $F(5)-F(0)$

[obsidian monolith]

TheLord26

[shadow summit]

no

unless you want to do riemann sums

[tight mortar]

ohh

[shadow summit]

but dw about that if you cant do an integral yet

[shadow summit]

so just plug in these numbers into the antiderivative

it should give you 17.5 i think

[tight mortar]

i can like do integration

im preparing for IIT

so

[shadow summit]

wdym?

[tight mortar]

i can do the integration sums

indian institute of technology

i just wanted to satisfy my one basic doubt

[shadow summit]

so you know how to do an integral?

[tight mortar]

yes

but i dont know where to use it in rl

[shadow summit]

im confused, why did you ask then?

[tight mortar]

..

so i asked it

[shadow summit]

its got a lot of uses in physics

[tight mortar]

hmm

[shadow summit]

for instance, if you know velocity of something you can calculate its acceleration.

[tight mortar]

but using derivative right??

[shadow summit]

thats if you are given the acceleration

[tight mortar]

bro

[shadow summit]

(i might be getting the acceleration and velocity graphs mixed up cuz i dont really study it)

[tight mortar]

acc means rate of change of velocity

so

[shadow summit]

its to find the one thats not linear

[tight mortar]

ohh

which depends on time t??

[shadow summit]

idk man, id have to have a refresher in physics, i havent really done it in a while

[tight mortar]

ohh

so are you a full fledged math teacher??

[shadow summit]

no

[tight mortar]

student at some university??

[shadow summit]

close enough

[tight mortar]

ohh

are u from india by any chance??

[shadow summit]

no

[tight mortar]

ohh

europe??

[shadow summit]

nope

[tight mortar]

lol

nvm

[shadow summit]

i really want to see where this guessing goes, so go on

[tight mortar]

ok then...

ru from asia??

[shadow summit]

no

HA

[tight mortar]

north america??

[shadow summit]

no

[tight mortar]

??

[shadow summit]

that was a laugh

[tight mortar]

does it mean hungary??

[shadow summit]

no

[tight mortar]

ohhh

[shadow summit]

thats in europe

[tight mortar]

yea

[shadow summit]

and i already said no to that

[tight mortar]

australia??

[shadow summit]

finally lol

yeah, im aussie

[tight mortar]

lol

[shadow summit]

anyways, if you want to know about riemann sums i might be able to help, but im not really good at explaining them

honestly, id just reccommend watching a video by khan academy or the organic chemistry teacher

[tight mortar]

how r they??

like hard or easy

[shadow summit]

not that hard, just a lot more work than an integral

[tight mortar]

ohh

is it like

using summations in integrals??

[shadow summit]

no

using sums

[tight mortar]

ohh

then thats definite integrals right??

[shadow summit]

no

[tight mortar]

lol

[shadow summit]

its very similar and calculates for the same thing

[tight mortar]

how come i manage to get everything wrong

[shadow summit]

its not tehinically wrong

[tight mortar]

ohh

[shadow summit]

it does the same thing that a definite integral does, it just doesnt use integrals.

[tight mortar]

ohh

i get it now

its just a different mechanism

[shadow summit]

yep

[tight mortar]

ok then

its been fun

and thank you for ur time!!

[shadow summit]

ok

[prime gazelle]

Can someone explain what happened to the constant c1 in denominator of 2nd last step

[glad widget]

idk what happened either lol\

c1 just said "aight im out"

c1 is meant to be there ur not missing anything lol

[prime gazelle]

Exactly , maybe its a textbook misprint

[granite quiver]

Anyone else using this in their Precalc class?

[hushed sphinx]

Forced perspective. If you look closely, you can see the ball is passing several meters behind the hoop.

[viscid thistle]

where does the 3 come from? thought d(cosx)=-sinx is there a rule?

[summer ruin]

chain rule

[viscid thistle]

oh thanks

[hushed sphinx]

Use #calculus for questions about differentiation, by the way.

[granite quiver]

Because math. I’m assuming kids basketball lol

The balls path when thrown represents that of a polynomial graph I assume

Maybe that’s the reason for the cover

[vestal bison]

can anyone recommend me some sources to study pre calculus?

and calculus

[keen wharf]

hey yall i have an exam tmr and one of the parts of it is like identifying if the given general form is a Circle or an ellipse or a hyperbola or a parabola and i just wanted to know how i could tell them apart without transforming it into standard form

[keen wharf]

Okay yall i just chatgpt'd it and can yall verify if this is true at all

[willow bear]

!nogpt

[tender quest]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[keen wharf]

o

[shadow summit]

If you are allowed to convert to standard form then do it. Also don’t trust chatgpt.

[kind valley]

interesting

[keen wharf]

what if im not 😭

[shadow summit]

Skill issue

[keen wharf]

smh

[willow bear]

why not

!xy

[tender quest]

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

[glossy tendon]

can anyone help me out

[clear glade]

Question?

[shadow summit]

!da2a

[tender quest]

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/

[chilly badger]

I don't understand this reduction.

https://tutorial.math.lamar.edu/Solutions/CalcI/TrigEquations_CalcII/Prob9.aspx

Kindly explain this reduction to me. <@&286206848099549185>

[summer ruin]

if you combine all values of 2pi * n and (2n+1)*pi, then they're the same as all values of pi*n

because you combined all odd and even multiples

[chilly badger]

where did you learn this from?

i don't recall any such rule

[summer ruin]

this is basic factoring and reasoning

[chilly badger]

what?

[summer ruin]

2n is even for any integer n

2n+1 is odd for any integer n

[chilly badger]

ohhhh so you factor the second one

[summer ruin]

pi + 2pi*n = pi * (1+2n)

[chilly badger]

makes snese i didn't factor it at first

thanks a bunhc

[somber current]

So, I have figured out what I actually want to ask about iteration.

Say you have an equation, (3x-1)/5x=1 One way you could solve this would be through rearranging the equation to get an x on one side, so x=(3x-1)/5. Then you plug in any value for x(n) and the output of that function (3x-1)/5 will be x (n+1). If you repeat this enough times, you will come to the solution. (This is of course for converging sequences, If it diverges e.g. f(2x) you can find the inverse of the equation, then do the before mentioned steps.)

I just learnt about newtons method, and was wondering what the differences are, and why you would use one over the other.

Thanks!

[old isle]

newtons method works for almost every function

[somber current]

And how do they work with trinomials, do they only give 1 solution?

[old isle]

u mean quadratics?

or nth degree polynomial?

[somber current]

That

[old isle]

u sort of have u guess the root first, or an approximate position of the root on the x axis

then it will converge to the closest root

like if a polynomial has roots 1,7,-5
if ur guess is -6 initially, it will converge to -5

[somber current]

Regardless of its funtion?

[old isle]

yeah

[somber current]

I might try graph it, feel like it will be easier to understand

Thanks for your help though!

[old isle]

wait i got mixed up with fixed point iteration, idt newton's method will converge to the closest root

[somber current]

Is that what the first method I said is called?]

[old isle]

yeah

[somber current]

Alr

[summer ruin]

well you don't know which root newton's method converges to

the dervative could be close to zero in which case newton method will make a step far away from the current point and will converge to some far away root

[nova musk]

hi is anyone available right now to help? on functions and graphs

[shadow summit]

either open a help forum for more general stuff or just state the question you are having difficulties with.

[nova musk]

thanks, i posted in the help forum

[valid parrot]

technically my question belongs here : without using L'Hospital's rule, or integrals, or Taylor polynomials, but by using the sandwich (can use absolute value cause we want to know if it tends to 0), how would you evaluate this limit :
[ \lim_{x \to 0} \frac{\sin(x^n) - x^n}{x^n} : \text{?} ]

so i've already gotten the point that it's 0

(i know it's true)

and

[ \lim_{x \to 0} \biggr| \frac{\sin(x^n) - x^n}{x^n} \biggr| = \lim_{x \to 0} \biggl| \frac{\sin(x^n)}{x^n} - 1 \biggr| ]

oh and we cannot let t = x^n, that'd be too easy

my only goal is to find a sandwich and then apply epsilon delta definition of a limit

oh wait

also my limit's wrong

it's x to <à

0

[valid parrot]

(it's the proof that x^n is the taylor polynomial of degree n of sin(x^n))

[summer ruin]

limit sin(t)/t as t->0 is 1

and limit of -1 is -1

[valid parrot]

:(

I know how to do it geometrically

But I wanna do it the sandwich way

[viscid thistle]

L-hos rule would be best to solve this
Its lengthy with sandwich theorem "/

[valid parrot]

ja thanks, but none of these 💀

i genuinely don't care about length

the goal is to prove it, not to evaluate it

oh shit

i wrote evaluate in my question

naaah i'm dumb

[swift stone]

openstax precalculus should be enough to prepare for MIT's Calculus course right ?

[river drift]

most likely, yes. just make sure you do plenty of practice problems to get comfortable with the concepts. if you ever see a topic you're not familiar with in calculus (that isn't the one being taught) you can look that up as needed

[swift stone]

thanks !

[wild torrent]

hey peeps, i have a question about linear regression through the least squares method. Its in my precalculus text book so im posting a question here

basically, im trying to understand why you would do the specific steps, rather than how to do them. like, you have a table of x and y values. You find the average of the x and y's, then subtract each specific value by the mean to get delta x and delta y. I think you do that because your finding how far the value is from the mean (how far it is, because youre trying to make a line that shows where the data is headed) Something im confused about is that you multiply delta x and delta y, then divided by the sum of the sqaures of delta x. I get youre finding the slope there, but how does multiplying delta x and y get you the 'run' (of rise over run, the way my middle school teachers described the slope) and why would you multiply specifically? why not do something else?

generally my goal is to understand why you would do specific steps, and why those steps specifically. like, is there something special about multiplication in this case? i have no clue

[spice steeple]

youre trying to minimize the error in both x and y
so you can multiply the error in x by the error in y

[spice steeple]

total error at a certain point would be the error in x multiplied by the error of y

a square

[wild torrent]

so if i have a specific value of x thats 5 and the average of all the x values is 15, the 'error' is -10 for that value
you then add up all the error values of x, and of y
and when you multiply them you find the total error? like why not just add them? You said you get a square, but why is that important?
thanks for talking with me btw

[spice steeple]

theres an error in both x and y right

[wild torrent]

ye

[spice steeple]

the particular method here is to minimize the squared sums

some of it is convenience

for instance the errors might cancel out if you just decided to add all errors

so we decide to square it

[wild torrent]

yeah i was thinking about that

[spice steeple]

its a similar logic for standard deviation

[wild torrent]

i had a feeling you multiply them, just to divide by sumx^2, to get rid of a negative value or something

like :

(delta x)(delta y)
/
(delta x)^2

just cancels out to

(delta y)
/
(delta x)

which makes sense cuz of the rise over run, (up y over x)

[spice steeple]

the error can be thought of as the square root of the sum of the squares of each error

in euclidean space it represents distance

[wild torrent]

ok so i wasnt dumb in describing error as "far" lmao

[spice steeple]

although tbh i am not super understanding of this

[wild torrent]

well, i did the same example as in the book but just did sum(delta y) / sqrt(delta x ^2)

[spice steeple]

a lot of it is making it easier to process computationally

since programs and the such run linear regression

[wild torrent]

yeah that also makes sense

[wild torrent]

and got .01 instead of .9

idk, thanks tho learned some things

[spice steeple]

it also has interesting properties assuming the residuals follow an approximately normal distribution

[wild torrent]

like a bell curve?

why?

[spice steeple]

least squares form is the maximum likelihood estimator

provided that this is true

u can read some about it

absolute value is also weird to differentiate while quadratics are pretty trivial

[wild torrent]

side question about this, when you multipy two different numbers is that called a square? i thought that only referred to when you multiple the same number together twice

https://www.investopedia.com/terms/l/least-squares-method.asp reading this rn lmao

[spice steeple]

i was wrong abt it it is the squares of the errors

as in multiplied by itself

[wild torrent]

gotcha

so i think i got my answer

like you multiple delta x and delta y because your finding the total area, then divide it by (delta x)^2 because your finding the ratio between total area and the 'perfect square' area

basically what it is vs what it should be

then you can make a line of best fit cause you have a slope

i asked it on math stack exchange, and im testing this myself on desmos currently

https://math.stackexchange.com/questions/4842023/question-about-finding-slope-from-my-textbook-walking-through-linear-regression

found a video that explains it pretty well https://www.youtube.com/watch?v=3g-e2aiRfbU

[verbal rock]

is this the right channel

is this precalculus

[swift stone]

yes baby girl, this is the right channel

[viscid thistle]

What's the name of this text book?

[swift stone]

like 70% sure it's the stewart precalculus book

[viscid thistle]

Ok thanks

[verbal rock]

Right one

[swift stone]

and I was wrong

[verbal rock]

This is the left one

Im pretty sure the right book builds off the content in the left book

[viscid thistle]

Is this a book you'd read before going to uni or while in uni?

[verbal rock]

im in 10th grade

[viscid thistle]

What would that be in terms of the uk school system?

[verbal rock]

im australian

[viscid thistle]

Yooo same

[viscid thistle]

May I know how old you are by any chance

[verbal rock]

14 turning 15

[viscid thistle]

10th grade is 15-16 lowest to enter is 14 highest is 17

[verbal rock]

why?

[viscid thistle]

Depends on the year your born

[viscid thistle]

So I guess that would be year 9-10 in the uk

[verbal rock]

uhhh idk

idk anything about the UK

[viscid thistle]

Same lol

[verbal rock]

except princess diana

[viscid thistle]

Queen Elizabeth

I need to revise all my highschool math

forgot most of it

Anyways, thanks for the textbook

[verbal rock]

NP

[verbal rock]

for topics like vectors and differentiation in the other book is this calculus?

i cant find in khan academt

[swift stone]

vectors will be in linear algebra

I meant khan academy https://www.khanacademy.org/math/linear-algebra

also not sure about differentiation haven't dug that deep into the PreCalculus yet

[verbal rock]

ok thx

i am going to bed now

[verbal rock]

oh that isnt good

like wat?

should be easy to relearn

[swift stone]

god speed my dude

[verbal rock]

muhwhahaahahahahahahhahahahahahaa

[obsidian monolith]

The current time for nutgun. is 02:59 AM (AWST) on Thu, 11/01/2024.

[glossy cave]

Can someone please explain to me how does Newton notation work... and what IS Newton notation

[viscid thistle]

It's been a long time since I've revised anything related to math

[verbal rock]

same im on summer brrak

break

[lofty tusk]

hello. Do u know a youtube channel called blackpenredpen? he had a video where he was solving an equation like P(x) ^ Q(x) = 1, and wolfram alpha found only 4 our of 6 solutions. Could u link me that video pls? cant find

[gaunt sand]

Just follow the WA syllabus. There is no explicit 'pre-calc' class in WA. Your school will cover the basis of what you need to be able to move onto the calculus related stuff

[gaunt sand]

Chapter 17 for the Methods 1/2 one introduces you into basic calculus, the rest ig is 'pre-calc'

Also Cambridge rlly is lazy lol. They really used the same layout of chapters from VCE methods to WACE 😭

prolly same questions too

[feral halo]

hi guys I need help with memorizing the unit circle I need it for my physics unit 5. however the thing is I haven't exactly learned it at all in my precalc class I've went over the basics in geometry but never went in depth. does anyone have any tips on learning the unit circle by yourself for rotational motion and gravity (the current unit that I've started in physics)?

[shadow summit]

<@&268886789983436800>

[river drift]

there are 2 parts to remembering the unit circle:

• knowing trig functions at special angles (0, 30° = π/6, 45° = √2/2, 60° = π/3, 90° = π/2). for this you only need the 2 special triangles (45°-45°-90° and 30°-60°-90°)
• knowing the quadrants. You should know 4 quadrants of the plane + which angles go in which quadrant to extend the trig values in quadrant I to other quadrants (remembering that x = cosθ and y = sinθ on the unit circle)

[verbal rock]

do u have a course outline i can have?

[gaunt sand]

Search up WACE methods syllabus

[gaunt sand]

https://senior-secondary.scsa.wa.edu.au/syllabus-and-support-materials/mathematics/mathematics-methods

[verbal rock]

ok thx :D so i just do this in order?

[gaunt sand]

Yep it'll outline what you can be assessed on. Anything not in there will not be assessed in your 3/4 exam

For when you start 3/4

[verbal rock]

most of this stuff i covered last year

do u think i should just do specialist?

[gaunt sand]

yeah a lot of the initial methods chapters

are basic math stuff

yea

[verbal rock]

what yr are u in?

[gaunt sand]

I do VCE methods

year 12 this year

[verbal rock]

ohhh ic

did u do specialist too?

[gaunt sand]

na i didnt

i didn/t do 1/2 and 3/4 picks up on quit a few things

so it was too much of a catch up

and i cbs

[verbal rock]

wtf

u are brave

[gaunt sand]

r u year 11 this yr?

[verbal rock]

10

[gaunt sand]

Ohh

so u're ahead

I see

[verbal rock]

ya

im also doing physics

[shadow summit]

ewww western australia

[gaunt sand]

😭