precalculus

[willow bear]

this is incorrect

just because the product of two numbers is 1, does not mean either one of them has to be equal to 1

it's called the null factor law for a reason.

[pale hazel]

Oh okay 👍

[primal quail]

a counter example would be (-1)(-1)=1 or any other number, call x, choose 1/x and we have they multiply to 1, (given x is not 0)

[sick quartz]

trigonometry was significantly harder

there's just a lot more to remember

but it's also more conceptually loaded, having to learn the unit circle

understand it

[lofty pine]

Interesting

[viscid thistle]

that would be 1 / cos y which can be rewritten as sec y.

in hindi?

what about post-calc?

[peak pasture]

That’s where it’s proofs and it gets tricky

[onyx night]

the amplitutde will be 2, and the period will be pi

[unreal cosmos]

hi

need help

can some one explain this

[willow bear]

gonna need some more context there chief

[unreal cosmos]

hmm no way to just define what this is saying?

[willow bear]

i mean

presumably s is a function of some kind, maybe with N as its domain

and A is some number

[unreal cosmos]

i just wanna know what each element is saying

[willow bear]

and the limit of s(n) as n goes to infinity equals A

we couldn't tell you why this would be true or indeed whether it's true at all, though.

[unreal cosmos]

s(n) is a sequence

in this case

[willow bear]

yeah

maybe with N as its domain

okay, so s(n) is a sequence

s(n) is a sequence which approaches A

[summer ruin]

we say that the limit of infinite sequence $a_n$ is (equal to) $A$ if for any positive $\varepsilon$ there exists a natural number $N$ (which could depend on epsilon) such that for all elements of a sequence $a_n$ which are enumerated with numbers starting from some number $n_0 > N$ all such elements satisfy the inequality $|a_n-A| < \varepsilon \\$

in other words all elements $a_{N+1}, a_{N+2}, ...$ are within epsilon distance away from the limit $A$

[willow bear]

or rather, taken at face value, the snippet you posted reads: "The sequence s(n) [which the reader already knows about] approaches A."

[obsidian monolith]

Transparent_Elemental

[unreal cosmos]

so. as n approaches infinity s(n) approaches A

[willow bear]

is this really helpful

anyway so what you're saying is you didn't know what the lim notation meant? and your question was about notation and not content?

[unreal cosmos]

well both ig

just how each element relates to the other

[willow bear]

element...

[unreal cosmos]

notation

[summer ruin]

well here it is, it will take some time to parse it, but it's worth it to understand what limit means

[unreal cosmos]

ok let me read it

[summer ruin]

I suppose you already have at least intuitive notion of what a sequence is

[unreal cosmos]

yes

at the very least

[unreal cosmos]

you there?

a question

are limits only used when f(x) is undefined?

[summer ruin]

no

[rapid inlet]

You can tell from the equation the x intercept, y intercept and gradient. Write those down and compare to the graphs 🙂

[leaden nimbus]

what program is this

[unreal cosmos]

i finally get it

took me a while to visualise it but damn it actually fit in my head

[warm glade]

anyone know good resources based on how my class is structured?
Chapter 1: Functions and their Graphs

Chapter 2: Polynomials and Rational Functions

Chapter 3: Exponential and Logarithmic Functions

Chapter 4: Trigonometry (Basics)

Chapter 5: Analytic Trigonometry

Chapter 6: Applications

Chapter 7: Systems

Chapter 8: Matrices

Chapter 9: Sequences and Series

Chapter 10: Analytic Geometry

[stone walrus]

Doing math corrections, can anyone explain how to do 16, 17, or 18? I need it for tomorrow

[light crescent]

mine was set up a bit differently last year since the 2nd half seems a bit different compared to the Units we had, but pauls online math notes would probably work although cant guarantee the units will be in order

[stone fog]

anyone tryna vc and help me out?

[light crescent]

goodluck finding that here

[stone fog]

pre calc is so annoying

like some things in it are like wtf

[tropic sage]

FR

Precalc is the bane of my existence

[lucid trench]

how

[inland ruin]

I think pre-calc is like the junk drawer of the math classes. It's got a lot of useful things, but they're just kinda all thrown into one drawer of "this is useful, but I don't know where else I could put it."

[opal tree]

Literallt

[opaque kelp]

no complex numbers?

[warm glade]

Did that last semester this is for this semester

[opaque kelp]

oh i see

i wonder, what year do u take pre-calculus

we have different systems where im from so im trying to understand the concept better

[lucid trench]

i'm in 12th grade taking precalculus

most people seem to take it 11th though

[waxen vale]

I'm a 10th grader and I take precalculus

there's a 9th grader in my class but all he does is use photomath on assessments

idek how our teacher hasnt caught on yet

[frank plover]

considering its name sake is just "before calculus" and not connected to any one section of mathematics, I guess it's to be expected

[night palm]

should i begin studying precalc?

rephrasing

when should i begin precalc

[brisk vortex]

That’s the normal curriculum some people are 1 year ahead and even more 2 or 3 years ahead

So that’s why

But you’re just where you need to be

[vapid plaza]

As early as you wish; if you get stuck, go back and review your knowledge

Better to be familiar with precalc concepts sooner rather than later

[fluid oxide]

I need help

Sinusoidal equations

[covert helm]

@everyone

join vc

[daring drum]

Don't try to ping everyone for math help please... it doesn't work and it's not appropriate

[vapid plaza]

Bro really told 130000 people to join vc

[analog glade]

and only 4 came

[unreal cosmos]

guis

why do we complete squares.

sorry if its a dumb question

i know how

i just wanna know why

till now ive only done it because book tells me to

[summer ruin]

because it simplifies the expression

e. g. show that the expression 2x^2 + 5y^2 + 6xy is greater or equal to zero for any x and y

[uncut mulch]

it converts expressions to an equivalent form from which certain info may be more easily obtained

[hazy hollow]

Write an equation for a cosine function with an amplitude of 1, a period of 4pi, a phase shift right of 5pi/6 and a vertical shift up of 3.

What would that be^?

[fringe pulsar]

asking for the answer here doesnt really benefit anyone

https://youtu.be/fo_q9mEAFp4

this is helpful

[gleaming prairie]

there are 2 general ways of plotting. The first is to follow transformation steps, ie horizontal compression with the A in the expression. The 2nd is to locate certain points on the graph like max or min and connecting the dots

[unreal cosmos]

how do i know what kind

[summer ruin]

?

[unreal cosmos]

what kinda info

im not really sure

actually nvm

i get it

[exotic moss]

does anyone have a recommendation for a precalc textbook?

[oblique ice]

Someone help me

I tried solving it many times

But my answer doesn’t match the final answer

[hot sigil]

someone mind explaining this rq?

[balmy blaze]

We can factor out cosθ, and we get cosθ(cscθ - 2) = 0. Now we can see that either cosθ is 0 or cscθ - 2 = 0. The only values of θ that make cosine 0 and are within the bounds are pi/2 or 3pi/2.

[balmy blaze]

If cscθ - 2 = 0, then cscθ = 2. We can substitute cscθ for 1/sinθ, which gets us 1/sinθ = 2, or sinθ = 1/2. The only values of θ that make this true and are within the bounds given are pi/6 or 5pi/6. So our final answer is θ = pi/6, pi/2, 5pi/6, or 3pi/2.

[queen ibex]

Am I doing this right?

[spark wolf]

not the five part

oh nvm im stupid

its 1/2 or 2

smh u wrote cosx=1

oh nvm 2 doesnt exist

[queen ibex]

💀 oh

[spark wolf]

im stupid

so only 1/2 ig im not sure eithe

r

[queen ibex]

You’re right

[spark wolf]

yeah only 1/2

giga chad desmos

[viscid thistle]

cos x = 1/2 cos x = 2

you got it right mostly except the last part

[spark wolf]

yeah

and cosx=2 doesnt exist

[queen ibex]

Thank you

[spark wolf]

np

[queen ibex]

I fixed it

[spark wolf]

https://media.discordapp.net/attachments/1051316377992044604/1063245746423476325/PewDiePie_Has_a_Mental_Breakdown_1.gif

[viscid thistle]

well done

[uncut mulch]

what's people classify as algebra 2 or equivalent covers mostly the same stuff
khan is a decent place to start

[viscid thistle]

Hello, can someone explain to me why arctan of -1 is pi over 4? In my head, I'm thinking it would be 7 pi 4 (going off of a unit circle) with consideration to the tangent restrictions. I'm guessing since 1 is negative, I should start clockwise?

[summer ruin]

because the range of arctangent is from -pi/2 to pi/2, 7 pi/4 is bigger than pi/2

so arctan(-1) is some number between -pi/2 and pi/2

specifically it's a number x such that it's tangent tan(x) = -1 given the constraint on the range of arctangent (and hence domain of this equation)

and the angle there isn't pi/4, but negative pi/4

7 pi/4 describes the same angle, but as I said it's outside of range of arctangent

[viscid thistle]

Thank you for answering. I think this makes sense to me now.

[viscid thistle]

cot - root 3 is - pi over 6*

[hallow thunder]

,calc -pi/3-pi/6

[obsidian monolith]

Result:

-1.5707963267949

[hallow thunder]

Which is -pi/2

$\frac{1}{a}+\frac{1}{b} \neq \frac{1}{a+b}$

[obsidian monolith]

jedben2

[viscid thistle]

can someone teach me calculus from beginning i have to do hc verma

[zinc fulcrum]

lmaoo idt anyone is going to do that

you could try learning some stuff on the internet or asking for some resources and coming back with more specific questions 🙂

[viscid thistle]

ok

[viscid thistle]

email hc verma to teach you

🙂

[viscid thistle]

lmao

[spark wolf]

three blue one brown is good

on youtube

he provides some pretty intuitive explanations for all the rules and stuff

intuitively understanding maths is like always helpful on top of concrete proof and stuff

at least for me so far lol

[spark wolf]

and btw this is precalc channel i just saw

[balmy gorge]

Got a 96% on my precalc midterm exam

[viscid thistle]

Is your name really Ryan Chapman? There’s a philosophy YouTuber with the same name. Congratulations btw on the score!

[balmy gorge]

Yeah that is my name lol

[hard tinsel]

what do you guys advice me to learn before precalculus?

[cosmic girder]

know your algebra

like moving around stuff in an equation should feel natural to you

[hard tinsel]

ok

that's a good advice

[viscid thistle]

so pre-precalculus

[viscid thistle]

3blue1brown
Blackpenredpen
The organic chemistry tutor
Eddie woo

Are all good youtube channels for those new to calculus. Although they also cover more advanced stuff as well.

[chilly hazel]

can a singular point have a limit?

and would this have a limit?

[cinder briar]

if a cubic graph has 0 as a function what does that do to the solutiobn

[sand quarry]

Hey, can I ask a simple question about limits?

It's really simple, it will take 2 seconds, I promise.

[viscid thistle]

if you post then maybe somebody can help

@sand quarry

[sand quarry]

I did. it's in help-27

It's not even a problem really, i'm just confused over some definitions.

[viscid thistle]

@viscid thistle try Professor Leonard’s Lectures on YouTube too

If you want something more like a classroom experience

Pair that up with Paul’s online math notes

[viscid thistle]

LMAO I watch the organic chemistry tutor for chemistry like periodic trends stuff I saw from him, I see math Olympiad questions from blackpenredpen others I don't know

[viscid thistle]

Okkkk

[untold spindle]

Yo, do you learn integration during precal or is that reserved for only calculus?

[drifting parrot]

yea but in the last chapter.

[untold spindle]

ah ok

thx

[twilit dew]

in what dimension are yall learning integration in precal wtf

[viscid thistle]

Lmaoo

In my high school introduction to limits and continuity is included at the end of precalc

[viscid thistle]

lmao what

[harsh vale]

Anyone good with unit circle stuff

[vapid plaza]

If you have a question, just ask; the worst that’ll happen is that you get ignored completely

@harsh vale

[uncut mulch]

@grizzled citrus
note that after
$$\br{x+\frac1x}^3 = x^3 + \frac1{x^3} + \underbrace{3x + \frac3x}_{3\br{x + \frac1x}}$$
$$f\br{\red{x+\frac1x}} = x^3 + \frac1{x^3} =\br{\red{x+\frac1x}}^3-3\br{\red{x+\frac1x}}$$
and hence
$$f(\blue{x}) = \blue{x}^3 - 3\blue{x}$$

[obsidian monolith]

ℝamonov

[grizzled citrus]

Oh, I just sub -1 on the second function to get -1 + a - b + c then do the same thing on the first function to get -1 -3(-1) from x³ + 1/x³

[fleet pendant]

that's normal

you even do some linear algebra in high school at my place, it's not too abnormal but yea

[viscid thistle]

easy

[fleet pendant]

if you replied to mines, ya duh, its high school math; not meant to be hard lol

[slim steppe]

Well hello

[fleet pendant]

omg hi 👀

im never usually active here

[slim steppe]

Yeah, only a total of seven messages from you

[fleet pendant]

oh damn ya

[viscid thistle]

I’ve been introduced to derivatives but my math textbook sucks because it doesn’t have enough optimization problems which is my weaker side. Do you have a good source for harder problems for free?

[slim steppe]

Albert.io, Khan Academy, or just make up your own problems

[elder token]

yo, does anyone have any recommendations for pre-calc textbooks

[maiden crest]

hello

i need help with this please

[viscid thistle]

aops book or even this website

nvm that website has been take down

lol

it was a illegal website

lukcily i downloaded the books but cant share here as file too big

[untold spindle]

🧐 📸

[lucid pebble]

does OpenStax have any?

[viscid thistle]

$$\trig$$

[obsidian monolith]

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

[viscid thistle]

$\trig$

[obsidian monolith]

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

[willow bear]

@viscid thistle what are you trying to achieve?

[viscid thistle]

literally nothing

i didnt even mean to do that in this channel

i wanted to do it in #latex-testing

[mental steppe]

I missing the day we learned about polar coordinates with squares. Can someone help explain this to me?

[viscid thistle]

well not illegal but the internet says otherwise. its libgen

[untold spindle]

usually, illegal websites like free movie websites are only illegal if you download any movies. i think it should be ok as long as you use a vpn. or so im told.

im not sure if the same thing applies to libgen

[haughty burrow]

Guys, is the general formula of a circle and graphing it considered as pre calculus?

[fluid oxide]

Hmm

Im guessing cause before calculations sounds like pre calculus

[fluid oxide]

So it has to be unsolved

[haughty burrow]

What is calculus anyways. I'm still quite new to algebra so I don't know what Calculus is all about

[fluid oxide]

Im not sure lmao

I dont even know what algebra is to

Its like we use coffe and water and not knowing anything about the differences lmao

[haughty burrow]

Lol

What year are you in @fluid oxide?

[fluid oxide]

06

[fluid oxide]

Or i am not sure what u r asking

[haughty burrow]

Like r u on secondary hs?

Idk man im not sure what other countries education system is using

[fluid oxide]

O

Im grade 11

Someone who is 16 year old

And has one year left of high school

Which is at grade 12

[haughty burrow]

Ohhh

[fluid oxide]

Yessir

[haughty burrow]

Im 1 year behind you

[fluid oxide]

You already know myles on top this shi

He always one way ahead lmao

[haughty burrow]

So which country do you live in?

[cosmic girder]

calculus is applied real analysis

real analysis is about looking at real valued functions

[cosmic girder]

do you know pythagoreas

[viscid thistle]

What makes you think someone who is new to algebra, and asking about what calculus is, will understand what “applied real analysis” and “real valued functions” means

[chilly hazel]

if you substitute a limit, and it outputs a non undefined answer, will that always be the answer to the limit

[summer ruin]

a sequence cannot have two or more limits

by the appropriate theorem

[chilly hazel]

though the value at f(x) can be different from the limit of f(x), so should I verify the limit with other methods to make sure?

or is substitution not calculating the value at f(x)

[summer ruin]

value of f(x) at a point has little in common with what the limit at a point is

[chilly hazel]

and substitution calculates value of f(x)?

[summer ruin]

and as I said earlier if you compute a limit it is not possible for that limit to have two or more different values

[summer ruin]

what

[chilly hazel]

for example

substitution gives -18

[summer ruin]

you can directly substitute only because 5x+2 is continuous everywhere and at x=-4 in particular

[chilly hazel]

should I skip substitution entirely if it only works sometimes

except for simple limits like this

[summer ruin]

I never said that

well for a more difficult limit you're not going to be able to directly substitute anyway

because you won't get any meaningful result

[chilly hazel]

so does this mean, if substitution gives a solution to the limit, then you don't have go any further with solving the limit?

just want to make sure

[misty helm]

hmm

[summer ruin]

yes

[chilly hazel]

thank you

[lean rover]

(z+1)^5 = z^5 implies |z+1|^5 = |z|^5
Which would imply |z+1| = |z|
Then write z=a+ib
This would imply (a+1)^2 + b^2 = a^2 + b^2
Thus, (z+1)^5 = z^5 has no solution

This is definitely wrong

But I can't see where the argument fails

We're over C

[untold spindle]

Wait, I'm not familiar with these but taking the 5th root on both sides gets you z+1=z. I dont think there is a solution to that. Is this a viable method?

[lean rover]

"The fifth root" doesn't make sense for complex numbers

It does have solutions over C

[untold spindle]

Ah I see. Ok

[lean rover]

I'm an idiot lol

(a+1)^2 + b^2 = a^2 + b^2
This has solutions

Ignore everything

Fundamental theorem of algebra still works

[eager adder]

Can someone please explain for me why when a plane intersects the vertex of a cone we have a degenerate conic section? In terms of rotations and stuff

[viscid thistle]

Just learned rationale zero therom today. Professor said "look only 23 possibilities"

[boreal escarp]

exchange x with -4

[azure gyro]

hi does anyone know how to find the exact value of csc(-3pii/2)

?

[summer ruin]

transform csc(x) into sine

[azure gyro]

i did that

then

[summer ruin]

what can you say about sin(-x)

[azure gyro]

no clue \

[summer ruin]

how can you express sin(-x) using sin(x)

[chilly hazel]

how do you cancel off an absolute function like this?

[summer ruin]

what is the sign of x+7 when x approaches -7 from the left?

[jolly sandal]

Can someone explain this briefly?

[pseudo hamlet]

Brother this is calculus not precalculus

[jolly sandal]

Ok I'll ask in the Uni chat. I'm not from the US and this is a part of our high school curriculum. I'm not really familiar with your terms of pre calc vs calc etc

[tardy thicket]

how do u solve this

[pseudo hamlet]

Construct a triangle

[tardy thicket]

Nvm I got it

[pseudo hamlet]

Hope it's not too late but I think it should be 18/x

[tardy thicket]

how come it 18/x

[pseudo hamlet]

because the height of the ladder is 18ft

[tardy thicket]

Ok

I got it

Thxxx

G

[pseudo hamlet]

np

[lucid trench]

here are some cool precalc notes i took #8 and #9 (sorry i forgot to post)

[burnt hare]

@lucid trench Your notes are so neat holy

[slim steppe]

Yeah, but do they understand the concepts>

[burnt hare]

real

I would hope so

[steady python]

https://tenor.com/view/clucking-hen-chicken-foraging-gif-16456650

heres how I write notes

[whole hound]

Bro those notes are god tier

[split hinge]

pov me in algebra

[lucid trench]

of course

[viscid thistle]

Nice pfp

[burnt hare]

ty

[solemn relic]

godly notes , best ones I've ever seen

[cyan jetty]

why is this, this

[summer ruin]

multiply numerator and denominator by x

[wintry mortar]

these type of notes get you straight Cs

[cerulean ruin]

bro the handwriting hater

the penmanship police

[wintry mortar]

Taking pretty notes is honestly a bad habit, I know cause I used to do it

The return on investment (the investment being time) is super low

[wintry mortar]

But this is really funny though, I chuckled

[barren lagoon]

hey i need help with how to start this, this is an exponential problem, it aint homework just extra stuff

basically exponential growth and decay stuff

[pseudo hamlet]

ok so the paper is .75 mm thick

and when you rip it, you have two pieces with a thickness of .75 mm

so stacking them would double the height of the stack

repeating the process will double the height again

until you've done it 50 times

[barren lagoon]

yes yes alright i got it

now what kind of equation you use for that? i mean i know there are a couple

[pseudo hamlet]

you know it's an exponential equation

which has the general equation of y=a(b)^x

[barren lagoon]

okay

[chilly hazel]

How do you spend your time more effectively in class?

[viscid thistle]

First of all, you pay more attention. And especially in Math and Physics, try to visualize and analyze the steps you are learning. Try to figure out if there are any other methods and etc. And take notes without without that much time.

[fleet pendant]

Can someone check my work? \
Find: $D_{f\circ g},$ given $f(x)=\frac{x}{x+5}, g(x)=\frac6{x}.$ \
$$R_g \subseteq D_f \implies \frac6{x}\neq-5 \implies \textcircled{1}, x\neq -\frac6{5}.$$ \
$$\because D_{f\circ g} \subseteq D_g$$ \
$$\textcircled{2} \therefore x\neq 0$$ \
$$\textcircled{1} \cup \textcircled{2} : D_{f\circ g}={x \mid x\neq 0, x\neq -\frac6{5}}.$$

[obsidian monolith]

Anonymous_H

[brisk pasture]

I got 5697.25

[slim steppe]

5679, 5697.25 isn't an integer

[brisk pasture]

Ah, I didn't even see the whole number part, but is my answer correct?

[slim steppe]

Yes

[brisk pasture]

Is it 5679 or 5697?

[slim steppe]

5697

[brisk pasture]

Ok thanks

[slim steppe]

Actually wait

@brisk pasture

That's wrong

On the first day the viewer count is 1590

It only then increases by 20 percent for the next six days

[brisk pasture]

I already sent it

[slim steppe]

It's 4202

[brisk pasture]

Bruhh

[slim steppe]

Just say to your teacher that you made an error and show your work

[pseudo hamlet]

how'd you get that?

[slim steppe]

1590*1.2^6

[pseudo hamlet]

ye but it's asking for the total number of views

so it'd be a series

[feral coral]

wow Math classes are reaching out to gen z hahahahaha

[brisk pasture]

?

[feral coral]

this is sarcasm

[icy merlin]

Can someone solve

Pls send the solution

[willow bear]

we do not give answers here @icy merlin

[icy merlin]

Then

Where

[slim steppe]

Can you rewrite the question

[slim steppe]

No where. This is a place to learn and expand your knowledge and not a place of freebies

[uncut mulch]

well supposedly the heading for your question d) which I'm assuming is part of question 1 would describe the type of method that would be used to solve that

and also this is calculus, not pre-calc

[limpid pine]

love the frog lol

[fleet pendant]

wow those notes are so neat jeez

[vale cargo]

how do you calculate this exactly

huh?

the limit is 4/3 but how do you end up with that

[fleet pendant]

Well, if you were to directly substitute it'd make the whole expression be 0/0, indeterminate form. That means you're able to evaluate the following by using L'hopital's rule. \
$$ ,If, \lim_{x\to a}\frac{f(x)}{g(x)}=\frac0{0}, \frac{\infty}{\infty}, then:,$$
$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}.$$

That should be in #calculus but pre-calculus

[obsidian monolith]

Anonymous_H

[vale cargo]

much appreciated

[fleet pendant]

👍

[vale cargo]

will keep note

[slender idol]

I know this is true, but how do I "show" that it is true?

[summer ruin]

mathematical expressions do not change if you use different letters

[worn geyser]

@lucid trench tysm!! Your notes are great

You should ping me whenever u post notes

I'm jowo

[slender idol]

fully aware, i just was curious how i would show understanding in my answer rather than writing "they are the same." i ended up just writing that they both produce the same values in a table and the same graph.

[cursive crag]

#help-27

[slim steppe]

l'hoptials

[safe forge]

L'Hôpital = bad

[obsidian monolith]

kappa

[hushed sphinx]

No, not even if you fix k=2.

(That gives one of the prototypical examples of a lacunary function, which is too ill-behaved in the complex plane to be described by a nice closed expression).

[pale marlin]

Thanks

[viscid thistle]

how did they get to that second step from the step before?

[summer ruin]

factoring out cosecant

[viscid thistle]

https://gyazo.com/2387f71d576a2b7dbd15a379cfaf9b5c

can someone help ?

[viscid thistle]

for number 4, i got cos^2x instead of 1-2cos^2x

is the answer key wrong or can somebody explain why the answer of 2sin^x - 1 is right

[orchid kindle]

for number 4?

act. 2sin^x - 1 =1- 2cos^x

cause 2sin^x - 1 =sin^x+sin^x-1=sin^x+(sin^x-1)=sin^x+(-cos^x)=sin^x-cos^x

1- 2cos^x=1-cos^x-cos^x=sin^x-cos^x

[rose raft]

how can i find the monotonicity of function f(x)=(x+4)/(x+1) ?

[hushed sphinx]

The typical systematic approach would be to look at its derivative, but that's hardly a "precalculus" solution...

[glass canopy]

Is there any point to memorise those Dl?

Cauz u could Always use Taylor formula

[orchid kindle]

I have no idea, I just practiced a lot and remembered

[glass canopy]

Thanks

[barren lagoon]

im looking to do a

i am so confused

the answers gotta be in radians

[pseudo hamlet]

The left should be sin theta

[barren lagoon]

i cross multiplied but i see hold on

sin theta = cos thetha?

theta*

[pseudo hamlet]

Ye

[barren lagoon]

okay now how do i get these radian answers?

[pseudo hamlet]

I'm not sure about a method, I usually just base it off of patterns

Ig you could rewrite the equation as tan theta=1 and then take the inverse

[pseudo hamlet]

Wait are there more answer choices not shown here?

[barren lagoon]

no no

a)

is the answer

thats the answer key

[pseudo hamlet]

I get how pi/4 and 5pi/4 are answers but not pi/2 and 3pi/2

[barren lagoon]

reference angles?

coterminal i think is the word

[pseudo hamlet]

But pi/2 is a 90 degree angle

[barren lagoon]

yes yes

i think

um

that

the sin, cos, or tan oif something is equal to 90*

then convert to radians at the end

thats what you do

[pseudo hamlet]

Idk it doesn't really concern me anyway

[barren lagoon]

its alright thank you though

[pseudo hamlet]

Np

[cloud crest]

can someone tell me what happened in the last step?

[willow bear]

a pair of common factors was cancelled out from the top and bottom

[slim steppe]

Factored out the four to cancel out the factor pairs

[thorn orbit]

if I am given a quadratic, and 2 factors, how would I find the intercepts?

[pseudo hamlet]

Set the 2 factors=0 and solve for x in each

[slim steppe]

Set the factors equal to zero

[gloomy pulsar]

You want to convert degree measure to radian measure?

[thorn orbit]

so if I have (-3x+7)(x-4), I just set (-3x+7) = 0, and (x-4) = 0and solve for both x-intercepts

[pseudo hamlet]

Yes

[thorn orbit]

coolio thx

[slim steppe]

Yes

[thorn orbit]

if there is no denominator to a function, does it automaticely make it unrestricted?

[summer ruin]

no

[snow gorge]

example: f(x) = ln(x) it is restricted to positive real numbers since ln function is undefined for x <= 0. There are other undefined things than division by zero

[lime frost]

How to simplify

[pseudo hamlet]

Pretty sure it's based off of cos^2(x)+sin^2(x)=1

Which can also be expressed as 1+tan^2(x)=sec^2(x) and cot^2(x)+1=csc^2(x)

[astral bone]

im lost on all of these but just 41 for now
i’m supposed to do 41-54 but the textbook and teacher arent much help

[vapid plaza]

,rotate

[summer ruin]

ln(a/b) = ln(a * b^-1)

[plush umbra]

Yo guys

Need help on this one

It about principle of mathematical induction and stuff

[remote ledge]

for any shape, given that the surface area increases by x cm squared per second and all, and the formula for surface area is S, how to find the rate of change as a general formula ?

[storm lodge]

Show n=2 works then do induction step with algebra

Doesn’t seem like precalc tbh

[junior rampart]

Hello, I wnated to ask a question about the domain of an inverse function

Can I send a picture of the problem?

[untold spindle]

Sure but I can't guarantee I'll be able to answer it

[junior rampart]

so this is the answer

but

originally i put that the x cannot equal 2

but that was wrong apparently. So what is this domain

[summer ruin]

domain of what

[junior rampart]

the inverse function

[summer ruin]

everything besides x = 2

[junior rampart]

or did i solve it wrong

i may have solved it wrong

oh

i put a negative on 2x

wait no

i think i’m right

alright i just forgot to write a negative

[viscid thistle]

is there a way to find local minimum and maximum values algebraically?

Dont need help with anything just wondering if it is possible

Without having to use a table and waste time

[summer ruin]

by showing that the function is bounded above/below by some value and then constructing a point which achieves this bound

or by taking first derivative and finding extreme points, if you can solve the resulting equation

[viscid thistle]

Oh that makes plenty sense

ill use that thank you

[mystic creek]

Quick question but if in a fraction, if the numerator and denominator are both negative, is it correct to simply them to a positive fraction even though the fraction hasn’t been evaluated?

[viscid thistle]

https://gyazo.com/c2ea426fefdc2cdae3c4327553ad1666

[naive shale]

https://youtu.be/QP0inFktTOo
found this video helpful on determining a limit of a rational function

[unkempt jolt]

What are some good online sources to learn and master precalc?

[viscid thistle]

yoo, is that sqa exam type ques,,???

[thorn orbit]

how would I do this?

[viscid thistle]

When a function is described like this: f : R x R -> R, does it means that its domain is R x R and its range is R?

[stuck lark]

what your definition of range

[viscid thistle]

hmmm

[viscid thistle]

kinda ambigious but i think of it as the set of what f(x) equals to for all x

[stuck lark]

ok do you know what a codomain is

[viscid thistle]

ive heard of it

but idk what it is exactly

[stuck lark]

its the set of allowed outputs

as opposed to the range which is the set of actual outputs

when writing f:A->B, A is the domain and B is the codomain

[viscid thistle]

thanks

ill search some more about codomain

[stuck lark]

thatd be good. to go with that heres an example

take $f:\bR\to\bR,~f(x)=x^2$

[obsidian monolith]

RokettoJanpu

[stuck lark]

the domain and codomain is R. the range is [0,infty) which doesnt equal the codomain R

[stuck lark]

$\trig$

[obsidian monolith]

RokettoJanpu

[slim steppe]

Have you studied limits with graph interpretation

[woven roost]

kind of. I got DNE, 1, and -3 for a b and c

idk if they are correct

do you know what the rest would be

[slim steppe]

B is wrong.

Redo

[woven roost]

would it be 0

[slim steppe]

Are you guessing

[thorn orbit]

is finding zeros with the quadratic equation the same as completing the square

[woven roost]

yes, I dont know how to do this

[slim steppe]

Okay, so, what is the defined function value at x=1

[woven roost]

1

[slim steppe]

Yeah, there you go.

C is correct.

[woven roost]

so b is 1?

[slim steppe]

Yes,

[woven roost]

A doesnt exist correct?

[slim steppe]

Correct

[woven roost]

thanks, how would I do d?

[slim steppe]

Do you see that minus sign above the number?

Called a superscript

The question is asking you: What function value is the function approaching to from the left of 1

The minus indicates that you are approaching from the left side

And what do you think a plus sign will indicate?

[woven roost]

approaching from the right side

[slim steppe]

Mhm

Okay, so using that, what do you think the answer to d) is?

[woven roost]

I think its -3?

[slim steppe]

You're approaching to positive 1 from the left side

Try again

[woven roost]

is it the value on the x axis?

[slim steppe]

Yes, you're approaching 1 on the x axis, and what is the limit as you approach 1 from the left side of it

Basically, to what function value are you approaching to as x-> 1

from the left side

[woven roost]

would it be -1

[slim steppe]

No, okay, look at (1,0)

[woven roost]

yes, there is a hollow circle

[slim steppe]

The question is asking you, what is the function value approaching to as the domain of the function approaches to x=1 from an infinitesimal distance

I'm going to draw it out for you, so you can see

[woven roost]

OH its 0

[slim steppe]

Yes, there we go

[woven roost]

lets go

[slim steppe]

Finally

[woven roost]

I believe e must be 0 as well?

[slim steppe]

Do you know what a hyperbola is?

[woven roost]

yes

[slim steppe]

Okay, so, do you know the behavior of it as the domain extends far out to positive infinity?

[woven roost]

[1,infinity) ?

[slim steppe]

Actually, scratch that

So, for e, right, look at the right of 1

[woven roost]

okay

[slim steppe]

It's an asymptote

[woven roost]

yes, i understand

[slim steppe]

That means, that there is an infinite discontinuity for that function at x=1

[woven roost]

okay

[slim steppe]

So, the function will approach to positive infinity from the right of x=1

and negative infinity from the left of 1

[woven roost]

yes

[slim steppe]

Do you understand why that is?

[woven roost]

so would the answer be infinity?

im sorry, Havent taken any math classes for over a year so im braindead

[slim steppe]

Okay

Take 1/x-1

And take some infinitesimal number to the right of one

like 1.000000000000001

[woven roost]

okay

[slim steppe]

and take an even smaller number

1.000000000000000000000000000001

and continue this

@woven roost Don't actually do this

This is basically intuitive

[woven roost]

yeah I get it

[slim steppe]

But, the point is, the closer you approach to 1, the larger your result will become

[woven roost]

okay

[slim steppe]

so, depending on your teacher

The answer can be positive infinity

or DNE

[woven roost]

oh

so why would it be 0 from the left? and why not negative infinity

because its in one piece right?

[slim steppe]

Because, the left side of the domain isn't given

just to the right of one

[woven roost]

ah okay

it might be dne, as it doesnt really exist

for e

[slim steppe]

Both work, but I prefer positive infinity

More discrete

than just saying "dne"

Okay, now, try problem f)

[woven roost]

is it a numerical answer

[slim steppe]

Can't tell you, you figure it out

[woven roost]

so its as x approaches negative infinity, the numebr gets smaller

[slim steppe]

Where is the function approaching to as x gets innumerably large

in the negative domain

[woven roost]

-2

on the x axis

[slim steppe]

Redo

Look carefully

[woven roost]

zero

it approaches 0 until it starts to get positive

[slim steppe]

What is the approaching function value as the domain of the functions approaches to greaters negative numbers?

[woven roost]

that is 1 on the y axis

[slim steppe]

Exactly

there you go

[woven roost]

so the answer is 1?

[slim steppe]

Yes

[woven roost]

okay finally last one looks too confusing i got no clue

[slim steppe]

For this one, you can just plug in 0 into f(x)

[woven roost]

OH

[slim steppe]

But, I don't want you to do that

Look at (0,0)

[woven roost]

so that comes out as 0

[slim steppe]

and what is the approaching y coordinate as x approaches to 0

[woven roost]

1

[slim steppe]

Good

Now substitute one for f(x)

[woven roost]

im getting -4

[slim steppe]

[(1)-3(1)+2]

is what

[woven roost]

no way im getting this wrong too

its 0 dang

@slim steppe

[slim steppe]

Yes, it's 0

[woven roost]

thank you very much, was a lengthy assignment lol

[slim steppe]

Honestly, this should only take you a few seconds

Just practice

[woven roost]

Yeah

I took a precalc class back in 2020 covid and it was just algebra stuff

[slim steppe]

I didn't even take precalc

I went from statsitics to ap Calc

[thorn orbit]

if I'm trying to find the points of intersection between 2 functions, would I just combine the 2 and solve for x?

[crystal star]

What kinda functions are they

Cuz you can just solve for x like you said

Then just plug the x values into the function that’s intersecting

Or any

To find the points where they intersect

[thorn orbit]

linear

[crystal star]

Yeah

Just do what I said I think it’d work

[thorn orbit]

coolio thx

[crystal star]

Np

[half pine]

is "Pre-university" like when your still in normal school?

[crystal star]

Yeah like high school

[half pine]

wait HIGHSCHOOL

nah

im in middles school

[crystal star]

Oh well that’s still

Pre university

Why you in precalc tho

[half pine]

well yeah

its the only channel i thought to ask this on

[crystal star]

Lol

[hushed sphinx]

He hasn't learned calculus yet, so it must be pre-calculus. Simple.

[thorn orbit]

ez

[crystal star]

You did the problem?

[hushed sphinx]

(sighs at bizarre American naming of school subjects)

[thorn orbit]

nah i was responding to tropo

[crystal star]

Oh

[thorn orbit]

lul

[crystal star]

So my instructions didn’t work or

[thorn orbit]

didn't say that

[half pine]

where do i go for my level?

which channel?

[crystal star]

Prolly pre algebra

[thorn orbit]

what's your level

[crystal star]

#prealg-and-algebra

[half pine]

ok

[crystal star]

Pre algebra or algebra

He’s in middle school so there

[hushed sphinx]

Have you even asked a question yet?

[crystal star]

Hurt did

[thorn orbit]

for all we know he could be the only PDE solving middle schooler

[crystal star]

I answered it

[crystal star]

LOL

[hushed sphinx]

Oh, I meant, its difficult to tell which channel RoastedChicken's question belongs in when we don't know what it is he intends to ask.

[crystal star]

Npnp dog

[thorn orbit]

the question has a quadratic and a linear to find the points of intersection for

[crystal star]

Plug in the x into the linear

@thorn orbit

[thorn orbit]

there was no x given

[summer ruin]

write what it means for two functions to be equal at a point

[thorn orbit]

I think it's asking for the points of the secant line, but i'm not sure how to find those

[summer ruin]

find points of the intersection of two functions
secant line

huh?

it's quite literally plugging in the definition of f(x) and g(x) and solving for x

[thorn orbit]

one is a quadratic, one is a linear

[summer ruin]

the problem states "solve f(x) = g(x)"

what's there about secant lines

[thorn orbit]

I interperated it as, when you graph each function, what would be the point of interseption. but now that i'm re-reading, there isn't even a possible secent line.

[ruby cloud]

If there was something related to secant lines, the task would mention them

[viscid thistle]

what is a good channel for maths courses?

pre-calculus and calculus

[compact bridge]

Would love a crack at this. Share answers after? If up for it.

[thorn orbit]

@compact bridge

[viscid thistle]

isn't this cal?

[woven roost]

Wdym

[viscid thistle]

what math are you in

[viscid thistle]

not really

just know algebra a little in depth

[viscid thistle]

Calculus

And combinatorics

Actually In my country, you need to study a lot of stuff in high school

Which are mainly college level stuff in other countries

[fading crown]

Finland got the best education system dunno what these other countries doing

Everyone should copy them

[slim steppe]

Having the best education does not necessarily intel the greatest outcome

Yes.

Solid point

It's a defined point

It's a graph

It can be a hollowed out or a defined point

A limit is defined as something that one is approaching to

A point is just a point

There is no left or right domain that extends from the point

Hold on, what grade are you in

No, I mean, what grade are you in in school?

What math class did you have in your senior year?

[compact bridge]

Thanks for sharing 👍

[slim steppe]

A function that approaches to 2 from the right side

[woven roost]

so a line?

[slim steppe]

If that line holds true for the other questions in the problem set, then yes

[woven roost]

im thinkng that The points (1,2) and (1,1) are graphed as solid circles to represent the limit as x approaches 1 from the right and left

for d and e?

[slim steppe]

They can be open circles, the question doesn't specify which

[woven roost]

okay, so for e, is there a horizontal line that goes from the asymtote, to 1,1?

[woven roost]

asymtote at x=-1

[slim steppe]

There's a jump discontinuity at x=1

Because from the left, it's approaching to 1

and from the right, it's approaching to two

Oh, you said negative one

hold on

[woven roost]

does this make sense as an answer for the whole thing

[slim steppe]

Thing is, the questions are so ambiguously stated

[woven roost]

yeah, there are many possible answers

[slim steppe]

Because b) the graph can have a negative range

and also a positive range

It doesn't specify to which "infinity" it is approaching to

a positive

or a negative

[woven roost]

does my graph seem reasonable though

[slim steppe]

I'd have to look at it later, I have to run now

Perhaps ask transparent

He can help you

[woven roost]

@summer ruin yo

can you tell me if my drawing makes sense

[summer ruin]

no

you didn't cover half of the questions

[woven roost]

oh

[summer ruin]

and even while f(2)=0 is correctly drawn you didn't put an empty circle on the graph to show that it's not continuous there

yes

[woven roost]

I don't get what else I'm missing

I can tell there isn't anything on the left side of the asymtote

[summer ruin]

b), c), f), h)

[woven roost]

I put b as an asymptote on x=-1. You can't really see it

And c is the point on 0,-1

F is the dotted line spanning from x=-1 to x= 1

Idk about h

@summer ruin you here

[summer ruin]

h) requires for two one sided limits to exist

and be equal

[woven roost]

so 2 lines coming from the right?

like where should i plot it

[summer ruin]

it's already plotted I guess

[woven roost]

oh really

[summer ruin]

but f) is not quite done

recall the definition of continuity from the left in a point

or from the right for that matter

[woven roost]

yeah. i dont understand how ill do that with the asymtote blocking the way

[summer ruin]

this has nothing to do with the asymptote

[woven roost]

oh

[summer ruin]

asymptote is not even in that region

[woven roost]

do i need to plot a solid point at x=1?

is f the last one i have not done

[summer ruin]

I don't know what your asymptote looks like

[woven roost]

it is what I did for the question b) i plotted a vertical asymtote at x=-1 spanning infiniteley

[summer ruin]

what does that mean

[woven roost]

i put a vertical line at x=-1

yo you there

<@&286206848099549185>

i dont want to start a new conversation with someone new

[summer ruin]

well that would be wrong

[woven roost]

oh really?

where should it be

im lost

[summer ruin]

have you ever seen an asymptote

[woven roost]

yeah, it is a line where the function cant cross

invisible line

[summer ruin]

that's not true

sin(x)/x has a horizontal asymptote at y=0 which it approaches as x approaches infinity

yet sin(x)/x crosses it's asymptote infinitely many times

[woven roost]

oh

[woven roost]

so in this case, i am able to plot the line through this asymtote?

[summer ruin]

and hardly drawing it as a vertical line is accurate

you're asked to draw a function

which meets these properties

[woven roost]

okay

[woven roost]

what would you suggest I fix

bro im losing braincells

7 hours at this

[summer ruin]

look at how any other asymptotes look

the exercise is not about drawing everything in some precise way

which you seem to be trying to do drawing straight lines

[woven roost]

okay, does the asymtote exist at x=-1 though?

[summer ruin]

what do you think based on limit f(x) = infinity as x-> -1?

[woven roost]

its negative 1

so this graph seems right now

im actually nauseous now

[summer ruin]

why is your function going to negative values if the limit is infinity

you should also draw what it behaves like as it approaches x = -1 from the left

[woven roost]

i dont get it, do I need to make 2 lines that look like a mirror image on each side of the asymtote?

that curve up?

[summer ruin]

yes, though not necessarily mirror image

[woven roost]

curving up corrrect?

@summer ruin

[summer ruin]

it should be f(1) = 1

besides that it looks correct

[woven roost]

what do you mean

[summer ruin]

left continuity

[woven roost]

oh a hollow point at -2,1

[summer ruin]

?

[woven roost]

Ohh do you mean I should extend the line that cuts off at 1,1

[woven roost]

Should I make it go the whole way

To like 5,1

[summer ruin]

what

[woven roost]

What do you mean by it should f(1)=1

@summer ruin

[summer ruin]

function f evaluated at x = 1 outputs a value of 1

because it says that f is continuous from the left at x = 1

[woven roost]

Okay... so what do I need to do

Thanks for the help btw

[summer ruin]

think about what's wrong with your current drawing

and why it doesn't meet the left continuity at x = 1

[woven roost]

Because its discontinued

[summer ruin]

that's too broad of a reason

there are discontinuous functions which are left continuous

no

that actually didn't change anything

[woven roost]

do you want me to change what I already have or build onto something

can you markup edit it and show me

[summer ruin]

I want you to look up the definition of left continuity of a function at a point

the change is so small it's not even worth trying to give a hint because that'll be the entire answer

[woven roost]

is it changing a hollow circle into a solid one

[summer ruin]

which one

yes

[woven roost]

is that it?

[woven roost]

rest is good?

[summer ruin]

yes

[woven roost]

alright, thanks man

[woven roost]

even though the function spans from [-5,5], I can have a solid circle connecting? in the center?

[summer ruin]

how are these concepts even related

[woven roost]

im confusing 2 things arent I

[summer ruin]

I don't know

[woven roost]

anyways, thanks

[slender idol]

for radical functions with an even root, the domain is only restricted by what produces a negative radicand?

ex. f(x) = 4 sqrt(x+1) - 3
isolate radicand into inequality
1. x + 1 >=  0
2.   x   >= -1

that is proper work for finding the domain here?

[summer ruin]

yes

[chilly hazel]

how do you calculate this?

[slim steppe]

The exponent is the same in the numerator and in the denominator

So take the ratio of the coefficients

And that is 81

and 3 to the 4 is 81

[odd hamlet]

can someone help w #40

b subpoint

[willow bear]

,rccw

[willow bear]

have you done part a?

[willow bear]

!status

[tender quest]

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

[tardy thicket]

highlight in red

since the division have the same base why is it -n+(n-1)

Instead of 2^n-1-(n-1)

[zealous trout]

Hi

Someone knows how i can study derive

I have an exam in two days

[tardy thicket]

read the text book

for your class they usually help and give out example how to do each problem and variation

of each problem

[zealous trout]

Maybe zill?

Someone knows about a good book?

[snow surge]

Uhhh im confused

What ariah walking got to do with this

Thats as close as i can get

[hushed sphinx]

Hmm, the exercise appear to make most sense if you assume that the boat's velocity relative to the water stays the same before and after it "encounters a current" -- even through I'm not sure that's a particularly realistic assumption.

[snow surge]

Like does it change from 35 to 7?

Its a little confusing for me

[hushed sphinx]

I would understand it as saying

• the water moves with a velocity of (12,7) relative to the Earth
• the boat moves with a velocity of (0,35) relative to the water
• Ariah moves with a velocity of (-5,0) relative to the boat
  and you're supposed to find (the magnitude of) Ariah's velocity relative to the Earth.

[snow surge]

Ohhh

Ok that actually does help

[tardy thicket]

Unsure about books but ask your professor for the recommnded book

[short crescent]

https://www.youtube.com/@macpryma2167/playlists 10c is all the grade 10 math, 20-1 all the grade 11 math for pre cal, 30-1 math is all the grade 12 math for pre cal

[viscid thistle]

Got my first Pre Calc exam this Thursday wish me luck!!! Im feeling pretty good going into the test.

[viscid thistle]

Guys i reqlly need help with this problem Proving trig identities pleaseee help me now with steps or imma fail soon😭😭😭

[slim steppe]

Butterfly rule

[viscid thistle]

That doesnt help me

I said show steps bro

Please

[viscid thistle]

Tysm

[shut skiff]

Some one please solve this easy problem which my idiot head can't process

[willow bear]

bad typesetting

[viscid thistle]

$\sin(y) = \floor{\frac{\sqrt{1+x} + \sqrt{1 - x}}{2}}$

[obsidian monolith]

Ryuzaki

[viscid thistle]

what are you guys thoughts on rotation matrixes?

matrices*

[fierce dock]

<@&268886789983436800> spamvertisement?

[pseudo hamlet]

Another way would be to replace (1-cos(x)^2) with sin(x)^2 using the pythagorean identity

[gusty pasture]

https://media.discordapp.net/attachments/1069618650832719996/1072923824464592936/image.png

help plz

[hushed sphinx]

You don't need all the information in the problem there. What is the simplest way you can imagine to find out what n is?

[gusty pasture]

2 + 5

would n be 7

for the first one

[hushed sphinx]

For both ones.

[gusty pasture]

wait how is the second one 7?

[hushed sphinx]

I mean, it's the same expression for both parts of the question -- n doesn't vary between them.

[gusty pasture]

alr

what do i do with 7?

[hushed sphinx]

When you know n, you can apply the binomial theorem to (5x+4y)^n.

[gusty pasture]

so its (5x^2 + 4y^5)^7

[hushed sphinx]

No.