Like take y=x^2 for example
#precalculus
obsidian monolithBOT
Parsec
magic remnant
Mhmm
dry lantern
You just look where the function slopes downwards and that's your decreasing interval
Then you look at where it slopes upward for the increasing interval
magic remnant
I get that but there’s multiple functions
dry lantern
So you do it for each function
magic remnant
Like from -inf, -1 it remains constant
magic remnant
So you do it for each function
So three different intervals
magic remnant
And then U between
dry lantern
Yeah
magic remnant
So like (-inf, -1]U(-1,1)U[0,infinity)
dry lantern
Wait are there two pieces that are overlapping
Oh nevermind
I don't know where you're getting [0,inf) from
stoic vine
Hi
lethal sand
is this not trig form for complex numbers?
stoic vine
I'm new where should I start
echo sinew
From posting your question
Here (if it is about precalculus) or, better, in one of the available channel #❓how-to-get-help
undone sage
granite star
@undone sage
granite star
we'll need to split the integral
undone sage
we'll need to split the integral
what if i got the definite integral of the absolute of the two functions
would that work
like this
i saw it somewhere
granite star
would that work
no since the area woul be negative for f x and gx in the region where the graph goes below the x axis
granite star
what if i got the definite integral of the absolute of the two functions
if you tak absolute then still splitiing of limt is neccesary
undone sage
if you tak absolute then still splitiing of limt is neccesary
oh
what would i split the limit into
granite star
what would i split the limit into
like for mod x integrated from -1 to 1 we write integration of -x from -1 to 0 and then + integration of x from 0 to 1
granite star
what would i split the limit into
first calculate the area under graph for f x and for g x
by splitting the limit
undone sage
?
granite star
like for mod x integrated from -1 to 1 we write integration of -x from -1 to 0 a...
..
like for sinx from 0 to 2pi we wirte integration of sinx 0 to pi + integration of -sinx pi to 2pi
undone sage
huh?
granite star
then ar(fx) - ar(gx)
undone sage
whats ar
granite star
huh?
sin is postive in 0 to pi region and negative in pi to 2pi region thats why take -sinx in pi to two pi integral to cancel out the negative in pi to 2pi
undone sage
sin is postive in 0 to pi region and negative in pi to 2pi region thats why take...
oh yh
undone sage
isnt the integral of sin 0 to pi still negative tho
granite star
isnt the integral of sin 0 to pi still negative tho
no
sin from 0 to pi/2 is increasing thne pi/2 to pi its decreasing and then after pi it becomes negative
undone sage
yes? int of sin = -cosx
undone sage
oh yh so its 0
undone sage
why would it be cos 0 - cospi?
wouldnt it be cospi-cos0
-1+1=0
wait no
its two lol
granite star
yeas
whole void
0 right
red storm
if you can prove that there is no equation between delta and epsilon you can pretty much say that it's discontinuous at that point
whole void
or just sin(pi/x) is not defined at 0…
red storm
T rue true
to prove a limit exists at some x = c, you need both a delta (a value greater than x by some small difference) and an epsilon (a value greater than y by some small difference)
we know that if this is true
then x - delta and x + delta will have a very small distance
whole void
yes
red storm
and because epsilon implies delta then y - epsilon and y + epsilon will have a very small distance from y
yes
kind of like that
whole void
look up the epsilon delta definition..
red storm
it is the intuitive explanation for it
whole void
It’s ok
digital sage
funny how we never learnt epsilon-delta definition for limits here
just plug and chug (also most of us know l'hopital but never taught at school)
red storm
i decided to study it for fun and realized how messy a real analysis proof could be
also the first time i encountered the triangle inequality
digital sage
it's also a shame that we also never learnt the definition of e
red storm
that one was clean asf
digital sage
we just treat it as a normal number
red storm
l oved the limit
digital sage
and somehow derivative of e^x is itself
digital sage
it's also a shame that we also never learnt the definition of e
I struggled in some limit problems i saw because of this
whole void
just plug and chug (also most of us know l'hopital but never taught at school)
most people learn l’hopitals I think
whole void
yea we arent taught that at school here
?? so e is just something completely random?
digital sage
yes
whole void
I dont like the definition of (1 + 1/n)^n
digital sage
and somehow (e^x)'=e^x
digital sage
I dont like the definition of (1 + 1/n)^n
I love it
whole void
I like f(x) = f’(x), f(0) = 1
whole void
why?
whole void
yeah
digital sage
garbage ministry of education doesnt give a shit
at least I give them some credit for making grade 10 entry maths exam more related to real-life problems
whole void
at least I give them some credit for making grade 10 entry maths exam more relat...
like how so?
whole void
garbage ministry of education doesnt give a shit
The overreach is very stupid. How come u rarely see people advocating for less standardized tests and things
red storm
garbage ministry of education doesnt give a shit
ours is worse
i was ass at 11th grade math until i locked in
for some reason i passed 10th grade without knowing basic asf algebra
shut canopy
and somehow (e^x)'=e^x
its not "somehow" there is an actual reason and there are two ways to prove it
digital sage
do you understand the context I was talking about
whole void
its not "somehow" there is an actual reason and there are two ways to prove it
what ways do u know?
digital sage
use the limit definition and definition of derivative
whole void
oh yeah. oops i was thinking of showing that f(x) = f'(x) -> f(x) = Ce^x
the only way i know is separation of variables
high pelican
I dont like the definition of (1 + 1/n)^n
I mean that’s one of the definitions
Idk if it’s the first one
I kinda like that one
river drift
the limit definition is nice because it requires no calculus, you can even handwave the limit a bit if that's unfamiliar
whole void
the limit definition is nice because it requires no calculus, you can even handw...
but the number equal to the limit of (1 + 1/n)^n is "the most important) in math? thats why i dont like it it seems too random
river drift
i mean the main utility of the natural exponential function is obviously its calculus properties but it's good to have a definition which can be introduced before calculus
and it can be motivated with continuously compounding interest
whole void
and it can be motivated with continuously compounding interest
yeah, still doesnt make it seem fundamental.
i dont know why e comes up before calculus but anyways
real wraith
jagged pawn
yeah, still doesnt make it seem fundamental.
i dont know why e comes up before ...
Yoo need to discuss something real quick
whole void
Yoo need to discuss something real quick
?
jagged pawn
?
Yooo
I wanna discuss trig and exponential functions have something in mind that's bothering me
echo stone
!1c
tender questBOT
Please stick to your channel.
left wasp
yo i have a question can someone answer me?
whole void
yo i have a question can someone answer me?
just ask
left wasp
so the derivative of e^x is the same is that means any constant^x is the same as well?
or thats just for e
whole void
are u saying is (a^x)' = a^x?
try desmos. or better yet, grab a peper
left wasp
how to derivate things in desmos
rigid burrow
or thats just for e
it's just for e. For any other constant base (a), the derivative is (a^x)*ln(a). For e, since ln(e) is 1, this just comes out to e^x
rigid burrow
how to derivate things in desmos
you can either type:
f(x) = e^x
f'(x)
or you can do
(d/dx)e^x
that was for them to figure out...
and figure out the error factor...
rigid burrow
that was for them to figure out...
that's fair. Though idk if simply graphing it out like you proposed would've been enough for them to reach that conclusion
sick fjord
Im trying to do more complex numbers problems
willow bear
Im trying to do more complex numbers problems
you swallowed a ± in the last two steps btw
timid widget
can someone teach me on how to solve this problem..
digital sage
is this precalc?
sick fjord
you swallowed a ± in the last two steps btw
Oh yeah lol mb it supposed to be 6 at the bottom
timid widget
is this precalc?
yes- analytic geomtry
willow bear
can someone teach me on how to solve this problem..
ok let's just transcribe this so that nobody else has to struggle with the handwriting
digital sage
we don't even have a concept of "precalc" here
sick fjord
Oh yeah lol mb it supposed to be 6 at the bottom
Wait no i Alr cut it
willow bear
Find the equation of the circle tangent to x + 2y - 7 = 0 at (5,1), with its center on the line 2x - y + 5 = 0
timid widget
ok let's just transcribe this so that nobody else has to struggle with the handw...
thanks
digital sage
we don't even have a concept of "precalc" here
just jump straight in in grade 11/12 lmao
willow bear
alright @timid widget maybe you could open a help ticket and we could move there
post this question and your progress on it (if you have any)
timid widget
ok let's just transcribe this so that nobody else has to struggle with the handw...
well.. its on my pre calc subject as analytic geometry;-;
timid widget
post this question and your progress on it (if you have any)
sure
remote lodge
Yes
sick fjord
remote lodge
Yea I think it’s how it works
sick fjord
Ok thanks
willow bear
Should i just put square root 23 i
one important note
when writing in plain text you should always put brackets around the things that go under a square root
sqrt(23)i
not square root 23 i
just as an example, \verb|square root x + 1| is ambiguous -- does it mean $\sqrt{x+1}$ or does it mean $\sqrt{x} + 1$? these two are not the same, but \verb|sqrt(x+1)| and \verb|sqrt(x)+1| leave no room for doubt.
obsidian monolithBOT
Ann
small solar
About square roots, do we agree on the fact that $\sqrt{1+i}$ and $\sqrt{-3}$ dont make sense ?
obsidian monolithBOT
gottawakup
small solar
Wait wait wait, when you react with ❌ , does it mean you agree that it doees not make sense, or you don't agree with my message ?
noble lava
Don't agree with the message
small solar
What
small solar
Because how can you choose between sqrt(3)i and -sqrt(3)i ?
Ok maybe you'll pick the positive one
But : we have a problem
small solar
If we want sqrt(i), we both have (1-i)/2 and (i-1)/2
echo sinew
Because how can you choose between sqrt(3)i and -sqrt(3)i ?
You don't. They're both correct
small solar
So : sqrt(-3)=-sqrt(3)i and sqrt(-3)=sqrt(3)i ????
small solar
You said both were correct
echo sinew
So : sqrt(-3)=-sqrt(3)i and sqrt(-3)=sqrt(3)i ????
Also you can't take i outside of the root
Yes
echo sinew
Because how can you choose between sqrt(3)i and -sqrt(3)i ?
But I was referring to this
noble lava
Also you can't take i outside of the root
?
i= sqrt(-1)
It has to be out of the root
echo sinew
$\sqrt{3i} \neq \sqrt{3}i$
obsidian monolithBOT
Alberto Z.
echo sinew
I meant this
noble lava
Oh alr
small solar
I meant this
Yes of course, how could this be true. I meant sqrt(-3)
echo sinew
So : sqrt(-3)=-sqrt(3)i and sqrt(-3)=sqrt(3)i ????
Oh ok you've edited, sorry I didn't see
Yeah it's correct now
small solar
But if sqrt(-3)=sqrt(3)i and sqrt(-3)=-sqrt(3)i, then sqrt(3)i=-sqrt(3)i, and then i=0 !!
willow bear
every complex number (aside from 0) has two square roots.
small solar
Yes but it can't be a function like sqrt(-3)
willow bear
if you want to use the symbol $\sqrt{z}$ you have to fix a choice of root for each $z$. maybe you do it in such a way that its argument lies in $(-\pi/2, \pi/2]$ or something.
obsidian monolithBOT
Ann
small solar
So it's not well defined
willow bear
if you want to die on the hill of "sqrt doesnt make sense in C!!!!!!!!!" then i cant really stop you
willow bear
Principal is (-pi,pi] btw
for the square root
noble lava
Ah okok
small solar
if you want to die on the hill of "sqrt doesnt make sense in C!!!!!!!!!" then i ...
There's a difference between the square root we write sqrt(something) and the square roots of a number, we have in the complex world
echo sinew
I don't see any difference
It just depends whether you're working on R or on C
And that has to be specified or deduced from the context
tough lake
Hello
I am in pre calculus 11 and tried very hard and got 98% about to do pre calc 12 and then calculus 12,
I found out that pre calculus 12 is all graphing, so I asked my seniors who have taken pre calculus 12 AND calculus 12 wether it is worth it to try to get a 100% or 98% im pre calc 12 like I Did in pre calc 11 and they said yes you should get 98% in pre calc 12 as well
But they said that calculus is not all graphing and a little bit different
Question for you: given the pre calc 12 curriculum:
Arithmetic and Geometric Sequence and Series
Unit 2
Transformations
Unit 3
Polynomials and their graphs
Unit 4
Exponential and Logarithmic Functions and Equations and graphs
Unit 5
Rational Functions and Conics (just very basic Conics)
Unit 6
Trigonometric Functions and their graphs
Unit 7
Trigonometric Equations and Identities
Is it worth to try hard in pre calc 12 to the point where I am sacrificing physics 12
chrome trench
I am in pre calculus 11 and tried very hard and got 98% about to do pre calc 12 ...
It depends on your end goal
Do you prefer physics or math?
If so, to what extent?
tough lake
Do you prefer physics or math?
Well if I were to be good at one I would say math
I would rather get 100% in math and 95% in physics rather than get 100% in physics and 95% in math
I would pick math to be best at
Usually but now how useful is pre calc 12 to learn calculus
Because if it is not that diverse then I can just drill down on physics 12, because the only topics are analyzed in a lot more detail
torpid crane
that depends on the position of the complex number on the argand diagram afaik
and in polar form its r(cosθ+i sinθ)
i think
magic remnant
that depends on the position of the complex number on the argand diagram afaik
well it I'd assume it's js Z(re) = 3
and Z(im) = -3
so (3,-3i)
torpid crane
mhm
magic remnant
and in polar form its r(cosθ+i sinθ)
but like how would I get there
I can solve for z using pythag
and then I can find the angle formed byt just doing arctan(3/3)
But where do I go from there
torpid crane
you simply write r (cos θ + i sin θ)
where theta is the angle you figured out
and r is basically the argument you get using pythag
as u said
torpid crane
yeah
my bad
the argument is the angle itself
and the modulus is Z
i used to call it r lol
small solar
Why don't you just factorize it by 3 to get : 3-3i=3(1-i), knowing the polar form of 1-i ?
drifting oyster
Chat just take The magnitude of Z and argument of Z and slap it into polar form...
Not that complicated
hushed sphinx
"Oh, just solve the exercise, it's not that complicated"
spice mica
how do you this 😭
use ur handy dandy equations. remember r = sqrt(a^2 + b^2) and theta = arctan(b/a)
willow skiff
and the modulus is Z
that's actually not correct
you should be using |z| for the modulus
z = a + bi, the actual complex number
torpid crane
you should be using |z| for the modulus
thats what i meant my bad
i usually avoid this kinda discrepancy by calling it r instead
willow bear
Do i use this formula here
your goal is to simplify $\frac{\frac12 + \frac{\sqrt{3}}{2}i}{\frac12 - \frac{\sqrt{3}}{2}i}$?
obsidian monolithBOT
Ann
sick fjord
your goal is to simplify $\frac{\frac12 + \frac{\sqrt{3}}{2}i}{\frac12 - \frac{\...
Yes by division
willow bear
are there special instructions or are you just saying things
sick fjord
sick fjord
Do i use this formula here
Do i use this formula or nah
willow bear
there's nothing wrong with using that formula.
if you want to do the division in the same way you'd divide any two complex numbers, then go ahead.
sick fjord
willow bear
mmm depends on what exactly you mean by that.
if you try to rewrite $\paren{\frac{\sqrt{3}}{2}i}^2$ as $\frac{3}{2}i$ that'll be pretty wrong
obsidian monolithBOT
Ann
sick fjord
sick fjord
But you have a strategy error
I went in blind lol i have no idea how the pattern works
willow skiff
You should be multiplying top and bottom by 1/2 + sqrt3/2 i instead
That's the conjugate of the denominator
sick fjord
Wait
willow skiff
It's salvageable cause that's your new denominator
sick fjord
So i gotta multiply first
willow skiff
You should be multiplying top and bottom by 1/2 + sqrt3/2 i instead
You multiplied top and bottom by the wrong thing
willow skiff
I just followed a yt video’s pattern
Yes, now that's correct
willow bear
But you have a strategy error
arguably the much better strategy would be to converrt num and denom both into polar form lol
sick fjord
Uh im kinda stuck here
willow skiff
Uh im kinda stuck here
literally multiply the two numerators and the two denominators together
echo sinew
$$\frac{A}{B}\cdot \frac{C}{D} = \frac{A\cdot C}{B\cdot D}$$
obsidian monolithBOT
Alberto Z.
echo sinew
This, in other words @sick fjord
sick fjord
I don’t understand this is it using the polar form
willow skiff
I don’t understand this is it using the polar form
okay, what's (1/2 - sqrt(3)/2 i) * (1/2 + sqrt(3)/2 i) ?
you've calculated this before, remember?
willow skiff
no
willow skiff
I just followed a yt video’s pattern
what you wrote here is correct
sick fjord
Wait the answer is the same as the question
echo sinew
**Alberto Z.**
I don't get it, what stops you from applying this fraction multiplication? @sick fjord
sick fjord
I don't get it, what stops you from applying this fraction multiplication? <@936...
So if I multiply it it just came out as 1- squareroot 3
echo sinew
echo sinew
Are you referring to this?
echo sinew
There's no fraction multiplication here
sick fjord
So what i do here
willow skiff
I just followed a yt video’s pattern
you need to do $\frac{(1/2 + \sqrt{3}/2 \ i) (1/2 + \sqrt{3}/2 \ i)}{(1/2 - \sqrt{3}/2 \ i)(1/2 + \sqrt{3}/2 \ i)}$
echo sinew
Uh im kinda stuck here
The same thing you did here, but for some reason you've lost it in the next steps
willow skiff
fight the urge to cancel everything
expanding everything in the numerator and denominator is the way to go
sick fjord
Wait ima multiply rq
obsidian monolithBOT
south
sick fjord
So do I multiply again for the bottom
willow skiff
(a - bi)(a + bi) = a^2 - (bi)^2
willow skiff
So do I multiply again for the bottom
what is going on with your numerator
sick fjord
Yeah i def did it wrong
willow skiff
This seems wrong did I multiply the wrong way
AH you keep copying my stuff wrong
sick fjord
But is the multiplying correct at the 4+4+4+4
sick fjord
you're forgetting the i
Okey i Added the i
willow skiff
But is the multiplying correct at the 4+4+4+4
no, it's wrong
willow skiff
Okey i Added the i
great, now go back and do $\left( \frac{1}{2} + \frac{\sqrt3}{2} i \right) \left( \frac{1}{2} + \frac{\sqrt3}{2} i \right)$ again
obsidian monolithBOT
south
willow skiff
Is * just multiply
yep
sick fjord
What is square root is 3 x square root of 3 is it just squareroot of 3^2
willow skiff
What is square root is 3 x square root of 3 is it just squareroot of 3^2
$\sqrt{3} \cdot \sqrt{3} = \sqrt{3^2}$, correct
obsidian monolithBOT
south
sick fjord
$\sqrt{3} \cdot \sqrt{3} = \sqrt{3^2}$, correct
So does that mean i can cut the root
willow skiff
So does that mean i can cut the root
what do you mean by that?
as in, what does that equal now?
sick fjord
what do you mean by that?
willow skiff
yeah, so that equals 3
sick fjord
willow skiff
And 4x2 =8?
why are you doing 4x2 = 8 for this question?
willow skiff
you need to do 2 * 2 = 4 multiplications
by this, I mean you need to multiply every term in the 1st bracket with every other term in the second bracket
if you have (a + b) * (c + d), you need to do:
a * c = ac
a * d = ad
b * c = bc
b * d = bd
and then add everything, so the result is ac + ad + bc + bd
sick fjord
Woah
willow skiff
and here's a picture
sick fjord
by this, I mean you need to multiply every term in the 1st bracket with every ot...
Okey ima try again
willow skiff
you are missing the terms $\frac{1}{2} \cdot \frac{\sqrt3}{2} i, \frac{\sqrt3}{2} \cdot \frac{1}{2} i$
obsidian monolithBOT
south
willow skiff
1/2 * 1/2 = 1/4, that's good
sqrt(3)/2 i * sqrt(3)/2 i = (sqrt3 / 2)^2 i^2, also good
sqrt(3)/2 i * 1/2 = sqrt(3)/4 i, good
sick fjord
Okey so what to do with the numbers we got
sick fjord
Lemme check
willow skiff
Okey so what to do with the numbers we got
you add them all together
sick fjord
but then you have 1/2 * sqrt(3)/2 i = ...
Theyre both the same numbers so like can i put them in ()^2
willow skiff
Theyre both the same numbers so like can i put them in ()^2
no
if you have x + x, where we are using x twice for the same number
that's just 2x
sick fjord
How do I multiply numbers in square root
willow skiff
sqrt(3)/2 i * sqrt(3)/2 i = (sqrt3 / 2)^2 i^2, also good
you're talking about this right?
sick fjord
but then you have 1/2 * sqrt(3)/2 i = ...
willow skiff
right, so you have $\left( \frac{\sqrt{3}}{2} \right)^2 = \frac{\sqrt3}{2} \frac{\sqrt3}{2}$ by definition of squaring
obsidian monolithBOT
south
willow skiff
$= \frac{\sqrt3 \cdot \sqrt3}{2 \cdot 2}$
obsidian monolithBOT
south
willow skiff
but if you remember your previous work, $\sqrt{3} \cdot \sqrt{3} = 3$
obsidian monolithBOT
south
willow skiff
to illustrate, $\frac{1}{2} + \frac{2}{3}$ is most definitely not $\frac{1 + 2}{2 + 3}$
obsidian monolithBOT
south
willow skiff
and here's a picture
according to the diagram
sick fjord
sick fjord
try *simplifying 1/2 + 2/3 and (1 + 2)/(2 + 3) yourself
Okey
willow skiff
also when trying to correct, you replaced it wrong
replace both the (1 + sqrt3)/4 i with sqrt(3)/4 i
sick fjord
willow skiff
right! and how about (1 + 2)/(2 + 3)?
sick fjord
right! and how about (1 + 2)/(2 + 3)?
willow skiff
right! and how about (1 + 2)/(2 + 3)?
no, by that I mean $\frac{1 + 2}{2 + 3}$
obsidian monolithBOT
south
willow skiff
that's why this doesn't make any sense
you can't combine the 4 fractions into 1 fraction by adding everything
sick fjord
Okey got it
zenith lantern
POV: Composing functions HEALED you 🌅
magic remnant
how would you go about solving this/
soft plover
how would you go about solving this/
isn't it just 16% of 72 g?
obsidian monolithBOT
Result:
11.52
Or you could calculate how much onion powder there in grams is if it's all seasoning blend, and how much 20% onion powder is, and then see what percent the difference is
magic remnant
this is what they gave me as explenation
and I got no clue where the -m part came from
hushed sphinx
72-m is the amount original seasoning blend there's in the bottle.
The idea is that the 72 grams in the bottle will be part seasoning blend with 4% onion and the other part 100% onion.
magic remnant
The idea is that the 72 grams in the bottle will be _part_ seasoning blend with ...
ohhh
then you just distribute and then omg
that makes sm sense 😭
thanks 🙏
arctic swan
can skmeone give me an integral to do on a six hour flight … possibly without trig sub cuz idk how to do that yet
obsidian monolithBOT
Enterlessguy
drifting oyster
Enjoy your flight 
safe brook
Could someone explain to me how z = 3 + 4i, evaluated to arg z^2 is not just arg z then squared. The answer of arg z is 0.927, how is arg z^2 not 1.854
noble lava
So you're asking why $(arg z)^2 \neq arg (z^2)$?
obsidian monolithBOT
Axe cutter (ask on server b4 dm)
safe brook
obsidian monolithBOT
safe brook
I’m guessing that it’s arg (z)^2 ?
noble lava
Yes
safe brook
Can I come back to in 2 minutes? I’m goijg to do it that way
noble lava
K
safe brook
I’ll show my working so it’s easier to show my thought process
drifting oyster
Bro doesnt know trig sub and this is what we give him <:bleakkekw:91334411798199...
I gave him a long ass partial fractions
💀
noble lava
drifting oyster
I mean he does have 6 hours
But its gonna be the most boring 6 hours of his life
arctic swan
Enjoy your flight <:opencry:586078614865444865>
LMAOOO
if that 1 wasn’t there this question wouldn’t even take 30 seconds
crazy
drifting oyster
I mean yeah thats how integrals work
arctic swan
no joke i’m not even sure where to start with this
arctic swan
if itll keep me occupied
cause the way ive been making sure my questions take ages is by adding a bunch of random sigmas and produxt operators for fun
noble lava
Lolz
obsidian monolithBOT
noble lava
,rcw
safe brook
Because I haven’t squared tan
noble lava
,tex.wrong square
obsidian monolithBOT
Axe cutter (ask on server b4 dm)
noble lava
That's what you've done
safe brook
Isn’t that what I’ve done with uh z^2
Like I squared it so I got 24i and -7
And then subbed that in
arctic swan
yo is this even possible wtf
noble lava
**Axe cutter (ask on server b4 dm)**
this i was talking abt the option 2 uve written
safe brook
I just don’t understand it because if I do arg z then times it by 2 to get the arg z^2 and then times it by 3 to get z^3
Not really sure if that helps
vagrant grove
any ideas on what figure C is, though kinda resembles cylinder?
willow skiff
any ideas on what figure C is, though kinda resembles cylinder?
a semicircular prism
vagrant grove
a semicircular prism
thanks, mate
vagrant grove
a semicircular prism
could u explain why it can't be half of the cylinder?
willow skiff
could u explain why it can't be half of the cylinder?
it is also a half-cylinder
but then the "half" doesn't specify the direction that the cylinder is cut
vagrant grove
but then the "half" doesn't specify the direction that the cylinder is cut
if i need the volume of the 3rd figure, would it be like (pi4²h)/2
at the same time, there is no formula for semicircular prism, right
oh waiiit
hushed rune
Can anyone teach me precalculus conic sections
vagrant grove
i got it thanks, the forula for semicircular prism would be the same
noble lava
What if y = 0
plain shard
prisma salmon
would be best in the algebra channel
hidden sun
**Axe cutter (ask on server b4 dm)**
False
hidden sun
idk what you're getting out of this but like, you are wrong
consider x or y = 0
willow bear
nobody claimed $(\forall x, y)[(x+y)^2 \neq x^2+y^2]$
obsidian monolithBOT
Ann
whole void
both cases they are false
🙄
willow bear
congratulations you are very smart (derogatory)
errant shard
How do you calculate the derivative from first principles
I learnt how to use the various rules (yay), but never through FP
chilly ruin
How do you calculate the derivative from first principles
you use limits say you have the function f(x)=3x^2+5x
now do as the formula says
lim h->0 {[3(x+h)^2+5(x+h)]-[3x^2+5x]}/h
so you just evaluate this limit
desert mural
Oops I forgot divide by h
chilly ruin
sorry i would type in latex but i forgot everything i havent touched all this stuff in 1 year
heavy pewter
school should really teach the difference between identity and equation
waxen goblet
you use limits say you have the function f(x)=3x^2+5x
now do as the formula says...
Derivative formula
desert mural
school should really teach the difference between identity and equation <:sully:...
I mean it’s pretty simple
heavy pewter
people can mess up on simple things 😔
desert mural
people can mess up on simple things 😔
Haha true
near dirge
hi guys im trying to study precalculus using precalculus 7th edition by larson hostetler, and Im at Mathematical modeling and I was wondering, is it much better to just using a graphing utility rather than to find the linear regression model by hand?
wispy yarrow
Hi guys i have the function 3Log2(1-x) +1 and the ask said me to find the inverse so my result was -2^x-1/3 - 1, im not sure if its ok, the Ai gave me another response so im not sure
iron meadow
did i do this right? sorry if my handwriting is bad its my first time writing on laptop with no mouse
quasi brook
did i do this right? sorry if my handwriting is bad its my first time writing on...
yep, good job!
iron meadow
yep, good job!
thhank you
modest bolt
Hi guys i have the function 3Log2(1-x) +1 and the ask said me to find the invers...
AI was right 
We can tell where you made mistake if you share how you did it
wispy yarrow
We can tell where you made mistake if you share how you did it
Right where's the arrow
In a bad sense I multiply for -1 because the problem before this was a bit similar
digital sage
forgot to change the sign in the last step
modest bolt
Right where's the arrow
last step
2^(..) - 1 = -y
-2^(..) + 1 = y
wispy yarrow
last step
2^(..) - 1 = -y
-2^(..) + 1 = y
Wait
Oh forget, the step the ai did was different but at the end is the same
Ty
digital sage
AI 
arctic swan
how do you prove the derivative of lnx is 1/x using first princiles wat
hushed sphinx
That's not really PREcalculus.
But it depends on what your definition of $\ln$ is. Sometimes the definition is
$$\ln(x) = \int_1^x \frac{1}{t},dt$$
in which case it's just the fundamental theorem of calculus ...
obsidian monolithBOT
Troposphere
small solar
But it depends on what your definition of $\ln$ is. Sometimes the *definition* i...
how could the definition change ???
hushed sphinx
The author of a textbook goes for a walk and decides which of the several equivalent characterizations of the logarithm they're going to call "definition" in the book they're writing.
heavy pewter
different people can define the same thing differently 😔
solemn olive
How do I go about solving inequalities like this?
digital sage
find the minimum value of 3x^2-6x+5 in the given interval
solemn olive
find the minimum value of 3x^2-6x+5 in the given interval
As a function of m, then let it be greater than or equal to zero?
digital sage
no you take m to the other side of the inequality
since the inequality must be true for every x in that interval, m must be < (or <= if you look carefully into the interval) than the minimum value of the left hand side in that interval
solemn olive
since the inequality must be true for every x in that interval, m must be < (or ...
Oh, I see it. Thanks
willow bear
https://tenor.com/view/future-internet-computer-penguin-smart-gif-26091293797546...
!nogpt
tender questBOT
https://tenor.com/view/future-internet-computer-penguin-smart-gif-26091293797546...
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).
digital sage
wrong reply lol
noble lava
yh
echo stone
idk what ppl are thinking these days :(
oblique ivy
How do I go about solving inequalities like this?
We have:
[ 3x^2 - 6x + 5 \geq m \iff 3(x-1)^2 + 2 \geq m ]
[ \iff (x-1)^2 \geq \frac{m-2}{3} \quad (*) ]
\textbf{Case 1:} If $\frac{m-2}{3} \leq 0$ or equivalently $m \leq 2$,
then the set of solutions is $S_1 = (2, +\infty)$.
\textbf{Case 2:} If $\frac{m-2}{3} > 0$ or equivalently $m > 2$,
then (*) is equivalent to $|x-1| \geq \sqrt{\frac{m-2}{3}}$.
Since we're solving for $x > 2 > 1$, $|x-1| = x-1$,
hence that's equivalent to $x \geq \sqrt{\frac{m-2}{3}} + 1$.
Now since $m > 2$:
\begin{itemize}
\item If $\sqrt{\frac{m-2}{3}} + 1 \leq 2$ or equivalently $2 < m \leq 5$,
the set of solutions is $S_2 = (2, +\infty)$.
\item If $\sqrt{\frac{m-2}{3}} + 1 > 2$ or equivalently $m > 5$,
then the set of solutions is $S_3 = \left(\sqrt{\frac{m-2}{3}} + 1, +\infty\right)$.
\end{itemize}
obsidian monolithBOT
Slomenist
oblique ivy
you just play around with cases very carefully
digital sage
you just play around with cases very carefully
!nosol
oblique ivy
?
digital sage
do not give out solutions
oblique ivy
why?
digital sage
also your solution is way too overcomplicated
oblique ivy
they asked for help on how to solve such inequalities and so i did help
digital sage
!nosols
tender questBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
digital sage
I also helped them earlier
leaden wind
did i do this right? sorry if my handwriting is bad its my first time writing on...
there's another (easier way imo) way to do this: choose the biggest expoenet in the each the numerator and denominator (x^2 for the numerator and x^4) then take away the other numbers beside it (3 and 2x, keep 5x^4 and x^2), then take out both x^2 from the numerator and denominator, you'll get 1/x^2, when x appreaches infinity it should give you 0. this only works when x appraoches infinity btw.
leaden wind
can i finish all of this in like a week?
are you trying to finish all of precalc in a single week
steep inlet
are you trying to finish all of precalc in a single week
yeah
im gonna take single variable calculus
and i have to take a placement exam
steep inlet
i mean if you're studying 18 hours per day then sure
nahhhhh
leaden wind
but you're gonna go crazy
steep inlet
actuallly
steep inlet
i mean if you're studying 18 hours per day then sure
maybe i will
leaden wind
man wtf
steep inlet
when are you gonna take it
not sure but i have until like july 31
preferably earlier
leaden wind
if you dont know a single thing in precalc then you're cooked bro
leaden wind
preferably earlier
try to learn the lessons asap
then after you're done with that go solve questions or precalc problems for the rest of the month
until its just basic knowledge
you'll have to shave off all your rest hours for this one
you can also check previous placement exams to test your level
lethal sand
precalc is basically a repeat of algebra 2 with trig
so just learn trig and you will be fine
steep inlet
okay i submitted the course request
steep inlet
precalc is basically a repeat of algebra 2 with trig
i didn't take algebra 2 though
after algebra 1 in 7th grade i just did selective practice
lethal sand
so you are cooked lmao
lethal sand
what grade are you in
steep inlet
gonna be 10th
lethal sand
do you like know the algebra 2 concepts
steep inlet
ik about logarithms
this year i did circle properties so theres that too
what else
lethal sand
adding
subtracting
diving
multiplying rational functoins
do you know how to do that
steep inlet
those are the 1/x right?
lethal sand
yeah but its not gonna be simple like that
lethal sand
what you know about it
steep inlet
uhhhh
lethal sand
do you know solve 3x3s.4x4s,5x5s etc?(systems)
lethal sand
if given 3 equations and 3 unknowns can you solve
lethal sand
all of ite
steep inlet
its like midnight here
lethal sand
how long do you have to do this btw
steep inlet
how long do you have to do this btw
not sure the minimum but maximum is like until end of july
maybe in a few days
the placement test for calculus
lethal sand
that will be very hard to actually retain that information
if you dont know a lot of the stuff
steep inlet
ehh i know a lot of the stuff actually tbh
like on khan academy
the guy's explaining the topic and then when im doing the practice problems
lethal sand
do you know unit circle
steep inlet
yeah
lethal sand
do you know all your indentiteies
steep inlet
the guy's explaining the topic and then when im doing the practice problems
it becomes intuitive
steep inlet
do you know all your indentiteies
yep
steep inlet
do you know the ranges of each trig function
i know for tan
solemn olive
We have:
\[ 3x^2 - 6x + 5 \geq m \iff 3(x-1)^2 + 2 \geq m \]
\[ \iff (x-1)^2 \ge...
Love it. Thanks
whole void
do you know the ranges of each trig function
why do u need to memorize all of these random things? u can likely figure it out on the spot
lethal sand
why do u need to memorize all of these random things? u can likely figure it out...
wdym
the ranges for a trig functoin
a lot of trick questions arise from that
whole void
a lot of trick questions arise from that
do u have an example
lethal sand
a calculator only can see the 1st an d 4th quadrant
lethal sand
do u have an example
let me see if i can find one
if arcsin(-sqrt(3))/2)
= theta
what is theta
whole void
-pi/3
pseudo canyon
sharp monolith
if arcsin(-sqrt(3))/2)
I think arcsin function domain is from [-1,1]
lethal sand
-pi/3
yeah correct
but some people would say
5pi/3
and thats not in the range
see how that could mess someone up
whole void
Yeah those questions are kinda dumb imo though
lethal sand
im so confused why people put calc in precalc
whole void
even in more compliucaed problems
Do u have an example
lethal sand
Do u have an example
id have to dive into my textbook
whole void
id have to dive into my textbook
If u don’t mind, I would be curious though
void charm
im so confused why people put calc in precalc
wrong channel sry
modest bolt
im so confused why people put calc in precalc
cause pre-calc isn't standard term in every country. In India, precalc is mixed with other concepts, so the term 'pre-calc' isn't common here. When I first time saw this channel, I thought it's for high school calculus problems and #calculus is for hard calculas problems
drifting oyster
what's the issue
steep inlet
i didn't watch the khan acdemy video before doing the practice
drifting oyster
Yeah but what's the issue...
steep inlet
oh i didnt put the minus sign
drifting oyster
steep inlet
i understand it now
noble lava
<@&268886789983436800>
steep inlet
what
lethal sand
cause pre-calc isn't standard term in every country. In India, precalc is mixed ...
in the description it litteraly says "anything in the US precalc curriculum goes here, examples include: trig, logarmithic and exponethial functions"
modest bolt
my fault for not checking description 
clear cipher
What falls under calculus?
willow bear
broadly speaking, anything to do with derivatives, integrals or infinite series
clear cipher
Ok thanks
lethal sand
my fault for not checking description <:pandaohno:513070260471988226> <:pandathi...
js saying lol
true geode
cause pre-calc isn't standard term in every country. In India, precalc is mixed ...
I'm not quite sure why you got 👎'd here; you're not wrong to state what you said
I've had to read around to properly check this, but "precalculus" is likely a uniquely US-ian word
polar heath
Hey guys I’m doing some random questions and solved sin(2x)=sin(x) and got x = 0, Pi/3 and 5Pi/3. now I understand for the x= 0 solution it’s just npi as sinx= 0 at each n value of pi, however solutions have the other correct answers listed as pi/3 +npi and 5pi/3 +npi. I am just wondering why it isn’t + 2npi instead because that’s the period of sine and cosine
willow bear
Hey guys I’m doing some random questions and solved sin(2x)=sin(x) and got x = 0...
can tell you pi/3 + npi is wrong bc for n=1 that gives a non-solution
so the answer key is screwed up
polar heath
can tell you pi/3 + npi is wrong bc for n=1 that gives a non-solution
are you able to please explain
willow bear
putting n=1 into pi/3 + npi gives x = 4pi/3, but x=4pi/3 is not a solution of sin(2x) = sin(x)
in case it wasn't clear or you missed it somehow, i am saying the answer key is wrong
polar heath
so its just 2npi because thats the period correct? but u still have to consider it properly coz cases like sinx=0
steep inlet
whats npi
clear cipher
Where do I find those lessons on khan academy?
drifting oyster
<@&268886789983436800>
clear cipher
<@&268886789983436800> here too
steep inlet
vectors easy asl
arctic surge
anyone want to study calculus?
sly zenith
Any one needs help with calculus algebra and statistics
hidden sun
anyone want to study calculus?
Go to roles and select "undergraduate math"
steep inlet
it's crazy how much you can learn in like 3 days
untold talon
Any one needs help with calculus algebra and statistics
i do
placid idol
hi hi smart pips! need sum tips on how to like easily figure out problems about finding the equations of the circle: passing through intersection with center (points given), with center at tangent to the line, and SPECIALLY WHEN 3 POINTS ARE GIVEN -- (not rly a math person but i practice daily)
basically tips on like which method should i use and yeah
willow skiff
hi hi smart pips! need sum tips on how to like easily figure out problems about...
what does the centre at tangent to the line mean?
do you have a diagram you can show?
versed ledge
i am wondering aswell
but usually for equations of the circle given points just make use of distance and midpoint formulas
versed ledge
no worries
willow skiff
it's actually using distance btween point and line to find radius
oh that's just a formula
placid idol
oh yes
willow skiff
willow skiff
ah okay
steep inlet
WAIT THE DIFFERENCE QUOTIENT IS LIKE PRIMITIVE CALCULUS
WTH
So THATS WHAT THE H IS
wheat harness
WAIT THE DIFFERENCE QUOTIENT IS LIKE PRIMITIVE CALCULUS
its a perimeter cube?
willow skiff
WAIT THE DIFFERENCE QUOTIENT IS LIKE PRIMITIVE CALCULUS
indeed!
daring aspen
Differentiate 2^x
willow skiff
Differentiate 2^x
this isn't the #calculus channel
lethal palm
willow skiff
it isn't B or D
No, it's B
novel girder
I tried all the options the answer was C
sonic crescent
how do i solve this (im still starting highschool math n precal so no judging)
calc*
obsidian monolithBOT
daring aspen
Differentiation of Inverse trigonometric functions at a glance
Basically, we use + for tangent and cotangent and - for sin and cosine and their co functions
In general terms I am speaking
I think I got the d/dx of cot inverse wrong. Guess it yourself
uneven valley
why are yall talking about calc in precalc
uneven valley
I think I got the d/dx of cot inverse wrong. Guess it yourself
"the proof is left as an exercise for the reader" ahh
modest bolt
Never learning this, gonna derive the formulas everytime.
(||why trig has non ending list of formulas 
||)
noble lava
What is this even in answer too 💀
Or did you just feel like coming to the precalc channel and blessing people with your (wrong) calculus formula sheet 
whole void
how do i solve this (im still starting highschool math n precal so no judging)
bash for the points A, B, D
modest bolt
how do i solve this (im still starting highschool math n precal so no judging)
differentiation of a polynomial gives its slope at every point and maxima, minima are the points where the slope is zero
hushed sphinx
I don't think we can assume differentiation in _pre_calc.
whole void
ok u can find local mins/max on a cubic without calc
daring aspen
Or did you just feel like coming to the precalc channel and blessing people with...
It's not wrong in any way
Point out the mistake
whole void
mostly useless
heavy pewter
ok u can find local mins/max on a cubic without calc
how else will you find local minima and maxima without calculus?
because it is pretty straight forward with calculus
river drift
you can define local extrema without calculus just fine
whole void
how else will you find local minima and maxima without calculus?
A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
As per Brilliant. I like this
heavy pewter
bad wording
erm okay but
how are you going to find or know that a value is a maximum or a minimum without calculus generally?
river drift
you can find maxima/minima of cubics without calculus, although it requires more algebra
see for example https://www.youtube.com/watch?v=yJNuAXGqtRY
whole void
bad wording
erm okay but
?
whole void
how are you going to find or know that a value is a maximum or a minimum without...
for a cubic, there’s a nice technique
Suppose a cubic say P(x) has a local extrema
Then there exists a value of a such that P(x) - a = (x - b)^2 * (x - c), for some constants b and c
and b will be the x-coordinate for the local extrema
gritty haven
is khan academy good
willow skiff
is khan academy good
yes
humble pine
willow skiff
congrats!!
kind geode
thank you!!
split elbow
oh
kind geode
it’s the highest fail rate test in the country
split elbow
its passing so thats good ig
split elbow
it’s the highest fail rate test in the country
in the country? damn
you passed though
so congrats
split elbow
oh
whole void
it’s the highest fail rate test in the country
No it isn’t. but in the top half
tough lake
i was thinking of this
What physics do I need to compete AP physics
kind geode
What physics do I need to compete AP physics
algebra 2 is a requirement iirc
winter comet
Shouldnt the answer be 1 or -11
yup, looks wrong to me
silver mason
precalc shouldnt exit bruh
winter comet
precalc shouldnt exit bruh
precalc shouldn't exit bruh ❌
precalc shouldn't exist bruh ✅
precalc should exit bruh ✅
odd heath
Am I stupid or is my curriculum wrong?
the curriculum for sure
what are you doing the work on?
echo stone
We passed 🗣️
mental wyvern
old pollen
precalc shouldn't exit bruh ❌
precalc shouldn't exist bruh ✅
precalc should ex...
Indeed
river drift
depends on what the regular precalc class in your school is like, they can vary a fair amount
drifting trout
im taking junior year math next year and thats like still precalc right
also like what types of things would I be learning
untold sphinx
Is ap pre calc harder than pre calc
No
lethal sand
Is ap pre calc harder than pre calc
ap precalc is like way easier than normal precalc
ap precalc has like only 4 units
and they arent even all tested on the ap exam
odd heath
Is ap pre calc harder than pre calc
honestly it can depend, AP precalc has less topics that could be more complicated to some, regular precalc has multiple topics that can be way harder for others
tender heath
yey
tender heath
congrats , but what is the name of that site?
ty btw
mortal basin
tender heath
ty
foggy cloak
spring plover
Im trying to prepare for precalc this summer since I sucked horribly in algebra 2, anyone have any prep suggestions? I dont really know what the curriculum exactly is tbh
forest hearth
sly zenith
Im trying to prepare for precalc this summer since I sucked horribly in algebra ...
@vian00395 yes
Precalc might have basic differentiation and integration and some applications of calculus in business like optimisation
willow skiff
Precalc might have basic differentiation and integration and some applications o...
no, precalc does not have basic differentiation and integration, cause that's part of calculus
willow skiff
Im trying to prepare for precalc this summer since I sucked horribly in algebra ...
take a look at this
you can skip matrices as they aren't covered in most precalc courses anymore
and also conic sections
red storm
you can skip matrices as they aren't covered in most precalc courses anymore
wasn't there gaussian elimination in some of them
like wtf
willow skiff
best is to ask your teacher what exactly you'll be learning
noble lava
Conic skip y
willow skiff
it's nice but not necessary for calculus
willow skiff
wasn't there gaussian elimination in some of them
some of what?
red storm
precalculus
willow skiff
yeah
noble lava
it's nice but not necessary for calculus
Ig yh
willow skiff
but the Khan Academy course goes into matrix multiplication and inverses
which is totally unnecessary
lethal sand
no, precalc does not have basic differentiation and integration, cause that's pa...
mine did
i took honors tho so maybe different
willow skiff
i took honors tho so maybe different
oh maybe your teacher just taught it early
lethal sand
well 'precalculus' is a US (and possibly Canada)-specific term
i go to a us school
lethal sand
oh maybe your teacher just taught it early
yeah
it was pretty basic js like reimann sums
willow skiff
it was pretty basic js like reimann sums
ahhhh
okay yeah so going into the theory behind integration and differentiation
without making you learn all the derivatives and integrals of various functions
lethal sand
also difference quotient and limits . basically like the very basics of calc so its not totally foriegn next year
willow skiff
also difference quotient and limits . basically like the very basics of calc so ...
yeah the theory
I see now, so that fits with "not technically teaching you calculus"
but it is still part of calculus if you look at it
willow bear
<@&268886789983436800> scam
lean jasper
ay does anyone here know where I can find hard precalc problems? thx
sly zenith
ay does anyone here know where I can find hard precalc problems? thx
Yes. I can give you
lean jasper
Ohh go ahead
sly zenith
junior dagger
smoky helm
Im trying to prepare for precalc this summer since I sucked horribly in algebra ...
I have some
If you sucked at algebra two you need to lock in for unit one
rational equations is algebra two on steroids
unit 2 is also an extension of algebra two with logs and a lot of graphing
units 3 and 4 are mostly seperate unless you learned the unit circle already
smoky helm
no, precalc does not have basic differentiation and integration, cause that's pa...
ap precalc does have basic differentiation and integration if you take bc
but its super easy so if you just practice rational functions and logarithms and the graphs youll be fine
whole void
How do u do the one with e^1/x
red storm
you don't
look at the integral bounds
and try exploiting a property
hint: this won't lead to a neat answer
whole void
hint: this won't lead to a neat answer
wdym?
red storm
look at the integral bounds
.
whole void
what’s your point? The function isn’t odd
red storm
use king's rule
red storm
multiply by the conjugate
red storm
yeah you can use identity x^2 - y^2 = (x + y)(x - y)
red storm
whats that new theorem
an algebraic trick you can always do is multiply the numerator and denominator by something
this may help you simplify problems like this
which have nice cancellations
in this case, the best thing to do is multiply by the conjugate
void charm
in this case, the best thing to do is multiply by the conjugate
I mean is there second way
except that complex theorem
red storm
no
void charm
what ya think if I screw the rules by squaring that function
red storm
the problem is
you can't really distribute exponents in (a + b)^2 form
you have to expand it
also what i told you regarding numerator/denominator multiplication
only strictly applies to multiplication
void charm
ok i got it :))))
velvet meadow
how do i go about learning limits and continuity
whole void
The hospitals