precalculus

[winter comet]

but the fact that you didn't draw the line until x = 2, and you had a hole, is correct

its just in the wrong place

9 - 2x = -2x + 9, if that helps

[fallow field]

It’s a slope then

[winter comet]

what?

the slope is -2

(going down)

[fallow field]

Oh I see it

[winter comet]

yeh

and also, the part of the absolute value after x = 2 shouldn't be there

[fallow field]

But it turns into 2 no?

[winter comet]

wdym

if you draw the entire absolute value function

but erase everything before x = -3

and erase everything after x = 2

then draw in a hole at x = 3, and a filled in point at x = 2

then thats part of the piecewise function

[fallow field]

I have x=2

There

Wait

Wait so

Like this?

[winter comet]

there shouldn't be a point 2, -4

nah

uhh

[hexed tangle]

the y intercept should be 9

for 9-2x

[fallow field]

Do I point that?

[hexed tangle]

a function cannot have two outputs for one input

[fallow field]

So do I remove the right arrow

I mean the arrow

And the right point

Both equations hit the same x right?

They have the same x?

[hexed tangle]

do the vertical line test

try plotting a bunch of points and then connecting them for 9-2x

[hexed tangle]

the absolute value was right

remember that the 9-2x part is defined for x>2

[fallow field]

Am I suppose to plug in a number then point it?

[hexed tangle]

you can plug in for example x = 2 and x = 3 and draw a line with arrow going right

[fallow field]

Just in case

The equation on the left

That’s y right?

And the other is x?

[hexed tangle]

f(x) is the y coordinate

[winter comet]

the big idea is that you want to draw the line |x|, but ONLY between x = -3 and x = 2, including 2 and discluding 3 so you shouldn't have any part of the line before or after.
then, you want to draw the line 9 - 2x but ONLY after x = 2, discluding 2, and you shouldn't have any part of the line before.

[fallow field]

So do I take out the line

[winter comet]

which line

[fallow field]

Abs

[winter comet]

this absolute value line was correct

the 9 - 2x part was not

[fallow field]

So what point should I start on

[hexed tangle]

start on the point x = 2 and draw the 9-2x line after that

and draw |x| between -3 and 2

[hexed tangle]

only draw the 9-2x after x = 2

[winter comet]

right now your 9 - 2x line is before x = 2

[fallow field]

Do I close x = 2?

[winter comet]

and its also not the line of 9-2x

[hexed tangle]

the lines need to not cross

or be on top of each other

you could also try just evaluating the function at different points like x = -3, -2, -1, 0, ...

[fallow field]

Wait

Wait a second

If I plug in x

For the 9 equation

Will that be a point for y

[hexed tangle]

f(x) = y so yes

[winter comet]

this part you already did correctly, but the idea is that you have a full function but you limit it to only being within the given bounds

its the graph of |x| but you cut it off at x = -3 and x = 2

so with the other line, its the same as the regular line except you don't draw any part of it before x = 2

[fallow field]

WAIT

[hexed tangle]

the lines cannot be on top of each other

[fallow field]

?

[hexed tangle]

9x-2 needs to be to the right of x=2

[fallow field]

Does it start on x=2

But it’s closed?

I mean open

[hexed tangle]

yes

the function is equal to 9-2x only after x = 2

[fallow field]

Open 2

[winter comet]

im not sure what u drew but if its what i think

this line is not supposed to exist before x = 2, but here it exists at x = 1

you want it to only exist after x = 2

[hexed tangle]

better but the value of your function is wrong

for x = 2, f(x) = 9-2(2) = 9-4 = 5

[fallow field]

X can’t equal to 2 tho

[hexed tangle]

open at 2

[fallow field]

So x = 3 then

[fallow field]

So is the graph right then?

[hexed tangle]

no the values for 9-2x are wrong

[fallow field]

?

I plugged in 4 and 3

Oh hold on

[hexed tangle]

open point should be at (2,5)

[fallow field]

It’s -2

[hexed tangle]

your line should also be more steep

slope of -2

[hexed tangle]

at x = 5 it should be -1

[fallow field]

Do I point that

[fallow field]

Closed circle?

[hexed tangle]

you don't have to point it just make sure the line passes through (5,-1)

[fallow field]

My graph isn’t straight

[hexed tangle]

if it helps you graph you can

[fallow field]

So for domain if it’s closed I include it right?

But what if there’s an open circle

Still closed?

[hexed tangle]

if a value is in the domain of the function use closed

[fallow field]

So is it

-3, inf

-inf, 5

[hexed tangle]

its defined at x = 5

[fallow field]

Wdym

[hexed tangle]

so at x = 5 use a closed point

[fallow field]

Top is Domain

Bottom is Range

[hexed tangle]

?

[fallow field]

Domain is (-3,inf)
Range is (-inf,5)

[hexed tangle]

you don't need to draw a closed point at (5, -1) but it will help you draw a straight line for graphing

[fallow field]

[ is closed

Bracket is closed

[hexed tangle]

im not talking about the domain and range just saying that f(x) should be -1 at x=5 but I guess it's fine

[fallow field]

Okay

Is my domain right?

And range

@hexed tangle ^

[hexed tangle]

yes

[fallow field]

Okay

For this i do rise over run

I got like

2/6x+4

[peak hornet]

guys

does anyone do tutring

for precalc

cuz like im doing it in summer for school

cuz im kinda doing calc bc in 11th grade

[hexed tangle]

you can ask your questions in this channel

[peak hornet]

ok

ill stay updated

thx'

[hexed tangle]

but if you need a tutor I would recommend looking for local opportunities

like many libraries or schools will have tutoring services

[peak hornet]

hmm that looks good too

[torn kestrel]

i know my local university offers free tutoring to anyone

[peak hornet]

i was gonna use khan academy💀

i mean it does work pretty good

[torn kestrel]

well i mean also precalc is like just recommended not even needed

like literally just today i tested into calc only having done algebra 2

i mean its just like normal calculus im pretty sure

like calc 1 and 2

shouldnt be too hard

my school doesnt even offer ap calc

we got like 3 ap classes

[fallow field]

I’m stuck in this

It’s asking to complete the square

f(x)=a(x-h)^2+k

[winter comet]

if you factor out a, what do you get

[fallow field]

(-2x+4)

[viscid thistle]

Yes :))

[torn atlas]

Quick question, can I just remove the negative signs all together if I divide both sides by -1? Cause that way I won’t get a fraction of 1/16 when getting the logarithm of 2^-4

[hexed totem]

why not

its a equation

[willow bear]

yes, multiplying both sides by -1 (or dividing by -1, which is the exact same thing) is fine

[torn atlas]

Yea you’re right I’m overthinking this

My teacher said i can’t evaluate by exponentiating and I’ll lose marks

Anyone know why that is?

[torn atlas]

Thanks

[willow bear]

wym "evaluate by exponentiating"?

[hexed totem]

i think you can loose some solutions

or get more

because that logarithm have a division

idk if its what u talking about but yeah

[summer ruin]

the log is defined only when the input is positive

[torn atlas]

Something like this

[willow bear]

...

that's not allowed???

[torn atlas]

She said I can’t raise them both to the power of 27

[willow bear]

what the actual fuck?

[torn atlas]

And I’ll lose marks if I cross out the log

[willow bear]

so then how are you supposed to solve the equation log_27(x) = 4/3 if you're banned from doing 27^(both sides)?

[willow bear]

you mean raise 27 to their power. there's a difference

[torn atlas]

Yea my bad

[torn atlas]

Maybe she meant I just lose marks if I cross out the logs

She said something like I can’t cancel logs

[timber herald]

27^(4/3) = x
3^3(4/3) = x
3^4 = x
81 = x

[hexed totem]

help

so i have the right answer but i didnt understand why

is D

[viscid thistle]

can someone help me with this

[willow bear]

,rccw

[viscid thistle]

what am i doing wrong

[willow bear]

,rccw is just the command to rotate the last-posted image counterclockwise

i did that so i could read the thing

how did you work out $4 - 8 + \frac{12}{5}$?

[obsidian monolith]

|Ann⟩

[willow bear]

it sounds like you made a sign error or something.

[viscid thistle]

-b/2a

-4/2

is -2

and i plugged it in

[split reef]

am i able to ask questions here if i already made a ticket?

[willow bear]

yes you plugged it in, but what did you do afterwards

do you have your arithmetic written down or did you do it all mentally

[viscid thistle]

i’m trynna find the vertex so i just plugged it into the equation

did 4-8 to get -4

and -4 + 12/5 is 1.6

so 1.6 is our y

and we already found out x -2

[willow bear]

-4 + 12/5 is not 1.6

[split reef]

thats negative 1.6 dear

[viscid thistle]

oh

thanks

[split reef]

ann can i ask questions here if i already have a ticket open?

[willow bear]

posting the same question in multiple places is frowned upon

but if it's a different question go ahead

i mean what do i care, i'm not even a mod or anything

[split reef]

oh okay i won then

just noone else was answering

u think you can look over it for me rq?

#help-12 if u want~

[willow bear]

busy rn

[viscid thistle]

how would i go about this question

[proper pagoda]

u know how to do polynomial long division?

[viscid thistle]

not really

we learned it a while ago

[proper pagoda]

mmmmm i forgot the specifics give me a second

[hexed totem]

you need to apply ruffini rule

[viscid thistle]

what’s that

[proper pagoda]

i wanna know too i thought it was polynomial long division

[viscid thistle]

ya me 2

i’m not in no smart math

[proper pagoda]

if its is polynomial long division u basicially wanna set it up like its long division

[hexed totem]

this thing

[proper pagoda]

oh the

box method

[viscid thistle]

that’s synthetic division

you can’t do it with this one bc the highest value is only squared

so it wouldn’t work

[proper pagoda]

polynomial long division stats off like this iirc

[hexed totem]

?

[proper pagoda]

do u understand this or should i explain further

i dont know ANY math terms so sorry

[viscid thistle]

could u explain more

[proper pagoda]

ok so if i dont do a good job watch this guy https://www.youtube.com/watch?app=desktop&v=_FSXJmESFmQ

[viscid thistle]

thanks

[fast tulip]

Chemistry tutor 🐐

[proper pagoda]

but its just long division but to the left

frfr

[viscid thistle]

ya nah this question on some bs

[proper pagoda]

since the first thing is 4x^2, you wanna get as close to it as u can with x+2. sinx x times 4x = 4x^2 you wanna put 4x on top like i did

[viscid thistle]

nah it would be 3x on the top right?

[proper pagoda]

NO wait u right 3x mb mb

[viscid thistle]

ya

but then you get x^2 + 3

[proper pagoda]

nah

the +2 is muiltiplied by 3x

so u get 6x

[viscid thistle]

i’m talkin ab the left over

after u subtract that

u get x^2 +3

how would u subtract that

[proper pagoda]

oh

[viscid thistle]

nah this question buggin

i’m cooked on this test

and it’s the most important test i ever took

[proper pagoda]

no it is 4x innit...

cause its like distribution

yeah it is 4x

[viscid thistle]

then what do we do with the negative

[proper pagoda]

put -2 in the top

but then you have a remainder of 7

i think u just leave that tho

so the answer would beeeee

[viscid thistle]

u js leave the remainder?

[proper pagoda]

4x-2+ 7/x+2

[viscid thistle]

it says it’s incorrect

[proper pagoda]

damn this is inccorect?

[viscid thistle]

oh like that

lemme retype it

damn wtf

it was correct

glooks gang

[proper pagoda]

OH DAMN!!

[viscid thistle]

oh shit

tysm

[proper pagoda]

ok so like do u understand or naw

[viscid thistle]

ya i’m js surprised we did 4x

but other than that i get it

i didn’t know u could do that

[proper pagoda]

yea cause its like distribution

[viscid thistle]

ya

[proper pagoda]

ok cool, good luck on ur test man

[viscid thistle]

im so scared for the test

it’s the most important test i ever took

[proper pagoda]

u got this!! finals?

[viscid thistle]

nah

[proper pagoda]

aps?

[viscid thistle]

its some college test

[proper pagoda]

well if its not finals u'll be fiiiiine

[viscid thistle]

and if i don’t do good i can’t take dual credit math next year

[proper pagoda]

oh damn

[viscid thistle]

and if i can’t take dual credit i drop a math class

[viscid thistle]

idrc ab finals

i never study for my finals

[proper pagoda]

i have to pass this math final or i fail the class ^^

[viscid thistle]

wtf?

[proper pagoda]

im studying rn... its 2 am

[viscid thistle]

what’s your grade

[viscid thistle]

nah wrd

[proper pagoda]

im failing rn lol

[viscid thistle]

i got a b in math so if i fail my final im good

[viscid thistle]

what math class u in

[proper pagoda]

precalc lol

[viscid thistle]

oh shit

[proper pagoda]

doing double angle identities

[viscid thistle]

i’m not even in precalc

i’m in normal alg 2

[proper pagoda]

i should've taken alg 2...

my EGO

[viscid thistle]

what grade are u in

sophomore

or freshman

[proper pagoda]

im a college freshman

[viscid thistle]

oh shit college?

wtf

nah i’m in high school

[proper pagoda]

yepyep

[viscid thistle]

i took precalc freshman year

alg 2 this year

[proper pagoda]

lmao

i think it was reverse for me

[viscid thistle]

and ap stats next year if i don’t fail this test

[proper pagoda]

i took alg 2 then precalc

then i think geometry or sm

and then calc

[viscid thistle]

damn

i’m in florida so shits different

[proper pagoda]

ohhh

[viscid thistle]

i took geo in 8th grade

[proper pagoda]

ny over here

i would give to be back in algebra 2

my ego it was too big

i thought i could handle precalc

[viscid thistle]

precalc in hs is pretty easy

prob way harder in college

[proper pagoda]

fs

it definetly is

[viscid thistle]

js 1 more week of school

then summer

[proper pagoda]

true ture

just gotta get through this

[viscid thistle]

im finna get some sleep thanks for the help

[proper pagoda]

no problem, sleep well

[agile sparrow]

Sleep well

[fallow field]

Im stuck here

[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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fallow field]

Don’t know where to begin

[willow bear]

ok, do you know your way around linear functions in general?

slope intercept form, that sorta thing

btw are we talking about letter a or letter b?

like which one of these do you need help with

and if both, which first

@fallow field

[fallow field]

with a

Can you just tell me where do i put the numbers

like what letters do i replace with what

because im not so sure how they got this

I also gotta sleep rn

[willow bear]

well uh. ok. go sleep then i guess

[willow bear]

you don't "just put the numbers"

you first find the slope of your function, then either apply slope intercept form directly or solve for the y intercept

[arctic sundial]

when do ap precalculus frqs get posted

its been two days, but is it posted when the last exam was given or at the time the exam was given for EST time zone people

[gritty ibex]

Hey guys, I recently just did tons of trig problems~~(identities, applying double,half,angle, product to sum formula, trig inverse, etc)~~ that I unconsciously memorized unit circle. If you ask me any important point(like pi/3, pi/4, pi/6, -3pi/4, 7pi/6, 5pi/3 etc) in the unit circle i will probably able to give you the exact trig value within 5 seconds without looking it up on the unit circle.(prolly still slow compare to you guys but im proud.)

Im doing great right?😊 I hope getting a good grasp of unit circle and those concept will give me a good start in starting calculus. Im still like half way in precal lessons yet.\

[arctic sundial]

Yes that’s really good!

Unit circle is prob most important thing in precalc

To memorize

I used mnemonics to help me memorize, like when the fraction has a denominator of 3, so that means it’s closer to the y axis and sin will be at its max/min there -+root3/2

[willow bear]

i mean like

[arctic sundial]

And when the fraction has a denominator of 6, so that means it’s closer to the x axis and cos will be at its max/min there -+root3/2 while sin will always be less +-1/2

[willow bear]

the unit circle is kind of like trig's version of the multiplication table

[arctic sundial]

Ye lol

Also do u know when ap precalc frqs get posted on college board

[willow bear]

no i'm not even american lmao

[viscid thistle]

Today's paper was easy

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[viscid thistle]

3

I need help with I_1

[willow skiff]

How did you go about doing limit 1? Like did you use the difference of two cubes for (x^3 + x^2 + x)^(1/3) - (x^3 - x^2 + x)^(1/3) to make it a fraction?

[willow bear]

t := 1/x to turn it into a limit at 0

[gritty ibex]

oh, i b4 that i actually memorized already like trig value of pi/6~pi/3 of sin, cos tan, I just used "3 2 1, 1 2 3, then 33 1 1" to memorize them first. For quadrant 2~4, i have to use symmetric identities(properties?)to visualize them. Once i figure out when the signs i just applied the 3 2 1, 1 2 3, 33 1 1 thing. It was kinda pain at first, but once i get used to it, I feel more comfortable with them and without spending minutes to convert them on paper. My lecturer told me to memorize them but i feel like this is the better way to go about it(visualizing, imaging ), instead of forcing them into your head.but yeah i just get pretty quick in convert them in my head. say sin 5pi/4. I know its somehow relate to pi/4, so i think from pi then going down pi/4 which is in quadrant 3, sin in q3 is negative just applied what i memorized than add a minus sign

[viscid thistle]

0/0 form so l hospital ?

[viscid thistle]

That is what I need help with

[willow bear]

imagine me making a disgusted grimace as if you handed me a rotten animal corpse

[willow skiff]

I misread, it's actually the sum of two cubes cause you have -a - b = -(a + b), anyways

$a + b = \frac{a^3 + b^3}{a^2 - ab + b^2}$

[viscid thistle]

I will try it again

[willow bear]

a^2 - ab + b^2*

[obsidian monolith]

south

[willow skiff]

(confused with difference of two cubes arghhhhhh)
(yes there's always exactly 1 minus)

https://external-content.duckduckgo.com/iu/?u=http%3A%2F%2F3.bp.blogspot.com%2F_gnmNoWMeZU4%2FTC-E7ZPAHyI%2FAAAAAAAAAF0%2Fsht6Q--u_Y0%2Fs1600%2Fcubes.png&f=1&nofb=1&ipt=4237da5dfc7f5ad533b8e993271c65341e2f9d2e785693eb5146b73b5ce608cd&ipo=images

[willow bear]

anyway the limit ends up being equal to the 2nd derivative of a certain function at 0.

which is a lot less headache-inducing than having to l'hôpital 2 times.

[viscid thistle]

1 time would be enough

Got it

[willow bear]

who am i to stop you from nuking every single limit with l'hôpital?

[viscid thistle]

So are we supposed to substitute t=1/n whenever n tends to infinity ?

[willow bear]

no

[viscid thistle]

Okay

Thank you

[viscid thistle]

Wait

I didn't get it

@willow bear

[viscid thistle]

How to do it ?

[willow bear]

$\lim_{h\to 0} \frac{f(x+h)-2f(x)+f(x-h)}{h^2} = f''(x)$

[obsidian monolith]

|Ann⟩

[viscid thistle]

Should I remember this ?

[willow bear]

im not gonna force you either way

[viscid thistle]

What would you suggest ?

I was taught only Differentiation by first principle

For 1st derivative

[willow bear]

your limit, after substituting as i suggested (t := 1/x) and cleanup, becomes a limit like this one, for f(t) = sqrt(1+t+t^2), and with a -1 coefficient

[willow bear]

so you are banned from rules of differentiation such as the power rule...?

[viscid thistle]

No,nothing as such

[willow bear]

nothing as in you don't know those? or nothing as in no such ban?

[viscid thistle]

No such ban

And I don't know them

[willow bear]

ok in that case

uh

well ok that falls flat then

gonna need some time to think of something else

[viscid thistle]

Okay

[willow bear]

man, this makes shit give 10 times more headache

[viscid thistle]

Substituting x equals 1/t ?

[willow bear]

no, the fact that you dont know derivatives

the substitution probably makes no difference for difficulty

but then again if you dont know derivatives then l'hôpital is impossible

actually yeah how do you even suggest doing anything with l'hop when you yourself stated that you don't know how to take derivatives

[viscid thistle]

I do know derivatives

[viscid thistle]

This is what I do not know

I know derivatives

[willow bear]

but you said things like the power rule were unknown to you

[viscid thistle]

Do you mean uv rule ?

I know derivatives to a high extent

[willow bear]

power rule is d/dx (x^p) = p*x^(p-1)

the others are product rule, quotient rule and chain rule

[viscid thistle]

I do know that

I know all of them

[viscid thistle]

Except this

I have Never seen this

I am familiar with this one

[viscid thistle]

Lots of "this"

[viscid thistle]

How to convert this ?

Sorry but This is something new,so I can't get any further than what you are telling

[willow bear]

f(t) = cbrt(1+t+t^2)

will get you a limit in the same form as i originally suggested, times -1

im currently doing physical exercises and typing here in the breaks

[viscid thistle]

Dang

Okay

Got it

Thank you

[viscid thistle]

How did you know it?

That quick

[willow bear]

probably bc i've seen limits that look like that at some point in uni

had to work it out before saying that tho

[viscid thistle]

So practice,
Hmmm

Okay ty

[fallow field]

How did they get 3/4 tho

[willow bear]

the graph of your function is perpendicular to that of y = (-4/3)x + 2

do you know the relationship between the slopes of a pair of perpendicular lines?

[fallow field]

every time somethings perpendicular to something the other has its x and y flipped right?

[willow bear]

...no, bad

do you know the relationship between the slopes of a pair of perpendicular lines?

the correct answer to this was "the slopes of two perpendicular lines are negative reciprocals of each other"

[hexed tangle]

$$m_2 = -m_1^{-1}$$

[obsidian monolith]

jasoney

[native eagle]

if i have
$$\frac{x^3}{x^2+1}$$
can i simplify by doing this ->
$$\frac{x^3+1-1}{x^2+1} = {x-1}$$

[obsidian monolith]

Adam

[native eagle]

can i do this or this is not right?

[fallow quiver]

[\frac{x^3 + 1 - 1}{x^2+1}] is right but whatever you've done after that is not.

[obsidian monolith]

! What the hell am I doing here?

[native eagle]

I wanted to get rid of the denominator

[willow bear]

for what purpose?

[native eagle]

so I did divide x^3+1 / x^2+1

[willow bear]

divide like long division?

[native eagle]

to get the value of x the original question is : -2 = x^3/x^2+1

[primal river]

no you cannot cancel them out

[willow bear]

you should always begin by posting the original problem

also you are missing parentheses, presumably

you meant $\frac{x^3}{x^2 + 1} = -2$, yes?

[obsidian monolith]

|Ann⟩

[native eagle]

yes

[willow bear]

and that is the original question, yes?

[native eagle]

not really the very original xd, its part of my answer

here it is the question

[willow bear]

http://xyproblem.info/

[native eagle]

sorry mb

[willow bear]

what did you get for f'(x)?

[native eagle]

I did it like this
$$ y = x^{-2} + 1 $$
$$y` = -2x^{-3} $$

[obsidian monolith]

Adam

[native eagle]

.

[winter comet]

you have to use quotient rule

[willow bear]

$\frac{1}{x^2+1} \neq x^{-2} + 1$.

[obsidian monolith]

|Ann⟩

[native eagle]

why?

[willow bear]

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

[obsidian monolith]

|Ann⟩

[willow bear]

or to give you a concrete example

for x=2:

1/(x^2 + 1) = 1/(4+1) = 1/5
but x^-2 + 1 = 1/4 + 1 = 5/4

clearly 1/5 is not the same number as 5/4

[willow bear]

excessive and full of opportunities for mistakes.

[native eagle]

so doing 1 / (x^2 + 1 )^-1 to flip the expression is not valid?

[winter comet]

hm ig

[winter comet]

what u had first was correct

[willow bear]

the problem isn't rewriting 1/(x^2+1) as (x^2+1)^-1

the problem is when you try to distribute the power into the parentheses

bc it doesnt work that way

[native eagle]

I didnt get why it doesnt work that way, Im sorry lol

[willow bear]

ok then we have to address that before all else

ok first

[winter comet]

1/(2+1) = 1/3
u tried to do
1/(2+1) = 1/2 + 1/1 = 1/2 + 1

[willow bear]

$(x^2 + 1)^{-1}$ is NOT, in general, equal to $x^{-2} + 1^{-1}$.

do you agree, do you disagree, or are you confused?

[obsidian monolith]

|Ann⟩

[native eagle]

Im confused shouldnt we multiply the powers?

[willow bear]

these two expressions are not equal to each other, and give different values for the same value of x.

you are probably thinking of one of the exponent laws, like (a * b)^n = a^n * b^n

yes?

[native eagle]

mhm

[willow bear]

but for that law, the stuff inside the parentheses must be a product.

not a sum as it is for us.

[native eagle]

ooh

so this rule works only if inside the parentheses are products only

or division right

[willow bear]

yes

i think you need a thorough algebra review

bc frankly you have no business doing anything calculus if you are making such faceplant-level blunders with algebra!

[native eagle]

I might have some gaps here and there in my algebra but I have a calculus exam soon what could I do lol

[willow bear]

💀

you say gaps, i say kilometer-wide abysses

[native eagle]

you are exaggerating xD

[fallow quiver]

Laws of exponents is like middle school.

[native eagle]

yeah thank u 💀

[willow bear]

yeah actually what grade are you in

maybe my exaggeration is not that great

based on you saying you have an upcoming calculus exam i'm going to ballpark your grade as 11

[native eagle]

I will use the quotient rule here then instead

yub Im grade 11 actually lol

[fallow field]

where did they get -6 from

[primal river]

don't worry Adam, just use situations like this one to fill in the gaps and eventually you'll catch up

[native eagle]

$$y` = \frac{(x^2+1) * (0) - (1) (2x)}{(x^2+1)^2}$$

[primal river]

for example now would be a good idea to read about rules of exponents

[fiery creek]

if you want to do x0 you can write it as x_0

hwhat

[native eagle]

mhm I will try my best

[native eagle]

its wrong?

[fiery creek]

ah you're using quotient rule here

[native eagle]

yeah

[fallow field]

how did they get -6?

[fallow quiver]

yes, there's supposed to be a - in place of +

[fiery creek]

i think it's wrong

they distributed wrong

[native eagle]

oh yeah, right my memorization is kinda bad lol

[obsidian monolith]

Adam

[willow bear]

$\frac{3}{4}(x-8) = \frac{3}{4}x - \frac{3}{4}\times 8$

[obsidian monolith]

|Ann⟩

[fallow field]

?

wait

3/4 x 8/1 = 24/4 = 6

[native eagle]

so from the original question
$$\frac{-2x}{(x^2+1)^2} = \frac{1}{x^2+1} $$
$$ -2x = \frac{(x^2+1)^2}{x^2+1} $$
$$ -2x = x^2+1 $$
$$ x^2+2x+1 = 0 $$

[fallow quiver]

You forgot the -1 even after I told you that you got it wrong.

[native eagle]

x = 1

is that right or im missing anything

[primal river]

how are the first left and right expressions equivalent?

[willow bear]

they aren't; the problem says to solve the equation f'(x)=f(x).

[primal river]

I know they aren't.. I just wanted Adam to think about it

[willow bear]

eh?

[primal river]

did I misunderstand something?

[fallow quiver]

And I thought help channels were at their all time low.

[obsidian monolith]

Adam

[native eagle]

x = -1

[native eagle]

the first is the derivative and the other is the original

[willow bear]

i mean you asked a misleading question imo

[native eagle]

mb

[willow bear]

like, i know that if i were in adam's shoes i would be confused by it

[native eagle]

https://tenor.com/view/sad-cat-sunakook-tired-exhausted-gif-24687868

oh bro...math xD

[primal river]

aah I see now sorry I missed the part where the derivative should be the same as in the original

[fallow field]

where did they get +4 from

[native eagle]

plus 4 for both sides

[fallow field]

oh i found it

something to do with

(a-b)^2

[native eagle]

🤨

[fallow field]

thats how i got it

x^2-4x = (x-2)(x-2)

x^2-4x+4

[willow bear]

it's called completing the square

[fallow field]

yeah and how did they get 7/2?

pos

[willow bear]

...what does "pos" mean?

[fallow field]

positive

[willow bear]

ok so it doesn't mean "piece of shit"

anyway they just added the -1/2 and 4 ...

you might wanna practice fraction arithmetic some more so that simple shit like this doesnt trip you up

[fallow field]

is there a reason why

is it because its moving it to the left

[willow bear]

from here to here?

no, there's no "moving". it's just cleanup. no more, no less.

[fallow field]

yeah how did they get 7/2

[native eagle]

by addition

of these

[willow bear]

i literally told you. they added the -1/2 and 4 together.

$-\frac{1}{2} + 4 = \frac{7}{2}$

[obsidian monolith]

|Ann⟩

[fallow field]

oh i see

[native eagle]

help?

[fallow field]

How is this negative 4?

[willow bear]

ok i think one of y'all should go to a help channel

cause 2 convos in 1 channel is bad

[fallow field]

hold on i got it

i have to extend it

[primal river]

use implicit differentiation

[viscid thistle]

Status 1

[willow bear]

4x^2 - 4x + 1 is a perfect square. that migt help a bit.

and the denominator smells like some bullshit could be done to it, but i don't quite see what yet

[viscid thistle]

That was a guess

[willow bear]

split 12x^2 as 8x^2 + 4x^2

this will make the denominator into the sum of two perfect squares.

[willow bear]

why do you keep writing your x's like æ ???

[viscid thistle]

Old habits

[willow bear]

they're getting less and less recognizable as x as you go on

anyway

you didn't really need to bring that 8 under the square.

it can stay outside.

[viscid thistle]

Got it

[viscid thistle]

Key point ?

[willow bear]

i don't understand your question, please rephrase.

[viscid thistle]

Nvm

Thank you

[fallow field]

Why does the work say (x-1) when it said the middle one is 2?

[echo sinew]

Yeah that's a typo for sure

[sour phoenix]

Hello please I need help here🙏🏿

Thanks

[willow bear]

typo in either the textbook or the written work

can't rly tell which one is supposed to be trusted more, but you're right that it's a discrepancy

[echo sinew]

Can you send the uncropped picture?

[sour phoenix]

What do they mean when they say that t <=a???

[echo sinew]

Literally what it's written, t is less than or equal to a

[sour phoenix]

I did it bc I had a pb for that specific question out of all the others

[echo sinew]

If you instead are asking why you need t ≤ a, that's because of the domain of that square root
@sour phoenix

[sour phoenix]

Ok thanks but I need the solving please at least explanation on how to proceed

[winter comet]

trig sub

wait im stupid i didnt see the x

outside

you can just do u sub

[agile sparrow]

Integrate either using x=sin u or just a^2-x^2=u
The t<= a just means that the value inside root will be positive no matter what

[hidden lagoon]

transformations relating to x are the opposite of what you'd "expect" because if you solved the equation for x you'd end up doing the opposite of the transformation to get x by itself

because that's how you isolate a variable

idrk how to explain "why" because it just is

[jovial coral]

Can anyone help me with limits

I am not really good at them

If there are any videos or books about limits pls tell me about them

[willow bear]

ochem tutor + khanacademy, they both have a bunch of limit videos

for here, you should post a particular problem you struggle with

[jovial coral]

Ok sorry but thank you

[dawn zealot]

Khan academy was pretty good for limits from what I remember

[jovial coral]

Thanks

[dawn zealot]

Once you understand them they are one of the easier units in precalc

In my opinion

[viscid thistle]

Wrong channel

Status 5

Go to #calculus

[viscid thistle]

Okay,thank you

[viscid thistle]

The locus

(Don't judge my parabola)

Status 1

[viscid thistle]

This is no calculus question but ok

[agile sparrow]

arg (that)= π/2

π/2 = tan^-1[ img part/real part]

img part/ real part = 1/0

[viscid thistle]

ANN said it's calc

[viscid thistle]

That won't help

It will at some point but not at the start

@willow bear please

[willow bear]

what.

[viscid thistle]

[willow bear]

im too fucking tired for this.

i saw your problem.

[viscid thistle]

A hint ?

[willow bear]

if i had something to say then i would have said it.

if i had something to say then i would have said it.

[viscid thistle]

Okay

[vapid plaza]

<@&268886789983436800>

[viscid thistle]

my friend wanted to know the conjugate of a set of complex numbers in a coordinate system

I just sent him this

A for effort?

[willow bear]

[hexed totem]

Wdym with that

[hushed sphinx]

Complex conjugation corresponds to mirroring the complex plane across a horizontal line.

[native eagle]

y = f(x)^n
dy/dx = n(f(x))^n-1 * f`(x)

dy/dx = dy/dt * dt/dx

which one is the chain rule?

[willow mortar]

The first one

[native eagle]

and whats the second

[winter comet]

both, more or less

[willow mortar]

Also the chain rule, for y=f(t) and t=g(x), so y=f(g(x))

But in the specific instance that you were computing you might want to use the first one

Though the second one is exactly the same

[winter comet]

the first one is usually used for functions, the second for applications like related rates

[native eagle]

mhm thank u guys

[native eagle]

but how though?

they look different

[willow mortar]

Well for a function y that is a function of t(x), say y(t(x)), then dy/dx=dy/dt*dt/dx,

[native eagle]

ooh I think I see now so when we substitute dy/dt with the derivative and dt/dx with also its derivative it give us the first formula?

[willow mortar]

Yeah

That is correct

[native eagle]

oh thank u

[willow mortar]

No worries

[warped cipher]

have you learned long division or sythentic division

I forgot what they called

[proper pagoda]

too tired to solve

actually i will jsut ask the help forums

[pseudo zealot]

when drawing from a standard deck of 52 cards, what is the probability that you draw 3 distinct pairs and 1 unique card in a 7 card hand?

i did
(nCr(13,3) * nCr(4,2)^ 3 * nCr(40,1)) / nCr(52,7)

is this right

[willow bear]

that seems correct but why write C(40,1) instead of just 40

[pseudo zealot]

oh ye

[willow bear]

is this a test?

i see the question has a point value attached to it

otherwise,

!status @desert swallow

[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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[willow bear]

if you are given the graphs of two functions y = f(x) and y = g(x), how do you find visually the solutions of the equation f(x)=g(x)?

i said visual.

how do you see on the graph the solutions of f(x)=g(x)?

the places where they intersect.

ok, so see your graph.

can you show me the point(s) where the red and green graphs intersect? if there are no such points, then say "There are no such points."

3 and 1.3?

neither of those looks like a solution to me.

btw what kind of format do they expect work in?

paper?

do you get a text box or do you get an "upload file" thing

cause "graphical method", "approximate solution" and ""mathematical reasoning"" don't mix all that well do they

.... thats a different question?

with different functions

[viscid thistle]

?

I wonder why...

[willow bear]

the other person deleted all of their messages.

[primal river]

one still remains

[charred epoch]

Why does x^-2 equal 1/x^2?

I know it's a fundamental rule but I'd like to understand how it works.

[willow bear]

ok so you know how when you first learn about exponents, there's this rule that they follow:

x^(m+n) = x^m * x^n

[willow bear]

and initially you only know what it means when m and n are natural numbers, but still the rule holds @charred epoch

like is this sth that makes sense to you?

[charred epoch]

What @primal river posted makes perfect sense, but now I'm trying to understand why the rule in your reply works as well lol

[willow bear]

i was actually not yet done

i was now gonna explain why x^0 is defined as 1, and x^-n is defined as 1/x^n

and the reason for that is to keep that rule

[charred epoch]

I figured out why x^0=1 yesterday

Well I figured out x^(3-3) = x^3/x^3 = 1 = x^0

But now I realize I'm confused why x^(3-3) = x^3/x^3 😆

[shut monolith]

lol

[charred epoch]

Is it true x^(4-3) = x^4/x^3? That seems confusing if it is

[shut monolith]

try to use what Shidoro said to verify it

[willow bear]

$x^{m-n} = \frac{x^m}{x^n}$

[obsidian monolith]

|Ann⟩

[charred epoch]

This is helpful and I also need to hammer it into my brain that exponents are like, the number of times the base of the exponent appears.

[willow skiff]

Yeah with enough practice it's going to become second nature to you

trust in the process

but that is exactly the right reasoning for why this is true

[daring tapir]

I know this isnt intended answer but it just looks like pain

[lapis sphinx]

huh?

wdym isnt the intended answer

[willow bear]

what is that supposed to mean

[daring tapir]

I dont recall having "pain" as the intended answer to any problem whatsoever lmao

[daring tapir]

A weird tetration id assume

[willow bear]

also who posted it

[lapis sphinx]

me

yea its tetration

i dont get why its weird lol

[daring tapir]

Having a power tower m-n long is kinda weird if you ask me

[lapis sphinx]

is there another way to represent it is what im asking

[willow bear]

id be surprised if there was any nice identity for this

there probably isn't

[lapis sphinx]

ah ok rip

[daring tapir]

I dont think so?

[daring tapir]

I havent really seen any cool identities for tetration yet

[lapis sphinx]

apparently this is a recursive way of writing it

which makes sense

its how its defined ig

[daring tapir]

Isnt this just the definition formally

[lapis sphinx]

but idk how to write it without the recursive part

[lapis sphinx]

yea

all my homies hate slog

[daring tapir]

Without the recursive part ig there arent any formal definitions

[lapis sphinx]

i see

alr, thanks for the help

[sour phoenix]

Hello everyone

I was solving this intégral and I was blocked at the last step.....I expanded and it gave me nothing interesting......😭😭😭

[winter comet]

whats the og problem?

integral of dx/((a+6) * tan(x)) ?

or integral of dx/(a + 6tan(x))?

[winter comet]

i can't read that very well unless i was correct 💀

[sour phoenix]

It is a+btanx

[winter comet]

oh

[compact stump]

your substitution is not right

in your case t = tan(x/2)

oh wait nvm the substitution is fine, but what happened to your dx?

also is there specific form that you want to show the integrals equals to?

[sour phoenix]

nothing happened to my dx

[winter comet]

don't you need to substitute dx with something with dt?

i dont see dt in the uh

integral

unless its there and im bliend idk i cant really read ur thing too well lol

[sour phoenix]

are u able to solve the integral?????

[granite quiver]

What are prerequisite math topics I should know before I learn matrices?

[hushed sphinx]

Nothing except a basic grasp of high-school algebra.

[granite quiver]

I see

Matrices involve a system of equations correct?

[hushed sphinx]

That's one use case for them, and often the first one to be presented because it is (a) pretty concrete and (b) independently useful.

[undone sage]

do all piecewise functions have a discontinuity?

[past dune]

No

[willow bear]

piecewiseness is a property of formulas btw not of the functions themselves

[winter comet]

just as an example, this is a continuous piecewise function

[undone sage]

thank u

[winter comet]

:D

by the way

i meant x<= 0

the function i wrote actually is not continuous, the function i drew is 💀

[willow bear]

i mean your function is continuous on (-∞, 0) ∪ (0, +∞) and can be extended to one that's cts on R

[winter comet]

R is all real numbers? isn't 0 a real number?

[willow bear]

i don't see how what i said implies 0 is not real

[winter comet]

also i think generally if they ask if a function is continuous they mean (-infinity,infinity)

[winter comet]

uhh

maybe i don't know what you mean by "can be extended"

the function as it is right now is not continous on R, but it is continuous on (-∞, 0) ∪ (0, +∞) ri

[willow bear]

the function as it is right now is not defined on R but only on R \ {0}

but it can be extended to a function with domain R by declaring f(0) = 0

[winter comet]

the "extension" being if i said <= or >= on one of the intervals?

[willow bear]

that's one way you could write it down yes

but generally

given a function f: X -> Y and a proper superset X' of X, an extension of f to X' is a new function g : X' -> Y which agrees with f on X (i.e. for all x ∈ X one has g(x)=f(x))

[winter comet]

i don't get it

💀

i don't know what a lot of that notation is, idk what a superset is, thus i dont know what an extension means exactly

and i dont know what it means by a function "agreeing" with another function

[willow bear]

"X' is a superset of X" means X is a subset of X'

[willow bear]

i literally explained that one right at the end

[winter comet]

what does f: X -> Y mean?

[willow bear]

"f is a function from X to Y"

X and Y are sets

X is called the domain a.k.a. input set and Y the codomain a.k.a. output set

[winter comet]

oh alr

[minor dragon]

hi im new to calculus

[winter comet]

hi, also this is the precalc channel

[minor dragon]

ok

[pastel fossil]

Hey yall

Did I do something wrong?

I was marked wrong but all the math bots and Chegg agree with my answer, if I am wrong perhaps someone could explain where?

I was told the answer is -110

[winter comet]

what's the og problem?

[pastel fossil]

I was marked wrong but everyone and all math tools say I’m right, I also want to know why I’m wrong if that’s the case

[pastel fossil]

So the og problem

Is asking for rate of change

Lemme get a photo for you

Might take I while, I seem to be missing my book lol

[winter comet]

XD

[pastel fossil]

Here it’s B

[winter comet]

the answer is definitely -108

lol

maybe he was just "estimating" too poorly

like not just estimating, the answer IS -108

i don't see how he could get -110 unless, again, the person who told you that was estimating poorly or smthn

[pastel fossil]

Okay, my school took marks off

And I genuinely couldn’t figure out how it was -110

[winter comet]

bruh 💀

[pastel fossil]

You might have just saved me a whole percent

If I can convince them

[hidden lagoon]

can confirm it's -108

[winter comet]

you can tell them to take the derivative, if they know calculus

[pastel fossil]

Thanks guys, appreciate it a lot

[winter comet]

f'(x) = -4x^3, if you plug in x = 3 the answer is exactly -108

[fresh gorge]

Hello everyone

Anyone good at differentiation here?

[willow bear]

!da2a

[tender quest]

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

[willow bear]

also probably better in #calculus, since yknow. it's calculus.

[winter comet]

(e^(4x+2))^2 is the same as...

[thick meadow]

but it said to keep it in the simplest form

[winter comet]

it said to give your answer in simplest form

and arguably this is more simple form

you have to multiply the outer exponent by the inner exponent

[thick meadow]

simplest form is this

[thick meadow]

.

[winter comet]

that may be the answer

i didnt do the math

but you can simplify (e^(4x+2))^2

[thick meadow]

hmm

[winter comet]

and then you can do u sub if you want

[winter comet]

do you know that (e^(4x+2))^2 = e^(8x+4)

[thick meadow]

yeah

[winter comet]

ok

[thick meadow]

i did that

[winter comet]

so you're actually just taking the integral of that

alr

do you know u sub?

[thick meadow]

sorry but i didnt understand what u said

[winter comet]

(u substitution)

[thick meadow]

oh yes

[winter comet]

can you use it to get the antiderivative?

[thick meadow]

i did upto this step

i am not understanding what to do next

[thick meadow]

to get this

[winter comet]

ah

whats e^[ln(2^8)]

sorry wait

ther

[thick meadow]

e^ln256?

[winter comet]

and whats that equal to?

[thick meadow]

256

ooh

[winter comet]

yeah

[thick meadow]

i got it

thnx

[winter comet]

yeh

[torpid perch]

is it giving any options or

[desert swallow]

nah i figured it out

[torpid perch]

Using what method

[desert swallow]

i sub points into y= a*b^-x

since decay

y intercept

to find a value then i sub anot her to find B

[sour phoenix]

plese does anyone have an idea

[willow skiff]

Weierstrass is the right approach but

1. 2 * 6 = 12
2. you need dt: in fact dx = 2/(1 + t^2) * dt

[barren jewel]

Does someone know how to find an equation for this graph(like y=2x+5 or smth)

[hidden lagoon]

It’s a sideways cubic. Look at it at a 90 degree angle

[barren jewel]

Yea

I meaning smth like y=x^2

[hidden lagoon]

Write it like you’d write a normal cubic, only flip the x’s and y’s

[barren jewel]

They don’t look the same

[hushed sphinx]

You'll need to move and scale it.

[barren jewel]

Like y^3+1

[willow skiff]

that would be up by 1, yes

[hushed sphinx]

Right by 1.

[willow skiff]

Can you read off the coordinates of the point of inflection (the part where the tangent is vertical)?

Oh wait

[barren jewel]

I’ll make a table

[willow skiff]

x = y^3 + 1 ah

[hidden lagoon]

the normal cubic function is this flipped over the line y=x, so you can use it for reference

[barren jewel]

Here is the table

[hidden lagoon]

how is this going to help you?

[barren jewel]

I have no idea

[willow skiff]

it probably doesn't help unless you want to substitute your points into x = a(y - b)^3 + c

[barren jewel]

I can try that option, but I don’t know how…

[willow skiff]

For example, (x, y) = (-2, -1.63) and this is an approximation ofc

gives -2 = a((-1.63) - b)^3 + c

ah shit this isn't going to be linear

it doesn't work unlike with other functions

[barren jewel]

I can just solve for the variables. Right?

[hidden lagoon]

you can just find them off the graph