precalculus

[whole void]

why?

what

i have no idea what u r saying

use this then

[white rapids]

Is there a certain rule

Where any cubic is symmetric and any quartic is not

[winter comet]

symmetric about what is important

[white rapids]

Ok ok

So if we're looking at quartics

[winter comet]

i would say no, because x^3 + x for instance is not symmetric anymore

[whole void]

can u pls actually answer this

if u want to get the problem thats all u need to know

[white rapids]

Whether x is going to negative infinity or positive, y is always going to be infinity, & for cubics it's going to both y infinity and negative infinity

In quartics, its never gonna reflect the negative y

In cubics it does

[winter comet]

when you reflect a point about another point, you just go the same distance away from the point in the opposite position. A reflected about B is C

[white rapids]

I guess like that ye

[whole void]

oy vey

[whole void]

still doesnt answer this

@white rapids

[white rapids]

Well what do you want me to say

[whole void]

i want u to answer it

[white rapids]

reflecting off the y axis

[winter comet]

if he doesn't know how to answer, how should he answer 💀

[whole void]

can u answer then

[winter comet]

it's because the every point on x^4 - 4 on the left side of x=0 is not rotated about the point (0,-4) 180 degrees :l

honestly i don't really know what you want as an answer either lol

[white rapids]

I dont get hockeydude

[winter comet]

basically, because it doesn't follow the definition 💀

I aint a proof guy

it simply isn't

lol

[whole void]

the point (1, -3) lies on the graph of f(x) = x^4 - 4 but (-1, -5) (the reflection of (1, 3)) isnt

thats all it is

so its not symmetric about the point

[winter comet]

and thats true for any pair of (x,y) value given by the function

but an even better thing than saying what its not

is saying what it is :D

[whole void]

wdym?

[white rapids]

Exactly

[whole void]

bruh

ofc u say that

[white rapids]

You straight up gave an definition from the internet

And i used it to explain my reasoning

[winter comet]

i mean if you have an (x,y) point, an even function will never give another (-x,-y) point

where x and y are constants btw

eh i'm still not making much sense

[white rapids]

I'll take note of this

[winter comet]

actually i was rotating around 0,0 there

[whole void]

nope i never consulted the internet except to type in google notes to create that image

[winter comet]

don't

💀

its kind of wrong

💀

[whole void]

reasoning

[viscid thistle]

What are you guys even saying

[winter comet]

idk bruh

[whole void]

yeah i think it is but one sec

[viscid thistle]

._.

[winter comet]

no i know it is

[white rapids]

Alright

[winter comet]

its not what i was trying to say 💀

just like

giving an example where it is not true

is not a great reason for saying its not true

even tho it does prove its not true in all cases

its better to make a general statement

and you know whats even better

[whole void]

there isnt a general statement to be made

what general statement?

[viscid thistle]

yeah

[winter comet]

not talking about what it isn't 💀

[whole void]

?

[winter comet]

you gave an example with a specific point

[whole void]

exactly, one example is enough to prove something isnt true

[winter comet]

sure, but it isn't really a reason it isn't true

it just proves its not true

[whole void]

so whats the reason then?

[winter comet]

a generalization isn't really a reason either, but at least its a rule that you can follow

[winter comet]

i'd have to think about it 💀

[white rapids]

Uh so

[winter comet]

its not a fun question and it doesn't really help anyway

[white rapids]

What can i conclude about this

[winter comet]

because we're talking about what it isn't instead of what it is

[viscid thistle]

@winter comet What did he ask

[whole void]

theres not rlly, because there is a point on the graph that is symmetric about (0, -4)

[white rapids]

Or is this sill going on

[winter comet]

if you're rotating a point A about another point B, then point A will be on the opposite side of point B, and will be the same distance away from point B

[whole void]

bruh i didnt even use the internet why did u accuse me of that

[winter comet]

there is a general rule

[viscid thistle]

So origin symmetry?

[winter comet]

there has to be

[winter comet]

yea 💀

[whole void]

oh actually i was slightly more precise than the internet

[winter comet]

math like this is defined, not wishy washy

[white rapids]

So like if (x,y) then (-x,-y)

[winter comet]

nah nah ignore that

💀

i was rotating about the origin but its not true if you aren't

basically to rotate around a point, it has to be the same distance away in the opposite direction

[whole void]

what needs further explanation

[whole void]

no thats to reflect

[white rapids]

Ahh ok alright

[winter comet]

what

[white rapids]

Thanks for the help hockey and viper

[whole void]

?

[lusty harness]

this is probably a dumb question but if i wanted to find the angle elevation of the sun, which angle should i use ?

[winter comet]

rotating 180 degrees is reflecting

about a point^*

[whole void]

yeah u said to rotate around a point is to do that

thats to reflect

[whole void]

i can rotate a point 37 degrees and this wont be true

[winter comet]

yea i shoulda said reflect u right

[whole void]

@winter comet

[winter comet]

i was specificaly thinking rotating 180 degrees 😂

[winter comet]

idk you tell me lol

oh

i mean

the thing that you proved was not true wasn't a reason or a rule as to why it wasn't true, it just proved it wasn't true

which is ok but doesn't help as much

doesnt rly matter now tho

[whole void]

u dont rlly prove something isnt true u just disprove

but here is a slightly more formal way

translate both the supposed point of symmetry and the function up by four

then f(x) = x^4 is an even function and wont be symmetric about the point we care about, now (0, 0)

[winter comet]

proof by contradiction vs proof by induction

[whole void]

sure proof by contradiction but thats not rlly applicable

[whole void]

this works

[winter comet]

yea

[winter comet]

exactly, you did a proof by contradiction

which is ok but i just thought a general rule was better

but i couldnt come up with anything so

🤣

[whole void]

i mean for rigorous math its completely fine if u just show theres a counterexample

but to prove something true

[lusty epoch]

does anybody know good resources to self learn precalculus

[nova obsidian]

Did I do this right?

Question in first image^

[white elbow]

No I think

h-¹(x)=1
x=h(1)
x=4

[obtuse nexus]

isn’t h(x)^(-1) equal to 1/h(x)?

If it is, then 1/h(x) = 1 => h(x) = 1 => -12x + 16 = 1

[crude solstice]

Nah

Well the way u wrote it maybe but the way its written in the question means its the functional inverse

[obtuse nexus]

Oh, I see

Thanks

[harsh field]

Question

[white elbow]

Answer

[harsh field]

Question

Ive tried utilizing the feature to "help me solve this" but the answer only asks you to get points for the equation w/ o the vertical transformation and doesn't solicit you to provide points for the full function.

I've put the points on the right into a graphing program and the points are true. .... I'm at a loss

[white elbow]

( , )

[harsh field]

all comma's are in place.

[white elbow]

Parentheses

[harsh field]

they're there as well

In the screen, yes, they are absent, however..... I have the window open and currently have attempted the same numerical answers w/ parenthesis.

[white elbow]

Okay then sorry idk

[north nebula]

Side explanation is wrong?

Differentiation of|x|

[elfin cargo]

It is correct

[north nebula]

What

Huh

|x|/x is not wrong?

[elfin cargo]

$\frac{d}{dx}|x|$ can be $\frac{x}{|x|}$ or $\frac{|x|}{x}$

[north nebula]

I am asking about right side explanation

[obsidian monolith]

Closer

[north nebula]

Really?

[elfin cargo]

Yeah

derivative of |x| is 1 if x>0, -1 if x<0 and undefined if x = 0

so both are correct

[solar olive]

If u want a funny way to derive this, try |x| = sqrt(x^2) and differentiate that

With chain rule, it becomes 1/2sqrt(x^2) * 2x
= x/sqrt(x^2)
= x/|x|

[north nebula]

.close

[white elbow]

.reopen

[pallid valve]

bro is too smart for harvard

[gritty dirge]

I have a bit of trouble with this

Can anyone help?

[winter comet]

what exactly do you need help with?

thats literally the solution 💀

[gritty dirge]

I know

I don’t know it got to there

[winter comet]

it did a u substitution

u = 2-e^x
du = -e^x dx

[winter comet]

i don't know what you understand and what you don't

[gritty dirge]

Yeah I understand that substitution

[winter comet]

ok

[gritty dirge]

The only thing I don’t understand was how ln3 into -1

[winter comet]

you understand that they changed the bounds

[gritty dirge]

No I don’t

[winter comet]

u = 2 - e^x, so they changed the bounds: x = ln(3) changes to u = 2 - e^(ln(3)) = 2 - 3 = -1

[gritty dirge]

Ohh alright

[winter comet]

and they did it witht he lower bound as well

[gritty dirge]

Now I get it, this is the only problem I had in integration, but anyway thanks

[winter comet]

yea

with u sub you can either change the bounds or substitute the function back in after finding antiderivative

[gritty dirge]

Yeah I get that, it’s just my crappy school decided to teach this at the last 2 sessions

Well thanks for your time

[winter comet]

precalc?

[gritty dirge]

No

Fundamental theorem of integration

[winter comet]

o

[gritty dirge]

Yeah but there is a ton of factors for this years math lessons, since the recent crises the country has been the government published changes to the education curriculum, for example, in my Grade, for only this school year, we do not study inverse, irrational, and trigonometric functions, we also don’t study Conics and Logic.

[winter comet]

bruh

then what do you study

well integrals ig lol

[gritty dirge]

The only Chapters we studied this year were space, exp and natural logarithm, numerical sequences, direct plane similitudes and complex form in transformations, complex numbers, exp and ln functions

Also for some reason translation was removed from the curriculum

Transformations we dealt with was sim, rotation and dilation, or composite. Sometimes sequences gets mixed in with too

[gritty dirge]

I forgot to mention probabilities and counting

[winter comet]

oh nice

what are direct plane similitudes?

[gritty dirge]

Its a study of when a shape changes it’s size and rotates by an angle

It’s a little more complicated than that though

[gritty dirge]

Yeah not so much, because students applying for STEM fields have to study what they are not taught

[plain ice]

If i plan on taking precalculus this summer and taking ap calc ab this school year, should i take ap precalculus or just precaculus this summer
i wont take the ap test if i do precal tho

[willow skiff]

just precalculus is fine

[plain ice]

thanks

[willow skiff]

np

[untold sparrow]

help

[winter comet]

can't, don't know what it is 💀

[untold sparrow]

ok

@winter comet

help

is 6-7 right? i dont get question 8

[wicked estuary]

For what domain of the x axis is all the y values of the graph less than 8

Just looking at it it would be like x>3 or x>4

You need the graph equation I think to find the exact number

[hushed sphinx]

It looks like h(2) is probably supposed to be 8, but the point where the graph passes up beyond 8 is at 3-and-a-bit and not really possible to read off more exactly than that.

Answering "1" to question 6 is clearly wrong; the graph is clear enough that there are several x where h(x)=1.

Question 7 doesn't ask "how many values", but "what values", so there my best answer would be "minus two-and-a-bit".

On the other hand, if the function to the left of x=3 is supposed to be a quartic polynomial with roots at -2 and 0 and 0 and 3, then the local maximum between 0 and 3 is actually not at x=2, but x=2.1472 (thanks, Wolfram Alpha), but that's definitely not "based on the information provided by the graph".

Conclusion: The creator of the problem is a moron.

[narrow briar]

Hi!

Does anyone know what did I wrong?

[winter comet]

W (ln(2)e^ln(2)) = ln(2), not 2

[narrow briar]

Ohhhh thank you so much

What a silly mistake

[winter comet]

lol

[uncut mulch]

<@&268886789983436800> adverting

[short sorrel]

@vale oak dont post unsolicited ads

[winter comet]

:l

[bitter wedge]

i need helpbyall

why is there and s and a t

[willow skiff]

The 47th term and the sum to 25 terms

[bitter wedge]

ohhh

wait thay makes sense thank you :3

how do i find the sum to 25 terms?

[gloomy bluff]

@bitter wedge , for no. 4 you had a much easier way of doing it

(161-25)/8+1=18

[gloomy bluff]

(t_25+t_1)*25/2

[bitter wedge]

thank you fr

[willow skiff]

It's n/2 (a + (a + (n - 1)d)) in general

That's why you have 2a

[bitter wedge]

how does this look?

what is the formula for question 7?

[fringe ridge]

arithmetic progression

3, 3+16, 3+16+16...

[subtle pond]

the one I know is $\frac{n}{2}(a+l)$

[obsidian monolith]

菜月

[subtle pond]

where a is the first term, l is the last term, and n is the number of the terms you're summing

so you would have to calculate n in this case

[bitter wedge]

n is 19 i think

i got 2793 for my final answer

i have 30 questions to get done for my assignment yall im cooked

[fringe ridge]

i got 2739

[subtle pond]

I got 2793 too

could you write this in the form of variables?

[fringe ridge]

wait

[fringe ridge]

ans 2793

my mistake

[subtle pond]

please @fringe ridge

[fringe ridge]

Im having trouble with arithmetic...

[subtle pond]

calculator

[fringe ridge]

in my country calculators are not allowed on the exam

[subtle pond]

same

I use it at home to make my life easier

[gloomy bluff]

For no 5, why is it negative?

[gloomy bluff]

The common difference is +8? Not -7?

[subtle pond]

yeah, it's wrong

@bitter wedge no. 5(a) is wrong

same with (b)

[midnight harness]

Hey guys I need help understanding this question, ive tried looking over my lesson and notes but I just cant get the grasp of it

[viscid thistle]

what on earth is math💀

[viscid thistle]

the language of the universe

teach me about.....

number theory

🥺👉👈

#book-recommendations there's lots of experts there who knows number theory lol...

i only know the types of numbers i prefer not to get too much in depth since i dont need it btw this should be in #No-access

...

I don't have enough mental stability to read a book lmao

[viscid thistle]

you can check out lectures in YouTube

Anyway you will be forced soon to read a book

and yea don't worry what book will you read (ofc as long as it's the topic you needed)

but the books will be limited lol

you can't be choosy

I have subscription for this entire session in a coaching, but their syllabus doesn't have to cover number theory

subscription in what?

online coaching

i mean what does it cover?

they're preparing me for a different exam

?

[viscid thistle]

..

[viscid thistle]

syllabus of jee advanced

ohh

bruh

Jee

which doesn't include number theory

you should fucking prepare

ig so...

i know someone who ranked #64 in JEE

i dont remember but it's below #100

[viscid thistle]

someone whom you know?

[viscid thistle]

nope

[frail hazel]

$\frac{n}{2}(2a+(n-1)d)$ aswell

[obsidian monolith]

Mustafa مصطفى

[frail hazel]

if you know the number of terms but dont know the last term

[gloomy bluff]

I don't understand this

Isn't |(x - x_0) + I(y - y_0)| = |(x + iy) - (x_0 + iy_0)| ?

[random yoke]

Yes

Although if a=b then a<=b is also true

Idk why they wrote it there though

[gloomy bluff]

That's why

[winter comet]

why

probably context 💀

[random yoke]

Maybe something with triangle inequality but they messed up the absolute value signs

[gloomy bluff]

Well I guess I'll continue reading now

[gloomy bluff]

how do i prove (10) and (13)

It tells us to try and prove (10) and (13) and I have no idea where to start

[winter comet]

i'm actually curious how one would prove that 💀

[empty owl]

For 10
lim z→z0 [c × f(z)]

Since lim z→z0 c × lim z→z0 f(z), (Product rule)
Then = c × lim z→z0 f(z), (Limit of a constant equals constant)

Therefore c lim z→z0 f(z)

[gloomy bluff]

it works, but the type of proofs they use use epsilon and delta

this is how they proved (11)

I'm looking for a way to prove (10) and (13) using their method

[rigid cove]

Epsilon delta

[rigid cove]

Start from the definition?

[shut monolith]

alternatively you can prove a lot of the properties regarding limits of functions very efficiently using analogous properties regarding limits of sequences

[rigid cove]

The way I prefer is to just prove multiplication and addition are continuous

[dull radish]

learnt about finding the range of a function by inverting the function, but how exactly do i get it to work in the case of : x^4+1/x^2 ?

[slender vault]

Get the domain first

Then invert

[dull radish]

care to explain wdym by this?

oh

ok

[slender vault]

Domain like the possible values of x

[dull radish]

alright lemme try it

ok so the domain is R-{0} isnt it?

now how do i proceed?

[slender vault]

For this one you can just invert and substitute

Then take derivative to find critical points

Put parentheses on it coz it might be different

[dull radish]

im feeling a bit lost here but can you like show it in steps?

this has been a major doubt for me throughout functions

[woven finch]

is it [0,inf]?

[dull radish]

unfortunately no, that is what even i got, but the answers say it's [2,inf)

[slender vault]

Ok

That makes sense

[dull radish]

care to explain?

[slender vault]

Take it as x^2 + (1/x^2)

Substitute y as x^2

Find the derivative

[dull radish]

with respect to?

[slender vault]

Y

[dull radish]

ok

[slender vault]

Substitute in original equation

You should get 2

That will be the min value

The max value is just lim (y approaches inf) --> inf

[dull radish]

so i get 1-1/y^2 as the derivate i should sub that in for y+1/y am i right?

[slender vault]

Yup

[dull radish]

and find the domain for that?

or..?

[slender vault]

You'll get the critical point

After you substitute

Set it to zero

You'll get y=1

Then substitute in y + 1/y

You'll get 2

That'll be min value

[dull radish]

hold up

won't you get 4 values of y when you sub it in?

considering there is no diff in +-0 won't it be 3 different values?

[slender vault]

Set 1-1/y^2 to zero

[dull radish]

ohhh

ok

i was setting y+1/y as zero

mb

[slender vault]

[dull radish]

ok i did get the answer for this but is there any particular algorithm to apply this to every question?

because i did understand the method

but not the reason to do so

[slender vault]

There is no algorithm

[dull radish]

oh

[slender vault]

You'll apply them through practice is what I would say

[dull radish]

any particular trick on how to spot which questions to use it on?

[woven finch]

but why it can't be 0?

[dull radish]

because differentiating was just quite out of the blue

[slender vault]

You get undefined

[slender vault]

It's just finding maxima and minima through double differentiating and substituting it in original equation

[dull radish]

oh shit so its basically a glorified horizontal line test

[slender vault]

One on one from y to x ig

[dull radish]

well so uh

can i use this on any function whatsoever?

holy shit ok it does work

@slender vault tysm for the point of view of a maxima and minima it made this wayyy easier

[slender vault]

Ok alright

You could've pinged me earlier too

[dull radish]

nono i just checked in 2 different questions

it did work

so i needed to thank you this saved me from such a headache

[slender vault]

I mean it should work for all functions

Coz the concept is just "maxima and minima of a FUNCTION"

[dull radish]

yeah but i didnt really understand the question when it asked for the range all i knew was range meant y axis

[dull radish]

nah nah i had a few things unclear thanks tho

[slender vault]

That's correct too lol

[slender vault]

[dull radish]

yes but it doesnt offer allat much of an intuitive understanding, atleast for me

[slender vault]

"intuitive" ic ic

[dull radish]

yeah lmao i gotta 'feel' the topic so i know i get it

idk man thanks a lot anyways

[slender vault]

Goodluck

[viscid thistle]

How do you motivate yourself to study

[slender vault]

Just start studying

[viscid thistle]

Is it

That simple

[slender vault]

Yes

Just start studying

[viscid thistle]

I get distracted when I try to study

What to do about that?

[slender vault]

Put up something to not get distracted

[viscid thistle]

Something like?

[slender vault]

Like a wallpaper or smth

[slender vault]

Just remind yourself what you're doing

[viscid thistle]

Yeah..

I might start studying

If I hve a good friend

Who studies very much as well

[slender vault]

[slender vault]

Which grade?

[viscid thistle]

12th

[slender vault]

You have a lot of people in this cord

[viscid thistle]

Calculus started a month ago

[slender vault]

It doesn't matter the grade

[viscid thistle]

And I am rlly struggling to finish just relations and functions

[slender vault]

You ask in help channels or here

[viscid thistle]

Haven't started inverse trigonometry yet and in the classes they are already teacher limits and differentiability

[viscid thistle]

I don't know I am quite new here

[slender vault]

You'll need inverse in physics later

[viscid thistle]

Oh..

Are you in clg rn?

[slender vault]

They are basics chill

Dw

You'll probably be using it all the time

[viscid thistle]

Yeah...

[slender vault]

Goodluck

[viscid thistle]

Yeahh thankss

[slender vault]

[gloomy bluff]

can someone please explain this to me

How did they get | z0 + z + z0 | >= |z0| - |z - z0| ?

and help with this one too please

Isn't | z^2 - z0^2 | = | z - z0 | | z + z0 |?

And how did they do | z^2 - z0^2 | < | z - z0 + 2z0 | ??

I'm so confused someone plssss help

[main path]

This is just another form of the triangle inequality (sometimes called reverse triangle inequality: $\left|a + b \right| \geq \left| |a| - |b| \right|$). As for $\left|z^2 - {z_0}^2 \right| = \left|z - z_0 \right| \left|z + z_0 \right|$, they probably meant to put equal instead, but the rest is correct. This becomes: $\left|z^2 - {z_0}^2 \right| = \left|z - z_0 \right| \left|z + z_0 \right| < \left|z + z_0 \right| = \left|z - z_0 + 2z_0 \right|$ then apply the standard triangle inequality ($z + z_0 = z - z_0 + 2z_0$, they just added an extra $z_0$ and subtracted one so the result didn't change, and we are given that $\left|z - z_0 \right| < 1$).

[obsidian monolith]

PowerUp

[gloomy bluff]

help pls what does it mean????

[gloomy bluff]

Thanks

[gloomy bluff]

Ty

It introduces us to the partial derivative symbol as boundary, and I just found out from Google that it is a partial derivative

But I don't know what is a partial derivative

Wait nvm

I just asked google and turns out its not that bad

But the way they defined u(x,y) and v(x,y) should be real values, so how would c2 be orthogonal to c1??

this is how they defined u(x,y) and v(x,y)

[digital aspen]

is this precalculus?

[gloomy bluff]

Idk I just send my complex analysis stuff here

They showed a graph but it doesn't make sense at all

[unique wolf]

What is the formula for permutation if the objects repeat? Like say, number of ways to arrange BANANA. Since A and N repeat, what would the formula be? I know it's not 6P6 =720 because the letters would be repeating

[hushed kestrel]

Factorial of the number of objects, then divide that by the factorials of the sizes of each set of duplicates

For your example that would be ||6! / (3! x 2!) = 60 since there are 3 As and 2 Ns||

[unique wolf]

There's 3 As

[hushed kestrel]

Yeah fixed

[unique wolf]

So, that only works if within the arrangement there are repitions right?

[hushed kestrel]

If there are no repetitions you just don't divide by anything

[unique wolf]

So for arranging MANCHESTER, what would that be

Hm, there is a reptilian for E

Repetition*

[hushed kestrel]

Orange would just be 6! = 720

[unique wolf]

Ah I see.

[unique wolf]

Then for Manchester, it would be 10!/2!?

[hushed kestrel]

Yep

[unique wolf]

Oh ok thanks

[unique wolf]

One more thing, for repetitions infinitely, like arranging letters A, B, and C. The formula would be n^r? For A, B, and C, it would be 3^3?

[hushed kestrel]

So like AAA, AAB, AAC etc? Yeah that would be 3^3 since each of the 3 positions can have 3 different letters

[unique wolf]

Yeah. Ok thank you

[lusty harness]

i have a logical problem which is kinda related to math but I don't know how to do it, can anyone help

[winter comet]

can't help you if we don't know exactly what the problem is :l

[heady pendant]

E

[white elbow]

Logic ≈ Math

[gloomy bluff]

Where should I put my complex analysis stuff?

[viscid thistle]

#real-complex-analysis

[lusty harness]

tried solving for theta, arctan(4/0) ?

[uncut mulch]

consider plotting the complex number on the argand plane

and it should be clear what the argument will be

[lusty harness]

oh yeah

i understand

[willow skiff]

it only works to the nearest pi radians, cause that's the period of tan

[brittle geode]

hi, can someone help me with this? idk that im doing wrong

[willow skiff]

your leading coefficient is not 3 (for x^3) but 1

[brittle geode]

ty

[white elbow]

No problem keep asking

[gentle aspen]

how to find critical and saddle point for

[summer ruin]

find partial derivatives and set them equal to zero, also #multivariable-calculus

[sour phoenix]

Is this question correct???

Since there are no limits on the integral

I tried numerous times but I think that i need the integral to be definite for me to proceed.

Any idea please??

[viscid thistle]

This isn’t precalc, post in #calculus or #competition-math ig

[boreal patrol]

Looks like IBP to me ... what have you tried?

[willow skiff]

yeah reduction formula blah blah

[white elbow]

Wow which country teach this in pre calculus

[sour phoenix]

Intégration by part ar the beginning then I wanted to substitute thé limits for the outcome but there aren't any

[jovial hare]

How to find b?

[hushed sphinx]

The limit will be finite unless you can make the denominator go to 0...

[jovial hare]

So b - x^2 = 0 => b = 0 ?

[hushed sphinx]

That's not quite the symbolism I'd have chosen, but b=0 is indeed the only choice that has a chance of working.

[jovial hare]

How can I write it better

[hushed sphinx]

b-x² goes to b when x -> 0, so if we want it to go to 0, b must be 0.

[wintry slate]

someone help me with this

[lethal gull]

For using trapeziums to estimate the area under a curve, how can you tell if its an overestimate or underestimate?

[willow skiff]

has to do with the concavity of the function

when the function is concave down, like on the left half, then it will be an underestimate
concave up will produce an overestimate

[lethal gull]

ok so log x would cause an underestimate and x^2 an overestimate?

[willow skiff]

yeah

[lethal gull]

sweet thanks

[willow skiff]

no worries that's why we use Simpson's rule etc

so that we have a method that respects the concavity

[lethal gull]

dont think im too familiar with that, the spec for an exam im doing just features this method so far

though thats pretty interesting

[wintry slate]

yo help me with this

[willow skiff]

yeah it would be pretty insane for high school stuff to cover Simpson's

[lethal gull]

Ironically it's on my next year's course

[willow skiff]

interesting

[lethal gull]

For what in the UK is called Further Maths

[willow skiff]

oh wait you must do Edexcel then

yeah Edexcel does some stuff comparable to first-year uni, but not too much in depth luckily

[lethal gull]

I know it's on Edexcel and I think it's on my board CCEA, but I would need to check

[willow skiff]

just the range of options is astounding compared to Cambridge

yeah totally forgot

about UK

[lethal gull]

I'm in NI so our board is weird

[lethal gull]

Does Cambridge have it's own exam board?

[willow skiff]

yes

[lethal gull]

Is that OCR?

[willow skiff]

top of the morning to you wrong country

[willow skiff]

no that's a different board

[lethal gull]

Right country lol

[lethal gull]

Ah I see thanks

[willow skiff]

well Cambridge is really popular internationally

as a board

[willow skiff]

just saying I love your accent

I had a teacher from NI in secondary and her name was Ms Henderson

it just goes up and down a lot

[lethal gull]

The accents here vary so much lol, but maybe that's cause I'm from here I can say so

[willow skiff]

oh true that makes sense too

[lethal gull]

I'm from like a small town so I didn't get a strong city one which I think you're describing or a country one either ahaha

Mines is more neutral, but still Irish sounding enough lol

Thanks though!

[willow skiff]

no worries

[viscid thistle]

how to get to know whether to substitute do by parts or partisl fractiojs?

[summer ruin]

experience

[random yoke]

Divine guidance

[winter comet]

brain

brain helps

[viscid thistle]

ok

[slender vault]

Real

(I hope so)

[white elbow]

Brain helps those who daydream

[echo axle]

not sure what chat this would be, but why doesn't this sum have an upper bound (multinomial equation)?

or the product

[sharp salmon]

Should I study precalculus on my own and take algebra 2 H at school? 🤔

[vapid plaza]

it’s another way to specify the things you are summing over, for example $\sum_{i=1}^n \text{(sth)}$ can also be written as $\sum_{1 \leq i \leq n} \text{(sth)}$

[obsidian monolith]

elon mask

[solar olive]

i think theyre asking the sum part, not the product part

[obsidian monolith]

impract1cal

[vapid plaza]

Yeah well the idea is the same

You’re summing over all possible choices $k_1, k_2, \dots, k_m$ (from context, they should be nonnegative integers) such that $k_1 + k_2 + \dots + k_m = n$

[obsidian monolith]

elon mask

[solar olive]

Ngl i dont get it

[slender vault]

I ain't even sure this is precalculus

[white elbow]

It is if it's in this channel

[slender vault]

I guess so

I hope so

Lol

[untold sparrow]

bro was right

[sharp salmon]

Lmaooo

[calm tiger]

can someone help me with pre calc

[random yoke]

Only if you post your question

[calm tiger]

k

[fringe yarrow]

excuse me yall

look at this

how in gods grace is this related:

also

for synthestic divison, can i flip?(like multiplying)

meaning that (x^3+x^2+3) * (1/x+4) instead of dividing?

[slender vault]

Yes, long division or synthetic division

Anything that's comfortable

But it's like really really long

Is this precalculus??

I thought #prealg-and-algebra exists

[calm tiger]

i know in highschool when i did trig/precalc we did it

so maybe

[lusty harness]

confused on how this is wrong, both of REF and RREF have the diagonal of 1s

[hushed sphinx]

Can you double-check your definitions of REF and RREF to see if they actually require that? (That would be quite strange and unusual definitions).

[lusty harness]

oh right, but on the 2nd to bottom row, would it be no variable = 1? I'm confused

[hushed sphinx]

Can you show the definition you think this matrix doesn't satisfy?

(Row 3 has a perfectly good leading "1" in column 4, and all other entries in that column are zeroes like they should be for RREF).

[lusty harness]

I just assumed the diagonals were all 1 because all the examples ive seen had that

[hushed sphinx]

I really hope you have an actual definition you can consult instead of attempting to generalize from examples.

(And by the way, this strongly belongs in #linear-algebra rather than here).

[lusty harness]

well I am learning it in pre calculus so I figured that it goes here

this math seems a bit shallow to be in linear algebra

[hushed sphinx]

It is, nevertheless.

[fringe yarrow]

well ye it is. its in my precalculus textbook for some reason

[echo axle]

got it, thx

[echo axle]

I don't think it is, but I wasn't sure where to put it

[slender vault]

Alright alright

[white elbow]

No problem

[fringe yarrow]

excuse me everyone

what would be the standard formula for synthetic divison? I can't seem to find this online and my textbook is as useless as it can be

also

how is te rational root theorom reltaed

im trying to find integral zeros for a polynomial number

[summer ruin]

look at wikipedia

[fringe yarrow]

?

how so

[summer ruin]

have you tried looking up both of these on wikipedia?

[fringe yarrow]

well not yet

but in math, wikipedia isnt much of help

[summer ruin]

try it

[fringe yarrow]

ok

[exotic granite]

hb yt ;-; ?

[white rapids]

Guys if I were to expand 4 log(3m)
Would it be 4log (3) + log(m) or 4log (3) + 4log(m)

I did a quiz so I did 4log(3) + 4log(m) since 4 is being multiplied with everything inside the () is this right

[lusty harness]

how do i do this?

[chrome ether]

what you put down is correct, 4log(3m)=4(log(3)+log(m))=4log(3)+4log(m)

[viscid thistle]

Hey, can anyone help with calculus and precalculus topics?

I'll be taking advance mathematics classes soon but I want to begin learning before going into the classes

[hushed sphinx]

Nobody will be able to help you unless you ask some questions about whatever it is that confuses you.

[viscid thistle]

I want to know that where should I begin from

Like what topics should I focus on

[uncut mulch]

algebra, functions, trig, exponentials,logs

[viscid thistle]

Thank you

Any sources that you would like to recommend?

[willow skiff]

https://tutorial.math.lamar.edu/ - Paul's Math Notes

and Stewart's Calculus, the textbook pdf should be somewhere online

if possible the early transcendentals version

[viscid thistle]

Perfect

Thank you!

[willow skiff]

no worries!

[daring tapir]

Piracy hmmmm

[willow skiff]

I'm being real with them

[white rapids]

Alright ty for the clarification

[proven night]

hello, guys

i have just solved the equation 4^x = 1/x

And my answer is W(ln 4)/ln 4

wolfram alpha says the same, but it also says that this answer is just 1/2. But i solved the equation using W Lambert Function and I cannot compute it on paper without computer

So, can i just leave W(ln 4)/ln 4 as my answer or did i do something wrong and the equation can be solved without this function and the answer will be just 1/2 then

[vapid plaza]

It can be “solved” to obtain the answer 1/2, but not with a fair bit of hopeful guessing

[obsidian monolith]

blast

[flint belfry]

the compiler thing broke :(

[flint belfry]

easiest way to determine without guessing is by graphing both functions and finding where they intersect

where the x coordinate will be equal to 1/2

[random yoke]

How are you gonna graph it accurately enough to read off the coordinates without a calculator?

[shadow summit]

Which function?

[solar olive]

i think they meant how to simplify a certain branch that gives W(ln 4)/ ln 4 = 1/2

[proven night]

So

Can i just leave my answer "as is"?. I mean, W(ln 4)/ln 4

[bitter marsh]

hi

[white elbow]

Hello

[slender vault]

Hi

[white elbow]

Hello

[flint belfry]

you dont necessarily need a calculator though

personally i could fairly easily do it

[random yoke]

Right in this case it's not too difficult because it's 1/2 which is quite easy to read

But you don't know that beforehand

[flint belfry]

let me explain my process rq

what you would do is make a table of both functions

for every value of x in intervals of, for example, 1/2, which is what i usually do

ill send a photo rq

its not right side up idk why

the values where both functions produce the same output is the solution for our equation

sorry if my handwriting is bad

[random yoke]

That's just systematic guessing

[flint belfry]

how is that guessing

i am plotting both functions on a table

[random yoke]

You don't know it's gonna be an integer multiple of 1/2

What if it's 4/3

[random yoke]

You're trying a bunch of values until you find the right one

[harsh field]

hello

[white elbow]

Hello

[solar olive]

i guess it depends on the answer form?

1/2 is clearly a solution, but if u dont want to check-and-guess, u would ahve to check brances of the lambert W function and see which one corresponds to 1/2

i dunno how to do that without a calculator, but this feels like those problems with cubic formula where it just spits results that are technically correct, but are useless to use in practice (they can result in nasty radicals even though by RRT, they can turn out to be really simple)

[viscid thistle]

How is that not guessing?

You choose points to plot your function on without knowing at which point it’ll give the same answer

[slender vault]

[white elbow]

[brittle geode]

hi, can someone help me with this problem

[willow skiff]

,w (6x^4-3x^3+29x^2) / (3x^2+13) quotient and remainder

[obsidian monolith]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by sooouth.

[willow skiff]

you have a small mistake, you should be doing 3x^2 + 13x - (3x^2 + 13) at the very end

ah one more little thing, you have a minus in front of your bracket, so it's -(-13x), double minus

so you should have 3x^2 + 13x and not 3x^2 - 13x right there

that gives your remainder as 13x - 13

[brittle geode]

okay

ty 🙂

[eager remnant]

How does this make sense?

[summer ruin]

it doesn't, it's wrong

[eager remnant]

Bruh my teacher is on something

[summer ruin]

e. g. d) should be x = 2t, y = 4t+3

[willow skiff]

exactly

[viscid thistle]

u use y = mx + b? (still on algebra just testing out)

[viscid thistle]

this is polynomial expression right?

[brittle geode]

yes

[viscid thistle]

looks hard i still don't know how to do one lol...

I've only done rational expressions. They're quite similar

the hard part for me is i still don't know trig

[winter comet]

eh

you have a parametric function in that form but i wouldn't really say you "use it"

with the parametric equations you want to get x as a function of t and y as a function of t such that if you solve for x in terms of t and then plug it into the parametric function of y, you get the original function.
which they did incorrectly 💀

[viscid thistle]

need to clarify my doubts in #prealg-and-algebra

[winter comet]

is more of a precalc subject but uh ok if you want to move there 💀

[viscid thistle]

i really don't still know functions

so I'm fucked for now

[winter comet]

hmm

[viscid thistle]

i really need help in #prealg-and-algebra...

[winter comet]

functions and equations are very similar lol

[viscid thistle]

in programming term i know what a function is

[winter comet]

with functions you're just more worried about the input/output part ig

[winter comet]

oh

[viscid thistle]

yes like print()

but I'm still not ready for that

[winter comet]

yeah i mean uh

y = 4x + 3
and
f(x) = 4x + 3
essentially mean the same thing

f(x) is used for functions usually, y is used for "equations"

but they're very closely related

[winter comet]

its similar to that but in math you can graph functions so :l

XD

[viscid thistle]

yea..

[winter comet]

like

i don't actually know how to explain really

i don't feel theres much to functions 💀

[viscid thistle]

ohh

[burnt yarrow]

struggling here

so orignal problem

then i was following photomath but why do we divide by 18

[winter comet]

makes the numbers simpler, and cuz we can

[burnt yarrow]

so simplify? alright

[winter comet]

yeh

[lusty harness]

Don is pushing a barrel up a ramp that is 1.5 meters long. He is using a force of 534 newtons acting parallel to the surface of the ramp and the ramp is at an incline of 25° from the ground. How much work is he doing to push the barrel up the entire ramp? (round to nearest whole number)

I've got 726 as my answer, however, it states that it is wrong. Am I missing something?

[brittle geode]

w=fxd

and because of the 25°

i think you will have to multiplied it cos(25)

534x1.5 x cos(25)

[fast furnace]

y being fancy ig

[thorny forum]

does anyone know how to do differentiation

[fading monolith]

Yeah(?

[fading monolith]

Do you need help?

[thorny forum]

yes

like im not able to do it

[fading monolith]

Can you show it?

[thorny forum]

4. sin (tan–1 e power-x)

[daring tapir]

do you know how to write tan-1 in the form of sin-1

[fading monolith]

Use latex or a screenshot. That way I cant understand it

[thorny forum]

yes

[daring tapir]

well do that then

(follow what alex said too)

[thorny forum]

i did it

[fading monolith]

Derivative of tan^-1(x) its 1/(1+x^2) so by applying chain rule you get -e^(-x)/(1+e^(-2x)) cos(tan^-1(e^(-x)))

[thorny forum]

can u solve n send the pic

[fading monolith]

$\frac{-e^{-x}}{1+e^{-2x}} cos(tan^{-1}(e^{-x}))$

[obsidian monolith]

Alex

[thorny forum]

ohhkk thanks alex

[fading monolith]

No problem

[white elbow]

[hazy axle]

do i understand this right: derviation is when f'(x) is belove zero then f(x) will go down and above zero it will go up?

[chrome ether]

positive derivative, function is increasing

negative derivative, function is decreasing

yeah

[icy sparrow]

if the derivative is positive it means the slope of the tangent line is positive and therefore the function is increasing and if its negative its decreasing

[hazy axle]

right, what i thought thank u guys

[viscid thistle]

i like calculus

[gusty galleon]

Isn’t this meant for #calculus channel

Or do they teach this in pre calc

[brazen urchin]

https://youtu.be/5M2RWtD4EzI?si=ZvPvb0KyCqZG1T80

[winter comet]

its really a calc topic, but sometimes they teach calc in precalc liek why even bother calling it precalc at that point but yk 💀

[celest mango]

Guys is this legit

[shadow summit]

Nerd

[winter comet]

saysa youa

[shadow summit]

I have the displeasure of doing statistics in class.

[winter comet]

isn't calculus so much better than statistics 😮‍💨

come to think of it why is there no stats channel

[shadow summit]

Yes

[shadow summit]

There is

You just aren’t good enough.

[winter comet]

LOL

i meant in pre-uni

[shadow summit]

It’s cuz stats is dumb af

[winter comet]

fair

[shadow summit]

It’s literally just notation and plugging stuff into a calculator and some integration.

Ping me if a good calculus question shows up.

[lusty harness]

how do I know if I should be adding a vector or subtracting it once I am given 2 points?

[shadow summit]

#linear-algebra

[shadow summit]

Also there’s not enough information.

[lusty harness]

both of the points are in quadrant 1

should i still be talking here?

[shadow summit]

That doesn’t explain what you are trying to do.

[lusty harness]

oh right

rewrite it in component form

[viscid thistle]

Sentenced to #real-complex-analysis

[shadow summit]

Oh no, how absolutely terrible. Thank god it’s not #probability-statistics

[shadow summit]

Wdym?

[lusty harness]

im not sure what you are asking for

[shadow summit]

@lusty harness can you give an example of what you are trying to do?

[shadow summit]

,,\vec{CD}=D-C

[viscid thistle]

Try plotting it out on a graphing thing to gain a better intuition

[obsidian monolith]

TheLord26

[lusty harness]

like this?

[shadow summit]

Remember straight lines.

CD=D-C

[lusty harness]

and when would it be addition

or would it just not be

[shadow summit]

Try to think geometrically

If you add two vectors you have to move in both vectors directions.

When you subtract you move from one vector to another point.

[viscid thistle]

With proper scales 😭

[lusty harness]

not sure i understand

[shadow summit]

Do you know what “tip to tail” is?

[lusty harness]

yes

like move one vector to the back of the other

[shadow summit]

That’s vector addition

[lusty harness]

but how do you know if it is "tip to tail" with only points

and not the graph

[shadow summit]

Tip to tail is just vector addition.

[lusty harness]

is there a way to write it similar to this

[shadow summit]

Let’s call the black vector A, red vector B, and blue vector C.

C=A+B

As that is “tip to tail”

And you can rearrange that to find A=C-B

Do you understand this?

[lusty harness]

yea

[shadow summit]

Alright, hope this helps.

[lusty harness]

wait so the answer to my original question would be <-2,-3> ?

[white elbow]

[zealous ice]

Someone pre calc dm me please

[white elbow]

[willow skiff]

if there is a precalc

is there a postcalc

[white elbow]

Yes there

If it has multiple xyz variable

I've seen

[viscid thistle]

i was being sarcastic

[white elbow]

Oh okay I thought you were serious

[eager remnant]

Im confused about what the inequalities are for, are they part of the rectangular form?

[winter comet]

just stating the domain and range

[steel iron]

Hey y'all, I just started with parametric equations and I'm having difficulties with this question

[winter comet]

consider the t value it takes to get from one x value (9) to the other (3)

then see if it takes the same t to get from one y value (5) to the other (15)

[steep kayak]

hey im doing precalculus 12.. i cant seem to get this question right..

Q. Determine the equation of the transformed image after the transformations described are applied to the give graph.
a) The graphy of y=log(6(x-3)) is stretched horizontally about the y axis by a factor of 3 and translated 9 units left.

My answer:
y=log(6(x-3))
y=log(2(x-3)) (After 1st transformation)
y=log(2(x+6)) (After 2nd transformation)

Textbook answer:
y=log2x

[whole void]

is it log base 10? the notation is slightly confusing this way

or log base 6

[white elbow]

e

[ebon ermine]

what would (1-sinx)²-(1+sinx)² be? after opening the squares you get (1 - 2sin + sin²) - (1 + 2sin + sin²)

how would you complete that equation

[winter comet]

distribute

and combine like terms

[ebon ermine]

so (1 - 2sin + sin^2) - (1 + 2sin + sin^2)

[winter comet]

i meant distribute the negative

[ebon ermine]

[winter comet]

☠️

[ebon ermine]

which negative

one in the middle yea?

[winter comet]

yea

[ebon ermine]

wheres she going

[winter comet]

• (1+2sin(x) + sin^2(x))

oof

its -1 - 2sin(x) - sin^2(x)

[ebon ermine]

oh zamn

not -4sin^2?

[winter comet]

where did that come from

[ebon ermine]

internet

[winter comet]

🗿

you should get 1 - 2sin(x) + sin^2(x) - 1 - 2sin(x) - sin^2(x)

and then you can combine like terms

💀

[ebon ermine]

oh i see

cause in my mind what throws me off if the equation would look like this for some reason

(1 - 2sin(x) + sin^2(x)) - (1 - 2sin(x) - sin^2(x))

and it would make it different for some reason

guess not

[winter comet]

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

[ebon ermine]

wowza

[ebon ermine]

looks like -4sin

[winter comet]

yeah

[ebon ermine]

[surreal fjord]

Hello everyone,

I'm returning to college after a very long break for Computer Science. My math skills need significant improvement to handle the required Calculus I, II, and Linear Algebra courses.

Where I am from we have this thing called CEGEPs which are basically Pre-university programs after high school. So I decided to take these I guess you can call pre-university level math courses to get me ready for the Computer science math courses:

1. Differential Calculus 103

2. Integral Calculus 203

3. Linear Algebra and Vector Geometry 105

I honestly have no idea how different these courses are from the college level ones, but they require them prior to science programs. I'm starting with Differential Calculus this Fall and have only 1.5 months to prepare. Currently, I'm working through Khan Academy's Algebra basics. I also found Professor Leonard's precalculus videos, but they are a little too advanced for me for now.

The Differential Calculus course covers:

• Functions and Graphs

• Limits and Continuity

• Derivatives

• Elementary Functions

• Trigonometric Functions

• Inverse Trigonometric Functions

• Optimization and Function Analysis

• Solving Optimization Problems

Given my limited time and math foundation, I'd greatly appreciate any advice on how to go about this. What should I focus on? Should I grind through Khan Academy Algebra and Trigonometry courses before I take the precalculus one? Or should I work backwards from a more advanced course if needed?

Sorry for the long post and Thank you in advance for your guidance!

[sinful halo]

1.5 months is cooked

[sinful halo]

Focus on getting a strong algebra foundation

Khan academy precalculus imo does not prepare for actual calculus

It's more like a leisure activity

[winter comet]

wdym

[sinful halo]

Idek

[winter comet]

the first part is just algebra and trig recap, the second part is series and polar and matrices and vectors and stuff to help with calc 2 and multivariable and linear alg

it may not be so useful in calc 1 i guess

[sinful halo]

Low-key you only gotta worry about polar and series for calc 2

[winter comet]

right

but precalc gives an introduction for these

i would say yeah its mostly calc 2 and much less calc 1

the preparation for calc 1 is basically the algebra and trig and such

and then it gives some topics that are introductions for topics taught in future classes

basically

thats how i see it

but yeah its skippable imo

imo cuz i skipped it 💀

[sinful halo]

I forgot everything about precalc 😂

[winter comet]

😂

[sinful halo]

Calc 1 and 2 just reteches you those concepts I'm p sure

Inverse functions is also good to work on, but again, it's one Google search away 😭

[winter comet]

exactly

so its not a leisure activity that doesn't prepare for actual calculus

but its not exactly that necesary

[sinful halo]

Might've used leisure activity wrong 😂

Oh well

Now the guy knows that he just needs to prioritize algebra

[winter comet]

yea XD

algebra is prolly most important

fundamental

[surreal fjord]

Thanks guys!

[white elbow]

No problem

[slow latch]

is there an expansion for tan^3 x using mclaren series?

[willow skiff]

yes

keep taking successive derivatives of tan^3 x and sub in x = 0

or you can cube the Maclaurin series of tan x, that also works

they're both nasty methods

[copper gyro]

if any precalc enjoyers wanna check out https://discord.com/channels/268882317391429632/1263504012926521494

feel free

[white elbow]

No enjoyment

[willow skiff]

<@&268886789983436800> above message is spam

[modern valve]

ty

[willow skiff]

bu yong xie

[opal jungle]

is this a normal precalc thing 😥

[somber root]

uff this is calc stuff

[white elbow]

But why that question considered as spam

[somber root]

are u talking about my question?

[agile sparrow]

@somber root yes

[willow skiff]

no lol

someone posted something else that got deleted

also I can't see your image

[somber root]

I ask same problem in #calculus

pls help if anyone have any Idea

[willow skiff]

oh then just post your question in one place only next time

[proven night]

hello, i have a question

How do i solve this equation (x^x=x^5) properly?

I understand that i should use logarithms on both sides, but

[hushed sphinx]

Yes. And then you can divide by log(x) on both sides.
(Remembering that you then need to check separately whether x=0 or x=1 are also solutions).

[proven night]

i changed the equation

1. Why can't i say that x = 5, since both bases are the same (they are x)?

2. Why wolfram alpha doesnt show -1 as an answer

[hushed sphinx]

x=5 is definitely A solution.

[summer ruin]

you can just divide both sides by x^5

[hushed sphinx]

Oh, and good catch on the x=-1 solution too -- everything negative will be lost by taking the logarithm too.

[proven night]

But exponential function cannot be negative, right?

So is -1 a solution?

[summer ruin]

x^x is not an exponential function

[hushed sphinx]

Yeah, that may be the better approach.

[proven night]

because the base is not a constant?

[summer ruin]

yes

[proven night]

okay,