precalculus

[timber blade]

who let u in

exactly

[quasi elbow]

i said what i said

and they actually a r e evil

you guys are just delusional

[timber blade]

but they cute

that reason alone is enough

https://tenor.com/view/cat-clock-death-help-i-am-going-insane-hi-boop-dog-gif-21354319

[quasi elbow]

opinion on hamsters?

[winter comet]

https://tenor.com/view/hammond-dramatic-overwatch-wrecking-ball-wrecking-ball-dramatic-gif-13947305

[quasi elbow]

where's this from? like which movie

[winter comet]

its from overwatch

a game

💀

[quasi elbow]

o

do not 💀 me okay

[winter comet]

💀

[quasi elbow]

what did i say

[timber blade]

his name is limey

[viscid thistle]

I've been on my phone for 10 hours straight, I can feel my brain melting.

[quasi elbow]

that is very cute

[winter comet]

._.

[quasi elbow]

is it your pet?

[quasi elbow]

sleep, child

[timber blade]

no

my friend's pet

[winter comet]

it looks like an anteater

[timber blade]

named him after me btw

[quasi elbow]

haha, cute

[timber blade]

he probably does

[viscid thistle]

I'll take it to 10 first.

[winter comet]

and then die of brainrot

or

brain melt :>

[tepid basin]

mine is 8hrs

[quasi elbow]

mine is 1.5 hours lol

[winter comet]

mine is 0 hours :l

[viscid thistle]

I've been simultaneously talking in 3 servers all along.

[quasi elbow]

but to be fair i am on my computer more

[tepid basin]

zamnn is that even possible 😭😭

[viscid thistle]

Heck!

[timber blade]

sleep bruh

[quasi elbow]

it was 13 hours one day if it makes it better

not very proud

[quasi elbow]

lies

[tepid basin]

guys we r supposed to talk about pre calculus remember?

[winter comet]

oh yeah

uh

[quasi elbow]

yes

sorry

[viscid thistle]

I didn't even do my homework, I'm cooked 😭

[tepid basin]

so tell me what is calculus?

[winter comet]

limits, derivatives, integrals :>

[quasi elbow]

d/dx and some

[winter comet]

calc 1 at least

[quasi elbow]

stuff

[tepid basin]

nice one good job

[winter comet]

thanks :D

[tepid basin]

send sm questions rn

[quasi elbow]

do i not get a "good job" as well

[timber blade]

ew homework are u a kid (jk)

[tepid basin]

but not very tough plz

[winter comet]

integral of sqrt(1/(x^2 + 1)) dx :>

[timber blade]

tbh I am not kidding, i don't talk to kids

[winter comet]

well its not very tough...if you know how to do it... 😑

[viscid thistle]

Aren't you one?

I mean 11th grade is a kid no?

[winter comet]

what is a kid tho 😔

[timber blade]

we call it assignment

[viscid thistle]

Oooh heavy words.

[timber blade]

feels good to say

deep inside we know it's homework only

[winter comet]

what's homework?...

[timber blade]

uh

work for home ig?

[winter comet]

not what i meant 😭

[winter comet]

"deep inside we know" IT is "homework only"

what is IT

[timber blade]

man is onto something or on something

can't tell

i hope u recover soon

[viscid thistle]

Lol you've been on screen for a day imo

[winter comet]

my question makes perfect sense wdym :l

[winter comet]

i just woke up wdym 😑

oh...

you call homework "assignment"

it is "assignment"

coulda just

told me 😔

[timber blade]

[viscid thistle]

Lol I thought you were philosophising.

[timber blade]

he doesn't know what homework is

[tepid basin]

i got it but i cant type it here

[timber blade]

do childrens also call it "assignment" where u live? @winter comet

[timber blade]

us

[tepid basin]

us

cat brothers

[viscid thistle]

Is 10 hours a day screentime really bad?

[timber blade]

how much do u sleep

[viscid thistle]

6 hours

[tepid basin]

thats enough

[timber blade]

it's like ... really sad

yeah I mean sleep is enough but screen time is not

[viscid thistle]

Life is sad there's so much to do.

I can feel my brain, I can feel it!

[timber blade]

euler 🗣️

[tepid basin]

yo from now on lets all of us share our screen time every night and tryna decrease it day by day

[viscid thistle]

How much is yours btw?

[tepid basin]

ik its kinda cringe but its helpfull ig

[viscid thistle]

I'm in, desperate in need of that.

[timber blade]

it sure is

[viscid thistle]

Doesn't seem cringe to me.

[timber blade]

shhhhhhh do NOT ask

[tepid basin]

nice then lets do it

but where do we share it ?

[viscid thistle]

In dms, is it only the two of us?

[tepid basin]

alright

[timber blade]

i would love to but due to mathematical reasons i cannot

[tepid basin]

ok brodtha

[viscid thistle]

Mathematical reasons.

[timber blade]

i use my phone for studies

there's no way my screentime is decreasing

[viscid thistle]

You can install an app, I use it for studies too

[viscid thistle]

For example it displays time spent like

[timber blade]

wow

will try that

[viscid thistle]

Regain is the name

It asks a lotta permissions though.

You'll see.

[timber blade]

done

[viscid thistle]

You in then?

Eh @timber blade ?

The more the merrier.

[timber blade]

sure

[willow skiff]

problem sets count as "homework" actually

but yeah we would just say oh I have work to do

subtle differences in the words we use for HS versus uni versus workplace probably

[winter comet]

we call it homework, assignment, work, whatever lol

"i have work to do"
"i have to do homework"
"i have to do an assignment"
just depends on the context 💀

[winter comet]

what was your process...

[winter comet]

productive: 14 minutes 🗿

[cerulean crown]

can someone help me with my pre calc test review

[viscid thistle]

Got a specific question ?

[tame pine]

Yo

[tepid basin]

Putting x = tan(u)

[winter comet]

i mean thats valid but you could also just remember that it's arctangent

[quasi elbow]

how do we solve question 26?

[steel nexus]

help

[tiny kestrel]

wtf

nah thats lowkey impressive

10 hours

[dense dagger]

I would expand all the sin2xs and sin3x and cos2x and cos3x

It seems like a lot of stuff wud cancel

Or factor

[tame pike]

I’d like support for these problems

Do I use special right triangles?

[lusty notch]

Ok no problem

I know how to solve it

[formal bronze]

Hold up

[lusty notch]

It asks you to solve the equation

[formal bronze]

It says “complete the solution and justify your answers”

[formal bronze]

It already is

Or I think so

[lusty notch]

If it asks you to justify, then the question is about what you did to solve it.

Just solve the equation and why

[formal bronze]

So I could pretty much say that the equation is solved bc both the answers aren’t more than 2, meaning both of them are valid answers

[lusty notch]

Sí exactamente

Yes exactly

[formal bronze]

Tysm

[tepid basin]

Yea I know the derivative of arctan and tried smthng like that but it didnt go well

[formal bronze]

Wait she said there’s another condition that should be considered,,

Hold on

[tepid basin]

Yo is this watchu talking about ?

Is this the correct answer?

[quasi elbow]

i do not think anything is

[lusty notch]

It is already solved

I could not have done the procedure but what I did was convert the sexadecimal degrees

[lusty notch]

Your handwriting is beautiful

[formal bronze]

Are there any other conditions here?

[quasi elbow]

here, wouldn't the answer be same if the interval was open at 2pi?

[timber blade]

yes

why u doing jee pyq though

[quasi elbow]

but then what difference does it make?

[quasi elbow]

because

yes

[tepid basin]

Thanks bruhh 🗿

[tepid basin]

Me too

Next year is my paper 😭😭

[timber blade]

basically

[timber blade]

nothing, coz ur final answer lied very well within.thr given range

if suppose one of the answers was x= 2π
then your answer would change for open interval and closed interval

however In this case, since x=0 and x= 2π is not a solution to this answer, the answer therefore remains the same for both open and close interval

[timber blade]

good luck man

[quasi elbow]

okay, thank you.

[exotic barn]

When you plug in x=1 you get 1 = -1

Squaring both sides here is critical if one side is negative

[formal bronze]

Thank you so much omg

I’m getting that bonus . @exotic barn I will make sure you see the heavenly gates. You have blessed my day .

[exotic barn]

Thank you, you too

[formal bronze]

🤍🤍

[uneven nexus]

why?

[tepid basin]

Bro that's totally correct

No no no

U getting it totally incorrect

Wait lemme send u sol.

Btw what's the answer for this Q.?

[uneven nexus]

ooh wow

got it thx

@tepid basin what about this one? any easy way?

[tepid basin]

Lemme try

Bro what's the ans?

[uneven nexus]

-1/6

[tepid basin]

Demn idk I wasn't able to solve it

Sorry

[uneven nexus]

it's ok, it's tough haha

[tepid basin]

So what's the solution?

[uneven nexus]

uhh this

[tepid basin]

No the solution like the whole process to this answer

I wanna know how to do this

[uneven nexus]

dude I don't know the soln... If I know the soln, why did I ask here

[tepid basin]

Oh ok

[daring tapir]

Since sinx and tanx are ≈ x near zero

[quasi elbow]

what's the best source to study inverse trigonometric functions? one that covers all things

[timber blade]

the best way to learn anything is to invent it first and then compare with what's already known

[shadow summit]

Limits aren’t precalc, they are calc.

[winter comet]

except when its, yk "precalc with limits"

like the extended reals 😁

[viscid thistle]

There's not much to them imo, any class 12 math book should be fine. You got SL Loney?

[quasi elbow]

i do not, but i will look it up. thank you.

[viscid thistle]

Indian? If so the twelfth grade book is enough for it.

[quasi elbow]

i get you, i just wanted to clear my concepts first

because trigonometry is a hard topic for me

[viscid thistle]

Yeah trigonometry sucks

[quasi elbow]

mhm! anyway, i am sorry; thank you for the recommendation

[viscid thistle]

Lol why are you sorry?

[quasi elbow]

it sounded like a stupid question

[viscid thistle]

What sounded like a stupid question?
Btw if you are absolutely new to trig give trigonometry by I M Gelfand a try.

I M Gelfand was a great mathematician btw.

[quasi elbow]

i see

thank you 🌸

[lusty notch]

Hi guys How are you?

[tepid basin]

Good

[tepid basin]

Wbu bro?

[lusty notch]

Well here I am bored reading a math book

And you?

[viscid thistle]

Can soemoen please help me with this question

[viscid thistle]

Is this polar coordinates ?

No

[neat ether]

part f please

[uncut mantle]

We do limits in precalc in my class ateast

[devout isle]

Was it done for you

[quasi elbow]

how do we solve tan(7x).tan(3x)=1?

[quartz pagoda]

Is mathematical induction precalculus?

[hasty lily]

Sure you could learn it in precalc

or in calc

or after it

There's no definitive comparison

[quartz pagoda]

Ooh ok, I am so lost in all of this tbh🤣, what does induction even mean?

What do I need to know prior to mathematical induction?

If someone could like give me a roadmap, that would be awesome thank you if you do

[quasi elbow]

what is happening here

[distant ivy]

have you watched this video?
https://www.youtube.com/watch?v=wblW_M_HVQ8

You could learn proposition/predicate logic if you wanted to get a deeper understanding, but theres a bit you have to cover before you can get to induction

[distant ivy]

It looks like hes finding the range of values for theta on the LHS and range of values for r on the RHS

[viscid thistle]

Write it as tan 7x = cot 3x.

[viscid thistle]

Basically how many pairs of values of r and theta satisfy the given equation.

Then he rewrites r⁴-2r²+3 to show that it's greater than or equal to 2.

So he finds the intersection of the ranges of LHS and rhs to find the values.

An artificial question, as expected from coaching centres.

[limber sentinel]

hey arjuna

[quasi elbow]

yeah but what next? do we make it a quadratic equation?

[viscid thistle]

The same old trick cot 3x = tan(90-3x)

[quasi elbow]

ah

got you

[viscid thistle]

11th?

[quasi elbow]

i am in uno

uni*

[viscid thistle]

Arjuna good though?

[viscid thistle]

I see.

[viscid thistle]

I'm asking because my parents bought the course yet I've never attended any class.

[quasi elbow]

do not do that

if you have spent money on it then utilize it

you are going to learn something either way

[viscid thistle]

But it's too lengthy though like 10 lectures of 2 hours each.

[quasi elbow]

should have thought that earlier

i mean

[viscid thistle]

My bad

[quasi elbow]

what are you preparing for?

jee?

[viscid thistle]

Oxford

[quasi elbow]

oh

[viscid thistle]

And ISI Bangalore

[quasi elbow]

what grade are you in, if you do not mind me asking?

[viscid thistle]

11th

[quasi elbow]

well

like i said, rather than thinking about how lengthy the videos are, just start watching them

also

why did you buy the course? is it just not available on youtube?

[viscid thistle]

I didn't buy it my parents did.

[quasi elbow]

i mean sure not 100% but 70%, maybe?

[quasi elbow]

eh

wow

[viscid thistle]

They didn't know.

They bought it for me. You know everyone's buying it nowadays.

[quasi elbow]

crazy

but it is what it is

so make the most out of it

[viscid thistle]

Fair, thanks

[quasi elbow]

what am I doing wrong here? it says the answer is npi+-(3pi/2)

[viscid thistle]

What's the seventh line?

Sixth, my bad

[quasi elbow]

sin^2x= (1/root2)^2?

[viscid thistle]

Nvm, it's correct but unnecessary.

Lemme see.

[quasi elbow]

why?

[viscid thistle]

I see you are doing it step by step.

👍🏻

[quasi elbow]

yeah sorry for that

[viscid thistle]

It's a good habit.

Sin x = ±1/√2

[quasi elbow]

sure but

i am using the formula for sin^2x

[viscid thistle]

Apparently you've done it all right.

[quasi elbow]

npi+-theta

[quasi elbow]

oh

wow

[viscid thistle]

Like if it's npi ± 3pi/2 how's that going to satisfy the equation.

[quasi elbow]

got it

thank you

[viscid thistle]

I didn't though

[quasi elbow]

the answer is probably wrong

they mess that up sometimes

[quasi elbow]

why is the answer of #5 not (1) and (2) both?

[viscid thistle]

2 would imply 1 = -1

[viscid thistle]

I did it on paper I don't get 2npi - 90 as one answer.

[quasi elbow]

i used the formula of cos(theta)=cos(alpha)

[viscid thistle]

Isn't 45 deg added when it goes to the other side

[quasi elbow]

yes but

it's +- alpha

so wouldn't it be + pi/2 and - pi/2?

i checked the solution online and the reason that they're not getting the second one is that they squared both sides

but do not we generally avoid that in trigonometry?

also what is wrong with my solution?

[viscid thistle]

a - 45 = 2npi ± pi/4 no?

[quasi elbow]

yes

[viscid thistle]

a = 2npi - pi/4 + 45?

Or am I drunk

[quasi elbow]

what about a= 2npi+pi/4+45

oj

oh

wow xS

xD

[viscid thistle]

Yep, I agree that you'll get that

[quasi elbow]

yeah sorry

what i was doing is

i was adding the angles first

if that makes sense

[viscid thistle]

Then placing the plus or minus?

[quasi elbow]

yeah

i thought it's in bracket or whatever

but yeah makes sense i am sorry that was really stupid

thank you!

[viscid thistle]

Np

[quasi elbow]

but hey

what about 2npi then

[viscid thistle]

You can make sense of it by saying that cosec 2npi ain't defined. At least that's what I do

And that's not an option:)

[quasi elbow]

fair enough

[viscid thistle]

It's like those √(x²-x + 1) = 2x -1 algebraic equations where some solution doesn't make sense even though it's reached through an algebraically valid series of steps.

[viscid thistle]

No you have an even more valid reason

Like you multiply both sides by sin x, if x is 2npi then that step wouldn't have been possible.

[quasi elbow]

i mean ehhhh

what if the question asked about how many solutions does it have

let's say in period [0, 2pi]

[viscid thistle]

It only has one because the other one doesn't make sense.
Ever seen a question like "solve x^2 - 1 = 1/x, x ≠ 0", it's somewhat like that, for the question to even make sense it must exclude the possibility of theta being 2npi.

[quasi elbow]

well

oh

[viscid thistle]

You did functions? Like finding their domains etc?

[quasi elbow]

yeah

[viscid thistle]

Then you can sympathize.

[quasi elbow]

i mean

like you can see, i am really weak at math

it's not what i am majoring in

so i do not see some stuff directly like others do

[viscid thistle]

I can see that you are learning stuff pretty quickly.

[quasi elbow]

except

i am not

[viscid thistle]

You are actually, in my opinion at least.
Btw what's your major?

[quasi elbow]

you're kind

and

computer science

[viscid thistle]

Cool

[quasi elbow]

mhm!

[viscid thistle]

I need to start learning programming too!

[quasi elbow]

it is super easy

i would advice that start with C first

[viscid thistle]

You'll probably get used to it quickly.

[quasi elbow]

nein

[viscid thistle]

Sure!

If you think I'm just saying that to make you feel good, I'm NOT!

[quasi elbow]

also try to think about how actually stuff is working rather than focusing on syntax

[viscid thistle]

It's actually the case that you can become really good at it if you shut yourself up in a room for a month. Like really good.

[quasi elbow]

haha well i live with two other people, not happening lol

[viscid thistle]

Fair, thanks, I'll ask for help if I run into problems.

[quasi elbow]

plus it's my final year so there's a lot of projects and stuff

[quasi elbow]

sure thing

[arctic meteor]

$$\lim_{x \to -\infty}\frac{\sqrt[4]{x^4-1}}{\sqrt[3]{x^3+1}}$$

[obsidian monolith]

wolly5114

[arctic meteor]

their root is not the same

how do you calculate it?

[viscid thistle]

Like divide by x both the numerator and denominator?

You tried that @arctic meteor

Then bring the x into the root?

[arctic meteor]

My textbook says the answer îs -1

@viscid thistle

[viscid thistle]

I see, it should be -1 but the way I suggested seems to say it's 1

[willow skiff]

the issue stems from x^4 not being a 1-to-1 function

so $\sqrt[4] {x^4} = |x|$ actually

[obsidian monolith]

south's secret twin brother

[willow skiff]

that means the sign will be positive/negative = negative

[willow skiff]

hopefully you get this reasoning

[viscid thistle]

Fair

[willow skiff]

(similar to how the square root cannot give you a negative number, a 4th root is a square root applied twice, so same thing)

a 2n-th root is the same as the composition of a square root and an nth root

[arctic meteor]

can you conjugate the denomitor?

in my textbook it says it's possible

[willow skiff]

yes you can

it's not worth it in my opinion though

the way to justify it is to factor the numerator and denominator and then use the binomial approximation $(1 + x)^n \approx 1 + nx, x \to 0$

[obsidian monolith]

south's secret twin brother

[quasi elbow]

how do we do #13?

[arctic meteor]

and how do I conjugate the denominator?I'm clueless!

@willow skiff

the opposite would be $$\sqrt[3]{x^3-1}$$?

[obsidian monolith]

wolly5114

wolly5114

[willow skiff]

oh wait it's not even like x + 1 lmao, so it doesn't seem possible

so yeah textbook had a dumb idea that didn't work

[willow skiff]

it's factorable

I think

yeah $2c(2s - 1) - \sqrt{3} (2s - 1) = 0$

[quasi elbow]

do i write 4sinxcosx as 2sin2x?

[obsidian monolith]

south's secret twin brother

[quasi elbow]

wow

[willow skiff]

no

[quasi elbow]

right

thank you

[willow skiff]

no worries!

[uneven nexus]

Define f(x) = {x=0: -1, -x^2}, (-1 at 0 but -x^2 everywhere else), how can we know the limit of f at 0?

[quasi elbow]

isn't the value of sin1 approximately 0? then why is the answer of 20 not (3)?

[willow skiff]

it's sin 1 radians they mean

[quasi elbow]

oh

i am sorry

thank you

[willow skiff]

no worries yeah trig uses radians by default

if they are using degrees they will say so

otherwise it's bad notation

[quasi elbow]

makes sense

[lusty notch]

i already solve your questionnaire

[quasi elbow]

that is sweet of you, but i got it already! thank you still 🌸

[lusty notch]

ok

I'm glad you're okay because you already have it.

Someone would like to support me on tik tok, I'm uploading math videos that maybe can help you.

[quasi elbow]

i am not sure if this is a right server to advertise in

[lusty notch]

ohh

I see, it would be a very illegal way to advertise

[quasi elbow]

not "illegal" per se

also, question

are you using a translator?

[lusty notch]

yes i used the traductor

my english not is good

Sometimes I use the translator

[quasi elbow]

haha, fair enough

[lusty notch]

can you solve integrals?

[tame pine]

Yo

Anyone said integrals

@exotic barn

[lusty notch]

yes

[exotic barn]

wolfram

[tame pine]

No

[lusty notch]

no

[tame pine]

We can try

WE

[lusty notch]

not used IA

AI

[tame pine]

Ok

Fair

[lusty notch]

LOL

ok

I can give you an exercise and you solve it

[tame pine]

Oh K

[lusty notch]

ok

one moment

Let me open word, I have many exercises.

[exotic barn]

i dont think you are ready for this

[tame pine]

Maybe?

I am ?

Or am I?

[lusty notch]

ahahh lol

is loading

[exotic barn]

is this you on your pfp

[lusty notch]

yes

[exotic barn]

i like your fit

[lusty notch]

I am the one in the photo

[tame pine]

,av @lusty notch

[obsidian monolith]

kleiner_mq's Avatar

Click here to view the image.

[tame pine]

Nah u female right?

[lusty notch]

ohh thank you brother

why

i am not girl

[willow skiff]

pink diamond

[lusty notch]

i am men

[exotic barn]

oh you got she/her pronouns

thats why i was confused

[tame pine]

Men

Lol

[willow skiff]

I am the human race

[tame pine]

Chad

We are humans

Before man and wo man

[willow skiff]

women literally means us in Chinese

[tame pine]

And man?

[willow skiff]

that's nan

[tame pine]

Lol

[lusty notch]

Do you mean that I have traces of a woman?

[exotic barn]

what no

[willow skiff]

which is funny cause that's like grandma

in English

[tame pine]

Oof

[lusty notch]

ok

[willow skiff]

British and other Commonwealth people

say nan

[tame pine]

Ok

[lusty notch]

its already open

one moment

[lusty notch]

im from Colombia brother

[exotic barn]

I see

[lusty notch]

@exotic barn

@tame pine

[exotic barn]

what's u in 2.

[lusty notch]

why?

[exotic barn]

is it a function of x or a constant or what

or do you have to solve for u?

[lusty notch]

where cos3x.= u=3x.
cos u

[exotic barn]

these integrals are not hard but i dont get the u part

[lusty notch]

They are integral to Stewart's book

[exotic barn]

S cos(3x) dx = sin(3x)/3
then u = 9x/sin(3x)

[lusty notch]

you already solved the first one?

[exotic barn]

C = 0

first one is power rule

you can also switch the bounds

[tame pine]

Computer math moment

[obsidian monolith]

bacc the sigma😔🤞

[exotic barn]

Last one just split the fraction and use 1/e^x = e^(-x)

[lusty notch]

The first integral can be solved by separating into two, also applying the power rule and then using Barrow's rule.

[exotic barn]

Do you want an integral of me/oppailol?

[lusty notch]

both

maybe if you like it you can do the procedure and take a photo

[obsidian monolith]

bacc the sigma😔🤞

[lusty notch]

Do you want me to solve it?

[exotic barn]

ya

[lusty notch]

??

[lusty notch]

lol

[crisp bane]

Is there a reason these two functions look eerily similar

[winter comet]

it's telling you the substitution to use 😂

[summer ruin]

they're both related to probability distributions

[exotic barn]

oh you are right

[river drift]

near 0 they are very close together because the first two terms of their maclaurin series are 1 - x^2

[exotic barn]

i thought the . was a multiply symbol

[tepid basin]

yo guys wtf just happened after the red part

[exotic barn]

3pi/5 = 5pi/5 - 2pi/5 = pi - 2pi/5

[quasi elbow]

how do we solve question 9?

[tepid basin]

nahh bro like why did we do that and what was the sense of that step

[winter comet]

we don't

[quasi elbow]

i wish

[quasi elbow]

to convert it into cos(2pi/5) for some reason which you must be aware of

[tepid basin]

Here u go @quasi elbow

[quasi elbow]

oh

[tepid basin]

is this right ?

[quasi elbow]

so the basic idea was to calculate tan theta and then substituting its value

[tepid basin]

yea

[quasi elbow]

I don't know, I am not on my pc anymore. but most probably, yeah

thank you! 🌸

[tepid basin]

its alright

[tepid basin]

i wasn't attentive 😭

[exotic barn]

lmao

[tepid basin]

lol this guy is llike my teacher 😂

[quasi elbow]

please, you're studying math

[tepid basin]

yea yea im sorry

[exotic barn]

cos(pi-x) = -cos(x) and then -1 = e^(-i*pi) but i cant tell the context

[tepid basin]

yea i found out

dw

thanks

[arctic meteor]

$$\lim_{x \to +\infty}\frac{x^2}{e^x}$$ and $$\lim_{x \to +\infty}\frac{x^4}{e^x}$$

[obsidian monolith]

wolly5114

[arctic meteor]

if both equal 0 is there any proof without differentiation/L'Hospital?

[winter comet]

relative rates of growth/taylor series

[lusty notch]

Yes

[river drift]

that's not true, the denominator of the second one is e^(2x)

[quasi elbow]

how do we solve question 14? what would be the first step?

[viscid thistle]

Dedication 🫡

[viscid thistle]

Write tan(P/2) and tan (Q/2) in terms of tanP and tan Q respectively

[quasi elbow]

stupid question but how do I do that

[viscid thistle]

Mb

[quasi elbow]

brain is not braining

[viscid thistle]

Let me check if that works

[quasi elbow]

I just want to know how to approach the solution

don't give me the whole thing

[viscid thistle]

Ik ik

[viscid thistle]

Since we know nothing about the lengths of the triangle , we should start thinking if there is any relation between the roots

Now it's given that the roots are tan(P/2) and tan (q/2)

[quasi elbow]

hey

what if we multiply them? wasn't there a formula for

multiplication of roots?

or was it for something else

or add them for that matter

this probably makes no sense i am sorry

[viscid thistle]

Aha

Good idea

[viscid thistle]

What is angle P + angle Q?

[quasi elbow]

I don't think I'm thinking about the right answer

are you talking about the roots or?

[viscid thistle]

No

We have a triangle PQR right?

I'm asking what the sum of angles P and Q is equal to

[quasi elbow]

180-R?

oh

pi/2

[viscid thistle]

We already know that R is 90

[quasi elbow]

?

[viscid thistle]

Yes

[quasi elbow]

right

[viscid thistle]

Now,
Replace Q with 90-P and write down the sum of roots =-b/a and product of roots = c/a

You will be able see what to do after that

[quasi elbow]

sure I get it now but

question

[viscid thistle]

It's absolutely alright if you dont

[quasi elbow]

do you think there's another approach to it? since we only want to prove one of the relationships given between a, b and c

a faster way, maybe?

[viscid thistle]

Not sure

[quasi elbow]

fair enough

thank you 🌸

also, go to bed

[viscid thistle]

Maybe the fact TanP= tanQ would help you think of a different way

[viscid thistle]

Lol,alright

[quasi elbow]

where's that given

ah

never mind, got it

good night!

[viscid thistle]

Gn

[quasi elbow]

why is the answer of #10 (3) not (2)?

[winged pawn]

Can anyone help, how would I graph a radical function when the x variable degree is higher than 1?

[uncut mulch]

you can always start with a table of values

[winged pawn]

is there a way where I can just look at it and know? kinda like normal radical functions

[uncut mulch]

this type of function is pretty common

try graphing and you should recognise something very nice

[winged pawn]

oh i see, you just plot the root of the constant value for both x and y

[arctic meteor]

$$\lim_{x \to \pi}\frac{1}{1+cos(x)}-\frac{2}{sin^2(x)}$$

[obsidian monolith]

wolly5114

[arctic meteor]

in the limit calculator it changes the angle from pi to t+pi

Is this how you solve it?

the answer is -1/2

[winter comet]

just multiply the first one by 1-cos(x)

numerator and denominator

[uneven nexus]

How to do division about this?

[arctic meteor]

$$\lim_{x \to 0}\frac{sin^2(x)+2cos(x)-2}{(1-cos(x))sin^2(x)}$$

[obsidian monolith]

wolly5114

[arctic meteor]

the answer is -1/2

how can i get that answer?

i tried the half angle formula and it didn't work

[willow skiff]

you can definitely try finding everything in terms of cos(x)

then sub in $u = \cos(x), u \to 1$

[obsidian monolith]

south's secret twin brother

[quasi elbow]

how do we know which is the longest side in a triangle, if nothing is given?

[timber blade]

wow

i would say atleast something will be given if the question asks u to find longest side

[quasi elbow]

well

i see

[viscid thistle]

How does one go about doing 8 and 9?

In 8 how do I show that the error is numerically less than 0.0007 and in 9 how do I show that the error is numerically less than 1/6 x²?

[willow skiff]

what did you get for the binomial expansion of $(1 + \alpha)^{-3}$?

[obsidian monolith]

south's secret twin brother

[willow skiff]

you need to use the term in $\alpha^2$

[obsidian monolith]

south's secret twin brother

[viscid thistle]

Heck I forgot on which page I did that, I divided though.

Didn't use binomial expansion.

Wait.

If I'm not mistaken it's 1 - 3a + 6a² - 10a³+...

Fair got it.

What about 9?

[willow skiff]

it's $(2 + 3x) 3^{-1} (1 + 4x/3)^{-1}$, then use the binomial expansion

[obsidian monolith]

south's secret twin brother

[willow skiff]

and expand up to the x^2 term again

[viscid thistle]

I had tried division that didn't work, I wonder why, the book hasn't yet taught the binomial theorem.

Anyways thanks.

[willow skiff]

that is so weird

yes and we are using the fact that the maximum possible error is the next term

for when the next term is the largest in that domain

that's a fact from calculus

[viscid thistle]

It's a pretty old book.

[willow skiff]

but it looks pretty helpful

the book

[viscid thistle]

How so?

Imo it's a pain in the ass, so dry.

[willow skiff]

exercises look fairly interesting

ah but it must not explain well then, pity

[quasi elbow]

how do I proceed further? the options do not have a 'k' in them

[timber blade]

huh wait what are a,b,c?

[viscid thistle]

What's the question though?

[agile moat]

hello guys

do u guys konw how to convert the gfe of an ellipse to the sfe?

it looks simple for me but im just confused how if someone can help me thank you

[willow skiff]

complete the square to get $4x^2 + (y^2 + 2y + 1) = 36$ and now you should be able to continue

[obsidian monolith]

south's secret twin brother

[agile moat]

could u

uhhh

in cave man terms im so sorry

😭

[willow skiff]

which part don't you get?

y^2 + 2y + 1 is a perfect square

[quasi elbow]

sides of the triangle

[agile moat]

how do i know if its a perfect square and what do i complete the square with kinda

[willow skiff]

so $(y + k)^2 = y^2 + 2ky + k^2$

so we have $2ky = 2y$ and $k^2 = 1$ so.....

[obsidian monolith]

south's secret twin brother

[willow skiff]

https://www.youtube.com/watch?v=f6yhfmW41wI

honestly you need some revision; you should watch this

[agile moat]

THANK YOU SO MUCH

[timber blade]

whoever framed this question deserves to die.

[agile moat]

i just realized that i need to revise the entirety of algebra

[quasi elbow]

why xD

good luck, batter

[agile moat]

;-; but thank you so much u guys ong

life changing

[timber blade]

coz normally 3, 4, 5(A, B, C in this case)
are sides of a right triangle

nvm ig i m missing something

[quasi elbow]

you're right

i applied sine rule here

i just do not know how to cancel the k out

[agile moat]

im gonna be fr w yall

i still dont get it ;-;

im starting to think my processing is t he problem

[timber blade]

keep trying man

[quasi elbow]

ah, got it. thank you 🌸

[timber blade]

we all been there

[agile moat]

damn

[quasi elbow]

it's not. you got this!

[agile moat]

what did u guys do to ui know overcome

im having lots of trouble with lots of numbers shown to me

[timber blade]

start from scratch mate

start with basic linear equation and solving them

it will take time but it's way better than to develop a fear of numbers

[agile moat]

ok ill try

[timber blade]

bro was typing his wisdom but stopped midway@willow skiff

SAY IT

[agile moat]

is there like math logic books

any good recs

[willow skiff]

I don't have an exact solution but you can let 2R = 1, where R is the circumradius
then using the extended law of sines, you just need to simplify $\sin 45 + \sin 75 + \sqrt{2} \sin 60$

[obsidian monolith]

south's secret twin brother

[willow skiff]

which does happen to be equal to 3 sin 75

[timber blade]

hm

i didn't understand the significance of first half
u can just simplify the last expression u gave and find it to be equal to 3sin75

why did u put 2R= 1?

[willow skiff]

cause the options are all in terms of the sides

so by similarity, it doesn't affect the ratios between the sides

[agile moat]

i have great news guys, i got the gist of ellipse, turns out i was just confused abt the terms buit the functions i get

:3

ty u guys

[willow skiff]

no worries!

[quasi elbow]

what mistake am I making here?

it says the answer is 4

[timber blade]

i never learned the sine rule

but ig while calculating the area of triangle ABC

u took the side length as √2 instead of 2√2

?

(not sure if this is intentional or an error)

[royal zinc]

Yay my level

Who has questionsss

[quasi elbow]

oh, yes

but it is still not equal to 4?

how do we know when to apply sine rule and when to apply cosine rule?

(not directed at you, limey)

[timber blade]

huh how I think u r missing brackets

[quasi elbow]

right

[quasi elbow]

oh

xD

wow i am stupid

thank you!

[timber blade]

welcome

[quasi elbow]

bump

[uncut mulch]

choose based on what information is available to you

the rules give relations between sides / angle(s) in a triangle
note which pieces of info the rule uses and whether that info is present

[quasi elbow]

got it, thank you

[timber blade]

bro u speak like chadgpt

[quasi elbow]

how do we solve this question? i tried simplifying it using sin(x-y) but it's not really working

[quasi elbow]

what happened here

[viscid thistle]

there is a common term of a^2 + b^2 for cos^2 x / 2 and sin^2 x / 2

if thats what you are asking

[quasi elbow]

oh

i see it now

thank you

i have got a really stupid question

[lusty notch]

hi fudge

[quasi elbow]

if it's given that the ratio of a, b and c is 4:5:6, does it mean that a:c is 4:6?

[quasi elbow]

hello

[lusty notch]

how are you?

my keyboard is a shit

[quasi elbow]

i am doing okay, thank you. how are you doing?

[lusty notch]

i am fine

I need a little help from you

[quasi elbow]

hm?

[timber blade]

yes

and yes u can also say a:c is 2:3 (more simplified)

[quasi elbow]

got you

if c= cos^-1(1/8) and a= cos^-1(3/4), how do i prove that c=2a?

[viscid thistle]

cos(2 theta) = 2 cos^2(theta) - 1

this might help

[quasi elbow]

i am just confused with the inverse thing, does the formula get applied in the same manner? i have not studied inverse trigonometric functions yet

[lusty notch]

express the integral as a Riemann sum limit. not evaluate the integral

[viscid thistle]

formula where?

[lusty notch]

I do the procedure well, but from one moment to the next I get tangled and frustrated

[quasi elbow]

i am not making sense, am i

i think this goes in #calculus

[quasi elbow]

.

[lusty notch]

you can solve it?

[viscid thistle]

no ig

[quasi elbow]

unfortunately, no. i also think that #calculus would be a more appropriate place to ask this question, so you might want to head there.

[quasi elbow]

i will come back to it later, thank you still

[lusty notch]

I have to go because I'm very sleepy

[unborn brook]

Why doesn't the product rule of radicals apply to imaginary numbers?

,help

[obsidian monolith]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[river drift]

context?

[river drift]

in complex numbers roots can return multiple values (square roots can return 2 values, cube roots can return 3 values, etc.) so the value you get out of it does depend on the order of evaluation

[unborn brook]

Is there any specific reasons for why we defined the latter as the correct order of evaluation?

[river drift]

if we take the square root of a real positive number, we would prefer to get a positive result. so if we have something like $\sqrt{49}$ we would not want to do [ \sqrt{49} = \sqrt{(-49)(-1)} \qeq \sqrt{-49}\sqrt{-1} = 7i \cdot i = -7 ] so we don't want to split up square roots which have the product of two negative numbers. this is essentially the same rule in reverse

[obsidian monolith]

cloud

[unborn brook]

Now I get it, thanks 🍻

[viscid thistle]

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant and equals 10. If the distance between the two foci is 6, how to find the lengths of the major and minor axes of that ellipse?

[storm lodge]

length of major axis is equal to 10 as given

length of minor axis shoudl be sqrt(10^2-6^2)

[tame pike]

What method can I use to find the angle measures?

[winter comet]

the unit circle

[tame pike]

Thanks 🙏

Also, is there another method I can use besides the unit circle?

[winter comet]

i mean you can use a triangle but its literally the same so uh

not that i know of?

[tame pike]

Ok

[dense hawk]

can anybody help me out in proving this some how I can't understand the concept of the 2 sin theta/2 not being equal to sin theta

[timber blade]

if you are referring to [2sin(theta)]/2
then it is indeed equal to sin(theta)

however if you are referring to 2sin(theta/2) then yes it is not

longer reason is that sin(theta) isn't a linear function, you can remember it by saying sin(60°) = √3/2
however sin(60/2) = sin(30°) = 1/2
which is NOT equal to [sin60]/2

[grim bolt]

2sin(theta/2) is NOT equal to sin(theta) as the previous guy said, but according to trig identities,
sin(A + B) = sinAcosB + cosAsinB
hence, sin((theta/2) + (theta/2)) = 2sin(theta/2)cos(theta/2)

[quasi elbow]

can someone please explain this question to me? i do not get what it is asking for

[arctic meteor]

$$\lim_{x \to 1}\frac{x^{n+1}-1}{e^{x}-e}$$

[obsidian monolith]

wolly5114

[arctic meteor]

do you divide by x both the numerator and denominator?

[gusty storm]

I am a high schooler but I suck at doing simple high-school integration. Practice isn't the thing that I need, but I can't understand anything when my teacher explains something new to me.

[lusty notch]

Using l'hopital's rule the result is simple

[winter comet]

do you understand integration? or just how to do integration

[lusty notch]

o using factorization

If you don't understand integration, how the hell are you going to integrate?

[gusty storm]

I know how to integrate, the most basic thing. Like int x is x2/2

[arctic meteor]

@lusty notch without differentiation

[winter comet]

so polynomials in general? like x^3 + 5x^2?

[lusty notch]

Do you know the basic integration rules?

[lusty notch]

oh yes

[gusty storm]

x^4/4 + 5x^3/3

I hope I am correct

[winter comet]

yeah

do you know integrals of trig functions?

[gusty storm]

sine-> -cosine
cosine-> sine

[lusty notch]

is correct using the rule potenciation

[gusty storm]

hold up what what what?

[lusty notch]

tan?

xdddddd

[winter comet]

i mean you use u sub for tan lol

[gusty storm]

dont remember

[winter comet]

do you know substitution rule/u sub?

[gusty storm]

I mean they don't tell us why int of cos is sin. (maybe it isn't necessary?)

[winter comet]

do you get that integration is the opposite of differentiation?

[gusty storm]

yeah but I couldn't understand it properly

[gusty storm]

yes

[winter comet]

you can prove the derivative of sin(x) is cos(x) using the limit definition of derivative

[gusty storm]

thats the main problem. At that time when I was learning this rule, I understood nothing

[lusty notch]

I also know that rule but I can't understand it very well either. : c

[winter comet]

its based on the chain rule

you know the chain rule, d/dx [f(g(x))] = f'(g(x)) g'(x)?

[gusty storm]

I 'know' that my teacher taught this to me, but I coudn't understand it

[lusty notch]

is formula is long :V

[winter comet]

do you understand the chain rule tho?

[gusty storm]

no

[winter comet]

do you understand the limit definition of a derivative?

[gusty storm]

everything goes from the top of my head when someone explains me

[lusty notch]

is easy

[winter comet]

i mean, do you know it in general?

[winter comet]

oh

do you know the derivative of (2x+5)^5?

[gusty storm]

no

[winter comet]

ahh ok

[gusty storm]

my brain flooded with confusion

[winter comet]

u sub is based on the chain rule so i really suggest learning the chain rule first 💀

[lusty notch]

I almost don't understand Riemann's summation rule in the end.

[winter comet]

wdym

[gusty storm]

my teacher already taught us this. I even practiced on this. But I tend to remember the procedure rather than to understand it

[winter comet]

there's different levels of understanding

[gusty storm]

and idk how to 'understand'

[winter comet]

there may or may not be a 'intuitive' way to think about the chain rule; if there is, I dont know it

but the limit definition of a derivative is 'intuitive' (to me), and the chain rule comes from the limit definition of a derivative, and u sub comes from the chain rule

so even if u sub or the chain rule isn't intuitive to me, i could see how it builds off of things that are

you know what i mean?

[gusty storm]

so what you mean is, if I understand limit definition, I could see how other things work? like u sub and chain rule

[lusty notch]

The thing is that not everyone learns in the same way, many learn by watching and others by reading, and others also by solving.

[winter comet]

i meant limit definition of derivative 💀

i mean knowing the epsilon-delta definition of limit also helps bu

[gusty storm]

wow I heard that for the first time in my life

[lusty notch]

why epsilon?

[winter comet]

you might be able to see THAT they work, but you might not have a great intuition for why it works

like the quadratic formula

you can complete the square and see THAT it works

you can understand completing the square, and you can see that completing the square gives you the quadratic formula

[gusty storm]

I learn from solving, but what to solve if I can't understand anything

[winter comet]

but you still may not understand like intuitively why it works i guess

maybe thats a bad analogy 💀

[gusty storm]

um

[lusty notch]

I was like that too, well I still am but not as much as before, now I learn in many ways.

[winter comet]

are you trying to understand the process, or are you trying to understand 'why' it works?

[gusty storm]

i... don't know

[gusty storm]

good for you, i also am trying...

[gusty storm]

Maybe process. yes process I guess

[winter comet]

maybe you should practice the chain rule a lil bit more?

[winter comet]

alr

thats fair

[gusty storm]

why

[winter comet]

why what? why the chain rule?

[gusty storm]

why fair

[lusty notch]

Before I didn't like reading, now a little

[winter comet]

oh because imo the 'why' is not very intuitive and seems to basically come from manipulating intuitive concepts into something that no longer seems intuitive

my opinion but 💀

[trim citrus]

how do i do number 10? i tried substitution but it js doesnt work lmao

[lusty notch]

shit

[winter comet]

remember sin(2x) = 2sin(x)cos(x)?

[trim citrus]

i wrote it as 1/2 sinxcosx

[winter comet]

you mean... 1/2 sin(2x)?

[trim citrus]

i mean thta

yeah

[winter comet]

yeah so if u = 1/2 sin(2x), whats du?

[trim citrus]

wait where did the e go?

[winter comet]

don't substitute in the e part

[trim citrus]

oh...

why not?

[winter comet]

d/dx [ f(g(x))] = f'(g(x)) g'(x)

in order to use u sub, your integrand must be in this form f'(g(x)) g'(x)dx
so we let u = g(x)

in this case, we can let f(x) = e^x, and g(x) = u = 1/2 sin(2x), and then du = g'(x)dx = ?

[gusty storm]

you can use integration by parts method

[winter comet]

naw bruh 😭

why would you do that 😭

[trim citrus]

i tried but i got confused lmao

[gusty storm]

huh

[winter comet]

nah you could but dont

💀

[winter comet]

do you understand what im sayin or uh

💀

[gusty storm]

well thats the only thing I can remember, and if it was in our book, it would be in integration by parts method section

[trim citrus]

naw

[winter comet]

do you get that u sub is the opposite of the chain rule?

[trim citrus]

yes

[winter comet]

nah this is a clear u sub

[timber blade]

#calculus don't mind me I keep.losing the channel

[gusty storm]

how can you say very confidently

[winter comet]

so heres the chain rule right?

[trim citrus]

yep

[winter comet]

because i can see u sub is much easier than IBP, most problems in an IBP section are not subbable

[trim citrus]

is du cos2x

[winter comet]

yes

dx

du = cos(2x) dx

[gusty storm]

how can you 'see' your brain

[winter comet]

basically with the substituion rule, we hope that our integrand is in the form of the chain rule so that we can essentially do the opposite of the chain rule

[timber blade]

#latex-testing

[gusty storm]

If I had to tell you people my backstory, then I used to perform very well in math during primary, and secondary school. Because everything was formula-based. Now I am terrible at math

[winter comet]

uhh i try it out a bit in my brain

like imagine you're writing it down on paper

but where paper is air

and you're not writing it down

💀

[winter comet]

i mean its still relatively formula/technique/methodical based