precalculus

[sour ore]

Can't you graph it

[viscid thistle]

is this the best way to fill this out?

[proven siren]

...

do you mean "can you check all my homework"

answer is no

[viscid thistle]

yeah pretty much 👻

[viscid thistle]

to my question or yours?

[proven siren]

…

To yours

[hybrid spoke]

damm integration and differentiation is soo ez

[autumn wadi]

1. Wrong channel
2. Differentiation I suppose integration not really

now solve for the gamma function at 0.5 using its integral definition

[mental talon]

[soft cedar]

wait im confused, is deffrentiation part of ur guys' precalc

cuz this turned into the clalc chat

calc

calc channel

[autumn wadi]

No lmao

[gentle kettle]

u sure integration is easy?

[old isle]

its called precalc for a reason 😭

[gentle kettle]

what is precalc?

is it just algebra (hs)

[old isle]

trig and algebra

and proof writing

[gentle kettle]

oh

[old isle]

and complex number stuff

[gentle kettle]

so just algebra

and some trig

[old isle]

yes

[gentle kettle]

oh

precalc is just an us thing right?

[old isle]

no

idk

im not from the US

[autumn wadi]

Just ignore them they probably trolling or smth, or they just know nothing abt what it actually is

[gentle kettle]

yeah probably

[autumn wadi]

Not sure tbh, just a convention of classifying topics tbh

[gentle kettle]

i just wanted to write somrthinh

[gentle kettle]

ah

[autumn wadi]

Lmao I keep on using tbh

[gentle kettle]

its ok

🙂

:3

[old isle]

its addictive tbh

[short saddle]

Sidelines of an acute-angled triangle $T$ are colored in red, green, and blue. These lines were rotated about the circumcenter of $T$ clockwise by $120^\circ$ (we assume that the line has the same color after rotation). Prove that three points of pairs of lines of the same color are the vertices of a triangle which is congruent to $T$.

[obsidian monolith]

aSome1gussy

[proven siren]

do you just expect us to solve it for you?

[viscid thistle]

its easy when you have a calculator

[autumn wadi]

... no

If you refer to an ordinary calculator, then idk what Yr on about. If yr talking abt wolfram, then Yr not even doing the integration

[outer stag]

calculus isn’t meant to be done with a calculator

takes away the beauty

[bitter compass]

is the rzn for x=1, x=2, and x=3 not being continuous bcuz of the open circles?

[autumn wadi]

Rzn?

[hybrid spoke]

yeah

[autumn wadi]

._.

please bring your trolling to another channel

and if you are being serious, just know that you probably barely scratched the surface of what lies behind all of integration.

[hot flame]

i just wanna check

is this right

for part c: 7(6i -15j) - 4(-22i + 12j)

42i-35j - (88i-12j)

-46i - 47j

[violet kelp]

the numbers on the integral sign mean the values you're integrating from

yes

$\int_a^bf(x)dx$ represents the area under the function $f(x)$ between the values $x = a$ and $x = b$

[obsidian monolith]

blanket

[violet kelp]

bottom to top

you as well

[hot flame]

how can i find the angle between two vectors?

[violet kelp]

there's a specific formula for this

[hot flame]

oh there is?

[violet kelp]

yeah

Given two vectors $\vec u$ and $\vec v$, then the angle $\theta$ between $\vec u$ and $\vec v$ is defined to be
$$\cos\theta = \frac{\vec u \cdot \vec v}{|\vec u||\vec v|}$$

[obsidian monolith]

blanket

[violet kelp]

where the numerator is the dot product of the two vectors, and then || means the magnitude of the vectors

[hot flame]

oh ok

and i take arccos for theta

[violet kelp]

yep

[hot flame]

oh ok thxx

[solar olive]

do note the calculation numerically is somewhat ill-conditioned near -1 and 1 for arccos

[wary ember]

https://i.gyazo.com/3392b5937a4b254bf7c8e90a4bd611ff.png

This can be rewritten as xy/x + x/x correct? And therefore the x on the left cancels and you're left with y+1? I'm simplifying trig equations and trying to make sure I'm doing this right

[frigid comet]

yes thats correct

[wary ember]

Okay I thought so, thank you :> I have a ton of issues with complex fractions and simplification stuff so brain go brrr

[frigid comet]

yea i got you

[mossy sierra]

i dont understand whats going on with the numerator😭 can someone help me find the notation for the sequence?

[willow bear]

hold on

why is $\sum_{n=2}^8$ there? was that part of the problem statement?

[obsidian monolith]

Ann

[willow bear]

or was this something you wrote yourself

[mossy sierra]

sorry i shouldve cropped that out lol it was just me trying to solve it

[wise spoke]

hey, can i distribute each e to a seperate ln? like we can with derivative or no?

[willow bear]

ln(x+y) != ln(x)+ln(y)

[wise spoke]

Huh?

I remembered that $ln(A \cdot B) = ln(A) + ln(B)$

[obsidian monolith]

∫Inheritanc-e ♦

[wise spoke]

so how do i simplify this?

$rx + ln(e^{2x} - 2e^{x} + 1)$

[obsidian monolith]

∫Inheritanc-e ♦

[wise spoke]

the ln part

[willow bear]

well as it happens e^(2x) - 2e^x + 1 can be written as (e^x - 1)^2

for what purpose do you need all this tho

[wise spoke]

ahhhh

yes it can

[wise spoke]

i was solving a question and it required me to simplify this $ln(e^{rx }\cdot (e^{2x} - 2x^{x} + 1 )$

[obsidian monolith]

∫Inheritanc-e ♦

[willow bear]

can you show the question in full

[wise spoke]

It's alright, i did it. just forgot the logarithm part

thanks for the help

[carmine coral]

y = 2x^(x-1)

is there a name for functions like these?

[autumn wadi]

exponential functions

tetration is also used to refer to smth like x^x^x... though I don't think it really fits your case

[carmine coral]

the graph isnt anything like a exponential tho does it still classify under it?

[autumn wadi]

Well the exponential function is defined by this so I suppose so

[carmine coral]

ok

tysm

[solar olive]

yeah but the thing has x in the base and exponent so wouldn't it be morr appropriate to call it tetration

[autumn wadi]

well, fits the definition either way

[solar olive]

exponential function is when the base is constant tho

[autumn wadi]

well I don't really see that from the what we call an exponential function from a glimpse in the wiki page. Could u perhaps provide a screenshot or smth? This function can be rewritten as $2e^{(x-1) \ln x}$, which kinda fits the definition here, so I don't quite see the issue tbh. Also, what's more important in mathematics is the implications of such a function, and not so much of the semantics.

[obsidian monolith]

Kiameimon | Welt Rene

[autumn wadi]

heck, just call it a function and you'd be right

[viscid thistle]

can someone help me w my homework plsss

[soft cedar]

ck12.org

youll love it

[safe oak]

What on gods green earth is the formula for the abomination that is what simplistic graphed

[safe oak]

Take the differences of each numerator

1+2=3 , 3+4=7, 7+8…

2, 4, 8

2^n+1 for the nth term.

[viscid thistle]

Hey

[viscid thistle]

Hi

[modest whale]

2^n, 2^n+1 ...

for num
1: 2
2: 4
3: 8
4: 16

differences

[viscid thistle]

https://www.youtube.com/watch?v=eR-gpNyb0

[stoic haven]

Hey can someone help me with problem number 23

Here is what i did but the correct option is c. I know how to get that option but i cant understand where i went wrong

[tropic patrol]

In feynmann’s technique, is it ok to say “differentiate with respect to the integral”?

[hushed sphinx]

Neither of those words sound like they belong in PREcalculus.

[marble beacon]

Someone can help me ?? :'))

[proven siren]

#❓how-to-get-help

[opal tree]

Uh

No

$\oint \int^2 + 2\int \hspace{2pt} \dd \int = \frac12 \int^3 + \int^2 + C$

[obsidian monolith]

Umbraleviathan

[opal tree]

LOL

but in all seriousness, no

You need to specify it's $\pdv{t}$

[obsidian monolith]

Umbraleviathan

[opal tree]

Or whatever your Feynman integration variable is

[opal tree]

@undone sand I integrated with respect to the integral

[undone sand]

[lone plover]

Hey all; I have been working through solving rational equations; grunt work practice to kill some quiet time; and came across one question thats kinda made me think im missing something :P; I can work my way around it no worries; but used a math step solver app which provided a solution which has me scratching my head as to the how and why.....any chance someone can explain this one a little better?....(stby)

[wild badger]

i don't have much help to give sorry but i love your handwriting so much

right in between messy and very readable

idk it just looks great but carry on

[lone plover]

in the middle term of that equation the solver chucked in a -(2x-1) then canceled out the (2x-1) heaving the "-"; this i just cant get my head around. Obviously taking the (1-2x) and multiplying it by (-1) makes it the (1-2x) but....its got me stumped why its not a lcm of the whole equation. Enough to finally join a maths group and ask for help 🙂

[lone plover]

haha; thanks, thats a messy page 🙂 it dosnt seem as much fun if its mesy. 🙂

Im sort of thinking that the (2x-1) is a factor for all; but that is a product of (-1)(1-2x) and the (2x-1) is sort of 'already including the -1'; and when in this middle term the -1 is pulled back out and left over during the canceling of the denominator? you will have to excuse my descriptions; hope that makes sense?

works out fine when you leave it; I guess im stuggling with; why isnt (-1) then just a part of the LCM and should be applied to all?

[floral ore]

I'm having trouble with this question

When I solved it I got answers to be 1/9 and √3, but in the solutions the only correct answer is 1/9

I don't know how I'm supposed to get rid of √3 as a solution without substituting for x

[cursive holly]

Just replace x with √3 in the equation and observe if the equality can be in real numbers

[floral ore]

^

[cursive holly]

Oh, I didn't read the last part

[floral ore]

is there any other way that doesn't involve me wasting 2 minutes on every logarithmic equation

because if checking for x is the only way, then God help me

[cursive holly]

I think that's the only way to do it

You don't have to know if the entire equation can be in real numbers

For example, if you have:
$$√x - \frac{x - 2}{x^2\ln(x)} = a$$

[obsidian monolith]

Rub05

[cursive holly]

If, in that equation (imagine a is a number where the equation has a solution), x = -1, you don't need to waste time replacing x with -1. You can see that it's a √x there. That's enough to conclude that x = -1 is not a real solution

[floral ore]

yeah, I was thinking if we could apply something similar in my question

similarly x can't be 1 either

since that'd make ln(x) 0

[cursive holly]

Correct

[floral ore]

but I'm not sure what limitations I have for √3

without substituting √3 in place of x

[cursive holly]

If you don't have trouble with √3, then you did something wrong in the resolution

If you replace x with √3, the left side would be 2 instead of 0

[floral ore]

for a little more context, I solved it by assuming log_x 3 to be t

log 3 base x

and I squared both sides as well

so it probably did create an extraneous root

I ended up getting t = -1/2 and 2

[cursive holly]

That can be the reason

[floral ore]

but how do I detect the extraneous root is the problem

unless I'm meant to check the solutions of every equation I solve by squaring

[floral ore]

can we reject t = 2 here?

[cursive holly]

You need to do that

[cursive holly]

Replace and observe if it's correct

[floral ore]

when I put in t = 2 I get √4 = -2

[cursive holly]

And that's wrong

[floral ore]

I guess this happened because I squared -t

[cursive holly]

Yep

[floral ore]

Welp

I guess I'll have to keep it in mind then

thanks for the help

This was my solution btw

[half night]

I don't know the answer but what pen do you use? lol

[lone plover]

😝 Pilot Evolt (2+1) and the mechanical pencil is a uni Kuru Toga

The two greatest pieces of engineering in human history 😝

[lone plover]

I spent years looking for these, trying ever pen I could find/buy/steal knowing that out there somewhere was the perfect pen; made by centuries of samurai swordmaking bloodlines; untill the day I found them.....instantly I knew. 😝 (I would recommend)

[half night]

Hahaha, thank you some much

I am looking to buy some stuff, all I got is a pencil now

[lone plover]

The Evolt is red black and a pencil. It's awesome. (In my opinion anyway). Refills are hard to find, you gotta get the origional Pilot ones. (Can be found on eBay)

[lost crane]

How do I find the perpendicular of a vector? Given multiple choices.

[willow bear]

"the perpendicular of a vector" is not something you hear often

but if you're given some vector and a list of options and asked which one of them is perpendicular to your given vector,

then you can check them all one by one

do you know how to check if two vectors are perpendicular to each other, or do you need a refresher?

@lost crane

[lost crane]

Oh I forgot I have already received help. Using the dot product to find the perpendicular of a vector. Thank you for the reply though!

[autumn snow]

Anyone know how to explain what a segment is?

[summer crag]

do you mean "line segment" ?

[obsidian monolith]

r3g56

[bitter turtle]

While squaring both sides, should the interval of t change(idk)

[mortal tartan]

i am actually confused about this formula . I always used to know as in the attached picture

[obsidian monolith]

r3g56

[crystal girder]

1. A massa de substancia radioactiva em certa amostra é dada pela
   fórmula:
   ( )

Com em anos e ( ) em miligramas.
1.1. Quantos miligramas havia no inicio da contagem do tempo?
1.2. Quantos miligramas restavam decorridos 10 anos, desde o início da
contagem do tempo? Apresenta o resultado com uma casa decimal.

[half night]

Qual é a formula?

[warped cipher]

why you keep spamming this anyway?

[bitter compass]

can someon explain how -2 is being approached from below for the right hand side?

it makes sense for the left hand side of the graph but isn't the right hand side approaching zero?

[warped cipher]

you're not?

[vapid plaza]

because of how h(x) behaves around x = 1; no matter x approaches 1 from the left or right, notice that h always approach 2 from the bottom; so if we put h(x) on the horizontal axis again then it is always approaching 2 from the left

[iron fern]

hi, i need help understanding the sandwich theorem (limits)

[proven siren]

google it first

[iron fern]

okay

[half night]

Quantos mg?

[mossy sierra]

if n=0 in summation notation, do i plug 1 or zero into a1? basically does a1 mean i plug in 1 or does it mean the first term of the sequence (0)??

[proven siren]

Can you give more context

[mossy sierra]

sure let me send a picture of the problem

ok take 49 and 53 as examples

[half night]

your just gonna do 3(3:2)^0 + 3(3:2)^1 until 20

it's called sum so you basically replace the value as you would for a "x" but your adding with the previous value each time you do it

[mossy sierra]

yes but to find a1 would i plug in 0 since thats the first term?

[half night]

i'm not sure if your course demands a different kind of approach to this question, though

[half night]

wydm by a1?

[mossy sierra]

so the equation to find the sum is Sn= n/2(a1+an) but i need to find a1 first which is the first term in the sequence. if the sequence starts at 0, do i plug 0 into the equation to find a1 or do i plug in 1? so sorry if this is confusing lol i am also confused

cause a1 means plugging 1 in as n but it also means the first term which, in the case of those 2 problems, is 0

[vapid plaza]

Why would this even work? Isn’t that formula for arithmetic series but your screenshot is geometric series

[mossy sierra]

ok yeah it is geometric sorry but thats not what im asking cause my question would apply to both arithmetic and geometric

since the formula to find the sum of a finite geometric sequence is Sn= a1(1-r^n/1-r) i still need to find a1

[vapid plaza]

If your formula uses the “first term” just put in the “first term” in the series

[mossy sierra]

so it would be 0? since thats where the sequence starts in the sigma

[vapid plaza]

That’s not always the case

Number below the sigma isn’t always 0

[mossy sierra]

look at the problems

n=0

[vapid plaza]

i = 1 tho

(Although one could easily rewrite the question to start the index from 0

[proven siren]

no

[mossy sierra]

n and i are interchangeable theyre just variables

n=i

[proven siren]

it’s xy^0

=x

[mossy sierra]

what

[proven siren]

The first term is 300(1.06)^0=300

not 0

[mossy sierra]

thats the equation to find the terms

[proven siren]

yes and

the first term, if n=0 is the start, is when n=0

ignore the a1

Just think about the first term

[still nymph]

any tutors ?

[mossy sierra]

to find the sum i have to find a1

[proven siren]

no

You find the first term

[mossy sierra]

i need a1 to plug into sum equation

the first term is a1

[proven siren]

but what is a1

Get your head out of thinking just about a1

It’s the first term

That’s what they mean

[mossy sierra]

my whole question is about a1

[proven siren]

sometimes the first term is when n = -2

[mossy sierra]

the first term can be anything

[proven siren]

yes

a1 makes it seem like n =1

[mossy sierra]

im asking how to find the first term if n=0

[proven siren]

Which is not always the case

[mossy sierra]

yes but a1 means first term but it also means plugging 1 in an

[proven siren]

I’m explaining why that mindset is wrong

no it doesn’t

that definition is bad definition

You’re basing your understanding on something that is not generalised

[mossy sierra]

ok ill just talk to my teacher tomorrow

[proven siren]

just use the first term

That’s it

Whatever n=

[mossy sierra]

so id plug in 0

[proven siren]

If n starts at 0 yes

If n starts at 10 you plug in 10

[mossy sierra]

that was making me go crazy

💀

[untold field]

what are you trying to solve?

im rlly good at calculus

i can rlly do that in my head

[mint sapphire]

is this just cause I didn’t draw fx line?

[viscid thistle]

The epsilon should have L+/L- and the delta should have a+/a-

I can demonstrate it

Give me a minute

[mint sapphire]

ight

[viscid thistle]

Wait, let me fix one of the operations

[mint sapphire]

do we show the greater delta

or do we use the smaller delta and replicate it both left and right

[viscid thistle]

It says to sketch the delta-epsilon definition of a limit, and the only thing wrong you had in your sketch is forgetting a and L.

If you cant read my handwriting I can try fixing it

[balmy gorge]

Fun stuff

[grave forge]

Funni

Ok actually trig is annoying

[balmy gorge]

Nah

It‘s easy

I completed that work in about 5-10 minutes

[grave forge]

No its ez, but like not enjoyable

[balmy gorge]

I enjoy it lol

I love math

[deep cove]

whats a good beginner friendly calculus book?

[slim dew]

Michael Spivak's Calculus is a good classic you could look into. Try #book-recommendations for more recommendations.

[steep mountain]

belive me trig is easy

its calc thats tuff

[autumn wadi]

I wanted to recommend it too but I wouldn't say that it's "beginner friendly", if that is meant to mean "easy/gentle"

[deep cove]

i did not necessarily mean easy, but it must cover like basics and should teach u from the beginning

[autumn wadi]

Hm

What do u intend to learn calculus for? The computations or for the proofs?

[deep cove]

for uni + programming related

[autumn wadi]

Ah.... ic. Not interested in axioms, proofs etc then?

[deep cove]

i guess so

[autumn wadi]

Then I'd recommend stewart's calculus instead. Spivak is more rigorous and provides an introduction to mathematical analysis

Which doesn't really suit your needs

[deep cove]

ill check it out ty

[indigo halo]

Man i wish i understood that kind of math

[grave forge]

Wdym xd
Its high school math or middle school in some cases

U just gotta spend some time

[summer crag]

finding general solutions of trig eqns is more fun actually

you get to struggle more lol

[grave forge]

I think its boring
Im more of a
Proofs guy

I love proofs

[summer crag]

ohh, that's a pure math guy ^

[grave forge]

Real

[summer crag]

you must have enjoyed real analysis and abstract algebra , then ?

[grave forge]

Bro fr believe me
U will love the proof of uncountability of the real number set

[grave forge]

Yes
But switching from school math to pure and competitive math on my own is very challenging

I still struggle with algebra

[summer crag]

clarify , are you talking about abstract algebra or algebra

[grave forge]

Algebra

Abstract 💀💀💀

I haven't started

I have the prerequisites tho

[summer crag]

hmm, I too algebra is too vast and there are lot of theorems ,proofs and manipulations involved

[grave forge]

Number theory is the fancy math
Everyone loves it

Way too fancy

[summer crag]

you need to be good at formal proof writing and need mathematical maturity , is that it or are there any other prerequisites as well

[grave forge]

Im a diophantine equations enjoyer

[grave forge]

Elementary counting and number theory would help too

[summer crag]

I've no experience with number theory :/

[grave forge]

And also linear algebra for abstract vector spaces

[grave forge]

You are missing out

Go go

Learn NT

[summer crag]

linear algebra is extension of matrices and determinants and vectors , right ?

[summer crag]

yeah, gotta learn NT , will start from scratch.

[grave forge]

Wdym
Linear algebra IS matrices

It just generalizes matrices and vectors using vector spaces

Anything that obeys linearity can be treated as a vector

[summer crag]

ohh, yeah , sorry I meant in grade 12 (cbse) I learned all this , without the linear transformarions and vector spaces introduced formally

[grave forge]

Bro

Fuck indian schools

Its a shame that they weren't introduced to us

It would have made a lot of math enthusiasts

[summer crag]

yeah , totally, I watched the essence of linear algebra by 3B1B recently,and realized how fun all this stuff is , which is taught in such a dry manner in school

[grave forge]

Ye
When he said go play around with transformations, I actually did
Lmao it was a good experience learning linear algebra from scratch

[summer crag]

yeah, did you take a linear algebra course as well (in clg) ?

[grave forge]

CMI stopped asking from Linear algebra, i think they weren't able to come up with tough problems

[grave forge]

Ye
I hated the way it was told to us(keyword: Told)

[summer crag]

LOL , I expect colleges also aren't that good , the same school system is extended

yeah , except a few like ISI, CMI

and IIT's (maybe)

[grave forge]

In state Colleges yes
But IITs IISERs and other prestigious ones may be good

[grave forge]

IITM has a very good math department btw xd

[summer crag]

Not as good as the way 3B1B does tho ^-^

[grave forge]

CMI and IITM actually did a few collabs

[grave forge]

He is like born for teaching

But a drawback is that, he uses way too much visualisations, so he maynot do videos on number theory 😔😔

[summer crag]

yeah , I'm taking their level 4 (think out of the box course) , really excited how the lectues will be

[grave forge]

Ye IITM is really good

I really want to teach math to a large audience one day

Idk how it feels like

Must be good

[summer crag]

yeah , he has made vids on abstract algebra in the past , so maybe he can

[grave forge]

Its on group theory tho

Oh yes

He may do yes

[summer crag]

yeah, the guy can do anything

[grave forge]

U could've applied for CMI imo

If u really like math

CMI and ISI is even worth a dead shot

[grave forge]

Are u giving IATs?

[summer crag]

not very confident , not sure , coz I suck at phy ,chem and bio

[grave forge]

Just do it

[summer crag]

yeah

[grave forge]

Im giving IAT if i fail to get into CMI

My last resort on record before obliteration

[summer crag]

hmm, iiser's are really good

[grave forge]

Ye

Start preparing btw

Like 3 hours a day

[summer crag]

my shot is cuet , maybe I can get into some good uni via it

[grave forge]

If u know hindi
Definitely an awesome option

Im from TN so ye

[summer crag]

hindi ? wdym

[grave forge]

In TN there only one reputable institute for sciences via cuet
And its not that good
But in other states there are really good ones
But it is rumoured that they teach primarily in hindi

I only know tamil and Telugu 😔

[summer crag]

, like hyd uni teaches in english ig

and they have a good math course

[grave forge]

Ye its awfully hard to get in due to competition 💀💀

But ye

I should have given CUET

[summer crag]

ik , <_>

[grave forge]

But dont lose hope tho

[summer crag]

yeah , thanks buddy , hope you get into CMI / ISI

[grave forge]

Naw ISI is next level
I have some hopes for CMI
If i manage to solve 1+1/2 questions from part B
I have a good chance of getting in

😩banger syllabus

[summer crag]

YEAH

[grave forge]

The best part about the exam is that
It has very interesting questions

So if u solve one question correctly, the morale just increases wildly

Even if u partially solve, it feels good

[summer crag]

Yeah , the subjective questions are really hard , INMO level stuff

[grave forge]

Nah INMO is out of reach

I have tried INMOs and i couldn't solve one question without dying more than 7363times

It is ridiculously hard

Even the RMOs god damn

[summer crag]

even the prmo

now ioqm

[grave forge]

This one here is actually a good RMO level problem but the hint made it elementary

[grave forge]

Ye

And yes CMI cares well enough to give hints LMAO

[summer crag]

wth is that

NT ?

[grave forge]

Yep

One key fact to notice right of the bat is that one of the numbers divides the other

[summer crag]

We are taught almost no number theory in school, it becomes really hard to even solve the most trivial NT problems

combinatorics is also neglected

[grave forge]

Ikr
I was like
Struggling to solve even smol NT probs in SECTION A LMAO
then i just had this book called excursion in mathematics and gave a lot of hours to math

Now section is solvable and section B is really hard for me

And i have CMI in two days

[summer crag]

I've heard Challenges and thrills of pre college maths also got some good questions on NT , combinatorics , geometry (which are neglected in school curriculum)

[grave forge]

Ye

Its a good one and also mathematical circles

The Soviet book

[summer crag]

Does excursion in math also has theory in it ?

[grave forge]

Ye it covers everything except calc

[summer crag]

hmm

It's made for math olympiads ig

[grave forge]

Ye

[summer crag]

And math olympiads usually don't have calc

[grave forge]

Now i gotta go solve problems ig

[summer crag]

Yeah

[grave forge]

Calc can be used

It doesn't exclude calc
Calc is just not in the syllabus

[summer crag]

Yep , like how you used Taylor expansion to solve that problem

[grave forge]

Nani u saw that

It was a CMI mock

[summer crag]

Hmm , does CMI allow all that stuff tho

[grave forge]

i actually enjoyed that problem
Got elementary real analysis vibes

[grave forge]

Ofc

[summer crag]

, I understood nothing out of that , lol

[grave forge]

It is rumored that they actually weigh good proof writing over marks
But a rumour
Idk for sure

[summer crag]

hmm ,it could be

[vast cliff]

hmm yes maths

very smart

[grave forge]

They asked me to prove that the function is a line
It just doesn't have a second degree term
The second derivative stands on the second degree term, if it is zero, then the solutions are lines(the second degree term is the remainder)

But now
I gtg

Bye

[summer crag]

Yeah , bye

[minor forge]

wtf is derivatives in precalc

thats calculus

[candid chasm]

Does anyone know any good websites where I can learn precalc?

[terse thicket]

Have you heard of coolmathgames?

Yeah, so they have a sister site coolmath

It goes from elementary to precal and the person who wrote it is a great teacher

[royal flare]

is there a BC calc channel?

[autumn wadi]

#calculus or #multivariable-calculus depending on your needs

[royal flare]

thanks.

[thin stratus]

can someone help to to solve come ap calc ab questions?

"Some"

[hushed sphinx]

Wrong channel? Also nobody will be able to help you until you ask a question.

[terse thicket]

does exponential/logarithmic functions have horizontal stretch/shrink transformations

[thin stratus]

someone?

[willow bear]

this belongs in #calculus.

[viscid thistle]

Is there no general channel?

[hushed sphinx]

There's #discussion.

[gentle kettle]

i "solved" this by making the inequality $\sqrt{n}+\sqrt{n-1} \geq 100$ and then showing that for n<=2500 this isnt true and for 2501 that it is the smallest possible

[obsidian monolith]

Affe

[gentle kettle]

the given solution was the same

but i was wondering if there was another way of solving this since the way i did it feels weird

[hushed sphinx]

That looks like a pretty neat approach to me.

[gentle kettle]

oh ok

ty

[crimson canyon]

Is this right?

[autumn wadi]

I'm curious- why >= 100? Is it some.... conjugate property? (ah, yes, it is.... You multiplied both sides by the conjugate. Nice one)

[viscid thistle]

Is this right

[cold badge]

#math-discussion sorry i cant find the channel

[soft cedar]

3 is incorrect

or 5

i meant

because u found sine theta and not tan

everything else is right

i believe

[cursive cairn]

<@&268886789983436800> spam?

[gentle kettle]

f(x) is concave over interval I if f''(x)<0 over I and its convex if f''(x)>0 over I right?

now while learning calc, the thing I thought meant convex is called concave upwards

was I remembering something different?

or is concave upwards just the same as convex

[mild swan]

concave up/down

I've always been taught concave up/down

[gentle kettle]

concave down was what i remembered as concave and concave up the thing i thought meant convex right?

[mild swan]

concave up is like a cup, concave down is like a frown

[gentle kettle]

so its not just f''(x) >0 or f''(x)<0?

this is how i thought it was

[summer ruin]

well yes you want to be able to say the linear function is both convex and concave

[gentle kettle]

ok ty

[pulsar geyser]

To find the dot product of a pair of vectors, you just multiply their values together and then just add them, right? And then how would you determine if they’re orthogonal?

[autumn wadi]

Wdym "multiply their values and add them"? That isn't concise enough for us to tell if you understand how to do it computationally

And you can tell when they are orthogonal when their dot product is 0. Can you convince yourself why this is true? Or is it?

[pulsar geyser]

Im not quite sure honestly about the dot product and what it is. It seems simple but i don’t fully understand it.

[pulsar geyser]

Uhhhh

Is it something to do with the unit circle? Or am I thinking of something else?

[autumn wadi]

Mmm.... not quite

https://www.mathsisfun.com/algebra/vectors-dot-product.html

This explains the geometric interpretation of a dot product

Should make things clear

[north remnant]

Could somebody please explain how these steps are completed? I just memorized how to do it but I would like to understand the process.

the relation portion, I understand the derivative process

[stiff tapir]

product rule of derivitves

[north remnant]

Ohh okay, thank you

[stiff tapir]

np

[vapid plaza]

people will literally post anything other than precalc in #precalculus

[autumn wadi]

Who knew #calculus doesn't exist

[viscid thistle]

no clue how to do part c, part a and b i have done and is one help channel 1: https://discord.com/channels/268882317391429632/269573202018041856

[vapid plaza]

What’s your answers for a and b?

[summer crag]

A(x) is the area of pentagon in terms of x , right ? , so now we can differentiate A(x) wrt x and we get A'(x) i.e the gradient function of A(x) and we can equate A'(x) with 0 , to find where the slope of function A(x) is equal to 0, next step would be to the 2nd derivative test,

[viscid thistle]

i posted it in precalc for a reason lmao

[summer crag]

Ohh , sorry.

[viscid thistle]

all g understandable, i know calc but this q is in a non-calc sec of our content

but i figured out

a(x) is a parabola

u find the t.p.

however I don't understand why that is the max area

[viscid thistle]

@vapid plaza check teh thread

nvm i am actually straight up stupid

a(x) is area of the pentagon

its a model for the area

and the highest would be a the t.p

oml

when maths works out

no

cuz if u read q

the penagon isn't normal

it is made up of a equilateral triangle and rectangle

[vapid spire]

@viscid thistle when in doubt, use derivatives to find solution

Or in the case where you haven't done derivatives yet, you can try vertex analysis for the quadratic function written above. Get its zero points and pick the middle between them

[viscid thistle]

thanks

legend

[mild swan]

Asking that question makes the process slower for everyone

[patent tundra]

please help lets say I have 0 = (-x2^-x) * (ln(2)) + (2^-x) how would isolate x? is there a specific order I should follow like Bedmas or Pemdas?

[summer ruin]

factoring

[hot sable]

how do i factor this cubic trinomial when i know that (x-2) is one of its roots x^3-3x-2

[willow bear]

polynomial long division

or perhaps synthetic division if that is more your thing

either way knock it down a degree

[hot sable]

thx

[tawdry bloom]

I made a formula to calculate pi

[viscid thistle]

Bro it's ain't clear

Even though explain how we should do it

Hi

[torn parrot]

explain derivation + i did the same by taking the limit of a natual polygons inscribed triangles sums

little different to that greek guy tho

[burnt hare]

Could someone check if this is right

i wasn’t in class and idk if i’m doin it right lol

specifically how do i do #1 at the bottom

i’ll post in a helper section lol

[main terrace]

Can someone explain to me how (sqrt(2) / 2) * (sqrt(3) / 2) - (sqrt(2) / 2) * (1/2) = (sqrt(0) - sqrt(2)) / 4

Bc I’m coming up with = (sqrt(6) - sqrt(2)) / 4

[main terrace]

I mean it looks good based off the formulas you were provided, tho I can’t say for sure bc I haven’t done logs for a few months

[main terrace]

Nvm my teacher made the mistake

[stiff tapir]

Bro your profile photo 💀

[wanton vector]

Sorry in case you already got an answer in another channel, but why did you divide at 6)?

[burnt hare]

Yea i realized 6 was wrong lol
all the others r right tho

just a stupid mistake

[wanton vector]

Yeah. Did you find help for the last question too?

[burnt hare]

Yea my teacher was free

[wanton vector]

great.

[lime frost]

Thank god I already finished that part

[burnt hare]

wym

[eternal flint]

hi

[autumn wadi]

So, how would you derive the formula to find the slope of a line perpendicular to it, given that you know the original line's slope? i.e taking the inverse and reciprocal of the original line's slope

[viscid thistle]

when you have a function that goes x_1 + x_2 = 5

what would be the Y in this?

[summer ruin]

whatever you choose to be y

[viscid thistle]

when i graph this is x_1 considered x and x_2 considered y?

so like y = 5-x

since youre here, this is what im trying to figure out

[summer ruin]

the point is that it's irrelevant, it will only change the names of the axis so you can choose any one to be x and y

[viscid thistle]

so for example 5x1 + 6x2 = 30 it doesnt matter

[summer ruin]

yes, you just need to be consistent throughout with your choice

[viscid thistle]

alright then 🙂 thank you very much

[viscid thistle]

lol i learned something new

[summer crag]

nope, it is nx^(n-1)

[faint echo]

i am new to calculus . please help me get started

[green delta]

What do you want to start with?

[summer crag]

I believe learning about average rate of change of a function is a good place to start with (atleast that's how I started) , and some basic limits algebra and learning non rigorously what limits are

and then we can learn about instantaneous rate of change of a function , precisely the derivative of the function.

[autumn wadi]

man, where's that message where someone said in precalc channel we discuss anything BUT precalc?

[summer crag]

hmm , I feel there's a very thin line between pre calculus and early calculus , and most often when someone has got a elementary calculus question, they feel it would be better to ask it in the pre calc channel as opposed to the calculus channel (which is made for actual calc)

Nevertheless, calculus questions are more than welcome here ig , the server doesn't put any air tight restriction on where one can put their question, especially when one subject is sort of merging into another.

[vapid plaza]

how exactly does precalc merge into calc?

if it involves derivatives/integrals then its calculus

otherwise its not

[summer crag]

Yeah , I agree but usually pre calculus is the stepping stone for calculus, and I mean precalculus curriculum is also somewhat flexible , at some places limits algebra , functions , average rate of change of a function is part of precalculus.

[summer crag]

Yeah , that's why there aren't any actual differential and integral calculus questions asked here , the questions asked here are more about definitions or they are elementary in nature.

[vapid plaza]

i guess so

[hushed sphinx]

We frequently tell askers "that is not precalculus", but the "pre-" seems to be invisible to many.

[summer crag]

hmm , but still ig students are more hesitant to ask elementary calculus questions i.e questions involving definitions, or some really simple rules in the calculus channel, but stll I take my words back.

[autumn wadi]

So, how would you derive the formula to find the slope of a line perpendicular to it, given that you know the original line's slope? ( i.e taking the inverse and reciprocal of the original line's slope)

[hushed sphinx]

Similar triangles.

(draw a horizontal line through the intersection point, with a perpendicular 1 unit to the right of the intersection).

[summer crag]

Yeah , consider a line with slope m₁ = tan(θ) , now the slope of a line perpendicular to this line will be tan(π/2+θ) = -cot(θ), thus slope of perpendicular line is -1/m₁ , but the method troposphere has suggested is much more intuitive (and it's geometric).

[viscid thistle]

who can help me with comics parametric and vectors $$$

[autumn wadi]

[golden cairn]

How do I find the vertex of this

[slim steppe]

Use the formula (-b/2a)

[dull current]

Hi how do you solve this: A rectangle is bounded by the x-axis and the graph of y = 4 − x2. What are the coordinates of 4 corners of the rectangle so that that its area is a maximum?

[glossy whale]

Do you do the stretches within the parenthesis first or inverse first? Cuz these give two very different answers

[glossy whale]

Suppose bounded by x-axis, y-axis and first quadrant. Then it should be the half way point along the line y=-2x+4 which is (1,2). Therefore (0,0) (0,2) (1,2) (0,2)

[dull current]

Oh sorry i meant y=4-x^2

So a parabola

[glossy whale]

So in that case you would construct a formula that will give us the area of the rectangle. Which is essentially (x times y)=(x times (4-x^2))=4x-x^3. However, since it is not bounded by the y-axis, there are both sides of the area, so the (formula times 2) = 8x-2x^3. Just plug that equation into a calculator and you'll see the local climax between -2 and 2 is when x=1.155. Therefore, the rectangle would be max at (-1.155,0) (-1.155,2.66) (1.155,0) (1.155, 2.66)

[dull current]

That makes sense, thank you!

[snow whale]

can someone explain why a isnt a function

[wild kite]

First of y = sqrt(8-x^2)

Not sqrt(8-x)

[grave forge]

±

[snow whale]

doesn't the square root take out the square on x

[wild kite]

Thanks

[wild kite]

Idk what you’re takking bout
x^2 +y^2=8
y^2=8-x^2
sqrt(y^2)=sqrt(8-x^2)

The square doesn’t go

[snow whale]

i see and then the square would make it not a function

[wild kite]

I ain’t sure bout that

[snow whale]

explain pls

[wild kite]

Idk bro I need to look up the definition of a function

[slim steppe]

A function is something that has an input and output

[snow whale]

right and y cant repeat right

[wild kite]

I was trying to think of how to phrase that lol i had a brain fart thanks

[wild kite]

Y isn’t repeating

[slim steppe]

Take |x|

In that situation it repeats

[crystal wedge]

can i get some help on some optimization questions

[trim light]

precalc scares me

[lilac quail]

Take the differential and then solve when it is 0

But I kinda suck

Lol

But send anyway

[formal fox]

function: for each input, there is only one output. this is a circle, so you will get two outputs.

[snow whale]

right and thats what makes it not a function

[formal fox]

exactly

[snow whale]

jyup

[tepid narwhal]

im confused on probability

i dont get venn diagrams

or how to approach a problem

i think how i approach questions is half my battle

[echo owl]

What the

btw we had to round up our answers to the nearest minute

[willow bear]

you got the sides the wrong way around i think

[echo owl]

Reference angle is from the top of the tower, which is why it's refered to as angle of depression. Opposite side from said angle is 65.4m long.

[uncut mulch]

angles of elevation and depression are angles made with the horiztonal
these angles are congruent

[granite quiver]

What are your thoughts on the new AP pre calculus class?

[uncut mulch]

where

in what country are you referring to and what's the content

and how does it compare to the calc class and the stuff before it

[granite quiver]

In the US

idk what’s in pre calc

I’m in algebra 2 rn

And they gave me a choice of AP stat, AP pre calculus or AP calculus BC

[uncut mulch]

alg2 and pre-calc pretty much overlaps from what i've seen

[formal fox]

i would not reccomend AP stats. that class is not easy nor is it difficult. do pre-calc then stats or calc.

i am shocked they gave you the option to do stats before pre-calc

[granite quiver]

Stat doesn’t really have a pre requisite

[formal fox]

well in public education. college is different i guess

[granite quiver]

Those are the choices they gave me

At first I chose Ap calculus BC

[formal fox]

WHAT

[granite quiver]

But I was struggling a bit with an AP class rn

So I switched

To Ap pre

[formal fox]

yes

alg 2 -> Pre -> AB -> BC

[granite quiver]

Because I didn’t want calculus BC to end up like the class I was struggling on

[formal fox]

thats the standard order

BC is challenging

very

[granite quiver]

And they don’t offer AB

[formal fox]

the ap pre-calc probably covers a bit of AB

i am suprised i guess. go with what you want to, but i strongly advise you do pre calc first

[granite quiver]

Also I’m a sophomore

[formal fox]

so you have plenty of time

[granite quiver]

Idk how to feel about junior in AP calc Bc

My teacher said after you’ve done BC In junior, there’s nothing else after that for high school

Which is why she recommends BC as a senior

[formal fox]

okay so we are in a similar position.
i did alg2 in 10th, prec in 11th, then ap stats and ap calc ab in 12th

[granite quiver]

You can do both?

[formal fox]

depends what credits you have

school’s flexibility as well

[granite quiver]

They only allow 3 AP per year

[formal fox]

ideally you’d take calculus right after pre-calc

so maybe think about stats -> pre -> calc bc

ap stats is not difficult, but it is a lot of testing

calculator work

Testing as in running tests on sets of data. not like you sit in your seat and do an exam

also do dual enrollment if it is available for you 🙂 the best thing ever

[slow coral]

thats exactly what you'd do

a derivative is just a function to find the tangential gradient at any given point on the curve

dy/dx literally means the change in y divided by the change in x, which is how we define the gradient of a line

as the gradient at any given value of x is given by 2x - 5, you'd plug values of x in to that equation to find the gradient of the tangent at those points 😄

[carmine pollen]

Damn

Mommy wheres my robux

😭

I want robux plssss

[viscid thistle]

You good bro?

[carmine pollen]

No im not

[warped cipher]

This is a math server not a roblox server

[hushed sphinx]

That user is banned already.

[warped cipher]

I see

[granite quiver]

Do people like him appear often?

[uncut mulch]

yes

[wise spoke]

what would be the simplification of $-ln(-u)+ln(-2u)$

[obsidian monolith]

∫Inheritanc-e ♦

[wise spoke]

nvm

got it

[slow coral]

gradient = slope of a straight line

[slow coral]

yeah we call it gradient in my country

[formal fox]

sounds like you already got it, but if we have the form:
ln(-2u/-u)

can we cancel out the negatives inside the log?

if anyone knows

[hushed sphinx]

Yes, (-a/-b) and a/b always produce the same result, no matter whether you're taking the log of that same result after the divisions ...

[fervent gate]

Even more than that. Yes you can cancel the negatives, but 2u/u is just 2

if u != 0 of course

Very late response now that I look at it 😅

[formal fox]

okay, sounds good. ty 🙂

[icy sparrow]

What could you do if n = 100

Or a very large number

[formal fox]

Use a computer to help you 🫡

[icy sparrow]

Silly me

Haha but for real, what approach could you take to solve that?

[viscid thistle]

Are you asking how to find a specific term the expression?

Cuz yeah if your gonna expand a 100 degree polynomial, your gonna wanna have a chat with Mr Turing

Here, I plugged (a+b)^100 into wolfram alpha

[hushed sphinx]

There doesn't seem to be any problem to solve yet, just a statement of a theorem?

Is your task to prove the binomial theorem?

[viscid thistle]

I think he is asking if theres any trick to computing it when n is large

[hushed sphinx]

If you have concrete numbers? Add them first, then raise to the nth power.

[icy sparrow]

Yep thats what I was wondering

[icy sparrow]

Pheeww that’s interesting to see

[icy sparrow]

Didn’t really have a task, just learned about the binomial theorem and my first question was what if n is a large number.
For (a+b)^2 its pretty fast to get to a^2 +2ab +b^2

[dull current]

Hi can someone explain how to solve this?

[willow bear]

ordinarily you would make an expression for the total time spent rowing and walking in terms of x, then minimize it

here, however, a shortcut exists

[thorn pagoda]

At first glance it's very easy since the walking and rowing speeds are the same

Just use the ||triangle inequality||

[granite goblet]

yea

[hushed sphinx]

Well, the theorem is still true if n is large. That doesn't mean you're obliged to write out all of the dozens or hundred of terms, if you don't have a task to solve where that would make progress.
Writing out all the terms is not the only way the theorem can be useful. There are plenty of situations where you can get something useful out of just having the sum in its symbolic indexed form and reasoning about the general expression for the terms instead.

For example, if a and b are integers and p is prime, we can prove that (a+b)^p and (a^p + b^p) have the same remainder when divide by p: Expand (a+b)^p by the binomial theorem. The first and last terms are a^p and b^b, and all the ones in between are some powers of a and b multiplied by a binomial coefficient that is a multiple of p, and therefore each of those middle terms leave no remainder. We don't need to physically write them down to see that -- the general form of (p choose n)·a^n·b^(p-n) is enough to complete that argument.

This also shows a common theme that we're often only interested in a few of the many terms, and there's a common line of reasoning that justifies ignoring all the rest of them.

[wanton vector]

If you want to expand the polynomial fast without calculating each you could draw (or learn for small n) pascals triangle and use the numbers in the corresponding row as prefactors for the expander form

Those would be a few rows as an example, each number is the sum of the 2 numbers diagonal above it, the entry in the nth row and kth column is ${n}\choose{k}$ wich is why it can be useful.

[obsidian monolith]

OfiezierOfShadow

[icy sparrow]

Thank you both for the explanation!

[slow coral]

does anyone have the proof for the derivative of e^x being e^x handy

no explanations i’m reading online are making any sense to me

[hushed sphinx]

That's not precalculus.

(And it depends on which of the handful of possible equivalent definitions of e^x you're using anyway).

[formal fox]

not really a proof, but doing the pre-calc way of taking the limit:

https://math.stackexchange.com/questions/359023/using-the-limit-definition-to-find-the-derivative-of-ex

none of these are done the way a prof i watched show it to a pre-calc class though. a bit higher level than what i wanted

[slow coral]

idk what precalc is tbh i’m not american

[formal fox]

oh i do remember it now:
after you get to the part where it:
$(e^x)Lim_{h -> 0} [(e^h)-1]/h$

we took a part of the limit->
$(e^x)Lim_{h->0} [(e^0)-1]/h $
so that the numerator became 1-1 and anything dividing 0 is zero itself.
$(e^x) Lim_{h->0} (1-1)/h$

$(e^x) Lim_{h->0} (0)/h$
so we are left with e^x

[slow coral]

it’s pre-university stuff where i’m from

[formal fox]

cool stuff

[obsidian monolith]

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

[formal fox]

not too sure how nice it is, but i trust my prof and it was in a pre-calc class so it seems okay

[slow coral]

ahhh i assumed you could do something like that with first principles but didn’t know exactly how to approach it

ty

[hushed sphinx]

I don't know it in detail either, but by the name it has to be something that comes before calculus, and derivatives is what calculus is about.

[slow coral]

ah

we get taught exponentials and logarithms AFTER derivatives and integrals where i’m from

hence the confusion

[hushed sphinx]

Ah, I see how the channel description can be confusing then.

[slow coral]

all good now anyway

[viscid thistle]

Im confused, if your saying the limit as h approaches 0 of (1-1)/h = 0, then we would be left with 0, because we multiply that by e^x

[slow coral]

surely that’s just e^x * 0 = 0

oh wait

yeah now i’m confused too

gonna see if i can work through it on my own now i know where to start

[formal fox]

oh yeah that makes sense. it might have been addition between the two, i can try to remember it but it certainly along those lines

just trying to pull it from my memory, but i absolutely agree with what you say

[hushed sphinx]

You do need to cough up a definition of "e^x" before you can prove anything about its derivative, though.

[viscid thistle]

yeah, you gots to define it as a limit right?

[hushed sphinx]

I know at least 5 ways to define it:

1. Define exp(x) to be the unique function that is its own derivative and satisfies exp(0)=1.
2. Define exp(x) as the inverse function of the natural logarithm (itself defined as the integral of 1/x).
3. Define exp(x) by the power series 1 + x + x²/2 + x³/6 + .... + x^n/n! + ....
4. Define exp(x) as the limit for n->infty of (1+x/n)^n.
5. First define b^x where b is a positive real and x is rational, by powers and roots. Extend it to arbitrary real x by continuity. Let e be the value of b such the resulting function exp(x) = e^x satisfies exp'(0)=1.

They lead to quite different proofs for the derivative.

[viscid thistle]

Interesting

[slow coral]

how can you define a term

i don’t understand this

it’s just e raised to the xth power

[hushed sphinx]

I just showed (or at least alluded to) five different definitions.

[slow coral]

are they not all the same thing

[hushed sphinx]

They define the same function, yes.

[slow coral]

i don’t understand why you need to define it

would you need to define, say, 2^x

[hushed sphinx]

Yes.

Otherwise it's just random symbols that don't mean anything yet.

[slow coral]

all of math is random symbols that don’t mean anything until you start thinking about them

[hushed sphinx]

You can't think your way to the meaning of symbols. That's what definitions are for.

[slow coral]

is it not pretty self-defined

you take a constant, e, and you raise it to the power of x

that seems pretty cut and dry to me

what am i missing there

[hushed sphinx]

Without a definition, those words mean nothing.

[slow coral]

without wheels a car can’t go anywhere, that doesn’t mean i give every car i drive a new set of wheels before going on a journey

[hushed sphinx]

You seem to be a troll. I'm going to stop replying now.

[slow coral]

what

i’m trying to ask - at the high school level - how can you prove that the derivative of e^x is e^x

without getting philosophical about what exponentiation really means or about what e is exactly

[hushed sphinx]

And you refuse to reveal how you define the function you want a derivative of. If you don't have a definition, a proof is impossible.

[slow coral]

i define it as the constant, e, raised to the power of x

e multiplied by itself x times

[hushed sphinx]

That only works as a definition if x is an integer. A function that is only defined for integer inputs does not have a derivative.

Never mind that you have not defined what ""the constant e" means.

[slow coral]

euler’s number

[hushed sphinx]

That is not a definition.

[slow coral]

it’s a constant why does it need defining

[hushed sphinx]

Sorry. i should not have continued replying after I promised not to.

Good luck finding other victims or your trolling.

[slow coral]

wtf is this guy talking about

i just need a proof

[slow coral]

i got my proof

don’t worry guys

crisis averted

[wanton vector]

In case you use the 3rd defenition this is a possible proof. If you use any of the other defenitions you would either need to use a diffrent proof or first proof that the exponentionalfunction is really equal to that infinite sum

,rotate

[wanton vector]

using the limit defenition

[slow coral]

someone explained this proof to me last night

all is good now

or something to that effect

[formal fox]

mine was wrong though, i like what ofie said here. look at their’s

[stoic atlas]

Pls integrate (secx)(tanx)

[hushed sphinx]

No no, the definitions are equivalent -- you get the same function out of each one.
The point is that if you want to prove things about that function, that proof has to start from some definition. And if it's a different definition than then one you're using, then the proof won't be convincing to you -- or at least not without an additional proof that the definition the proof starts from is equivalent to the definition you've been using.
On the other hand, if you already know that all the definitions I listed are equivalent, then there's nothing to prove, because the first one them explicitly defines that exp is its own derivative.

[stoic atlas]

.

[hushed sphinx]

That's not precalculus. And even in the right channel, you won't get anyone to just do your work for you -- please read the advice in #❓how-to-get-help before asking.

I'm sorry, it seems to be difficult for me to get express the point in an understandable way.

[wild shale]

Does anyone any good videos about finding the equation of a graph & graphing them (like for (x-3)^2(x+2) etc)?

[viscid thistle]

Hey

[quiet stag]

hi

[untold spindle]

https://youtu.be/a0RW8B3RVIM This video explains how to graph cubic equations like the one in your example.

[abstract tusk]

can anyone solve this for d, f and g?

[vapid plaza]

d, f and g are the roots of x^3 - 3x^2 - 10x + 24 = 0

[marble leaf]

Just use substitution

[vapid badger]

https://nursingscholar001.gumroad.com/l/knrmg

[versed mesa]

Hello

Does anyone have any practice work sheets with these kind of topics? Im doing mathematical methods (australia) and just flopped on my exam

[limpid sand]

its really simple

its just the limit of (1 + 1/n)^n as n approaches inf

you can plug in the number for higher and higher values to get e

[limpid sand]

using taylor series

you can take the taylor expansion of e^x

differentiate each term

and voila

you get e^x again

oh wait at a high school level

[willow bear]

???

the derivative of e^x is not xe^(x-1)

[slow coral]

ya taylor series is too advanced for me lul

i found a proof using first principles

or using limits

they’re the same thing apparently

i’d never heard the phrase “taking limits” but the method was first principles

so i assume they mean the same thing

thanks for the help anyway tho

[grave swallow]

derivative of functions in form of [c^x ]where [c] is a constant (a.k.a exponential functions)is [ln(c) .(c^x) ]

yes

[limpid sand]

No problem

[slow coral]

log base e, yes

[limpid sand]

Y

Yes

It's called natural logarithm cause e appears in the nature

I think

Like it shows up in compound interest which is the most obvious fact

But yea

What else

I'm asking lol

What else has e

Natural growth

ye it will be e^(x/2)

Great

[slow coral]

convention

the answer for 99% of "why does this symbol represent this thing" questions is convention

ya

delta always means change in a variable

n is really commonly used in series and sets

etc etc

[rugged crater]

can someone help me figure out how to find what x cannot be. I have factored all of them down, but i don't understand how to find what x cannot be

[wraith sequoia]

Hi guys, I'm in grade 7 and rn I'm on differentiation, can anyone guide me or like help me like a map which tells me which topic to do after which so I can learn advanced calculus before 15

[wraith sequoia]

in an orderly manner

and I'm self learning, so that's why I'm asking here

[slow coral]

learn to differentiate simple algebraic expressions

learn integration alongside differentiation

[grave swallow]

ln(e) * e^(x/2) * 1/2

[slow coral]

then learn to integrate and differentiate logarithms and exponents, then trig functions

then start learning the more fiddly techniques for integration and differentiation like chain rule, reverse chain rule

product rule, quotient rule, integration by substitution, integration by parts

then you'll be at the level most high-schoolers are at before they go to university

[grave swallow]

stewart is a good book to start with

[wraith sequoia]

Right now, I am referring to Eddie Woo's playlist Introduction to Differentiation

[slow coral]

also try to really familiarise yourself with the first principles

where you find derivatives using limits

[wraith sequoia]

I've to do that only now

[slow coral]

thats good

[wraith sequoia]

I'm doing that only rn

[slow coral]

do you understand where first principles comes from graphically?

like what h represents

[wraith sequoia]

I'm not there yet

[wraith sequoia]

I'm going to

[slow coral]

it really helped me when i was first learning it to see the graphical representation

[wraith sequoia]

kinda rn

[slow coral]

otherwise it's quite daunting

h is the hypotenuse of this triangle

the idea is that with the limit, you make the perpendicular sides of that right triangle infinitely small and the hypotenuse tends towards the instantaneous gradient at a point

gradient = slope if you're american

[wraith sequoia]

yeah, I'm referring to that and I understand that

[slow coral]

that's good

practise using the equation to differentiate some simple expressions

like f(x) = 2x^3

[wraith sequoia]

yeah, the gradient = rise/run

[slow coral]

that's the one

[wraith sequoia]

I've differentiated 1 or 2 expressions

I'm using [f(x+h)-f(x)]/h

[slow coral]

keep practising first principles until you're super super confident with it, why it works, and how it works, then move on to learning all the nice shortcuts

[slow coral]

lim h->0

that's the one

[wraith sequoia]

yeah

we have to put it till h is denominator

because you can't divide by 0

[slow coral]

yeah you basically manipulate it until h can disappear if it were 0

[wraith sequoia]

yeah

[slow coral]

are you confident with what a derivative actually represents

[viscid thistle]

just learn l hospital rule works 80 percent of tym

[slow coral]

the idea that it's a gradient function

[wraith sequoia]

I'm Indian, but I use that

[viscid thistle]

and all euler identities

euler identities are lyf saver

[slow coral]

idek these

[viscid thistle]

like e^x expansion

[slow coral]

what

[viscid thistle]

sinx expansion

[slow coral]

huh

explain

[viscid thistle]

oh sorry its called taylor series

[slow coral]

ah

taylor series too advanced if you're only just learning basic differentiation

save that for later

[wraith sequoia]

Can I DM you, you seem like a really helpful person

[wraith sequoia]

ok

[slow coral]

no im much worse at math than i let on

[viscid thistle]

cosmos u going for jee

?

or isi

[wraith sequoia]

yeah, prob, I want to get in mit though

everyone does