help-36

[raven marsh]

yes

[brazen stump]

hy

thats it?

[raven marsh]

mhm

[brazen stump]

damn tysm

.close

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[raven marsh]

np

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[jagged flare]

is there a term for the fact that the first goes everywhere and the second only goes to some of it

[raven marsh]

whats orginal

[jagged flare]

used the fact that it must repeat so like ABCABC...

i split cases where:
all diffrent
atleast two is the same

for all diffrent, you can group them like (ABC)(ABC) and its p easy to see all n such that 3|n works

[jagged flare]

for atleast two is the same, wr alr tackled 3|n so we can consider 3 not dividing n, i asked this cause i noticed if you jump 3 everytime (like from the first A to the second A, so if you jump 3 they both must be equal) you reach every point, so you need every point to be equal, or n=m^3

but im not sure how to write the fact that it goes to every point, what about diffrent amounts of jumps

[onyx peak]

How about "you can reach every point"

or sth like that

if you are gonna repeat that word often, just define a new word for that

e.g. Call the ring "complete" iff you can reach every point

[tired walrus]

"is the number of points coprime to 3 or not"

[jagged flare]

hmm can i just write it as is

"if the number of points (n) is coprime to 3, then you can reach every point"

[onyx peak]

<@&268886789983436800>

[jagged flare]

noo i almost beat you to it but i accidentally pressed some random guys name instead

[onyx peak]

As long as it's clear what "you can reach every point" means from the previous context, i'd say yes

[jagged flare]

btw at what time should you name something? ive never really defined something extra for a question before

[storm haven]

When it appears a lot

[onyx peak]

if i had to write the same sentence defining some situation more than like 6 times, i'd define an extra word for it

it also depends on how long the defn is

if it's just 3 words, i dont mind it unless it appears really, really often

if it's 3 sentences, i define a word for that even if it appears just thrice

[jagged flare]

oo ok ty

.solved ty guyss

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[timber plume]

Ik what the question is asking except I’m confused on why it’s saying “for x>2”

[lyric obsidian]

1. x>0
2. We don't wanna run into ambiguities when taking the derivative and solving the equation

Given the nature of polynomials and such

[timber plume]

So it’s asking for stationary points of x values bigger than 0

[lyric obsidian]

Yes

[timber plume]

and for this question

Do we use the product rule

[magic coyote]

Or just write f as (8x^2 - x^4)^1/2

[timber plume]

Cant we just do x^1(8-x^2)^1/2 =(8-x^2)^3/2

Because x^3(x^4) = x^7

[terse crypt]

U need same base to add exponent

[timber plume]

Both are considered x tho

[terse crypt]

8-x^2 ≠ x

[timber plume]

Except the other x had an input

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[noble pawn]

hello can someone help me

[sullen gale]

!da2a, just post your problem :)

[final saddle]

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

[noble pawn]

ok, so i would like to know how to do Pi Radius Squared

[sullen gale]

Can you elaborate on that? It seems like pi*r^2 is a formula

[noble pawn]

it says here ur super nerdy and also good at piano good job

[sullen gale]

-# ty hehe

[noble pawn]

dw I always get like 90 to 100

anyway But this circle thing is harder thanu THINK

[sullen gale]

ok, can you post it then please? I try and see if I can do it

[noble pawn]

yes

Help the cicle theoroms

circle theorems*

pls tell me what I need to know about cirlces

[mental roost]

These are not directly about pi r^2, but angles

[sullen gale]

do you have a bigger picture?

[noble pawn]

yes, but I would still like to know the theorem

let me check

[mental roost]

If i remember right, in pic 5 the red angle is double the blue angle (not 100% sure)

[noble pawn]

Pls tell me everything about circle RULES

here u go

hello?

[sullen gale]

So…maybe tell me what you know. Do you know what the angle of BCD is, in terms of the arcs?

[sullen gale]

-# please be patient, I needed to find a picture :)

[mental roost]

Also i think this resource is good https://thirdspacelearning.com/gcse-maths/geometry-and-measure/circle-theorems/

[noble pawn]

ok, i gotchu

Also my fav formula is Pi Radius Squared

radius, diameter, chord, circumference, are all basics

We need to do grade 10 mathematics

[sullen gale]

Do you think you have the information you need now?

[final saddle]

@noble pawn Has your question been resolved?

[noble pawn]

Oh wai tI was afk

dont worry BOT

[sullen gale]

usually bots say this after 10-15 mins of inactivity. you can just press the cross right there and nothing will happen to this channel

[sullen gale]

also this^

[noble pawn]

Oh yes also

Just note that I am grade 9 maximum carrying capacity

in other words, I can only withstand 9th grade mathematics

10 to 12 I think I have no idea

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[split violet]

Very interesting question

<@&268886789983436800>

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[worthy wren]

<@&268886789983436800>

[dapper hull]

<@&268886789983436800>

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[dapper hull]

sniped

[wicked storm]

what he say??

[cyan kayak]

porn discord server spam

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[left trail]

I have a question regarding 13b

[echo solar]

yeah sure

let me just- oh

[left trail]

So when using 13a if you expand it let say for we have b = n+1, a =n and p=p+1

[echo solar]

-# these only go to 13b

[left trail]

Oh sorry thats what I meant

[echo solar]

oh then i amn't smart enough to solve this 🫤

[left trail]

So if you expand it you have that the expanded term is greater or equal than n^p p+1 and less than or email to n+1 p+1 times

[dapper hull]

I want to know is 13a even doable with polynomial division ?

[stone wagon]

email lol

sorry xd

[dapper hull]

😭

[left trail]

?

[stone wagon]

apply part a to
$$(n+1)^p - n^p$$

[soft zealot]

artemetra

[echo solar]

look at what you did, they're crying now

oh god

[stone wagon]

what do you get?

[left trail]

Oh I just realized lol

But what I what I was trying to say was you get that (p+1)n^p≤(n+1)^p+1-(n)^p+1≤(p+1)(n+1)^p

[stone wagon]

or rather $(n+1)^{p+1}-n^{p+1}$ i should say

[soft zealot]

artemetra

[left trail]

But it feels a bit iffy

[stone wagon]

that's correct

[stone wagon]

why?

you are 1 step away from the answer

[left trail]

Ye I divide by p+1

I understand that but the way I did this was I just check for a couple of specific n values that it works

[stone wagon]

yep

[left trail]

And it isn't that what throws me off

But saying look n^p less than each term so it is less than it p+1 times just feels unusual if you get what I'm saying

[stone wagon]

honestly not really

can you show your working?

[left trail]

I haven't written anything out really just wasn't thinking about it

But I didn't feel like writing it out like that what be the right way of saying it

[stone wagon]

words are harder to understand in this case

[left trail]

So your saying when wiring it up this is all that needs to be said then?

[stone wagon]

or visually shown

i can't reall LaTeX this properly but something like this is common:
$$\underbrace{bla}{\geq n^p}+\underbrace{bla}{\geq n^p}$$

[soft zealot]

artemetra

[left trail]

Sorry I don't really understand this

So your saying that each term is greater than equal to n^p

Ok I understand

So I just write out all the terms then have the...... And for each I write ≥n^p

Do I need something under the ..... though?

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[sharp scaffold]

does someone here know IK?

[vital crag]

What is IK and what is your question

[sharp scaffold]

Inverse Kinematics, used in robotics. I have no get from the right point to left one with trigonometrics

[vital crag]

You mean distance?

Which point on the left

[sharp scaffold]

i have to get the coordinates from the bottom left point, ending of the red and light blue line

[vital crag]

Draw a vertical line down continuing the 6mm and make a right triangle with your blue and red intersection point

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[drifting mica]

why am i not getting -1 in LHD
where is the error

[tired walrus]

f(1) is?

[drifting mica]

f(1) = (x-1)

[tired walrus]

no, f(1) means put x=1 into f(x)

[frosty geode]

yeah

[edgy mauve]

f(1) means placing 1 in values of x in the function

[drifting mica]

when x = 1, the piecewise function is (x-1)

[frosty geode]

he's differentiating using limits

[tired walrus]

yes so you still put x=1

and get f(1) = 1-1 = 0

[drifting mica]

thanks ann

.close

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[undone tiger]

The product of values of (cos(π/6+isin(π/6))^(3/2)

[terse crypt]

Demoivre?

[serene panther]

Write cis(pi/6) as e^i(pi/6)

[undone tiger]

of course

But i felt like when we do square or make it easier

The product changes

okay so we have e^(iπ/4)

1/√2+i/√2

@terse crypt

[terse crypt]

👍

[undone tiger]

product?

is lost?

[terse crypt]

Wdym product

[terse crypt]

Tf does that even mean

[undone tiger]

.close

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[serene panther]

Tf is that

[terse crypt]

Right?😭

It’s like asking what is the product of values of 1

[serene panther]

[old quarry]

1

[serene panther]

They've not even made an exponential sign

For 3/2

[old quarry]

Idk guys question seems fine to me

[serene panther]

Is that so

[old quarry]

Yeah

They wanted to confuse u guys

It's beyond advance level

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[turbid grotto]

!occupy

[zenith cedar]

No need for that

You can just send your question

[turbid grotto]

ahh i see

sry idk abt these

In the diagram below, PQRS is a cyclic quadrilateral.

Find the value of x.

68°

82°

106°

115°

[zenith cedar]

What have you tried

[turbid grotto]

im learning in a different language

[zenith cedar]

Can you roughly translate it

[turbid grotto]

i translated it

from malay to english

[zenith cedar]

No I meant your approach

What did you try here

@turbid grotto

[turbid grotto]

one sec im doin on my wb

[whole haven]

its 115 degree bro

[zenith cedar]

No

This keyboard

[zenith cedar]

!nosols

[final saddle]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[whole haven]

i just come to this channel for help sorry

[turbid grotto]

se if its right

[turbid grotto]

dw u good

[zenith cedar]

That is correct

[turbid grotto]

sry i use my mouse to write lol

[quartz leaf]

Correct! Good work.

[turbid grotto]

ty

one sec im doing other questions too

guys help me

[terse crypt]

what kind

[turbid grotto]

i think id be

[terse crypt]

of triangle is formed by diameter and those lines

[turbid grotto]

no u understand that the diameter is AB

[terse crypt]

yes i do

[turbid grotto]

so AB/2 = radious

[terse crypt]

the central angle of the other side is 180

[turbid grotto]

so u saying c is 90?

[terse crypt]

this is like

known property

[turbid grotto]

hmm

[magic coyote]

Welcome to the server jsrao!

[turbid grotto]

erm hi!

[raven marsh]

Welcome to mathcord @turbid grotto

[turbid grotto]

hello

lets continue the question

[candid pulsar]

or here's how you prove it (special case of another property)

[turbid grotto]

so /_ ABC = 180-90?

[candid pulsar]

,rccw

[terse crypt]

,rccw

[raven marsh]

,rccw

[raven marsh]

yay

[sacred night]

hi carbon

[terse crypt]

wonderful

[raven marsh]

Hello

[sacred night]

omg your handwring is so good

[terse crypt]

nice proof

[raven marsh]

Btw this uses the fact that OA = OB = OC

[raven marsh]

isnt mine

[sacred night]

oh ok

thanks actually a good diagram toh

[turbid grotto]

w handwriting

way better than mine

[turbid grotto]

thx for helping alot 🙂

[lament token]

isnt this the property of diameter of a semi circular arc to subtend 90 degrees

[candid pulsar]

yeah..

k already said it was a commonly known property

[turbid grotto]

but my explaination is

[candid pulsar]

yeah it's a given in most places

[turbid grotto]

w

guys reminder

i learn maths in malay so if theres anything yall dont understand yall can ask me

btw im kinda good at pre-algebra

[raven marsh]

we'll see about that

[candid pulsar]

good to know i guess..

[terse crypt]

pulls out a challeging alcumus problem

[turbid grotto]

💀

hb this

@here

[turbid grotto]

bro i need help

[raven marsh]

[raven marsh]

opposite angles sum to 180

[raven marsh]

the 5th thingy

[turbid grotto]

lets go i got it right

[raven marsh]

nice

[terse crypt]

for future ref

there is also this

[raven marsh]

this is derived from this

[turbid grotto]

now this :?

[turbid grotto]

@raven marsh

@here

i got the answer

x=180-104/2
x=38

[candid pulsar]

yeah

correct

[turbid grotto]

hey i got this question its kinda triccky

[severe verge]

calculate angle AOB

[turbid grotto]

∠BAC=180
∘
−90
∘
−20
∘
=70
∘

i mean ABC=180-90-20=70

my brain corrupted

@here

gotta be fkin fr

this is the fkin formula

[quartz leaf]

😭

[turbid grotto]

aaaaa

i took 30 mins doing tha shi

[quartz leaf]

What grade are you in?

I personally would NOT remember such values

(tan 20, 70 etc)

[turbid grotto]

idk what grade is a 15yo

cus we dont count grades

[turbid grotto]

70 is bc OBC = 140/2

[quartz leaf]

I understood that, I just would not remember the value of tan(70degrees)

[turbid grotto]

u can js claculate

and yh im a freshmen grade 10

[turbid grotto]

should i quit games and focus on studies??

[turbid grotto]

yo

wake up

[quartz leaf]

I'm not sure if chatting further here is appropriate, considering your question has been resolved.

[turbid grotto]

what

[turbid grotto]

bro u speaking like a bot

[magic coyote]

@turbid grotto is your question resolved?

[final saddle]

@turbid grotto Has your question been resolved?

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[stray flicker]

3 right?

[tiny oar]

Ye

[stray flicker]

thank you brother

for this graph A right?

because its a histogram

or am i wrong? kind of confused

or waitiiii its graph b it shows a clear range!!

the graph a is more messy and in graph b its easier to tell the shape of the distribution?

.close

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[cursive shore]

Why is this 7?

shouldnt it be DNE because

going to - inf, the limit is -7?

[rustic light]

That is a whole different limit

Going to -infinity is not the same as going to +infinity

You're probably mixing it up with one sided limits

[cursive shore]

No one sided limit has its own problems

see?

So im gonna guess its suppose to be +?

so then it is DNE

[deep condor]

if you're tending to positive infinity, the limit doesn't have to be positive

[cursive shore]

yeah but if it doesnt specify a sign then both sides has to have the same limit

[rustic light]

If it doesn't have a sign then it's positive infinity

That is the standard notation, at least in my experience

[cursive shore]

No if you see above it does have the + side if its going towards positive

every problem i had so far had it

and every problem requiring both sides did not include a sign

[rustic light]

There's no such thing as "both sides" of a limit tending to infinity.

[deep condor]

to clarify, $\lim_{x \to +\infty}$ is a two-sided limit to positive infinity (right side of graph). $\lim_{x \to \infty^+}$ is a one-sided limit

[soft zealot]

haseeb

[deep condor]

in terms of notation, what erk said is true

[lean magnet]

is it even possible to approach positive infinity from the right

[cursive shore]

oh

[deep condor]

no, which is why i like your notation better

but the point stands

[worn knot]

aren't limits to infinity always one-sided?

[rustic light]

Whether its positive or negative

[worn knot]

since you can't approach infinity from both sides

[rustic light]

Yes

[cursive shore]

whats the diff between +inf and inf^+?

[rustic light]

Inf^+ is just bad notation

[worn knot]

i've never seen inf^+ before

[deep condor]

thats cause it doesnt exist i was just making a notational point D:

[cursive shore]

i dont know how typing math stuff here works

but now im confused

[rustic light]

If you saw something like $\lim_{x \to \infty ^{+}}$, that is bad notation

[deep condor]

$\lim_{x \to +a}$ is the two-sided limit to positive $a$, but $\lim_{x \to a^+}$ is the one sided limit to (positive) a

[soft zealot]

haseeb

[cursive shore]

then its suppose to be +inf right?

[rustic light]

I've never seen something like that before

[rustic light]

Yes

[soft zealot]

Erk Gah

[cursive shore]

ok then wb my original question of no sign. x --> inf.

[rustic light]

Probably

[lean magnet]

that's just a normal limit to positive infinity

[rustic light]

If the infinity isn't signed, assume it's positive

Just like we do with numbers

[lean magnet]

limits to infinity can never be two sided though because you can only approach infinity or negative infinity from one side

[cursive shore]

then wth is +inf

[deep condor]

moreover, x --> -inf is not approaching inf from "the other side" (no such thing exists), it's in the exact opposite direction from +inf

[rustic light]

That is positive infinity as well. Just like 3 and +3 are the same thing

[lean magnet]

$+\infty$ is just another way of writing $\infty$

[soft zealot]

satvik

[cursive shore]

oh

i was not taught this 😫

[deep condor]

so if these limits aren't equal, it doesn't matter

[lean magnet]

that's just them making the explicitly clear

[cursive shore]

so inf^+ is wrong, but if you say 3^+ then its approaching 3 from the right side right

[lean magnet]

yes

[rustic light]

Exactly

[cursive shore]

and x --> +3 is just x --> 3

[lean magnet]

correct

[cursive shore]

ok thank you all. how do i close this

[rustic light]

Type .close

[cursive shore]

.close

[final saddle]

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[cursive shore]

.solved

[rustic light]

Just .close is enough

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[rough moss]

A

[rough moss]

Did I do something wrong it says it’s a cute

#29

Ah

Nvm

!close

Ok idk how to close

[narrow cedar]

.close

[lean magnet]

.close

[rough moss]

.close

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[rough moss]

how do I do b

[rough moss]

I did a and got like the thing

But then I forgot what to do after

Nvm

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[kindred sun]

help

[lean magnet]

with

[kindred sun]

how tf ami supposedto do ths

this is literally a homework question not even like an extra credit thing

im still writing the matrice

[terse crypt]

Holy fuck that’s horrendous

[solar glade]

There is no shortcut

[kindred sun]

ikr

[terse crypt]

What size is that matrix gonna be

[kindred sun]

11x11

[lean magnet]

😭🙏

[terse crypt]

Good luck reducing that😭

[kindred sun]

bro its due tommrow

im fucked

[rough moss]

Bro

😭🙏

[lean magnet]

goodluck soldier

🫡

[rough moss]

wtf is that thing

[kindred sun]

bro help me 😢

[solar glade]

And you should start doing it instead of hoping someone does for you xD

[kindred sun]

i cant even finish writing the matrcie

[terse crypt]

Bro’s training to be a computer

[rough moss]

ask ai or something bruh 😭🙏

[kindred sun]

okok atleast help with another one

[kindred sun]

cant even help bro it keeps spewing out ungodly fractions

its a 4x4

the other one

let me send

[rough moss]

Yea ur fried for ur 11x11

[terse crypt]

4x4 is manageable

But 11x11, at that point just plug in WA

Does WA have a matrix of that size?

[kindred sun]

nop

its only till 4

[solar glade]

It will say too many characters for sure

[kindred sun]

only quickmath orwtv has it

[terse crypt]

Damn

Cooked

[kindred sun]

im kidding thop that 11x11 is for extra creidt

[terse crypt]

Is that del or 2

[kindred sun]

i rlly need that tho

[kindred sun]

number 8 i need to solve

[terse crypt]

Convert this to an augmented matrix first

[solar glade]

Do you have to use any specific one?

[kindred sun]

i have never heard that

[kindred sun]

what do you mean

[terse crypt]

Like

Row operation?

Cramer’s rule?

[kindred sun]

oh

row by coulumn

ok

[terse crypt]

Then do gauss-Jordan elimination

Prolly the easiest method

[kindred sun]

the 1s and 0s one?

[terse crypt]

Yes

That’s called the row echelon form

[solar glade]

Start by setting up the augmented matrix.

[kindred sun]

ok i completed that

i also switched last row withfirst

[solar glade]

perfect

now 0 the first column

[kindred sun]

ok

one sec let me do that rq

[solar glade]

then u divide the second row by the leading term itself to get another 1

and repeat this step for second column

and so on

[kindred sun]

if there is a 1 uynder a 1 isnt there a trick

like a sign trick

is it same sign or opposite sign

[terse crypt]

Subtract by multiple of another row

Get it into

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

If u can

Or something that looks a lot like this

[kindred sun]

can soneome attempt the first colum of the 11x11 🙏

ok i got
[1, 2, -2, 3, 13]
[0, -4, 3, -5, -17]
[0, 5, -7, 8, 33]
[0, -5, 7, -7, -30]

there is not another 1

how do i get a 1 in the second row second column at second position where the -4 is

[terse crypt]

Now

[terse crypt]

Get the bottomed row to 0 by adding row 4 by row 3

And when u’re done u can divide row 2 by -2

[kindred sun]

what do you mean

add the rows?

is that allowed

[terse crypt]

Ye

[kindred sun]

i thought i would have to divide a certain row by one of the numbers to get that one number to be 1

[terse crypt]

There are 3 elementary row operations

1. Adding one row by a scalar multiple of another row
2. Multiplying a row by a scalar that is not 0
3. Switching rows

[kindred sun]

so if i want to add row 3 and 4 what would happen

wouldnt a whole row dissapear

[terse crypt]

No

[kindred sun]

tell me

also when multiplying matrices how do i say what it is like how many row x colu

is it row by col or col by row

[terse crypt]

There are ways to multiply a matrix

[kindred sun]

so how do i add the two rows as you were sayingbefore

[terse crypt]

https://youtu.be/eYSASx8_nyg?si=XV2PPwdjSvetAfJ5

Js watch this gng

🥀

[kindred sun]

https://tenor.com/view/man-praying-and-crying-black-man-praying-and-crying-black-man-praying-man-praying-gif-1984228927205209673

wait answer me this

[10]
[12]

x

[6, -2, 1, 6]

how can i do this multiplcation cuz it only has one colum

would it be just 10 x 6

and 10x -2

for a new number not add

wait i think i got it

nvm i got it

is there a difference in multiplying 2x2s and3x3s?

like is it still row1 by column 1 and then col 2 and col 3 and row2 col 1 col 2 col 3 and so on

[half salmon]

Are you trying to multiply a 1 column 2 rows with a 4 column 1 row?

[kindred sun]

no

i figured that out

the new one is this:
[7,5,-4] [2, -2, 3]
[-2,5,1] x [8, 1, 4]
[10,-4,-7] [-4, 2, -8]

is it still same way as multiplying 2x2 but now its with 3 different things to add for new one

help

[deep condor]

https://tenor.com/view/matrix-math-multiplication-multiply-matrices-gif-4323841554477167734

does this help establish the pattern?

[kindred sun]

yea i was just wondering if its the same

yea i was getting mixed up with identiies and shit

thakns

can someone help me withe the 4x4

[deep condor]

i forget every single time you're not alone 😔

btw your 11x11 is definitely cooked, there's not a single shortcut

[deep condor]

are you having trouble with the row reduction?

[kindred sun]

k said someting like adding rows

i thought i would have to divide a number by itsself to get 1 and everything else inthat row also gests divided by that number

idk how to add like he mentionaed

[deep condor]

yeah, but then you "use" that row to get 0 values underneath it

you want each column to have 1 appear only once

like $\begin{bmatrix} 1 \ 0 \ \vdots \ 0 \end{bmatrix}$ or $\begin{bmatrix} 0 \ \vdots \ 0 \ 1 \ 0 \ \vdots \ 0 \end{bmatrix}$

[soft zealot]

haseeb

[deep condor]

im an idiot but you get the idea

so to do that, we add the "1 row" to the other rows below it

[deep condor]

this video sums it up nicely

[final saddle]

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[spring nexus]

how to solve..?

[spring nexus]

.close

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[rocky scroll]

Can I make the summation start at 0 and not change x_i if n approaches inf?

[rocky scroll]

essentially im asking if it matters whether i = 1 or i = 0 in the case n approaches infinity for the definition of a integral

[bleak granite]

Whether you start form i=0 and go to n-1 or start from i=1 and go to n will give different values (that being the left and right-sided Riemann Sum). However, in the limiting case (n->inf) and for elementary purposes, these both will converge to the integral.

hello Adonis

[drowsy epoch]

I got compromised 😂

but hi

[bleak granite]

[drowsy epoch]

This is what would happen geometrically, if you started from i=0 instead (from a right Riemann sum to a left Riemann sum)

[bleak granite]

https://tenor.com/view/riemann-integral-calculus-definite-integral-gif-27532351

but as we get more and more rectangles (infinitely many), both give the area under the curve

[final saddle]

@rocky scroll Has your question been resolved?

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[tropic sun]

ANOTHER DAY ANOTHER QUESTION

[tropic sun]

how would u solve this without taylor expansion?

for more context

[tropic sun]

I already solved the limit of the first one and the result was -5

so it´s a continuous function

[ripe jewel]

taking the derivative of f

well

that assumes the derivative is continuous

if you dont assume that it's harder, sure

[tropic sun]

what is taking the derivative of f?

[ripe jewel]

i realized it wont work unless you know in advance f' is continuous

[gentle zephyr]

shouldnt we analyze continuity and differentiability at x approaching 0

maybe i am saying the obvious

[tropic sun]

hola renato

cuando derivas 10sen(x)/etc

[gentle zephyr]

buenas, como va?

[tropic sun]

te termina dando -5

por lo que la funcion es continua

[tropic sun]

va, que es lo que puse aca

[gentle zephyr]

when you took the derivative using first principles, you got 0/0, no? so shouldnt we use lhopital

[gentle zephyr]

a que te refieres derivar

[tropic sun]

perdona, quise decir

calcular el limite tendiendo a 0 de lo de arriba

[gentle zephyr]

para saber si la derivada de la funcion a trozos existe en el cero, osea si f'(0) existe tenemos que analizar continuidad en el cero y derivabilidad en el 0, osea tiene que ser f continua en el 0, al evaluar el limite cuando x tiende al cero por izquierda y por derecha tiene que dar -5, y lo otro para evaluar derivabilidad hay que ver si el limite de la derivada por definicion por izquierda o por derecha nos arroja el mismo resultado

por lo que veo, al evaluar derivabilidad en el 0, (si es derivable es continua) te da una indeterminacion (-5+5)/0 -> 0/0, no?, entonces por que no aplicas lhopital

[gentle zephyr]

si dices que es continua entonces limite X cuando tiende a cero del primer caso de la funcion a trozos, osea este limite da -5, 10sin(x)/(1-e^2x)

[gentle zephyr]

differentiability at a point i think implies continuity at a point

[tropic sun]

creo que ese metodo es complicarlo demasiado

cuando usas lhopital por primera vez

te vuelve a dar 0/0

[gentle zephyr]

vuelve a aplicar lhopital

[gentle zephyr]

tu dijiste que no quieres usar taylor

[tropic sun]

jajajaj

tenes razon igual

[gentle zephyr]

esto es analisis matematico de uba xxi?

[tropic sun]

no, cbx

cbc

uba

[gentle zephyr]

👍

aplica dos veces lhopital y deberias de llegar a tu respuesta (maximo es aplicar lhopital dos veces en estos ejercicios me parece), pero tienes que hacerlo por izquierda y por derecha para ver si es diferenciable

[tropic sun]

claro

[gentle zephyr]

aparte, si sabes que f es diferenciable en el 0, no es necesario ver si es continua en el 0

[drowsy epoch]

Do you have to compute the value, or find out if it exists?

[ripe jewel]

sure but that deosnt mean the derivative is continuous

[gentle zephyr]

fortunately we just need to find if f'(0) exists and whether if f is differentiable at 0, aswell as give the value of f'(0), I think, though charko hasnt confirmed

[ripe jewel]

right but my idea of taking the derivative of f using normal derivative rules does not work for f'(0)

because we dont know f' is continuous at 0

[tropic sun]

compute the value

[gentle zephyr]

lim sin(h)/h = 1

[drowsy epoch]

Although, hmm meh; up to interpretation, whether we can assume it exists or not - nevertheless, the idea is to make one common denominator and then apply L'Hopital.

[tropic sun]

do u think is easier to use taylor expansion?

[drowsy epoch]

Yes

At least, it seems so.

[gentle zephyr]

si estas rindiendo el primer parcial no deberias de poder usar taylor porq es contenido del segundo parcial, pero si estas rindiendo final, da igual

[tropic sun]

estoy rindiendo recuperatorio

[gentle zephyr]

can you send the problem statement (consigna) even if its in spanish

also, check this video charko https://youtu.be/6gSKFYzE6vg

[gentle zephyr]

siempre es mejor usar taylor pero tenes que usar lhopital tengo entendido jajaj, bueno me retiro mucha suerte charko, pingea a universe y a gfaux si necesitas mas ayuda

[tropic sun]

dale gracias chicos

.close

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[turbid garden]

hii this is what the markign key has done

[turbid garden]

and this is what ive done. is this a viable method ?

[loud sundial]

yes these are the same thing

$\frac{\ln 15}{\ln 3}+1=\frac{\ln 15}{\ln 3}+\frac{\ln 3}{\ln 3}=\frac{\ln 15+\ln 3}{\ln 3}=\frac{\ln 45}{\ln 3}$

[soft zealot]

Civil Service Pigeon

[loud sundial]

[final saddle]

@turbid garden Has your question been resolved?

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[sacred night]

$\frac {d}{dx} ({\frac {1}{x^3 - 4x}})$

[soft zealot]

calvin

[sacred night]

do i use quotient rule or chain rule?

and i am actually not quite sure where to begin

[pliant shore]

it would be easiest to write it as $(x^3 - 4x)^{-1}$

[soft zealot]

south

[sacred night]

oh ok

[pliant shore]

nothing's stopping you from using the quotient rule but it would be longer

[sacred night]

so then i apply chain rule?

[pliant shore]

yeah

[lofty sinew]

Both chain rule and quotient rule would work, but chain rule will be easier here

[sacred night]

so then $-(x^3 - 4x)^{-2} \cdot (3x^2 -4)$

[soft zealot]

calvin

[sacred night]

and we are finished?

[pliant shore]

yep! we're done

[sacred night]

tysm

👍

.close

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[sacred night]

$\frac {d}{dt} \sqrt{t^2 +9} = t^3 + 9t$

[soft zealot]

calvin

[sacred night]

can someone verify for me

please

[severe verge]

wrong

[magic coyote]

How did you come to this conclusion

[sacred night]

ill write my working

$$\frac {d}{dt} \sqrt{t^2 +9} = (t^2 + 9)^{\frac {1}{2}}$$
$$\frac {1}{2}(t^2 + 9)(2t)$$

t cancels

Hence, $ t^3 + 9t $

[old quarry]

uh

[severe verge]

Tell me what is the derivative of x^1/2

[old quarry]

thats not how power rule works

[soft zealot]

calvin

[sacred night]

wait FUCK

my bad

😭

i forgot to subtract 1

[magic coyote]

[sacred night]

is it

$\frac {1}{\sqrt{t^2 + 9}}$

?

[magic coyote]

No it is not that either

[sacred night]

wait what did i do

wait no

[magic coyote]

{} around t^2 + 9 not {)

[sacred night]

1/ \sqrt (t^2 + 9)

[magic coyote]

yes

that

And then chain rule

[soft zealot]

calvin

[sacred night]

isn't it just that

[magic coyote]

No

Chain rule where

[sacred night]

st

[magic coyote]

Also u forgot a 1/2

[sacred night]

2t is the

chain rule applied

right?

bc t^2 + 9

goes to 2t

and the 1/2 cancels it

[magic coyote]

Where is the 1/2 from derivative of sqrt(t^2+9)

[magic coyote]

uh huh

and the t?

[sacred night]

ohhh

im so dumb

so its $\frac {1}{\sqrt{t^3+9t}}$

[soft zealot]

calvin

[severe verge]

❌

[sacred night]

i am so confused

can someone help work it out w me pls

[magic coyote]

Idk what you're doing man, to find the derivative of sqrt(t^2+9) you first do the power rule, and then the chain rule

[sacred night]

ok lemme do it again

i might jus be rest arted

wait wait wait

ok so

$\frac {d}{dt} \sqrt{t^2 +9} = (t^2 +9)^{\frac {1}{2}}
= \frac {1}{2}(t^2 + 9)^{-\frac {1}{2}} \cdot \frac {d}{dt} (t^2 + 9)$
= \frac {1}{2}(t^2 + 9)^{-\frac {1}{2}}{2t)

wait am i right

@magic coyote @severe verge

[severe verge]

multiply not plus

[sacred night]

Ohhhhh shit

??

[magic coyote]

what

[sacred night]

is it $\frac {t}{\sqrt{t^2 +9}}$

[soft zealot]

calvin

[magic coyote]

Yes

[sacred night]

ok finalllyyyy

[severe verge]

nice

[magic coyote]

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[sacred night]

im not done

[magic coyote]

k

[sacred night]

Q8. $\frac {d}{dx} \frac {x^4}{\sqrt{x^2+4}}$

[soft zealot]

calvin

[sacred night]

to start off do i have to convert the sqrt of $x^2 + 4$ into a exponent

[magic coyote]

whoops

[soft zealot]

calvin

[magic coyote]

Sure

[severe verge]

quotient rule

[magic coyote]

or you can use the quotient rule

either is fine

[sacred night]

let me find it

[magic coyote]

,tex.diff rules

[magic coyote]

^

[sacred night]

$\frac {d}{dx} (\frac {f}{g}) = \frac {f'g - fg'}{g^2}$

[soft zealot]

calvin

[magic coyote]

yes

dont forget to use chain rule while doing g'

[sacred night]

uh

wdym

[magic coyote]

wdym what do i mean

chain rule

while finding diff of g

idk how thats unclear

[sacred night]

ohhh

i get it

ok so i got

$\frac {d}{dx} \frac {x^4}{\sqrt{x^2 +4}} = \frac {(\frac {d}{dx} x^4)(\sqrt{x^2 +4} - (x^4)(\frac {d}{dx} \sqrt{x^2 +4}){(\sqrt{x^2+4}^2}$

[magic coyote]

why r u adding so many dollar signs

[sacred night]

wait yeh

oh its cuz i was copy paste

[soft zealot]

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

[magic coyote]

$\frac {d}{dx} \frac {x^4}{\sqrt{x^2 +4} = \frac {(\frac {d}{dx} x^4)}{(\sqrt{x^2 +4} - (x^4)(\frac {d}{dx} \sqrt{x^2 +4}){(\sqrt{x^2+4}^2}$

[soft zealot]

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

[magic coyote]

bruv

so many wrong brackets

rewrite and post

[sacred night]

$\frac{d}{dx} \left( \frac{x^4}{\sqrt{x^2 + 4}} \right) = \frac{\left( \frac{d}{dx} x^4 \right)(\sqrt{x^2 + 4}) - x^4 \left( \frac{d}{dx} \sqrt{x^2 + 4} \right)}{(\sqrt{x^2 + 4})^2}$

[soft zealot]

calvin

[magic coyote]

yes

now do the derivative parts

[sacred night]

when im differentiating sqrt(x^2+4) do i have to multiply by the derivative of the inner term

(x^2+4)

[magic coyote]

yes

[sacred night]

ok thx

[magic coyote]

.

[severe canyon]

Yeah it's exactly the same process of the previous question: #help-36 message

[sacred night]

ok thx

wait is it

$\frac {x}{\sqrt{x^2 +4}}$

[soft zealot]

calvin

[severe canyon]

Sure

[sacred night]

yay

i goty

[magic coyote]

so, whats the complete diff

[sacred night]

complete

omgogmgmomgomg

i have a messy fraction

its

[magic coyote]

u can just show a photo

if u dont wanna latex

[sacred night]

$\frac {4x^3\sqrt{x^2+4} - \frac{x^5}{\sqrt{x^2+4}}}{x^2+4}$

[soft zealot]

calvin

[sacred night]

nah i like to enchace my latex skills

also yall can't read my handwriting

[magic coyote]

yes

is correct

[sacred night]

i hate messsy stugffg

now what do i do

wait is that it

[magic coyote]

yes but u can simplify

[sacred night]

how

pls pls pls pls pls show

[severe canyon]

Multiply numerator and denominator by √(x² + 4)

[magic coyote]

multiply and divide numerator

by

yeah that

[sacred night]

ok\

btw

when i multiply by $\sqrt{x^2+4}$ does that apply to the 4 in $4x^3$

[soft zealot]

calvin

[magic coyote]

wha

[sacred night]

or just the whole term

[severe canyon]

Wdym?

[magic coyote]

its multiplication bro

[sacred night]

i am very dumb

[magic coyote]

its commutative

[sacred night]

is it just

[magic coyote]

(a * b) * c = a * b * c

[sacred night]

ughhhh

so i have to do it to every single term

[magic coyote]

what

[sacred night]

im gonna run out of space

[magic coyote]

noo

[severe canyon]

??

[sacred night]

wait does it apply to the 4 or not

in my book

[magic coyote]

bro when u multiply

[sacred night]

i have like 3 cm left

[magic coyote]

its only multiplied once

u dont need to

distribute it

[sacred night]

so

[magic coyote]

(a * b) * c != a * c * b * c

is equal to a * b * c

[sacred night]

$(4x^3\sqrt{x^2+4})(\sqrt{x^2+4})$

[soft zealot]

calvin

[sacred night]

wait do i have to do that

like will it expand to

i am just confusing my self

what does that expand to

@magic coyote

[magic coyote]

write x^2 + 4 as having an exponent 1/2

rewrite sqrt as ^1/2

[sacred night]

yeah

[magic coyote]

sooo

[sacred night]

so it becomes just x^2+4

times 4x^3

[magic coyote]

into 4x^3

yes

[sacred night]

ok thx

i am so dumb

[magic coyote]

[magic coyote]

revise algebra

[sacred night]

i should

[magic coyote]

and exponent laws

[sacred night]

i know my exponent law

s

wait so its just

$(4x^3)(x^2+4)$

right?

[soft zealot]

calvin

[sacred night]

@magic coyote

[magic coyote]

yes

[sacred night]

ok thx

ok my final answer is

$\frac {4x^5 +16x^3-x^5}{x^2\sqrt{x^2+4} + 4\sqrt{x^2+4}}$

[soft zealot]

calvin

[sacred night]

@magic coyote

!!

i got it

yayay

[magic coyote]

wait

[sacred night]

..

what happened to my denoimatinater

i butchered the word

[magic coyote]

nm

denom is also correct

but u wrote it badly

[sacred night]

.yes

oh sh

[magic coyote]

u shud just write

[sacred night]

😭

[magic coyote]

(x^2 + 4)^3/2

[sacred night]

why

why ^3/2

OHHH

[magic coyote]

to make it look

bootifull

[sacred night]

t hx

ur a g ex

.close

[final saddle]

Channel closed

Closed by @sacred night

Use .reopen if this was a mistake.

[magic coyote]

[sacred night]

.reopen

[final saddle]

✅

[sacred night]

ok so i started a new q

and its

$\frac {d}{dx} (2x^{\frac{5}{2}}-8x^{\frac{3}{2}})^6$

[soft zealot]

calvin

[sacred night]

i applied the power rule

[magic coyote]

power rule + chain rule

[sacred night]

$6(2x^{\frac{5}{2}}-8x^{\frac{3}{2}})^5)$

then the chain rule

[magic coyote]

No

You forgot the 6

[sacred night]

my bad

[soft zealot]

calvin

[sacred night]

i forgot to add it i was accidentally on shift

[magic coyote]

kk

[sacred night]

then multiply by $(5x^{\frac {3}{2}} - 8x^{\frac {1}{2}})$

[soft zealot]

calvin

[sacred night]

$6(2x^{\frac{5}{2}}-8x^{\frac{3}{2}})^5(5x^{\frac {3}{2}} - 8x^{\frac {1}{2}})$

so this is my full answer

is that right?

[soft zealot]

calvin

[magic coyote]

whatchu do with 8x^(3/2)

[sacred night]

?

[magic coyote]

forgot to multiply 3/2

[sacred night]

ohhhhh

shit

its just 12 right

[magic coyote]

yes

[sacred night]

hx

thx

[magic coyote]

[sacred night]

.close

[final saddle]

Channel closed

Closed by @sacred night

Use .reopen if this was a mistake.

[sacred night]

.reopen

[final saddle]

✅

[sacred night]

$\frac {d}{dx} (4t^2-9)(t^4+8t^2-3)^9$

[soft zealot]

calvin

[sacred night]

idk where to start

product rule?

or chain rule