help-0

[rose raven]

It just happens to work out that when you differentiate a polynomial

[noble sinew]

wanna bet he doesn't know what first principles are?

its pointless

[rose raven]

So you can skip the whole deal with first principles and just do the rule

[noble sinew]

to say this can be proven using stuff he hasn't learned

[tight thunder]

man i feel like im the farmer and you are prince

with good school

so you go insane

[noble sinew]

same way for how they did derivative of 3x^3?

[tight thunder]

you even know menu in calculator

[noble sinew]

what is the difference in your mind?

[tight thunder]

and how to use it

[tight thunder]

man

[rose raven]

This is called differentiation from first principles

And if you look at that, you can see you end up with

2 * x^(2-1)

[tight thunder]

derivatives use limits?

[rose raven]

Haha it's not as complicated as it sounds

I promise

[tight thunder]

yes but i want to understand it

but dont get how to

[rose raven]

Sure

[tight thunder]

we didint use limits in school

[rose raven]

What country school and what grade?

[tight thunder]

we did learn limits

but like

not in this derivatives

[rose raven]

Yeah

[tight thunder]

this is the task we did yesterday

so like why it doesnt use limits?

[rose raven]

Because it's a shorthand way

[tight thunder]

hmm

[rose raven]

You know when I say 5 * 5 and you say 25

[tight thunder]

so its iq600?

or its low iq

[rose raven]

You didn't do 5 + 5 + 5 + 5 + 5 = 25

[tight thunder]

yeah

[rose raven]

You just knew how to do 5*5

It's the same principal - since you know already what it will end up as

[limpid spade]

or 5²

[rose raven]

You can skip the intermediary steps

[tight thunder]

hmm

[rose raven]

Let me tell you something

[tight thunder]

ok

[rose raven]

There is a 200 page proof that 1 + 1 = 2

Imagine if you had to do that every time you added up numbers

When you can skip all that and just write the answer

[tight thunder]

how would you proove that

[rose raven]

hahaha

[tight thunder]

like

2=1+1

[rose raven]

It's all complicated

But see the point

Imagine if you had to do all the steps in that proof

Every time you added a number together

Just to show it's the answer

[tight thunder]

i dont know because i dont know

how to proove 1+1=2

[rose raven]

Yeah

You don't know how to prove it

[tight thunder]

i dont even have idea

of concept

[rose raven]

Neither do I

[tight thunder]

but i heard about prooving

[rose raven]

I don't know either

But what we both know

is that 1+1 does in fact equal 2

So we don't NEED to prove it

[tight thunder]

fr

[rose raven]

it's the same thing here

[tight thunder]

so like

this just is

there is no need to proove it?

i still dont understand derivatives

[rose raven]

Not if you're just asked to state the first derivative, no

Maybe this helps

[alpine sable]

https://blog.plover.com/math/PM.html he proved 1+1=2 with simple math

[rose raven]

3x^1 - 1x^0

1 * 3x^(1-1) - 0 * 1 x^(0-1)

God I wish I knew latex

Let me try

[tight thunder]

man this is iq60000 club i dont belong to

[alpine sable]

maybe this will help

[tight thunder]

holy shit

[rose raven]

lol

I tried

But basically, the same thing is applied at every step

If you differentiate something like 5

You can write 5 as 5x^0 as you know x^0 = 1

And then if you apply the rule

[tight thunder]

man

w8

[rose raven]

Times by the power drop the power by 1

[tight thunder]

i dont even understand differentiate

wait

you mean

[rose raven]

The differential is the gradient function

It tells you the gradient at a given point

[tight thunder]

25 = 5*5

this is differentiate?

[rose raven]

No no

[tight thunder]

5+5+5+5+5+5

[rose raven]

That was just an analogy

That has nothing to do with differentials

Do you know y = mx + b

[tight thunder]

no bro

[rose raven]

The equation of a straight line

[tight thunder]

oh ye

[rose raven]

y = mx + b

What is m in that equation

[tight thunder]

i dont think we used m idk

[rose raven]

What did you use? I will use that one

[tight thunder]

y=ax+b

[rose raven]

Okay sure

y = ax + b

What does a represent

[tight thunder]

a is the thing that moves the line on x axis

b determines its position

right

[rose raven]

a is the gradient of the line

So every time x increases by 1, y increases by a

[tight thunder]

man

https://www.geogebra.org/calculator

w8 i go here to understand this

i understood this long time ago

[rose raven]

Once you understand it, try differentiating y = ax + b

and see what you get

Using the rules your teacher told you

[tight thunder]

hmm

i changed the a

but b is still 5

innit

btw @rose raven

like i just realised

to understand derivatives

i also must understand limits

and so on

like its insnae

yo

@rose raven

1 question rn

i just put the

i just put this in photomath

and app insantly offered solution for derrivative

so like my question is

is the reason we use derivatives

because we cant use something else?

for example

[rose raven]

What do you mean

[rose raven]

No you don't have to

The derivative of a function is just the gradient function

It tells you the slope (gradient) of the function at a point x

[lone heart]

@tight thunder Has your question been resolved?

[lone heart]

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[rancid narwhal]

how to find D's coordinates?

D should be = (9.5, 3)

pls help

,ti

[ocean seal]

The current time for Napoleon is 01:32 AM (+06) on Sun, 27/03/2022.

[rancid narwhal]

i need to go to sleep

tmrw exam

pls

someone

i need to go to sleep

[last ether]

Bro what we dont even know the lengths of the sides

[rancid narwhal]

gn 😢

[lone heart]

@rancid narwhal Has your question been resolved?

[lone heart]

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[eternal bison]

I just can't seem to wrap my head around visualizing this. I can calculate integrals well, but setting it up is the problem. Ive watched countless videos and looked at many online sites to no avail

<@&286206848099549185>

[lone heart]

@eternal bison Has your question been resolved?

[lone heart]

@eternal bison Has your question been resolved?

[lone heart]

@eternal bison Has your question been resolved?

[lone heart]

@eternal bison Has your question been resolved?

[woeful pulsar]

what integral did you set up?

[lone heart]

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[split slate]

I would assume that the area is going to be: y(8-x)-x^2; but the textbook says it is: (8+x)y−x^2...
Why would this be, and how would I get to that?

[slender gull]

There are multiple ways you could do this.

[split slate]

I just assumed that it would be like this:

[slender gull]

Try doing it like this.

Or wait, how did you do it?

[split slate]

Oh shoot

I realize my mistake

I put a - instead of a +

[slender gull]

Yeah.

[split slate]

Oh welp

[slender gull]

That is the only difference in your answer too.

Anyway, well done.

[split slate]

ty

.close

[lone heart]

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[earnest ore]

can someone help prove these 5 axioms?

[earnest ore]

i understand them but I'm not sure how to prove them

[tacit arch]

You don't prove axioms

[earnest ore]

it's an assignment q so i kinda have to xd

[tacit arch]

That's a different question

[earnest ore]

o

[tacit arch]

You know what the circle with + means?

[earnest ore]

closed under

add

[tacit arch]

$\oplus$

[earnest ore]

vector addition and

scalar mult

right?

Is this what rhe question was asking?

Or is it something else?

[tacit arch]

,rotate

[ocean seal]

riemann

[earnest ore]

I’m not sure I’m doing it right anymore

After you said that

If not could you let me know?

this is the whole q if that matters

[lone heart]

@earnest ore Has your question been resolved?

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[unkempt stream]

Am I able to do this?

Since both converges can J say the whole thing converges?

[foggy remnant]

I do not understand

[unkempt stream]

The question was asking whether or not the summation converges or diverges

[placid zinc]

Yes

[unkempt stream]

ty

.close

[lone heart]

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[sly comet]

Can someone please explain how for question ‘b’, the domain does not exist as x=-2

[lone heart]

@sly comet Has your question been resolved?

[vale wigeon]

@sly comet do you mean to ask why -2 isn't in the domain of f'?

[lone heart]

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[vale pulsar]

,tex $$2^{1401}-(2^{1400}+2^{1399}+2^{1398}+...+2^2+2^1+2^0)-2^0$$

[ocean seal]

Tanjiha

[woeful pulsar]

do you know how to sum a geometric series?

[vale pulsar]

No

[vale pulsar]

You mean 1+2+3+4+...+100?

[woeful pulsar]

that's an arithmetic progression

have you covered how to sum a geometric progression?

[vale pulsar]

Wdym?

[woeful pulsar]

an arithmetic progression has a constant difference

a geometric progression differs by a constant ratio

[vale pulsar]

n(n+1) / 2?
I know this formula

[woeful pulsar]

yeah but that only works for a specific arithmetic progression

it wouldn't work for the geometric progression that is involved in your question

[vale pulsar]

So how should I solve this?

[woeful pulsar]

there's a specific way, and a more general way\
have you seen a formula like this before?
$\sum_{i=0}^kx^i=\frac{x^{k+1}-1}{x-1}$

[ocean seal]

Element118

[vale pulsar]

Yes but this is not what I have learned in high school.

[vale pulsar]

Is the answer (1)?

[woeful pulsar]

hmm, what did you learn exactly?

[vale pulsar]

Power calculations and obtaining the result of a sequence

[woeful pulsar]

can you apply it here?

[vale pulsar]

Is it solvable without a formula?

[vale pulsar]

What do you want me to apply?

[woeful pulsar]

another way is to notice that $2^k=2^{k-1}+2^{k-1}$

[ocean seal]

Element118

[woeful pulsar]

and use it to split the biggest powers of 2

[vale pulsar]

,tex $$2^{1399}+2^{1399}-(2^{1400}+2^{1399}+2^{1398}+...+2^2+2^1+2^0)-2^0$$

[ocean seal]

Tanjiha

[vale pulsar]

I still have no idea

[woeful pulsar]

it was originally 1401

check again

$$2^{1400}+2^{1400}-(2^{1400}+2^{1399}+2^{1398}+...+2^2+2^1+2^0)-2^0$$

[ocean seal]

Element118

[vale pulsar]

Oh yes it was my mistake

[sly comet]

Yes

[vale pulsar]

I got 1
Is is correct?

[woeful pulsar]

did you remember to subtract the extra 2^0 at the end?

[vale pulsar]

Yeah!

[woeful pulsar]

idk how you got 1

[vale pulsar]

Then what's the right answer?

[woeful pulsar]

i got 0

[vale pulsar]

.close

[lone heart]

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[thorn echo]

pls teach me how to get the quotient

our teacher taught us how to get it, but only if the indices r the same, so idk how to get if it's different

[woeful pulsar]

they probably want you to write it over an integer denominator

[thorn echo]

what?

[crimson carbon]

rationalise the denominator

[woeful pulsar]

use an integer denominator for your fraction

[crimson carbon]

weird way to ask to do that

[woeful pulsar]

yeah, it's weird

[thorn echo]

ill try

how do i do the num?

[crimson carbon]

You can't simplify it further

so just leave it how it is

[thorn echo]

so like this?

[crimson carbon]

ye

[thorn echo]

ohh, no more multiplication sign?

[wary stream]

It's implied

[thorn echo]

which

[wary stream]

Because saying 4(5) is the same as 4 * 5

[thorn echo]

ohh okay thanks

[crimson carbon]

Ye juxtaposition of variables

which is implied multiplication

But again

[wary stream]

What is juxtaposition?

[woeful pulsar]

put next to each other

[thorn echo]

ooo thank you

ill try the second one now

[crimson carbon]

Ye for emphasis and contrast

[thorn echo]

okok thank you

same method with 2nd item right?

[crimson carbon]

Basically what it's asking is to rationalise the denominator

which is just making the denominator rational

[thorn echo]

yeah, just remove the radical symbol right?

[crimson carbon]

essentially

https://en.wikipedia.org/wiki/Juxtaposition @wary stream

Scroll down the page a bit

[thorn echo]

so this is what i did for no.2

is this correct?

[crimson carbon]

no

Because

[thorn echo]

?

[thorn echo]

oh yeah

[crimson carbon]

It'll be easier to see if you write your radical and express it as a fraction

[thorn echo]

ahh

[crimson carbon]

test message

test message 2

[thorn echo]

is this correct

[crimson carbon]

how'd you get 4 as a base

the exponent is right

but the base

[thorn echo]

OH sorry

is it wrong?

should it be 2

[crimson carbon]

ye

[crimson carbon]

Is what you have

you may leave it like that

but simplify it further

[thorn echo]

ok im trying to rationalize it further

is that allowed?

i will multply the expression w cbrt of 2

[crimson carbon]

you could

but

why would you

Look at

[thorn echo]

cos according to our teacher, we have to eliminate the radical sign

oh i can just cancel

thanks

[crimson carbon]

oh wait

ye you could've which would've lead to cancelling

[crimson carbon]

I was thinking of factoring

[thorn echo]

oh

[thorn echo]

is this correct

[crimson carbon]

If you factored ^3sqrt(12) you would get this yes

as well as rationalising ig

so ye you're correct

but simplify it further

[thorn echo]

cancelling is the fastest method right?

[thorn echo]

u can still simplify?

[crimson carbon]

well you'd end up cancelling anyhow 🤔

[crimson carbon]

yes

[thorn echo]

how

[crimson carbon]

factor

then apply a radical rule

[thorn echo]

which will i factor out

[crimson carbon]

well look at what you can factor out first

just recall your radical and exponent laws

observe

think

notice

apply

[thorn echo]

the six?

[crimson carbon]

yes

[thorn echo]

it'll be like this?

then?

[crimson carbon]

yes precisely

[thorn echo]

that's it?

[crimson carbon]

now apply some exponent laws

[thorn echo]

Ooo

[crimson carbon]

notice how you have radicand as 2 appearing in 2 radicals

[thorn echo]

yeah

[crimson carbon]

which then you could express that radical as fractional exponents

[thorn echo]

but they have diff indices

[crimson carbon]

then you have a common base of 2

[thorn echo]

ooo

then what?

[crimson carbon]

what could you do now

the next step is quite obvious

[thorn echo]

simplify the fraction

how tho

[thorn echo]

oh yeah

?

[crimson carbon]

exactly

and you're practically done

[crimson carbon]

Or express it as a radical

preferably

[thorn echo]

final answer?

[crimson carbon]

yes

[thorn echo]

thank youu

tysm bro

[crimson carbon]

There was actually a way to do this

without even rationalising

[thorn echo]

which is?

[crimson carbon]

just apply radical rules and exponent rules

We'll do it that way

[thorn echo]

Ohhh i see

[thorn echo]

our lesson is rationalizing actually

but i still wna try

[thorn echo]

factor out 12 right?

then itll bcome cbrt 2 n cbrt 6

[crimson carbon]

you mean factorise 12

[thorn echo]

yea

same thing i think

[crimson carbon]

Not really

[thorn echo]

ohh

okok

[thorn echo]

?

[crimson carbon]

When you factor out you take it out

for instance

[thorn echo]

Ohhh i see

[thorn echo]

Ohhh i get it

[crimson carbon]

like we're taking that quantity out of the picture

many ways we could factorise

[thorn echo]

Ooohh

[crimson carbon]

recall that we could write any number as a product, quotient, sum, and difference of other quantities

well depends on the set that number is contained in

But let's not digress

[thorn echo]

okay

[crimson carbon]

apply your exponent laws here

[thorn echo]

cbrt 2 and cbrt 6

[crimson carbon]

nice

[thorn echo]

then?

[crimson carbon]

(i'm typing wait)

[thorn echo]

oh okay sorry

[crimson carbon]

Step one. We express the radicals as a base and fractional exponents
Step two. We factorise 12
Step three. We apply our quotient rule for exponents
Step four. We simplify
Step five. We express 3^(1/3) as a radical

[thorn echo]

where did the exponent:3 go?

in 2^2/3

[crimson carbon]

test message

[thorn echo]

2-3?

[crimson carbon]

kitchen wifi poopy

[thorn echo]

lol

[thorn echo]

OH

[crimson carbon]

o

[thorn echo]

wuts that

[crimson carbon]

Ignore that message

I just wanted to see the difference in size

[thorn echo]

oh okayy

[crimson carbon]

Thought \frac was larger than \tfrac

[thorn echo]

let me try in scratch

ohhh i see

[thorn echo]

i get it

thankss sm

[crimson carbon]

.close to close the channel if you're done

[crimson carbon]

.

[thorn echo]

.close

[lone heart]

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[viscid wren]

i got that this converges at 1/e^2

but im not sure

i can provide my work

[lone heart]

@viscid wren Has your question been resolved?

[lone heart]

@viscid wren Has your question been resolved?

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[cloud junco]

question24

[wary stream]

Question 24 was a popular riddle question that went viral on the internet. You can easily look it up and watch videos on the solution

[cloud junco]

please

[wary stream]

Please what? I literally told you, it was popular on the internet a few years ago. Just look it up

[fresh coyote]

@cloud junco

https://en.m.wikipedia.org/wiki/Cheryl's_Birthday

scroll down and click on “Solution”

[wary stream]

This is literally the reason why I don't give people links because people are capable of doing it themselves

[fresh coyote]

he said his english isnt very good, im just trying to help

[wary stream]

If they looked up "Cheryl's Birthday", they would have found tons of resources

[fresh coyote]

from what ive seen he was having trouble understanding what you meant

[wary stream]

How would I have known? They never said anything about not understanding what I meant.

They probably could have said that to then make me or someone do the research for them

[fresh coyote]

you wouldn’t, they never directly said it

but

they have said this and replied “Please” to you telling them to look it up, which i believe is enough clues to know hes having trouble understanding

[wary stream]

But what? You're just assuming that they were actually having trouble. What if they were just saying that, like I mentioned

[fresh coyote]

@cloud junco make sure to close the channel if you don’t have any more questions

[lone heart]

@cloud junco Has your question been resolved?

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[alpine sable]

i mean im halfway on this one. because it COULD be zero, or u and v could be orthogional

[split oriole]

What is <> represent here?

[alpine sable]

inner product space

[forest turtle]

Hello. Uhm, is this server a place where we discuss maths and give tips on solving math problems?

[alpine sable]

yeah it is skarmory, you can ask a question in the math help (available) channels. I already reserved this one.

[alpine sable]

i dont see this in there, thise is u, v

not u, u

[split oriole]

It can be possible of vectors are orthogonal ,yes you are right ( if your inner product is sclaer product)

[alpine sable]

okay but because it could also be that one of the vectors is the zero vector its true

or one of the functions is a zero function

in this sense, function

[split oriole]

Yes ,but only writing one of them is 0 ,not a correct defination

[forest turtle]

Ill be in some academic tests to be accepted in a senior high school in abt 2 weeks so i hope this is the perfect place for me to ask about some math problems and get some tips on how to solve them quicker since the tests have time limits

[split oriole]

Like simple example is dot product

[alpine sable]

read the rules man and figure out the server. its kinda rude to pop into peoples help channels, but im a nice guy 😛

so just read the rules, and ask questions int he availble help channels

[forest turtle]

Good, im llokin forward to learn some important math knowledge

[alpine sable]

yeah yeah i get it, I think lmao. THank you.

.close

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[forest turtle]

Oooh, i didnt know it works like that but im sorry, though this is just some channel in the server

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[light tusk]

Is this $\text{sin}^2\theta=(\text{sin}\theta)^2$ true?

[ocean seal]

MoneyMaker

[gray isle]

yes

[light tusk]

Thx

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[queen anchor]

what does it mean by the triangle of ABY?

this triangle?

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[earnest lodge]

can anyone help me check whether this page is correct

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@earnest lodge Has your question been resolved?

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[tacit arch]

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[pulsar smelt]

hi i did these two questions and just want to make sure if the correct answers are A and D

thank you to whoever takes this up!

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[harsh swallow]

i get the same answers i think

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[cloud kiln]

how come this isn't homogeneous

[cloud kiln]

I can also represent the above and below functions in y/x form

Yo can you delete your question

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[glass tide]

what would you say the length here is?

[limpid spade]

?

[glass tide]

I figured it out

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[astral nymph]

Hi, I have a question regarding the parametrization. According to the answer, the parametrization is r(t)=ti+t^2j. Is this standard when you only have and x and y or is there a concept for it?

[limpid spade]

when it says y=x^2 parameter is (t, t^2), x=(3+y)^2 would be ((3+t)^2,(t)) for example

(0,0) and (4,16) is to find boundary

[astral nymph]

Ah I see

[limpid spade]

if it said let the line integral be a line from (0,0) to (3,0) then another line from (3,0) to (7,7) it would have 2 segments

and u find parameter by (1-t)(0,0)+t(3,0)

for first segment

and boundary is always 0 to 1 I think

[astral nymph]

But you only use the x coordinates for your integral right?

So you won't be doing anything with your y coordinates

for this question then

[limpid spade]

it depends on the integrandum

for you yes

[astral nymph]

ah okie, thank you for your help!

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[misty mortar]

\begin{tikzpicture}
\tikz \draw (0,0) coordinate (A) -- (0,1) coordinate (B)
--++ (250:1) coordinate (C)
pic [draw,->,red,thick,angle radius=0.5cm] {angle = C--B--A};
\node [red,right, text width=5cm] at (0,1) {30};
\end{tikzpicture}

How do I scale this image to be bigger relative to the page?
Is there a way to automatically make the 30 appear right next to the arc, instead of having to manually calculate its position (LIke the version that I drew on the paper)?

[ocean seal]

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

[timber cradle]

Maybe...

\path pic ["$30^\circ$", font=\footnotesize, draw, angle eccentricity=1.5]
{ angle=C--B--A };

[ocean seal]

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

[misty mortar]

Is the "font=\footnotesize" the thing that changes the size?

[timber cradle]

yes

[misty mortar]

Which line of code of mine am I supposed to replace with your line of code?

@timber cradle

[timber cradle]

\usetikzlibrary{calc, angles, quotes}

\begin{tikzpicture}
\draw
(3,-1) coordinate (A)
-- (0,0) coordinate (B)
-- (2,2) coordinate (C)
pic["$\alpha$",draw=orange, <->, very thick, angle eccentricity=1.2, angle radius=1cm] {angle=A--B--C};
\draw (B).. controls ($(B)!.2!(C)!10pt!90:(C)$) and ($(B)!.8!(C)!10pt!90:(C)$) .. (C) node [midway, sloped, fill=white] {$a$};
\draw (A).. controls ($(A)!.2!(B)!10pt!90:(B)$) and ($(A)!.8!(B)!10pt!90:(B)$) .. (B) node [midway, sloped, fill=white] {$b$};
\end{tikzpicture}

[ocean seal]

Cryska

[misty mortar]

How did you get that symbol to be right next to the arc?

[timber cradle]

angle eccentricity

https://tex.stackexchange.com/questions/175967/tikz-using-the-angles-library

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[astral nymph]

Hello can someone tell me how they derived the answers from the root?

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[steel crag]

So this question from earlier. I found Vmax (which is the velocity after the slope) = 3.42 m/s.

So I need to be able to find the distance it takes to go from 3.42 m/s to 0.75 m/s given the 0.2 coefficient of friction

[steel crag]

My brain is shot after these last 2 hours, so I may extensively ask questions about the problem. I completely got rid of the slope from the question by finding Vmax. It's only the horizontal section I'm worried about now

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@steel crag Has your question been resolved?

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@steel crag Has your question been resolved?

[tacit arch]

.close

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[plucky lynx]

First notice $$\frac{1}{6n^3+5} < \frac{1}{n^3}$$.

[alpine sable]

?

[plucky lynx]

Sorry, latex is down.

Notice the sequence of terms is eventaully positive for n > 7. So observe 1/(6n^3 + 5) < 1/n^3 which implies (n-7)/(6n^3 + 5) < (n-7)/n^3.

[alpine sable]

yes

[plucky lynx]

Simplify (n-7)/n^3 to (1 - 7/n)/n^2, we observe that 1 - 7/n < 1. Hence (1-7/n)/n^2 < 1/n^2.

Notice I am working with all n > 7 here.

Since 1/n^2 is known to converge, by limit comparison we have (n-7)/(6n^3 + 5) converges.

hmm, wait a sec, I have an error.

It should be 1-7/n < 2.

So we have (1-7/n)/n^2 < 2/n^2 which the rhs converges.

Do you have any questions in any parts of it?

[alpine sable]

alot

im still trying to understand

[plucky lynx]

Yeah, ask away. Sorry I wrote down the whole solution. I wanted to let you see how this stuff works so in case you have another question similar to it, you can apply it.

[alpine sable]

can you send a picture of your work

[plucky lynx]

Oh, I didn't do this on paper.

[alpine sable]

Rhs converges

[plucky lynx]

is that from above?

[alpine sable]

Yes but this is what I did

[plucky lynx]

Yep, your right.

Now, use that. Notice adding a 5 at the bottom of lhs, you have it smaller than it. So It converges by limit comparison.

Your solution was a lot nicer than mine.

[alpine sable]

no lol

i have no idea

[plucky lynx]

Ok, do you know (n-7)/6n^3 < 1/6n^2. Adding 5 to 6n^3 we have the bottom gets bigger hence the whole (n-7)/(6n^3 + 5) becomes smaller than (n-7)/6n^3.

[alpine sable]

yes

do i cross multiply here

i know that rhs converges

but that would be the direct comparison test

[plucky lynx]

Yep.

[alpine sable]

6n^2(n-7)/6n^3+5

[plucky lynx]

Your done already.

[alpine sable]

tahts it

i dont have to take the limit ?

[plucky lynx]

No, the question is above convergence and divergence.

[alpine sable]

O

thank you soooo much man

[plucky lynx]

np.

[alpine sable]

.close

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[wary stream]

I'm pretty sure that I explained how you do those questions

[cunning trout]

Yh but I can’t get this particular one

[wary stream]

What's the inverse of that function?

[cunning trout]

Y=x/3

[wary stream]

#❓how-to-get-help

No

[cunning trout]

Then what’s the inverse function?

[wary stream]

The no was for the user that posted and asked for help on their question

[cunning trout]

Ok

[wary stream]

y = x/3 is correct

So what is the trouble then?

[cunning trout]

What do I do now?

[wary stream]

The same thing you did for the first problem

[cunning trout]

But I’m not getting my answer

[wary stream]

You take f(x) and plug that into f^(-1)(x)

[cunning trout]

What x

What’s x I’m confused in that

[wary stream]

That's notation

f(x) is the function

Like the first question

[cunning trout]

Ok

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[alpine sable]

help pls this is confusing me i am dumb

[alpine sable]

ofc ik the area of the rectangle but not the six yellow sections

how would i do that?

ohhhhhh

yeah u right

so the diameter for the circles are 2 cm correct?

i guess so yeah

oh so i jus subtract the total area by the areas of the circles?

oh alr thx

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[alpine sable]

How does one improve in proofs?

[alpine sable]

Im taking discrete math and going through the textbook, it all makes sense in the explanations

But trying to do them on my own is very daunting

I really want to do well on the exams

And have a good understanding of the stuff

[wary stream]

Practice

[alpine sable]

Rip i guess thats the only way

Should i memorize important “definitions”

Like what is irrational number defined as

Etc

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[light tusk]

I don't understand the question (i)

[ocean seal]

MoneyMaker

[tacit arch]

what? dx/dy is the derivative of x with respect to y. typically the "gradient" is the other way around, the derivative of y with respect to x, and that's denoted by dy/dx

[light tusk]

if dx/dy is helping us to find "gradient of tangent"

what does dy/dx actually helps us to find?

[light tusk]

and with that, the answer key states: (for (i))

[ocean seal]

MoneyMaker

[tacit arch]

have you taken calculus before?

[light tusk]

Only introductions

[tacit arch]

https://en.wikipedia.org/wiki/Leibniz's_notation#Leibniz's_notation_for_differentiation

do you remember seeing that

[light tusk]

Oh I do

Change in y over change in x as change in x gets closer to 0

Ah i see

Ok then... ill try to do the rest of the parts first.

.close

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[unkempt stream]

Am I doing this correctly?

[tacit arch]

nahhhh

[unkempt stream]

I need to find if this series converges or not

Factor out 1/10?

[tacit arch]

that's a geometric series

have you learned about those

[unkempt stream]

Trying to self teach

My prof is rly bad

[tacit arch]

https://tutorial.math.lamar.edu/classes/calcii/series_special.aspx

just the first half. do all the examples in example 1

[unkempt stream]

Okay

[unkempt stream]

Thanks I get it now

[tacit arch]

[unkempt stream]

Wait one more

[tacit arch]

,rotate

[tacit arch]

nice look at that ratio test

[unkempt stream]

I used ratio test

Did I do it right?

[tacit arch]

yea

who needs a professor when you have lamar calculus

[unkempt stream]

Ty 030

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[lilac river]

Please help me with 108

[lilac river]

<@&286206848099549185>

[tacit arch]

read this

[lilac river]

I did

Sorry I'm new here

@tacit arch can you please help me

[tacit arch]

you missed the first 3 bullet points entirely

• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping @Helpers.

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@lilac river Has your question been resolved?

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[alpine sable]

@tacit arch can u please help me

[tacit arch]

don't ping me out of nowhere

[alpine sable]

Sorry bro

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[sly mantle]

@alpine sable pls use 1 channel

.close

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[tired axle]

i have the E F G alll solved, and i need additional assistance to see if they are orrect

[tired axle]

<@&286206848099549185>

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[wary stream]

#❓how-to-get-help

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[alpine sable]

Anyone able to help me here?

I'm making a mistake somewhere

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@alpine sable Has your question been resolved?

[limpid spade]

-e^2tcos^2(e^t)+e^2tsin^2(e^t)=e^2t*(-cos^2(e^t)+sin^2(e^t)=e^2t*-cos(2e^t)

-e^2tcos(2e^t)+cos^2t

[alpine sable]

Yep yep I see. Factoring it out :) tyty

.close

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[ripe rain]

Ηi how do I find lower value of range for the given function

[ripe rain]

I know that upper bound will be 1 at x= π/2

How do i find lower bound

[ripe rain]

Hence by looking at the options i can confirm it’s option (D)

[lone heart]

@ripe rain Has your question been resolved?

[ripe rain]

<@&286206848099549185> ?

[slender yew]

1a

Ips sorry

[lone heart]

@ripe rain Has your question been resolved?

[ripe rain]

,w plot (sin x)^(sin x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Deep.#6969

[ripe rain]

<@&286206848099549185> any idea?

[pine fable]

This is same as range(x^x) with range restricted to (0,1)

[ripe rain]

Ya but how do we prove it

If we can prove it then maybe its simply taking derivative of x^x

Then our jobs done

Right?

[pine fable]

Yea,find derivative and predict it's behaviour

You get it becomes zero at (1/e) and the function achieves it's minimum there

[ripe rain]

But how do we show it will be same as x^x, its the challenging part

By it i mean range

[pine fable]

let f(x)=sin x and g(x)=x^x
Then our function is g(f(x)) which is range of g restricted to range of f(x)

[ripe rain]

Ohhhh

I get it

Damn its that simple

Smh

Thanks @pine fable

.close

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[grizzled sundial]

Quick question: When I'm integrating by parts of a cyclic function, such as e^xsinx, i let u=e^x and v'=sinx for my first integration. But if I let u=cosx and v'=e^x in my second integral i end up with the equation 0=0 after my substitution. It only works when i let the second integral have u=e^x and v'=cosx, Why is that the case? Thanks in advance

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[devout latch]

I have a problem which I can't solve. Can you help me, please?

A rotation brings the point O (0; 0) in O' (-1; 0) and the point M (2; 2) in M' (√3; 1 - √3)
Write its equations and determine the rotation center C and the rotation angle α.

[devout latch]

this is the rotation formula when the center isn't the Axes' origin O (0; 0)

[lone heart]

@devout latch Has your question been resolved?

[grizzled sundial]

.reopen

[devout latch]

.reopen

<@&286206848099549185>

[vale wigeon]

@devout latch are you required to do it with algebra? or is some geometry okay

the center of rotation lies on the perpendicular bisectors of OO' and MM'

[devout latch]

so I have to do the bisector of OO' and MM'? And next?

[devout latch]

it's better with algebra

[vale wigeon]

better in the sense of "the teacher would like it if you did the algebra, but does not mind some geometry" or better in the sense of "you will get zero on the entire assignment if you so much as hint at anything geometric, so don't fucking dare"?

anyway, yes, construct the perpendicular bisectors of OO' and MM' and look at their intersection

that'll be your center of rotation

[devout latch]

The prof in this test wants obligatorily maths beacause she wants to know if we understood the application of the rotation formulas.

[devout latch]

okk I'll try

[vale wigeon]

"obligatorily maths" says nothing

if you mean algebra is obligatory then say algebra is obligatory, don't beat around the bush

also math != algebra

[worldly marsh]

hi
I need help :/

[devout latch]

yes excuse me, I wanted to say that algebra is obligatory

[vale wigeon]

@worldly marsh please read #❓how-to-get-help and take a channel in the Math help (AVAILABLE) category.

[worldly marsh]

oh ok thank you

[vale wigeon]

okay then plug both of your points into the equations you wrote there and suffer through the painful algebra

[devout latch]

So I have to substitute O' (-1, 0) in the place of x' and y' and then O (0, 0) in the place of x and y.
But how can I find cosα and sinα and Xc and Yc with algebra?

Should I do a quadruple system?

[devout latch]

and the same with M and M', but then remain three unknowns that are α and Xc and Yc

for now I start using your tip about the rotation Center

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[ancient shale]

Could someone explain to me why the first line implies the second line? How do you convert all the minuses to pluses?

[placid zinc]

Note the location of the =

In both lines

This is basically:
a - b = 0
a = b

Except b is a bunch of terms

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[prime sluice]

I am off the mark for some reason

[sudden hinge]

@prime sluice I get 152.58 for AC

Then using sin(42 deg) = AB / AC

[prime sluice]

Huh?

[sudden hinge]

Should get the right answer

[sudden hinge]

weird, that gives me 152.6

[prime sluice]

Hold on I will try my phone's calc

Yo my calculator is fried oof

Very weird

[sudden hinge]

lmao

[prime sluice]

I reset my calculator and am getting the correct numbers now,

[sudden hinge]

does it work with the new value?

because i didnt use the law of sines for the triangle ABC

[prime sluice]

Thanks for the help, never thought that my calculator would be the dumb one

[prime sluice]

Yeah 102

[sudden hinge]

perfect

[prime sluice]

Ye thanks!

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[white stump]

Uh got a translation to English?

[alpine sable]

Its asking for the degree and coefficient(?)

Coefficient of x³

[white stump]

Oh ic

[alpine sable]

yaa ikr

but thenn

[white stump]

So all you have to find is the highest degree

Which would be 5

[alpine sable]

so E?

but where does 15

[white stump]

And expand out the equation

Ohhh

Wait

I’m confused

[alpine sable]

,w expand (4x²-12x+9)(x³-x²+4x-5)

[ocean seal]

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Requested by ! !#2332

[slender gull]

Why are you doing their work for them?

[white stump]

I can’t read the e answers

Or the question

[alpine sable]

@alpine sable probably the question is incorrect

[alpine sable]

ahh oki

,w expand (2x-3)²(x³-x²+4x-5)

[ocean seal]

Results provided by WolframAlpha

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Requested by ! !#2332

[alpine sable]

so my work is correct?

[slender gull]

What language is that lol?

[alpine sable]

Yes

[alpine sable]

Indonesian i think

oki

[alpine sable]

yes

thank you

[slender gull]

I see.

[alpine sable]

I cannot understand but i can read Indonesian lol

.close.

how do u cclose

[slender gull]

There's no period after close.

.close

[alpine sable]

.close

[lone heart]

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[alpine sable]

:)

[lone heart]

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[balmy plank]

Let a,b∈N, with a>0 and b>0.
Let p,q,r,s be the unique integers such that
a=qb+r, 0≤r<b,
b=pr+s, 0≤s<r.
(In other words, r=a%b and s=b%r.)
Prove that s<b/2.

[balmy plank]

<@&286206848099549185>

[lone heart]

@balmy plank Has your question been resolved?

[balmy plank]

anyone

[oak perch]

b=pr+s>ps+s=(p+1)s>=2s

So b>2s