help-27

[tame spear]

give me a second

[old carbon]

k

[tame spear]

this should make it a bit more clear?

[old carbon]

a little bit clearer

i need a sec to think

[old carbon]

oh

thanks for thinking for me

[tame spear]

Tough question

[old carbon]

it is

can't wait to do the math for it

anyway I've been slowly differentiating the first one while we've been talking

and I'm getting a substantially different value than what I first got

[tame spear]

Fun fact: If you let yourself use any shape (not just a straight line), the biggest possible thing you can fit through the hallway is an open problem. Nobody knows the answer

https://en.wikipedia.org/wiki/Moving_sofa_problem

[old carbon]

woh

[tame spear]

Not really that surprising, your thinking looked confused. Quite easy to pick up an error somewhere

Hope you do well with the rest of the problems

[old carbon]

thanks, I need all the luck I can get

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[devout snow]

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[daring plank]

helloo could i please have an explanation on how to do this problem? it's hyperbolas

[kindred gulch]

what have you tried

[misty crest]

set the functions equal to each other

[kindred gulch]

😭

[daring plank]

i haven't really tried anything because i don't know where to start. i'm pretty sure i need to rearrange the equation but i don't really know how to do that 😓

[daring plank]

sorry, could you please elaborate? i'm really slow at math and i'm especially bad at this topic

[kindred gulch]

we have y=? and y=??, since y is the same value, try setting ?=??

[daring plank]

i'm really sorry, i'm already lost

[kindred gulch]

I'll give you a for free

y=1/x, y=3, so 3=1/x

or 3x=1 and x=1/3

[daring plank]

is it okay if you explain this please?

[kindred gulch]

just divide by 3, 3/3=1 and 1/3

you can do the same operation on both sides and the equality holds

[daring plank]

ohh okay i see

so the first point is (1/3, 3) ?

[kindred gulch]

yeah

do you know how quadratics work?

or I mean x^2

[daring plank]

somewhat, but i don't fully understand it

[kindred gulch]

try b like I did here

[daring plank]

i don't really know what to do after 4x = 1/x . am i meant to divide both sides by 4x?

[kindred gulch]

multiply by x, 1/x*x=1

[remote steeple]

bro seriously needs to review how to solve rational equations

[daring plank]

i'm a lost cause at math

i'm here for a reason

[kindred gulch]

I don't judge

[remote steeple]

neither did I. just an advice

[restive river]

what is rational equation

I’m cooked too I think

[kindred gulch]

equations involving rationals like 1/x

[restive river]

um.. what is a rational

a fraction?

[daring plank]

4x^2 = 1

[kindred gulch]

fractions involving polynomials

[remote steeple]

rational functions rather than transcendental functions

[restive river]

oh ok

[kindred gulch]

do you know how to squareroot?

something like this might help? idk

[daring plank]

oh yeah

[kindred gulch]

but when you take the square root of x^2 make sure it's + or -

[daring plank]

what happens next?

[kindred gulch]

you might also find this helpful

[kindred gulch]

we need to find x=? so we need to take the square root on both sides

[daring plank]

i don't really understand sorry 😓

[kindred gulch]

4x^2=1 look at the perfect square chart and use the rules for square roots to show that it is the same as 2x=+-1

[daring plank]

i'm sorry, i don't get it at all

[kindred gulch]

which part

do you see how 4x^2=2^2x^2?

and 1=1^2?

[daring plank]

i don't understand this

[daring plank]

but this one i definitely understand

[remote steeple]

4x^2=1 right

so x^2=1/4?

you know how to do this right

[daring plank]

i do not, could you please explain it to me?

[remote steeple]

ok.

x^2=a how to solve x

[daring plank]

i don't know that either

[remote steeple]

Hmm...

x^2=1 what is x

[daring plank]

1

[remote steeple]

-1 too?

[daring plank]

oh yes

-1 * -1 = 1 because two negatives make a positive

[remote steeple]

x^2=4 x=+-2 right

[daring plank]

yes

[remote steeple]

so x^2=a x=+-a^1/2?

see the pattern?

1^1/2=1

4^1/2=2

thats how you solved x^2=1 and x^2=4

[kindred gulch]

sorry I got busy

[daring plank]

i'm starting to get lost here

[daring plank]

no worries, prioritise yourself before others always

[remote steeple]

look at x^2=4. the way you arrived at x=+-2 is by taking 4^1/2

[daring plank]

yep, sorry for the late response, was looking back at this message

[remote steeple]

so you do have a pattern. taking +-a^1/2 yields answer?

[daring plank]

so what would i do now?

[remote steeple]

x^2=1/4

take (1/4)^1/2=1/2

add plus or minus

[daring plank]

i'm still lost, really sorry about that. thank you for your time and effort into trying to help me though (same for the previous guy). i'll skip over this question and come back to it and review this conversation to see if doing more hyperbola-related questions will help me further deepen my understanding as well as understand the steps for this question. have a good day/night ^^

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[viral zephyr]

which answer is exact and which is aproximate i forgot

[acoustic leaf]

the one in terms of logs is a formula which gives an exact answer whereas the decimals is approximate (because it really has infinitely many decimals which you have to round off)

[viral zephyr]

sorry can you rephrase the first part?

[acoustic leaf]

an exact answer is a formula which doesn't involve any decimal approximations

basically the thing you put into your calculator

[viral zephyr]

ah okay

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[whole raven]

i'm on my last attempt and i dont wanna waste it before im sure of my answer, why does my answer feel like it's wrong here

[whole raven]

my final answer is -137/3, just doesnt seem right for the question but i'm not sure

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[distant wave]

help i dont get it im wrong

[devout snow]

@distant wave Has your question been resolved?

[analog flume]

what have you tried

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[robust scarab]

Just a quick question I have a list of numbers (7,345.78, 604.77, -166.64, -120.69, 631.96, -4,421.43, -4,345.38, 2,299.27, -2,136.86, -293.14, 2,271.25, 698.79 ,-754.43, -1,504.32, 848.66, 2,476.32, -3,120.95, -414.77,68.33, 812.07,-1,605.58,-535.75,-1,330.55,306.01, 329.85) I know the average of these numbers are -106.78 does that mean there average gain or an average loss of 106.78

[wooden wraith]

It seems like there's some context missing (they should have told you that the numbers represent a gain or loss of some kind) but since the average is a negative number, I'd assume that represents a loss

@robust scarab

[robust scarab]

yah

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[harsh hazel]

can someone please explain why they are using cross product in this ms

[olive snow]

Normal vector to plan

[acoustic leaf]

the cross product between two vectors returns a vector perpendicular to both

[harsh hazel]

oh ok got it

so thatd be the normal vector to the plane

ok ok thanks guys

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[violet jacinth]

can someone prove identity 4 and
3 ? i tried to ask chat gpt but it kept messing up w the proof

[devout snow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[twilit comet]

also

[coral violet]

try simplifying the rhs..

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[twilit comet]

and yes, what luna said. it's fairly simple--just expand the RHS

not too hard

[violet jacinth]

yeah but then what after? why can’t we write it identity 3 in the form of L^3 + M^3 = (L+M) (L+M)^2 instead of that?

[violet jacinth]

also about this im literally trying to learn my math teacher just gave us this and told us to memorize it but i just wanna know where its deprived from

[violet wind]

Because that isn't true. Test almost any two values of L and M to see it

[twilit comet]

because

[sage burrow]

expand and simplyfy the rhs and you will get the lhs. there is nothing to do after.

[woven radish]

ren

[twilit comet]

which is what your identity has

[violet jacinth]

okaayy i will try that

[twilit comet]

if that were true, L^3 + M^3 = (L+M)^3 which is trivially false

[violet jacinth]

okay so i just expand then simplify for both?

and lhs and rhs should be equal?

alright tyy

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[granite bough]

Hello! I am trying to follow along on an example about the sum of an infinite series in my textbook. This one is about a geometric series.

[granite bough]

[ \sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^{n-1} = \frac{1}{1-\frac{1}{2}} = 2 ]

[woven radish]

Neo

[granite bough]

I am having trouble understanding the sum notation

[coral violet]

hmm… try to expand it..

[acoustic leaf]

what about it are you having trouble with?

[fervent hornet]

do you code?

[granite bough]

I think everything, I am not very familiar with sum notation

[granite bough]

No, sorry ,not really

We started learning Python but

No I don't code

[fervent hornet]

ah i see it would be easier if you knew for loops but alright

[granite bough]

I have only heard of for loops but I don't know what they are really

[acoustic leaf]

,, \sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^{n-1} = \left(\frac{1}{2}\right)^{1-1} + \left(\frac{1}{2}\right)^{2-1} + \left(\frac{1}{2}\right)^{3-1} + \cdots

[woven radish]

cloud

[granite bough]

okay

that makes it a little easier to understand

I tried the first problem in my textbook

is this correct?

[ \sum_{n=1}^{\infty} \left(\frac{1}{n^2 + 1}\right) = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} + \frac{1}{17} + ...]

[woven radish]

Neo

[granite bough]

I still don't understand how we would arrive at a number

Or would this just be infinity?

We're adding an infinity of small things so they should become infinity

[coral violet]

No… its approaching a number

[granite bough]

damn

okay

[coral violet]

Nope, not exactly

[granite bough]

How do I know which number it approaches

[coral violet]

That’ll be the concept of GP

[granite bough]

What's GP?

[coral violet]

Geometric progression..

[acoustic leaf]

sometimes for a sum like this it can be much easier to figure out whether it has a value at all than to figure out what that value is

[coral violet]

every consecutive term has the same ratio…

[granite bough]

Sorry my grandma called

[coral violet]

alright..

So here… ill explain you with s diagram why the sum is not infinity

do you get it?

[granite bough]

sry i will read it in a minute still talking to grandma

[coral violet]

Mkk

[devout snow]

@granite bough Has your question been resolved?

[granite bough]

okay

im sorry

grandma has been spoken to

i am going to read what you have written

I don't understand the s diagram, I don't know what an s diagram is either

I don't understand what the m represents

[devout snow]

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[granite bough]

.reopen

[devout snow]

✅

[granite bough]

Yeah okay

[granite bough]

To solve this, can I use the following formula?:

$S=\frac{a_1}{1-r}$

[woven radish]

Neo

[sudden harness]

what is the question?

[granite bough]

my bad

[ \sum_{n=1}^{\infty} \left(\frac{1}{n^2 + 1}\right) = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} + \frac{1}{17} + ...]

what am i doing wrong

[sudden harness]

$$ \sum_{n=1}^{\infty} \left(\frac{1}{n^2 + 1}\right) = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} + \frac{1}{17} + ...$$

[woven radish]

AnshumanNeon

[sudden harness]

this?

[granite bough]

yeah thanks

the lefthand part

[sudden harness]

we have to compute this sum?

[granite bough]

the right hand side was just for me to understand what was going on - i am not veyr familiar with sum notation

I tried to find answers on google

and was wondering if this formula works

$S=\frac{a_1}{1-r}$

[woven radish]

Neo

[granite bough]

where S is the "answer" of the sum if it can be computed

a_1 is the first term of the sum

so I assume 1/2 = a_1?

and then r = a_2 / a_1

[sudden harness]

this looks awfully close to geometric series formula

except what you have is not a geometric series

[granite bough]

okay that sucks

i dont know the differences between series yet

the original problem is in my textbook

it says this:

"Determine whether the given series converges or diverges

by using any appropriate test

The p-series can be used for comparison as can geometric series.

Be alert for series whose terms do not approach 0"

I don't know what a p-series is

I don't know what a geometric series is

Actually

a geometric series is you go from 1 to positive infinity?

[sudden harness]

geometric series is a series where each term is of form 1/(n^2)

oh no!

wrong

my bad

[granite bough]

no problem homie

[sudden harness]

its of form a^x

where a is starting term

x is the common ratio

commonly written as r

[granite bough]

i have a really hard time visualising that

[sudden harness]

https://en.wikipedia.org/wiki/Geometric_series

nth term = a^(n-1)

to get the next term you multiply the previous term by 2

so one such sequence is 2, 4, 8, 16, 32 ...

3, 9, 27, 81 ...

[granite bough]

in my textbook it says ar^(n-1)

[sudden harness]

1/2, 1/4, 1/8

[sudden harness]

shit man

yeah that's correct

i'm extremely sorry. its messed up in my head

[granite bough]

no problem, this messes up my head already

[sudden harness]

yeah but its true

[granite bough]

i dont understand why they are given names

do they have special properties

do we know that all geometric series converge or diverge

[sudden harness]

they appear a lot, simplify things and yeah have some special properties

[granite bough]

why are they named

[sudden harness]

https://en.wikipedia.org/wiki/Convergence_tests#p-series_test

p series is also a test

a test for convergence

[granite bough]

isn't there an infinite number of series

how would i know what test to use

[sudden harness]

i really don't know

i just do this out of curiosity

[granite bough]

thats gigachad

nice man

[sudden harness]

it looks like your series does converge

[granite bough]

i dont really find the answer interesting, but how you arrive at the answer

[sudden harness]

there is a ratio test which is very simple

[granite bough]

but how do i know what test to use

when i look at that series

[sudden harness]

take the ratio of two consecutive terms

[granite bough]

i have no clue what test to use

i understand there are tests

[sudden harness]

if n+1 th term divided by nth term is less than 1

then the series should converge

as n goes to infinity

[granite bough]

i feel like part of arriving at the answer involves overcoming the hurdle of choosing the correct test

i dont know how to choose the correct test

and do i need to memorize these tests

for exams?

this is messed up

thank God the exam is in january

[sudden harness]

i haven't reached that level yet

but i'd say keep a few in mind along with knowing when to use which

like often times more than one test can give you the correct answer

start with the one that's less complicated for you, the one you can apply most of the time and you like it

if that doesn't work, then go to the next

you should also take note of when to apply, cuz some convergence tests have conditions

[granite bough]

$$ \sum_{n=1}^{\infty} \left(\frac{1}{n^2 + 1}\right) = \frac{1}{2} + \frac{1}{5} + \frac{1}{10} + \frac{1}{17} + ...$$

[woven radish]

Neo

[granite bough]

so for this question

the expression inside the parenthesis is a_n?

while the terms listed to the right is a_1 + a_2 + a_3 ...

and so on

what does converge even mean

[fervent hornet]

,w convergence

[woven radish]

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[granite bough]

,w diverge

[woven radish]

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[sudden harness]

yes

[sudden harness]

yes

[granite bough]

,w divergence

[woven radish]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by screwtheodds

[sudden harness]

lol your username itself is convergence

[fervent hornet]

yes it is that

[granite bough]

very cool

convergence you seem like the right person to explain to me what a convergence is

wolfram alpha sasod

said

it is when an infintie series approaches a finite number?

[granite bough]

when i looked at this

i thought it would be infinity

so my intuition sucks

how can i tell that it approaches a number

how can i tell that is converges

it is by using tests

okay

what tests, since series look different from one another

[fervent hornet]

yes

[granite bough]

my textbook lists a few tests

but i am wondering why there arent more

and frankly some of these tests i do not understand very well because of lack of knowledge

e.g. bounded above and bounded below

i dont know what either means

it is something about a graph

i cant remember

[sudden harness]

there are many

[granite bough]

is there a couple of tests that encompass all infinite series?

also what does diverge mean

sorry for so many questions

,w diverge

[woven radish]

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[granite bough]

im not sure what not having a limit would entale

[sudden harness]

diverge means that if you compute the whole series, the answer will not be a single number. it will just approach infinity

[granite bough]

not having a limit means we approach something undefined?

[sudden harness]

like 1+2+3+...

it doesn't approach a single number

it just goes to infinity

[fervent hornet]

let me give you an example the set (1.infinity) its bounded below what it means is that the there is a value such that the elements in this set cant be any smaller

[sudden harness]

that's a way to think

[granite bough]

diverge goes to + or minus infinity

and converge goes to a number

[sudden harness]

but it doesn't approach something undefined. infinity is perfectly defined if i'm not wrong

[sudden harness]

yes

[sudden harness]

yes

[fervent hornet]

yes and no

but in general you can consider like that

[granite bough]

the elements cant be any smaller?

i dont understand that

there exists a value so that the elements cant be any smaller

[fervent hornet]

is there any element smaller than 1 in that set?

[granite bough]

there isnt even 1 in that set

so no

[sudden harness]

that's what it means

no element is smaller than 1

@fervent hornet did you write (1, infinity) as an interval?

[fervent hornet]

yes

[granite bough]

but what about 1 million

[sudden harness]

alr

[granite bough]

there are smaller elements

are we just saying there is a smallest element

is that what you are saying

im just very dense but i really want to understand what you have said

[fervent hornet]

not really

[granite bough]

ye sry i dont understand

there is a value so that the elements cant be smaller

and 1 and infinity are the only elements?

[sudden harness]

no

[granite bough]

okay so it is an interval

so anything between one and infinity

[sudden harness]

when he wrote (1, infinity) it is an interval (which is a set also)

[sudden harness]

yes

[granite bough]

then i am still confused i dont understand what is being said

[sudden harness]

so if everything is between 1 and infinity. then no value can be smaller than 1

also no value can 1 too, because we said "between"

[granite bough]

yeah

[sudden harness]

hence we do not include 1 as an element

[granite bough]

but how is this different then

isnt that what convergence is saying

[fervent hornet]

in the reals there is no "smallest" element there will always be an element smaller than the element

[granite bough]

can you try to explain this in a different way?

there is a value such that the elements in this set cant be any smaller

[granite bough]

that makes sense

i am just confused and trying to understand what you are saying

[fervent hornet]

its alright these are usually discussed properly in an analysis class

[granite bough]

im taking single variable analysis

is what the course is called

so i guess that would count as being an analysis class

maybe not

i know there is real analysis as well

and i am not taking that

[fervent hornet]

it is taught there but its proof based

[granite bough]

could you dumb it down

like in a non-math way

we have a interval/set (1, infinity)

[fervent hornet]

i can try

[granite bough]

and you said there is a value such that the elements in this set cant be any smaller

i thought that meant you were saying

that a value exists

so that the elements cant be smaller

i guess i dont understand

[fervent hornet]

alright let me just generalize this consider the interval $(a,\infty)$

[granite bough]

what or where that value is

[woven radish]

convergence

[granite bough]

okay ye

[fervent hornet]

so let we let any element in this interval be x

[granite bough]

okay

a is x, infinity is x

sorry

they are nto in the interval lmao

i meant anything between

[fervent hornet]

we can also say that $a<x<\infty$

[woven radish]

convergence

[granite bough]

yeah

there exists a value for x?

such that the elements in the interval can't be smaller?

i still dont understand what value that would be

and isnt the elements in the interval already set in stone

like they arent changing, so why would they ever become smaller

[fervent hornet]

generally whatever value x is greater than is called the lower bound of the interval (as long as a is not infinity)

[granite bough]

so for (1, infinity), 1 is the lower bound?

[fervent hornet]

yes

[granite bough]

and for sin(x)

-1 is the lower bound

just as an example

[fervent hornet]

yes

[granite bough]

1 is the upper bound?

[fervent hornet]

yes

[granite bough]

okay

[fervent hornet]

so when we have a lower bound its called bounded below and when it has an upper bound its called bounded above

do you get it now @granite bough ?

[granite bough]

not entirely, when would an interval not have an upper bound or lower bound?

[fervent hornet]

it completely depends on the set for example (-infty,infty) is not bounded above or below

[granite bough]

wait so

(1, infinity) is bounded below but not above?

[fervent hornet]

yes as there will always be an x such that x>whatever number you chose

[granite bough]

so if i chose one million

there is one million and one

okay

[fervent hornet]

yes

[granite bough]

$$ \sum_{n=1}^{\infty} \left(\frac{1}{n^2 + 1}\right) $$

[woven radish]

Neo

[granite bough]

for the original problem

i was reading through tests in my book after clearing up my confusion about the sum notation

one test said "If a_n is ultimately positive, then the series must either converge (if its partial sums are boundeda bove) or diverge to infinity (if its partial sums are bounded above).

and i am thinking a_n would be positive

[granite bough]

for this

[sudden harness]

a_n is positive here.

[granite bough]

and partial sums

is that just 1

and n^2 + 1?

no

LOL

wiat

i know what theya re

it is when you add the things up one by one n times

so S_2 = a_1 + a_2

or something

and

WAIT

is it bounded below

by 1/2?

[fervent hornet]

yes

[granite bough]

okay that's great but come to think of it that doesnt help me with this test since it was wondering what th bound above was

i dont know what the bound above would be

thats the whole point of the question i think

i still dont know how to find out whether that specific series converges or diverges

[sudden harness]

@fervent hornet does the ratio test work here, as a side question

[fervent hornet]

there are several test for that

[granite bough]

i am reading through them but none of the jump out at me

how would i check if the partial sums are bounded above?

a_1 + a_2 is 1/2 + 1/5

[fervent hornet]

no its inconclusive from ratio test

[granite bough]

Wouldnt a partial sum just be a single number

how can it have an upper or lower bound

[fervent hornet]

in this case you would not know but in some other cases you may know cant think of any example rn tho

[granite bough]

and if it means all the partial sums in general

i have no clue how i would check that

my problem right now is

i am reading through my textbook tests

and they say

"if this sum converges"

[sudden harness]

huh. how? shouldn't
$$\frac{n^2 + 1}{(n+1)^2 + 1} < 1$$
always

?

[granite bough]

or

[fervent hornet]

personally i would not use the method that you used

[woven radish]

AnshumanNeon

[granite bough]

"if this diverges"

but isnt the point of the test

to find out

if it diverges or converges

the tests in my book say that "if it converges"

but i dont know if it converges, that's why i need the test

i am so confused

[fervent hornet]

yes but when we get the limit to be 1 you dont know whether it converges

[fervent hornet]

you can use other tests to find the convergence of thsi series

[granite bough]

i found a page talking about "convergence tests for positive series"

i am gonna read it

FUCK

I am not kidding

that refers back to the

"if the partial sums are bounded above"

thing

from earlier

wtf man

what is this

it is a labyrinth

[sudden harness]

textbooks aren't exactly straigthforward tbh

but they are accurate

[fervent hornet]

what book are you even using?

[granite bough]

Calculus a Complete Course

10th edition

is there a cheat sheet

for the tests

it would help so much

if there was a cheat sheet for all the tests

OKAY WAIT

DONT LEAVE ME YET CONVERGENCE

Is this a p-series?

[granite bough]

is this a p-series

please tell me yes

[fervent hornet]

you can use p series for this

[granite bough]

YES

Okay

and then it is OBVIOUS that it converges

using p-series

because all those funny fractions

have a positive denominator

wait

i mean all the denominators

are > 1

WAIT

uhh

yes

yes.

[sudden harness]

shit, even this shit leads to reimann zeta function

[woven radish]

convergence

[granite bough]

this is too much for me

i am trying to understand

let me think a little longer

[sudden harness]

hmm

it kind of makes sense

[fervent hornet]

yeah its alright you can just state that it converges usind p series

[granite bough]

yes it makes sense

dividing by 1 + n^2

vs dividing by n^2

yeah it would be smaller because of the 1

[sudden harness]

well i found this:

[granite bough]

but i dont understand the and

[sudden harness]

https://en.wikipedia.org/wiki/Direct_comparison_test

[granite bough]

i will probably just stick to doing this

[sudden harness]

which is exatcly what this says

[granite bough]

my goal is not understanding, just being able to do it on the exam is enough

i dont hate math i just dont have any love for it either

[fervent hornet]

alright

[granite bough]

it is really cool though

i wish i had better intuition for it

1 +1 doesnt even make sense to me

thanks for the help

[sudden harness]

thanks for new knowledge @fervent hornet

👍

[granite bough]

knowledge collector

no, but seriously thank you for putting up with me

i am very dense

[fervent hornet]

if you are done close the channel,other people aslo need help :)

[granite bough]

of course!

.close

[devout snow]

Channel closed

Closed by @granite bough

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[fervent hornet]

you clearly have not seen me in a real analysis class kek

[granite bough]

.reopen

[devout snow]

✅

[granite bough]

i realized

the whole point of my original question was for me to calculate the sum

[sudden harness]

shit

[granite bough]

or see what number it approaches

i understand it approaches a number now

because it converges

same thing

kind of

but i dont know how i would actually decide what number it converges to

[sudden harness]

this is incredibly close to the basel problem

which makes use of the euler-maclaurin method to compute sums

but it might just be overkill

because it goes into integration, differential eqs, bernoulli numbers

and all the shit

[granite bough]

i sure hope thats overkill

[sudden harness]

it definetly

does

[granite bough]

okay

i checked

i didnt have to find the sum for that specific one

thank god

[sudden harness]

lol

i'll still try if i can do find the value

i probably won't be able to do it

but let's see

[fervent hornet]

there are many methods to slove it but they involve bit of thinking and by "bit" i mean a lot

[granite bough]

im gonna close this again until i have a semblance of an idea of how to start computing non-geometric series

.close

[devout snow]

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[devout snow]

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[surreal pivot]

hello

[surreal pivot]

please help me

hello any one there?

[glossy dew]

yeah

[pastel pasture]

did you notice that x = 1/y?

[glossy dew]

multiply each number with its conjugate in the numerator and denominator

[surreal pivot]

what?

whats a conjulate

?

[devout snow]

@surreal pivot Has your question been resolved?

[surreal pivot]

still do not understand

[devout snow]

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[valid garden]

guyss can someone explain the part where i circled pink, i got lost here

[valid garden]

im making notes and idk what to write for this part

[knotty sage]

He added the molar masses of CO2 1 carbon atom and 2 oxygen atoms

[valid garden]

OHHH okayy

TYY

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[void knot]

How to understand this?

[glossy dew]

add the three equations

[wheat pawn]

if those equations hold, any linear combination of the equations must hold.
In this particular case, if the equations hold, the sum of the three equations must hold.
Since x1-x2+x2-x3+x3-x1=0, then b1+b2+b3 needs to be 0, or the equations wont hold

[devout snow]

@void knot Has your question been resolved?

[devout snow]

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[void knot]

I want to ask what's the second pair here?

[random helm]

The second pair is: the column space (dim = 1) and the left nullspace (dim = 2).

[void knot]

Then what's the two lines😿

[devout snow]

@void knot Has your question been resolved?

[devout snow]

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[exotic vessel]

what is the shortcut formula for calculating the variance from grouped data using relative frequencies?

[devout snow]

@exotic vessel Has your question been resolved?

[supple knot]

Why do you think there's a "shortcut"

I guess you can cancel the n/n

[devout snow]

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[exotic vessel]

bc there was a shortcut for calculating the sample variance when using absolute frequencies

[devout snow]

@exotic vessel Has your question been resolved?

[devout snow]

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[plucky helm]

What do I do for finding absolute extrema when the derivative isn't factorable? For example my derivative is (-x^3 + 6x^2 - 18x) and like I was able to factor out a -x to get x=0 for a critical point, but I'm not sure what to do with (x^2 - 6x + 18) since it's not factorable from what I can tell

[warped night]

quadratic formula

even though it's really painful to do

it works

[plucky helm]

Alright thanks

I actually just realized I differentiated wrong so that was my issue

But good to know in the future

[warped night]

oh lol

-3x^2+12x-18

yeah I just realized

[plucky helm]

d/dx of 3x^3 =/= 6x^2

[warped night]

oh wait

[plucky helm]

My original function was -(x^4)/4 + 3x^3 - 9x^2

[warped night]

oh

-x^3+9x^2-18x

[plucky helm]

No it's just -x^3 + 9x^2 - 18x

[warped night]

oh wait i'm dumb

anyway

you understand now rightr?

[plucky helm]

There's a 4 in the denominator of the leading term

Yeah I think I should be good from here

[warped night]

alr

[plucky helm]

Was just confused what to do when my derivative isn't factorable normally or by grouping

So thanks

[warped night]

yw

[plucky helm]

.close

[devout snow]

Channel closed

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[warped night]

I don't think they'll make you solve by quadratics but idk

[plucky helm]

I've had to for a problem before in this class so not unreasonable

But only one out of a lot so

[warped night]

oh

ok

[plucky helm]

So critical points on that one then are x = 0, x = 3, and x = 6

Sweet

[devout snow]

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[rancid spire]

The rent is 225,000 ISK per month. That's 32.5% of my salary. What do I have as a salary?

[olive snow]

So 0.325x = 225,000 with x your salary

X% of smth <=> (X/100)*smth

[sharp moth]

692,308 ISK

Salary = 225,000 / 0.325

[rancid spire]

ty!

.close

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[supple knot]

!nosols

[devout snow]

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.

[sharp moth]

?

[raven cape]

So I'm practicing for a GED and I went to a site for practice questions i got given
x + 36 = 3x
The site simplified it to
x + 36 = 3x
x - x + 36 = 3x - x
36 = 2x

My questions Is where the hell did the 2x come from?

[sharp moth]

ok

[sharp moth]

huh?

u subtacted x from both sides

[raven cape]

I thought acting on an X variable with a X variable cancel teacher out and it would end up as 3x

[stone juniper]

x=18

[sharp moth]

3x - x=2x

[sharp moth]

he wants to know why ther eis 2x

[raven cape]

Yeah

[sharp moth]

but x variable still represents a constant

3x is x+x+x

so 3x - x = x+x+x-x

=2x

basic algebra

[raven cape]

That's

So bizzare

I remember the reason why I never liked this stuff now 💀

[winged tapir]

wdym bizzare

thats common sense

[raven cape]

For you probably because you're at a much higher lvl of math knowledge

But of all the equations I've been doing so far this was never mentioned

So like another example 10x - x

Would that be 90x?

[winged tapir]

9x

[devout snow]

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[silent sandal]

So my textbook says to use integration by parts by setting u =ln(2x+5) and dv=dx. Why is setting dv=dx allowed? Shouldnt there be two things multiplying each other in order to use integration by parts?

[misty crest]

yea it’s 1

1 * ln(2x+5)

that’s how i think about it

i also don’t use the trash integration by parts formula

just do DI or tabular as others call it

[silent sandal]

yeah i wish i didnt have to, but unfortunately im required to on my exam 😵‍💫

thank you for the help though, thats a useful way to think about it

.close

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[tawdry wave]

Hey

[tawdry wave]

My teacher told me i didn't have to use substitution

I can't see it

I can't see an easy way

[boreal lion]

tabular method?

[vestal dirge]

Or guess the antidervitive xD

[tawdry wave]

OHH x² is the derivative of x³

[hollow pulsar]

or double integration by parts

(which needs then a substitution afterwards)

[hollow pulsar]

u sure abt that?

[tawdry wave]

Yeah degree wise so i can manipulate the integral a bit by adding -3 instead and putting -1/3 outside

[hollow pulsar]

well 3x² is the derivative

but i get what u mean

[boreal lion]

or if you're bored, expand everything

[hollow pulsar]

woah

thats one hell of a good method

[boreal lion]

unless you make a tiny tiny mistake

[tawdry wave]

Lol thanks guys

.close

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[spark hound]

How do we know dat angle is in da second quadrant?

[spark hound]

Just looking at da unit circle?

I can convert to degrees which is easier, but I wan2 learn to visual radians

[acoustic leaf]

so we would like to compare $\frac{5\pi}{7}$ to the 4 quadrant angles $0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$

[woven radish]

cloud

[acoustic leaf]

to do this i would recommend you convert all of them to a common denominator

[boreal lion]

2nd quadrant is 0.5pi to pi

clearly, 5/7 > 0.5 and less than 1

[spark hound]

Thanks guys

.soled

.solved

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[blazing crest]

b

[supple knot]

!show

[devout snow]

Show your work, and if possible, explain where you are stuck.

[blazing crest]

i can write the sequence has 1/n - n

i understand from this that the sequence approaches -infinity as n approaches infinity

but im stuck at the proof part

[supple knot]

For any M < 0, can find an N large enough so that 1/n - n < M for all n > N?

Say M = -100

[blazing crest]

i think there si no l for any n in natural numbers for tn in which it holds that l <= Tn

[supple knot]

What

What's l and Tn and tn

[blazing crest]

if M - 100, we can take N is 1000 so for any n>N there is no M

[blazing crest]

l being a lower bound, and tn being the sequence (1-n^2)/n

[supple knot]

You should show what you did for a)

[blazing crest]

for a, i basically contradict the statement that there exists an L in Real numbers, for any n in Natural number s.t. l <= tn

contradicting this leads to for any L in R, there exists an n in N st l > tn

[supple knot]

You're missing for all n > N

[blazing crest]

contradicting this leads to: for any L in R, there exists an N in Natural numbers in which for every n>N , we have l > tn @supple knot

is this better

[supple knot]

Yea can you find the N for l=-100

[blazing crest]

Take N = 500, then for every n>N we have that it is smaller than M

i assume we have to now generalize l instead of taking a specific value

right?

@supple knot

[supple knot]

Right that works fine

Yes

[blazing crest]

but we need not for M = -100 but for any M in Real numbers..?

[supple knot]

yes

[blazing crest]

uh

[devout snow]

@blazing crest Has your question been resolved?

[devout snow]

@blazing crest Has your question been resolved?

[devout snow]

@blazing crest Has your question been resolved?

[unique mesa]

hi everyone

[devout snow]

@blazing crest Has your question been resolved?

[devout snow]

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[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[jovial spire]

can anybody explain to me why we subtract 180 from 210 if 210 is in the south?

[jovial spire]

because usually if that 210 was in the west it would be west south which doesnt exist so we would subtract 180

to get whats in the south

[winter patrol]

you're interested in the acute angle deviation from north or south

[jovial spire]

the south but is it bc it starts at north?

that we minus 180

[winter patrol]

starting from south, the bearing is that angle towards west

[jovial spire]

yeah

because i thought it was south210 degrees west

[winter patrol]

which you get by subtracting 180 from 210

[jovial spire]

wait but is that whole revolution not 210

[winter patrol]

yes

[jovial spire]

really?

OHHHHHHH

[winter patrol]

the true bearing, measured clockwise from N would be 210°

[jovial spire]

because it passes 90 degrees once, 90 degrees twice

which is 180

but not 210

so to find that little angle over there 210-180

[winter patrol]

yes

[jovial spire]

ahh are compass bearings never three digits?

[winter patrol]

no,

as mentioned, they indicate deviation from North or South
towards West or East, depending on which is closer

[jovial spire]

ok that makes alot more sense now

tysm

.close

[devout snow]

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[devout snow]

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[dreamy pelican]

I'm a bit confused on what the next step is, I've looked an example question and I'm still kinda confused

[dreamy pelican]

The topic is on the top left and the answer next to the green check mark is my working out but it's not fully correct yet

[delicate fossil]

They want you to rationalize the denominator

[dreamy pelican]

Ohhh

Hold up

I'm kinda stuck again now

I thought it'd equal to sqrt5 over 5

[delicate fossil]

seems correct

maybee they want to have a common denominator?

[dreamy pelican]

Ah yeah they did

It's still not correct yet though But I feel like I've got this now so I'll close this for now

Thanks for the headers

.close

[devout snow]

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[devout snow]

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[void knot]

Any idea is welcomed...I'm cooked

[lusty sapphire]

[fervent hornet]

try this it might work
$f_{n+1}(x)=f_n(x) +\frac{x^{n+1}}{(n+1)!}\
\left(f_n(x)\left(f_n(x) +\frac{x^{n+1}}{(n+1)!}\right)\right)=0$

[lusty sapphire]

Is this ever zero?

[woven radish]

convergence

[sage burrow]

if a product is null, one of the factors need to be 0.

[sage burrow]

for n=1 with x = -1.

[devout snow]

@void knot Has your question been resolved?

[remote steeple]

i think this thing is (e^x)^2 when approaching inf

so i dont see how it approaches 0

[sage burrow]

who is talking about approaching infinity? i see a given n, and f_n(x) times f_(n+1)(x) = 0 is solvable in the reals for some n, not all n i guess.

[remote steeple]

oh right

then i think it'll always have a root

depends on odd or even n

essentially expansion to what order

[sage burrow]

and as its the product of f_n and f_(n+1) there is always an odd polynom.

[remote steeple]

true thats the trick

[sage burrow]

but that gives only "at least one solution" as answer, but its asked for the number of real roots. could there be more than one?

[random helm]

prove by induction that f_n is positive for even n and increasing for odd n. So the product f_n * f_(n+1) has only one root.

[devout snow]

@void knot Has your question been resolved?

[devout snow]

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[restive river]

I think the textbook solution is wrong and should be 3units, I started with double integrals to find my xyz range to get my bounds.

[faint gorge]

I agree

If you were to compute the volume without integrals, but geometry you end up with 3 as well

[restive river]

appreciate the confirmation, now i just need to get the integral to work

[faint gorge]

are you struggling to find the bounds?

[restive river]

yes, i watched some videos on it too

[faint gorge]

Ok I will try to explain it

you basically need two integrals

this would be the easiest if you did dzdydx

now in dxdydz

you consider the yz plane

you integrate the purple surface over the region 0 <= y <= 2 and 1 <= z <= 2

and then you integrate the other surface x=1 over 0 <= y <= 2 and 0 <= z <= 1

I kinda messed up the drawing with the yellow it should hit z=1 ofc

[restive river]

ok, ill try that. ty

[faint gorge]

here is the desmos site btw

https://www.desmos.com/3d/f1xpqxkx4v

[restive river]

like this?

[faint gorge]

yup

[restive river]

😁 👍 ty for you time

[devout snow]

@restive river Has your question been resolved?

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[whole bear]

Im doing complex numbers. Im last year in highschool and i have a problem in my calculator. I need someone to please help me fix it urgently cause i have an upcoming exam. Idk how to explain it step by step but i can explain what im doing and show u my calculator and my friends one and hope u can please help.

[fossil locust]

okay, just ask your question

also which calculator model do you have?

[whole bear]

Okay so i wanna transform the algebric form into an trigonometric form. I wanna find the R and θ using the calculator. In order to do that, i press shift mode setup and put Rad so i get the angle in rad. I press mode setup and put cmplx. After i write my equation (-1-i) i press equal, then i press shift-> 2 or shift-> [cmplx] and choose the 3rd one r<θ. And there i should get an answer which ill send in a picture, but ill also send my wrong answer.

Calculator model : fx-991ES PLUS CASIO

[whole bear]

I should get this

[whole bear]

But im getting this

[fossil locust]

oh turn on exact mode on your calculator

[whole bear]

Sorry to say but idk what it is

[fossil locust]

https://www.youtube.com/watch?v=UGBvg4iU5Uo

[whole bear]

Tyy ill be right backk

[fossil locust]

one sec

[fossil locust]

press shift then menu

[whole bear]

Menu is mode?

[fossil locust]

yeah

[whole bear]

Okay i did

[fossil locust]

wait what are the options on your calculator now?

is there an option called fix?

[whole bear]

Yes

I press they put 0~9

[fossil locust]

ah shit that gives you the number of decimal places

so not that one

[whole bear]

Okay

I get the R right but the θ wrong

Just in this particular rquation of -1-i

Usually it works fine on othee equations

[fossil locust]

,calc -3/4 * pi

[woven radish]

Result:

-2.3561944901923

[fossil locust]

it's correct

you just want your calculator to display this in exact form

which means a multiple of pi in this case

[whole bear]

Like is it fixble?

[fossil locust]

it should be but I don't know how

to fix this in the meantime, I would recommend you use degrees

so press shift + mode

press the number that corresponds to degrees; I think it's 1

[whole bear]

Yeah yeah i can have it in degrees but i dont want to mess up converting degree into rad by my own calculations

Is therw a way to do it on the calculator to like show from deg to rad?

[fossil locust]

yes press shift + Ans

then press 1 for the degree

that will convert degrees to radians

yes that converts from degrees to radians now

[whole bear]

Wait ill try

[fossil locust]

but your calculator has to be in radians mode

[whole bear]

Okay ill try

Ill put -135 press equal

Than i ress shift ans

And press r?

It gave me what i wrote

Sorry if im wasting ur time or something

But im really stressed about it

[fossil locust]

wait I might have the answer

just press mode

[whole bear]

Ty alot btw