help-0

[scenic heath]

@abstract goblet

[abstract goblet]

okay i will try again

after i try again i will notify

then it becomes a Geometric Progression of ratio 1/3

[charred flint]

yup

[abstract goblet]

but i am not able to find any uniformity in the question which will show the next step

[gray isle]

wdym

[scenic heath]

you calculate the limit

[glass lichen]

Per Plum's idea, consider the natural log of the limit, thus turning the product into a sum.

[scenic heath]

can't he just evaluate the limit of the geometric progression and add the numerator and denominator?

of the irreducible fraction

[lone heart]

@abstract goblet Has your question been resolved?

[scenic heath]

everything collapses nicely due to (1+b)(1-b) = (1-b^2)

[abstract goblet]

then the expression becomes (1-1/9)(1-1/81)........(1-1/3^2^(n+1)

with the same limit

[scenic heath]

yes but (1-1/9)

is (1-1/3^2)

you now multiply that with the next one

and it becomes (1-1/3^4)

and so on

[abstract goblet]

oh so basically a repetitive multiplication with the conjugate term ?

[scenic heath]

the numerator collapses into (1-1/3^(2n+1))

yes

as n goes to infinity that just becomes 1

so the only relevant part is the the conjugate

that remains in the denominator

and thats just 2/3

[abstract goblet]

thanks a lot brother

[scenic heath]

n+m is just 2+3 now

[abstract goblet]

yeah thanks for the help

[pearl loom]

Find the volume of the solid generated by rotating the region bounded by y = x - x^2 and y = 0 about the line x = -2

Can't solve this

I'm stuck...

[scenic heath]

ask in one of the open help channels

@pearl loom

[pearl loom]

oh

sorry

[lone heart]

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[grave lance]

Ok I'm having to ask this question again because I was told an approach earlier by another member, however I thought I got another way down to solve it but it turned out I made an error so it was wrong and now I'm stuck again with this being unable to solve it. The advice was let sqrt(x) = u but I don't know where to go with that

[grave lance]

This regular approach leads to nowhere

I'm supposed to solve without complex numbers and I know for a fact that there is one correct answer which is 1

[late bridge]

the line after 4x = 9-6x+x^2 is wrong

[grave lance]

oh crap yeah

Alright that solves that

but I'm still curious on how replacing sqrt(x) with u would help?

[glass lichen]

u^2+2u-3=0...

Instead, you could have asked directly instead of ignoring it then asking.

[grave lance]

Oh yeah that one goes on me

I tried that but then saw the other method of solving and just decided I solved it but now I was curious

that does it anyway ty you guys

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[fallow gorge]

Greetings. I'm looking for a solution for a certain exercise about proportions. In which chat can I ask the question?

[glass lichen]

Dont ask to ask.

[fallow gorge]

Oh ok. I though posting in a wrong chat would mean violating the rules (that I haven't read) xD.

I'm currently doing an exercise related to proportions and I have stumbled upon one of them that I cannot solve. The exercise reads the following:
If person A and B work together, they finish a job for 2 days. People B and C finish the same job for 4 days, while A and C can finish it for 12/5 days.
How long would it take for person A alone to finish the same job?

[scenic heath]

1/a + 1/b = 1/2

1/b + 1/c = 1/4

1/a + 1/c = 5/12

solve for a

[late bridge]

wouldn't walking them through the process of coming up with the equations be helpful tho?

[scenic heath]

a,b,c are in days.
1/a means that in one day, a makes 1/a of the total job.

Lets look at the first equation

We have that a and b need 2 days together

that means that in one day, a and b make 1/2 of the job

1/2 of the total job in one day is made by the sum of the work a has done and the work b has done

a has done 1/a in one day

b has done 1/b in one day

putting the equation together:

1/2 = 1/a + 1/b

we do that for every equation

@fallow gorge

you have to think in terms of jobs/day

jobs per day

Alternatively: (a,b,c are in 1/days)

(for the first equation)

a and b need 2 days together

that means that every day they manage 1/2 of the work

a + b = 1/2

you do that for every equation

but now you don't get the days but the fraction of work they do as a solution

you have to take the inverse of the solution to get the time spent

Both ways are equivalent

@fallow gorge does this make the solution clearer?

[fallow gorge]

It does, thank you so much.

The 1/a, 1/b and 1/c were bothering me at first, but now everything is clear.

[lone heart]

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[formal dune]

hello, i have been studying logarithms and couldn't understand what exactly natural logs are and where they are used. According to my notebook they are used in the change of base formula, which doesn't really make a lot of sense to me, since their base is E (2.7...) , and according to this formula the base can be anything. I searched about them in the internet and apparently they are used to make function graphs or something like that. I might have wrote it wrongly on my notebook, i'am a little bit confused x-x

[glass lichen]

natural logs are logs with base e (not E)

[formal dune]

whoops i meant e not E

[glass lichen]

and they're just the convinient math log, as opposed to log which is base 10 and used more in science / logarithmic scales

[formal dune]

but what makes them more convinient than the normal log?

[glass lichen]

w/o calculus knowledge: Nothing

w/ calculus knowledge: They simply behave the best under differentiation

and e kinda tends to just show up when we look at continuous things, so ln pops up with it

example continuous compound growth, Newton's Law of Cooling, Drag forces all rely on e

[formal dune]

mhm i see, so they are a type of log that fits better in certain situations?

[glass lichen]

yes

exactly that

You pick the base of the log that just makes things nice

[shell widget]

might help: https://www.youtube.com/watch?v=4PDoT7jtxmw

[glass lichen]

for example in science, everything is in base 10 (recall scientific notation). So log w/ base 10 is just the most sensible one to pick

however if you look at say half life functions, you're better off w/ log base 2 since the base of the exponential is 2

[scenic heath]

change of base works with any log with any base

its just that look up tables mostly use ln()

[glass lichen]

Half life in the form $P=P_02^{-t/h}$

[ocean seal]

Kangaroo Gang Mosh

[scenic heath]

entropy needs log with base 2

information etc...

because information is stored in bits

[formal dune]

so in the change of base formula they aren't necessarily the formula, they can simply be used there because the base can be anything?

[glass lichen]

yes

the base is any positive number except 1

[scenic heath]

include all numbers except 1 if you feel complex

[formal dune]

i think this is what i saw in google, they behave better in that function graphic is that it?

[glass lichen]

nope, it technically is harder to graph because irrational numbers

[formal dune]

:/

[glass lichen]

but as you do more math you'll realize e has a tendency to pop up more and more

[formal dune]

I see

[scenic heath]

economics:

https://stats.stackexchange.com/questions/27682/what-is-the-reason-why-we-use-natural-logarithm-ln-rather-than-log-to-base-10

reason for ln() without calculus knowledge

[formal dune]

i think i understood it, thank you!

[scenic heath]

https://youtu.be/4PDoT7jtxmw

https://youtu.be/m2MIpDrF7Es

second video might be better

[formal dune]

i will watch all of them, im starting to study maths independently

[scenic heath]

might have to look at some calculus videos for the second video

if you don't know about derivatives/slopes

[formal dune]

k

[lone heart]

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[sterile vale]

Hi, I am asked to find the limit of this function when it tends to +infinity

[sterile vale]

I keep obviously getting the wrong answer but I really don't understand why?

Thanks 🙏

[noble sinew]

x^2(1/x+1/x^2) is not equal to x(x+1)

[urban inlet]

x(x+1) = x^2(1+ 1/x)

tru

[sterile vale]

ahhh crap

Went too fast

Thanks a bunch

.close

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[gloomy forge]

Still getting this wrong 😅

[icy trail]

its just looking for length of c?

[gloomy forge]

meant to put a there

[icy trail]

oh kek i see

sus i got 158.36

[gloomy forge]

can you explain steps?

[icy trail]

i just put it in my calculator lol

im tryna find where you went wrong

,w cos 113

[ocean seal]

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[icy trail]

it looks like you put 0.9952 for that instead

[buoyant kayak]

your calculator is still in radians

you're working with degrees

[gloomy forge]

ty

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[harsh ocean]

I need someone to check if I did any mistakes doing these derivatives and arranging algebraically.

[harsh ocean]

The order is checking from 2nd image to 1st

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[harsh swallow]

Integrating the volume for this gives me a negative volume for R > r > 0

[harsh swallow]

the jacobi matrix is this

jacobian is this

and integrating this gives me a negative volume

i don't understand

nvm

i'm stupid

gotta take the absolute value of the jacobian

.close

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[lone heart]

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[raw shard]

yes

well, in the limit definition of the derivative for the function, the limit exists

[frozen python]

f being differentiable is a stronger form of continuity

e.x. |x| is not differentiable at x=0, but its continuous at x=0

[raw shard]

mattdog just gave an example of that exact thing

yeah i think

because you could be looking at something like \ $y = \frac{(x+3)(x-5)}{(x-5)}$

[ocean seal]

quantum

[frozen python]

yeah that's discontinuous at x=5 but has a limit of 8

so continuity at a point guarantees a limit, but discontinuity does not mean there is no limit

smh

[sly mantle]

@errant marten rly?

[frozen python]

i cheated
mods show up
naw im just kidding bro

[gray isle]

not something you should joke about

[frozen python]

[sly mantle]

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[alpine sable]

How is sin(3pi/4) equal to sqrt(2)/2?

[raw shard]

because it just is?

[alpine sable]

how?

that would mean sin(pi/4) = sin(3pi/4)

[raw shard]

,w sin(3pi/4)

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[alpine sable]

hmm

wait

[raw shard]

wait

yeah

i just realized

my gosh that took way longer than it should have

sin(x) = sin(pi-x)

[alpine sable]

yeah nvm, figured it out

thanks

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[whole lake]

Is the complexification of the complex plane a field?

[whole lake]

That is, if we define F = C^2 with pointwise addition and (a,b)*(c,d) = (ac-bd,ac+ad), is F a field?

I suspect it is but I can't seem to find any literature on it

[lone heart]

@whole lake Has your question been resolved?

[ancient saddle]

Hello, it is a field according to this
http://pirate.shu.edu/~wachsmut/complex/numbers/numbers.html#complex_field

[whole lake]

wow thanks!

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[lucid tinsel]

So in trying to find the sqr rt of 40, I am trying the repeated subtraction method. The website said this is convenient for perfe t squares, but it did not say it's not compatible with non-perfect squares. I am down to 4-13. What do I do from here?

[severe sluice]

you can't do that

use taylor series

[gray isle]

what are the exact instructions of your problem

[raw shard]

you mean linear approximation if anything

[lucid tinsel]

It's just to find the Square root.

[alpine sable]

The intended solution probably begins with writing sqrt(40) = sqrt(10*4)

[lucid tinsel]

No, it's square root thing then inside is 36+4

Wait, I mean that's how the problem is written

[severe sluice]

well, that works, but i meant taylor series (but linear approx is still easier to do)

[lucid tinsel]

Solution says 6.32

I'm relearning all this stuff and this is a problem in the skill review at the beginning of a geometry book.

So should I try the linear approximation or Taylor series?

[alpine sable]

Pretty question if literally all it said was to “find the square root of 40” and the answer is 6.32

[raw shard]

neither

it probably just wants you to approximate it using a simpler method

[lucid tinsel]

"Evaluate the radical expression. Round your answer to two decimal places.

[severe sluice]

2 decimal places in a geometry course?
well, i think they just wanted you to put it in a calculator

[alpine sable]

You should have mentioned that earlier lol

[lucid tinsel]

Sorry

[gray isle]

pretty much just calculator

there is an algebraic way for approximations that's a little tedious

[lucid tinsel]

I'd like to know how to work it out myself

[gray isle]

look up square root by hand

or something

[lucid tinsel]

Okay. Thanks.

.close

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[gray isle]

you could also consider pythagoras

and draw a right triangle with legs 2 and 6

and measure the hypotenuese

[lone heart]

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[tawny fable]

Hey there

[tawny fable]

I am trying to prove that

But the only thing I can use is that f+g and f*g are differentiable

and I can't get the solution with that

[placid zinc]

Are you trying to prove it, or are you asked if it is true/false?

[tawny fable]

I am asked if its true or false

sorry

Let me guess xD

Its false?

lol

[placid zinc]

Looks a little bit false, trying to think of a counter example

[tawny fable]

Please

if you can

try to explain to me your thoughts

I want to try and understand how do you get to a counter example regarding differentiable functions

we learned about |x|,

and some more

I can't seem to find any that its false for them

[mystic mulch]

In my mind this feels very germ-like and should be true

[tawny fable]

If it's true

I am stuck on the defenition

I have some 2limits

[placid zinc]

Got it. Consider this function:
f(x) = 0 for x≤0
f(x) = 1 for x>0

g(x) = 1 for x < 0
g(x) = 0 for x ≥ 0

Then f + g = 1
And fg = 0

But clearly niether are differentiable at x = 0

[tawny fable]

and some equations with no connection, at least not that i can see

could be also derichlet?

[lone heart]

@tawny fable Has your question been resolved?

[placid zinc]

What did you still want to know?

[tawny fable]

I wanted to understand what did you think about when you got to the counter example

[placid zinc]

I usually generate very very simple examples

I think you'll agree that f and g are pretty easy to think about here, and that helps a lot with reasoning and honing in on counter examples

Use 0, and 0-like objects often, they're always really good

[tawny fable]

Got it Kaynex

Thank you for the explanation

@placid zinc

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[spice kelp]

need to check if it is correct

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[spice kelp]

<@&286206848099549185>

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[spice kelp]

.close

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[pearl musk]

i have no idea how to go about this.

[lone heart]

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[pearl musk]

<@&286206848099549185>

[vale sapphire]

are you allowed to use l'Hôpital's rule?

@alpine sable #❓how-to-get-help

[alpine sable]

@vale sapphire ah, thanks!

[lone heart]

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[vale sapphire]

@pearl musk I reiterate, are you allowed to use L'Hôpital's rule?

[pearl musk]

sorry I didn’t see your message

no i’m not

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[noble sinew]

Multiply through with conjugate

[pearl musk]

conjugate?

[scenic heath]

conjugate of a+b is a-b

[scenic heath]

(a+b)(a-b) = a^2 - b^2

[pearl musk]

should I multiply with the conjugate of the denominator or numerator?

[noble sinew]

Denom

You want to rationalize the expression

[lone heart]

@pearl musk Has your question been resolved?

[pearl musk]

why should I think to do that?

[noble sinew]

Because you have a sqrt in the expression

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[lone heart]

@silk terrace Has your question been resolved?

[rich basin]

(d)

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[flat saddle]

What does A raised to Jesus mean?

[vale sapphire]

needs more context

are you sure it's not just a footnote?

it's a common symbol to denote those

[flat saddle]

Involution Law:

[vale sapphire]

i'm strongly leaning towards a footnote

check the bottom of the page

[flat saddle]

oh yep

thanks

.close

[lone heart]

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[alpine sable]

this is a wonderful quote

[lone heart]

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[plain zodiac]

if x:y = 3:4 and x:(y+z) = 2:5, what is the ratio of x:z?

[flat saddle]

try get the ratios to have the same numbers

[plain zodiac]

both of the x?

[flat saddle]

yeah

try it

[twilit dune]

if you already know that it is enough information [i.e. there is one and only one possible ratio x:z] then you can just plug in values for x,y that satisfies x:y=3:4

[lone heart]

@plain zodiac Has your question been resolved?

[plain zodiac]

is it -3/2

?

[gray isle]

show work

[lone heart]

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[late parcel]

I’m pretty lost on this

<@&286206848099549185> the fact that’s I’m only given POIs is what’s confusing me

I defiantly think that x=4 is a maximum so I’m sure III is correct

I think I need a full walk through for I

[lone heart]

@late parcel Has your question been resolved?

[late parcel]

Any thoughts?

[severe sluice]

what's the question?

[late parcel]

@severe sluice

That’s it

[severe sluice]

ok @late parcel we'll go through the points

firstly, I

why do you think that it's correct

[late parcel]

Well

Based off my sketch 4 is a max

How I’m lost on 1

I think 1 is neither because it’s first derivative is 0 at 1

But I’m not sure if that’s correct sense @severe sluice

[severe sluice]

what does this mean?

[late parcel]

Neither a min or max

At x=1

[severe sluice]

what does first derivative = 0 mean?

[late parcel]

It means the function is flat there

[severe sluice]

yeah, so?

i mean

[late parcel]

So I think no min or max

[severe sluice]

first derivative = 0 means that the point is either a min or a max (or the function is completely flat, in which case the second derivative will be 0 as well, but it isn't)

[late parcel]

So it’s a min or max

[severe sluice]

yeah

[late parcel]

How would you tell which kind

[severe sluice]

based on the second derivative 🙂

if the 2nd derivative is negative, it's a max

if it's positive, it's a min

[late parcel]

Negative is min

[severe sluice]

no

[late parcel]

Oh second derivative

Oh ok

But they only give you POI

[severe sluice]

wait, what's a POI?

[late parcel]

Point of inflection

That’s all they give you

[severe sluice]

oh
POI happens when the second derivative is 0

try taking the derivatives of y=x^3 at x=0

[late parcel]

It’s 0

[severe sluice]

yeah, so it's an inflection point (you can also see that on the graph)

[late parcel]

Ok

So wait after all that

[severe sluice]

so is I true?

[late parcel]

X=1 is positive for second derivative

Meaning it’s a max

So 1 is not true

[severe sluice]

right

is II true?

[late parcel]

Wait

Well it is true

But III is also true

I think

And their is no answer choice for II and III

[severe sluice]

why?

[late parcel]

Oh wait X=4 is a min

Oh so B is the correct answer

Thanks

[severe sluice]

can you do .close?

[late parcel]

.close

[lone heart]

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[raw shard]

lol

[severe sluice]

0 open help channels soon

[late parcel]

I have another question

If this is still open

[severe sluice]

this is like the 4th time we've done this (hype is dead)

[severe sluice]

.reopen

[raw shard]

doesn’t really matter

if it’s just a quick question

[late parcel]

Not really that quick

[lone heart]

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[bold pebble]

I was doing a little trolling, a little programming when I came across google saying 859806257774723102 mod 3 is equal to 0 while 859806257774723102 mod 3 in my program is 2 and on demos it's 0 and on wolfram it's 2 so why is it 2 in python and on wolfram but 0 in desmos and google

[vale wigeon]

it's a pretty large number, so google and desmos might be treating it as a float rather than an int and hence it gets rounded off which messes with the mod

,calc 8+5+9+8+0+6+2+5+7+7+7+4+7+2+3+1+0+2

[ocean seal]

Result:

83

[vale wigeon]

yeah, the correct answer for (your number) mod 3 is 2

[alpine sable]

Poor Sam.

[bold pebble]

is this a modulo trick that I didn't know about

[vale wigeon]

it's divisibility by 3 (and 9)

[alpine sable]

Google "divisibility rules".

[vale wigeon]

it's pretty well known that a number is divisible by 9 iff the sum of its digits is divisible by 9

(the same trick works for 3 obviously)

[alpine sable]

Once tried to prove it but failed. 😔

[vale wigeon]

it's not very hard to prove either

[severe sluice]

10 = 3x3 + 1 (basic modular arithmetic from there)

[jagged imp]

hint for the proof:10^k=1 mod 3 where k is natural

[alpine sable]

My 9th grader brain is not that advanced.

[vale wigeon]

is your ninth-grader brain capable of knowing what positional notation is and how it works?

[alpine sable]

Positional notation?

[vale wigeon]

you know

the notation you use to write numbers

place value and all that

[alpine sable]

I know place values.

[vale wigeon]

like the 6 in 42069 refers not to the number six but to six times ten

[alpine sable]

Yep.

[vale wigeon]

yeah well

if you subtract the sum of a number's digits from the number itself, you'll be left with

the tens digit times 9, plus the hundreds digit times 99, plus the thousands digit times 999, and so on.

[alpine sable]

Hold on, I didn't get this part.

[vale wigeon]

would you like me to write it in symbols?

it might get a little harder to comprehend if i do that

or i could give you an example

[alpine sable]

Try both.

[vale wigeon]

which one first :p

[alpine sable]

Example first.

[vale wigeon]

ok

let's consider the number 5287

this is really 5 * 1000 + 2 * 100 + 8 * 10 + 7, yes?

[alpine sable]

Yep.

[vale wigeon]

now subtract 5+2+8+7 from it

rearranging some stuff we get (5 * 1000 - 5) + (2 * 100 - 2) + (8 * 10 - 8) + (7 - 7)

which is 5 * 999 + 2 * 99 + 8 * 9

[alpine sable]

Oh like that.
I was thinking about 5287 - (5+2+8+7).

Ahhhh got it.

[vale wigeon]

i mean that IS what we're doing

we are subtracting (5+2+8+7) from 5287

[alpine sable]

Yeah, got it now.

[vale wigeon]

i'm just writing it in a way that makes it clear the result is a multiple of 9 no matter what

[alpine sable]

But doesn't that mean that all numbers will be divisible by 9?
Like
ABCD - (A+B+C+D)
= 999 * A + B * 99 + C * 9 + D*0?

[vale wigeon]

it does not mean that "all numbers will be divisible by 9"

but all numbers that result from this subtraction will be divisible by 9, yes. that was my point.

[alpine sable]

I mean when they will be subtracted with their sum.

Okay.

[vale wigeon]

and with some abuse of notation, you wrote it out in the case where the number has four digits.

[lone heart]

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[bold tapir]

Hello, this is my first time using this server. I have just started using the chain rule to differentiate and understand how to solve simpler questions, however, I am stuck on how to differentiate $(\frac{1}{x^3+\frac{1}{x})^5$ with respect to x.

[ocean seal]

samarium 62

Hello, this is my first time using this server. I have just started using the chain rule to differentiate and understand how to solve simpler questions, however, I am stuck on how to differentiate $(\frac{1}{x^3+\frac{1}{x})^5$ with respect to x.
```Compilation error:```! File ended while scanning use of \frac .
<inserted text> 
                \par 
<*> 570368640923336704.tex
                          
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```

[jagged imp]

missing a brace

[bold tapir]

$(\frac{1}{x^3+\frac{1}{x}})^5$

[jagged imp]

for the denominator

[ocean seal]

samarium 62

[raw shard]

\left(stuff\right) if you want tall parentheses

[bold tapir]

Ok thanks, not that experienced with latex

[raw shard]

so where are you lost here?

this would just be the quotient rule on the inside function

[bold tapir]

Oh....

Ok, i think I can solve it now! thanks

[raw shard]

no problem

[bold tapir]

.close

[raw shard]

remember to .close

[lone heart]

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[raw shard]

oof

[bold tapir]

.close

[lone heart]

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[glacial coral]

Hi

[warm brook]

what’s your question

[lone heart]

@glacial coral Has your question been resolved?

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[rapid nova]

Let $\qty(X, \mathcal{A}, \mu)$ be a measure space, $A, B \in \mathcal{A}$ and $\forall, C \in \mathcal{A} \quad \mu \qty( A \cap C ) = \mu \qty( B \cap C )$. Calculate $\mu \qty( A \bigtriangleup B )$

[ocean seal]

rept1d

[rapid nova]

By calculate I mean express in terms of $\mu(A)$ and $\mu(B)$

[ocean seal]

rept1d

[shell widget]

#advanced-analysis might be more helpful

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[lone heart]

@rapid nova Has your question been resolved?

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[vernal egret]

#linear-algebra Hey guys! Can anyone help me to underestand these statement please?

[shell widget]

What do you think about 1?

[vernal egret]

As I underestand a Matrix is inconsistent if there us no solution for the matrix

But in 1 I am not really sure what the quetion means...

I am lost in what "rank" means?

in that context

[shell widget]

Rank = no. of linearly independent column/rows in row echolon/reduced row echolon form

All you need to know is that for a consistent system, we need rank(A)(coefficient matrix) = rank(A|B)(the augmented matrix)

[vernal egret]

Okay

[shell widget]

anyways, we have rank A < n

but does it say anything about rank(A|B)?

[vernal egret]

No

The statements is the only informations I have

[shell widget]

Yes, so we can have rank(A|B) = rank(A), both less than n

and what happens when rank A = rank (A|B)?

[vernal egret]

Then we will have a solution for the matrix

[shell widget]

the system, yes

and hence a consistent system

[vernal egret]

Okay, so the statement comes false?

[shell widget]

Yes.

[vernal egret]

okay, thank you

[shell widget]

think a bit for 2

[vernal egret]

.close

[lone heart]

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[short thistle]

Hey guys,
I would like some help with finding the primitive of this one
I tied a change of variables but stuck

[short thistle]

the x is a typo

it should be a t

This is what I should find, again they put x instead of t

[gray isle]

I tied a change of variables but stuck
show work

[short thistle]

ok

[gray isle]

bad choice for sub

[analog olive]

ig substituting t^2 - 6t + 13 is better

[gray isle]

usually you'd go for one of the more complicated parts

and recognising certain derivatives helps too

[short thistle]

oh so u = the one below without the exponent

[severe sluice]

well, try taking the derivative of the denominator

what do you get

[short thistle]

i get the t-3

[severe sluice]

(i mean t^2-6t+13)

[short thistle]

2t-6 mb

[severe sluice]

yeah

and that is.....

well

that's the numerator

$\dv{u}{t} = 2t-6$

[ocean seal]

just sаm

[severe sluice]

so you have

[short thistle]

oh

I/u^n+1

right?

[severe sluice]

$\int \frac{1}{u^{n+1}} \dd u$

[ocean seal]

just sаm

[severe sluice]

yeah...

[analog olive]

also you could have proceeded with this too but thats like 2 steps.
You could have substituted u^2 + 4 = q again and then dq = 2udu.. which is numerator

[short thistle]

I see

That would be more complicated

[severe sluice]

hi [redacted]

[short thistle]

So I should always look to substitute the most complicated part?

[analog olive]

hi :0

[severe sluice]

don't
choose u so that you can easily get du/whatever the differential is in the integrand

[severe sluice]

hi!

[analog olive]

Hi

[severe sluice]

how are you redacted

[short thistle]

Okay thankyou

[analog olive]

I am fine

wrong channel

[analog olive]

Also, you could have a look over this to see a nice problem on substitutions : https://www.youtube.com/watch?v=GfA-Orj0Hgs

[short thistle]

I will thank you for the link

I have another question

This is the original problem
They chose these u et v' for the integration by parts

First when I tried I chose like (t-3)^2 as u struggled to get the other part
Is there a way to choose the right combo like here?

Or is it just instincts?

[gray isle]

recognising certain derivatives helps

[severe sluice]

they chose u so that it's easy to differentiate, while v' should be easy to integrate (unless i completely messed up the variables)

[short thistle]

I understand, I guess I just have to do more ibp 😦

Thank you guys for the help 🙂 👍

.close

[lone heart]

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[pliant estuary]

Hey guys, I have a bit trouble understaning what is the connection betwen Hilbert spaces and Fourier series.

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@pliant estuary Has your question been resolved?

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[pliant estuary]

.reopen

[lone heart]

✅

[lone heart]

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[cursive badger]

a b (and c) are all coefficients

note that the first a and b, and the a b and c are completely different variables

they just happen to share the same name

I don't have any values, so I can't help with the actual problem

but to get a and b for the linear model (where a is the y intercept, and b is the slope), I would put your values into point slope form, then expand and solve for y

so y-output1=slope(x-input1)

but you need actual values to do that

as for the quadratic function, that's written in vertex form, where (b,f(b)) is the coordinate of the vertex

first you would ideally have the x coordinate of the vertex, which is the b value plain and simple

then using two other points (x1,y1) and (x2,y2) (one of those points can be the vertex, they just have to be different) that the quadratic passes through you can solve for a and c as a kind of system of equations

I mean, I think they need the values too

well, in that case

in the linear model,

'a' is the y intercept - it is the value of the function at t=0. That means that f(0)=a: the amount of aspirin already excreted from the body at t=0 is 'a' grams/units/elephant-pounds/whatever

'b' is the slope - it is the rate at which the amount of aspirin changes

for every 1 x axis unit (so every second, or every minute - whatever the change from 0 to 1 is on the t axis), 'b' is how much the amount of aspirin changes

so a 'b' value of 2 means that every second (for instance, not sure what your time values are), the amount of aspirin that has been excreted from the body increases by 2 units

I mean, I think of it as 'total mass excreted' and am calling it a day, but yeah, it could have other meanings

not really a rate function

as for the quadratic

amount=a(time-b)^2+c

so, 'b' is the time at which the function hits its maximum or minimum

'c' is the value of the function when it hits its maximum or minimum

not really sure how to describe 'a', since it's not just a slope

but it does govern the rate at which your function predicts aspirin will be excreted

here would be a good place for a line break

or, you can slightly change the meanings of all these if your functions aren't of the amount of aspirin excreted at any given time, but of the rate at which aspirin is being excreted at a given time

in which case for the linear function, 'a' is the initial rate (at t=0) that aspirin is being excreted, and 'b' is the acceleration, the speed at which the rate aspirin is being excreted is being changed by.

and for the quadratic function, (b,c) are the coordinates of the maximum/minimum (depending on if a is negative or positive, respectively) rate of aspirin excretion. And 'a' becomes a slightly more abstract rate at which the rate changes of the rate changing, in addition to changing how the rate changes - less directly understandable.

I'm more than happy to help with any questions you may have!

[rapid summit]

Okay thanks!

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[silk steeple]

help

[silk steeple]

how do I do A and B

[plucky storm]

for part a start with letting a=1 then set up a ratio

[silk steeple]

hm

okay let me try that

does c = 1 too

[plucky storm]

no

how could you represent c in terms of b

if we know that a=1

also wait why is the b on the left capital

[silk steeple]

oh that’s a mistake my bad

in the book it says to make it a/b = b/c

but I don’t understand the reasoning behind that

[cursive badger]

a/b=b/c, c=a-b

because the ratio of a to b is the same as b to c

that's given

that's the premise on which the whole problem is founded

[silk steeple]

hm

wait let me test this out with numbers I don’t fully understand this

[plucky storm]

that's why we set a=1

[silk steeple]

I’m sorry but I don’t understand

why is it not a:b

[cursive badger]

a:b=a/b:1≈a/b (for our purposes)

[silk steeple]

okay I get it now

so we have a/b = b/c

So now I think we have to get a common denominator?

[plucky storm]

remember we set a=1

[silk steeple]

Yes

[plucky storm]

so instead we have 1/b=b/c

and we can also write c in terms of b

[silk steeple]

A-b?

[plucky storm]

exactly

[silk steeple]

Okay so now I have 1/b = b/a-b

do we make into a common denominator?

[plucky storm]

and we set a=1 at the start

so a-b is just 1-b

[silk steeple]

lemme rewrite my equation 1 second

1/b=b/1-b?

[plucky storm]

from here we just solve for b

[plucky storm]

yeah

[silk steeple]

so I think we move b to one side

[plucky storm]

just get rid of the denominators

it will be a quadratic

[silk steeple]

true

so how do we remove the denominators

Cancel?

[plucky storm]

multiplying

[plucky storm]

yeah

[silk steeple]

so b(1-b)

Or (1+b)

[plucky storm]

yes

multiply both sides by that

[silk steeple]

I think something went wrong

I have 1/b^2-b^3 = b/(-b^3-2b^2-b)

[plucky storm]

wait what

[silk steeple]

damn

[plucky storm]

no wispy

no wait

that thing just popped up

ok so hmmmm

let's see

you have to try to get rid of the denominator

[silk steeple]

we need to get to that form

so I think we might have to use the quadratic formula

[plucky storm]

see that image just popped up while i was typing

idk what it was

[plucky storm]

yes

but first you get rid of the denominators

[silk steeple]

I multipled both sides by b-b^2

[plucky storm]

yeah

oh you multiplies the denominator by b-b^2

that's why you got something wrong

[silk steeple]

yes

what do I multiply

[plucky storm]

ok so our equation is 1/b=b/(1-b)

we first want to get rid of the left fraction

we multiply by b to get

b(1/b)=(b*b)/(1-b)

[silk steeple]

wait so we multiply the numerators

[plucky storm]

which simplifies to 1=(b^2)/(1-b)

[plucky storm]

yes

[plucky storm]

from here we multiply both sides by (1-b)

[silk steeple]

wait do we not multiply the denominators at all

[plucky storm]

no that's not how multiplication works

[silk steeple]

oh…

okay then…

back to the question

I have 1-b=b^2

do we move to one side

-b^2 -b + 1 = 0

A= -1
B = -1
C = 1

okay

I got it

well sort of

So close though

and we also need the :1

hm

<@&286206848099549185>

[analog olive]

what's your doubt

[silk steeple]

it’s not the right answer

It’s similar but there’s a issue

like the minus 2 should be 2

And not a minus

[inland shale]

is this the question?

[silk steeple]

no

[inland shale]

Ok.

[silk steeple]

this is the question

sorry I don’t know what that was

[inland shale]

Ok so what is the trouble?

Do you need help with part a or part b?

[silk steeple]

a

So we’ve gotten close

[inland shale]

Alright.

So whats the issue?

[silk steeple]

so the answer I gave

I don’t know what to do next

To get to that answer

I think it might have been a calculation error

[inland shale]

What answer did you give?

[silk steeple]

But I checked and I can’t find

1 plus or minus surd 5 over - 2

[inland shale]

Oh ok.

I think I see the problem.

I'm pretty sure you're correct with the reason it's a calculation error.

[silk steeple]

hm

[inland shale]

Try starting over with the ratio and first see the difference with lines a and b.

I think starting over will help.

[silk steeple]

okay I’ll be back in a few minutes

[analog olive]

this equation isn't right ig for ratio

[silk steeple]

hm

[analog olive]

ratio will be root of equation
$$x^2 -x - 1=0$$

[ocean seal]

[redacted]

[inland shale]

Oh yes i didn't see that.

[silk steeple]

If I rearrange it a bit more differently

okay I’ll move it to the right hand side then

Now I have 0=b^2 + b - 1

I’m going to use the quadratic formula on this and hopefully it’s right this time

[analog olive]

if you are using b for the length only, then this isn't right and if for length, then idts one could get an equation for that

[analog olive]

nah it will give same answer as you got before as equation is same

[silk steeple]

I got this now

but now we have a different problem

[analog olive]

$$a = b+c$$
$$ \frac{a}{b} = \frac{b}{c}$$
$$\frac{b+c}{b} = \frac{b}{c}$$
$$1 + \frac{c}{b} = \frac{b}{c}$$
We need to get the value of ratio i.e. $ \frac{b}{c} = x$
So
$$ 1 + \frac{1}{x} = x$$
$$ x^2 - x - 1 = 0$$
$$ x = \frac{1 \pm \sqrt(5)}{2}$$

[ocean seal]

[redacted]

[silk steeple]

uh

[analog olive]

ig this channel is occupied , so post in some other channel

[indigo storm]

Oh

Ok

How to move this question

?

[analog olive]

delete from here and post it again in other channel

[indigo storm]

Ok

[analog olive]

@silk steeple see this

[silk steeple]

wait

What did you do here

[analog olive]

(b+c)/b = b/b + c/b

[silk steeple]

oh

B/b=1

My bad

then In the next step

how did you do that

[analog olive]

I just substituted b/c = x

as we had to find the ratio

which is b/c

[silk steeple]

oh

but I don’t understand

How you made x^2 positive

you multipled both side by x?

[analog olive]

yeah

and then took lhs term to rhs

[silk steeple]

OH

If I had it on the left side

Would I still get the same answer?

[analog olive]

yeah

[silk steeple]

alright thanks so much

.close

[lone heart]

Channel closed

Closed by @silk steeple

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tawdry saffron]

how to start with this limit?

[analog olive]

try making use of sin x / x form

[tawdry saffron]

I know about the $\frac{sinx}{x}$ part

[ocean seal]

Ruffy🎄

[tawdry saffron]

but how do I reform it

[shell widget]

multiply/divide by x^2

[analog olive]

^

[tawdry saffron]

ah right

rusty with these limits

[alpine sable]

Where question?

Oh

[tawdry saffron]

it's the same for $\frac{x}{sinx}$ right?

[ocean seal]

Ruffy🎄

[echo socket]

Yes

[tawdry saffron]

what about this one

I also have to make different cases for even and uneven n

[echo socket]

Try writing that as $\frac{x^{-n}}{e^{\frac{1}{x^2}}$, might help

[raw shard]

you wrote [x^2}

[ocean seal]

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

[tawdry saffron]

l'hopital?

[echo socket]

Damn it

[echo socket]

Yeah

[raw shard]

Try writing that as $\frac{x^{-n}}{e^{\frac{1}{x^2}}}$, might help

[ocean seal]

quantum

[raw shard]

missed a }

[echo socket]

Thanks

Yeah knew it, typing LaTex on phone id suffering

Is*

[raw shard]

gets confusing when there’s so many pairs of {}

[tawdry saffron]

yea

even on pc when they do it for you kekw

now I have $\newline$ $\frac{n}{2} \lim_{x \to 0} \frac{x^{n+2}}{e^{\frac{1}{x^2}}}$

[ocean seal]

Ruffy🎄

[tawdry saffron]

yea idk

how to continue

@echo socket

[echo socket]

Yeah not really sure, but maybe a substitution could help

u = 1/x^2

If it doesn't work too, thdn idk

[tawdry saffron]

how do I replace the x on top then

[echo socket]

u^(-n/2) I guess

[tawdry saffron]

and the limit?

or does that not work

ah

infinite

i guess

[vale sapphire]

u=1/x² didn't work for me, but u=1/x did

[tawdry saffron]

then what's the top u

I suck at substitution changes

://

[vale sapphire]

top u?

oh wait

[tawdry saffron]

uhh what's the english name

[vale sapphire]

numerator?

[tawdry saffron]

denominator and something else

yea

[vale sapphire]

anyway i just started from the original expression

not your reworked one (which honestly i do not know how you got)

[tawdry saffron]

l'hopital

and then some handling

[vale sapphire]

from what i can tell, x=1/u sidesteps this altogether

[tawdry saffron]

did you get 0

@vale sapphire

[vale sapphire]

yup

[tawdry saffron]

ok

[vale sapphire]

wolframalpha agrees

[tawdry saffron]

nice

was able to do it from my reformed limit

but guess I needed more steps then required

anyways that was the last one for today

thanks for the help all!

.close

[lone heart]

Channel closed

Closed by @tawdry saffron

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[abstract prairie]

Please help me solve this problem: 9x - 7i > 3 ( 3x - 7u )

[vale sapphire]

what is the question

[tawdry saffron]

^

[abstract prairie]

9x - 7i > 3 ( 3x - 7u )

I don’t get it

[tawdry saffron]

but what are they asking

and is i a parameter or the complex number?

[abstract prairie]

Complex number

But please help me

[noble sinew]

There aren’t inequalities in complex numbers

[abstract prairie]

I don’t know what you are saying

I just said complex number

[noble sinew]

Complex numbers isn’t an ordered field

No inequality in it

So your question doesn’t make sense

[tawdry saffron]

yea

[abstract prairie]

Bro

Algebra

And stuff

Could you please help me solve the question

9x - 7i > 3 ( 3x - 7u )

[noble sinew]

What is x, i, u?

[tawdry saffron]

show a picture of the entire question please

[abstract prairie]

That is the question

[abstract prairie]

Nothing

Just a variable

[noble sinew]

Likely not posting the whole question

Missing information

“Solve the question
9x - 7i > 3 ( 3x - 7u )”
Isn’t even a question - solve for what?

[abstract prairie]

Like when you have 3(6x - 2y)

It’s 18x - 6y

[noble sinew]

Then the problem would say: “simplify the following” (or some variation of that)

So why don’t you just post the entire question

[abstract prairie]

I am not english

When I put it in google translate it says ‘reduce’

[noble sinew]

There we go

Start with simplifying 3(3x-7u)

[abstract prairie]

6x - 21u

Right

I don’t get the > part but let’s go through it step by step

Please

[noble sinew]

Try again

[abstract prairie]

Oh I am stupid 9x - 21u

My bad hahahaha

I am tired

[noble sinew]

Subtract 9x on both sides

[abstract prairie]

So that makes 7i >3 -21u??

Of am I being stupid again

I don’t have paper with me