help-0

[charred musk]

wtf is

log 10

by itself

what is it asking

[remote heron]

if youre just learning logs

log means base 10

ln means base e

[charred musk]

base 10?

[remote heron]

logs always mean

$\log _b (x) = a$

this means

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

to what power is the based raised to get x

[charred musk]

so whenever it says log X there is always a 10 before?

[remote heron]

if they dont specify a base it usuallry means 10

this is the base of the log

[charred musk]

uhh

[remote heron]

you know how 10*10 is 100

express this in log form

[charred musk]

i have a few questions here that says caclulate without a calculator

for example

A) Lg 100
B) Lg 10^3
C) ln e^3
D) ln e^1.5

[remote heron]

yes

[charred musk]

so with A

they are asking

10^x=100

[remote heron]

A is the question i just asked you lol

yes

log (100) = ?

[charred musk]

2

[remote heron]

to what power do we have to raise 10 to get out 100

[charred musk]

so the base of log 100 is 10

[remote heron]

if you see "log" written with no base assume its 10

unless someone tells you otherwise

or you are in uni

[charred musk]

ah ok im starting to understand

so question b

is 1000?

or 3

[remote heron]

heres the generic form

$\log _b (b^p) = ?$

sorry every time my cat meows i do a brain dump

im going to throw him out the window

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

here

brb

[charred musk]

hmmmmmmmmmmmm

[remote heron]

its a circular question

to what power do you have to raise base

to get base raised to power

whats always the answer

[charred musk]

with b^p

idk

[remote heron]

what kind of sandwich do you have to eat

to eat a ham sandwich

[charred musk]

ham sandwich

[remote heron]

ham, yea

you can solve this with more complicated log properties

[charred musk]

[remote heron]

you should be able to just look at it and tell

if you understand what a log is asking, though

[charred musk]

so what is lg 10^3

[remote heron]

this is for you to determine

[charred musk]

3?

[remote heron]

by understand what a log is

you need to stare at the definition

or maybe write it down and box it

[charred musk]

to what power do you have to raise base
to get base raised to power

[remote heron]

burn into your mind

[remote heron]

i mean more generally

what log(N) = x is asking

a log is a question

if you dont need a calculator to solve it, then its a stupid question

[charred musk]

ahhhhhhhhhhhh im so confuseddddddddddddd

[remote heron]

a log is asking

[charred musk]

give me an example question with common log

[remote heron]

create your own example

its a good exercise

write down a log equation with no remaining variables

write down one you know is true

or maybe rather

[charred musk]

log n=x -> N= 10^x

[remote heron]

think of something you know is true, and write it using logs

no variables

use numbers

[charred musk]

IDKKKKKKKKKK

log 10 = log10^10 = 1

idk

[remote heron]

are you saying $\log (10) = 1$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

ye

[remote heron]

okay

why is true

[charred musk]

because 10 that goes into 10 goes 1 time

[remote heron]

no

you are thinking of division

[charred musk]

[remote heron]

rewrite $\log (10) = 1$ without a log

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

an equation using only numbers

say the same thing but without a log

[charred musk]

10*1=log10

[remote heron]

this is not an equation

youve used a log

[charred musk]

10*1=10

[remote heron]

this is correct but its not an equivalent statement

use an exponent

[charred musk]

10^1=10

[remote heron]

yes

you have constructed your own example problem

$\log (10) = ?$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

now you just have to do it like

a dozen more times lol

logs are really just

[charred musk]

10^1

[remote heron]

you have to build comfort

okay $\log (10 ^5) = ?$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

5?

[remote heron]

why do you think this is the answer

[charred musk]

because you need to raise the base with 5 to get the same power as the exponent

[remote heron]

yea

[charred musk]

wait i was right?

[remote heron]

yea

[charred musk]

[remote heron]

ln is just the same thing but with e's instead of 10s

[remote heron]

if they say dont use a calculator it means the answers are dumb

or you just need to have practiced for 20 minutes and you can do it without turning on your brain

[charred musk]

ln e^3

[remote heron]

yup

[charred musk]

is 3 ?

[remote heron]

are you saying e^3 = e^3

[charred musk]

[remote heron]

yea thats the right answer though

e^3 = e^3 is the justification

lol

[charred musk]

[remote heron]

see EZ

[charred musk]

i thought i was wrong!!!

[remote heron]

i mean i shouldnt have to tell you

if you know how to do it

convince yourself

[charred musk]

it's 4:40 am ok

me is tired

[remote heron]

lol im sayin

you know how to do it now

[charred musk]

i mean i think so

[remote heron]

so think of how you can know youre right

rewrite the equation without a log

using the answer you think correct

and check

youve done this already

[charred musk]

hmm

[remote heron]

for another problem

try it now with this one

or any of them

convince yourself that $\log _b (b ^p) = p$ is true this way

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

is it really this easy?

[remote heron]

since basically every question you can do without a calculator is this but with numbers substituted

yes lol

[charred musk]

how about

[remote heron]

they have to nerf log stuff if you cant use a calculator

also people are terrified of logs since they have math anxiety

[charred musk]

10^lg 1000

[remote heron]

even change of base you can rederive yourself on the fly

[charred musk]

what is the question to this

[remote heron]

if you dont let panic get the better of you

[charred musk]

[remote heron]

$10 ^{ \log 1000}$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

i wonder what the answer will be

[charred musk]

3?

[remote heron]

if only i knew the powers of 10 off the top of my head

j/k that sounded overly snarky

[charred musk]

[remote heron]

im not a jerk

idk wym 3

evaluate the expression

[charred musk]

10^3=1000

[remote heron]

so what is your answer

$10^{\log 1000} = ?$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

3?

[remote heron]

stop guessing lol

[charred musk]

loooool

[remote heron]

think about it for some time

[charred musk]

idk what this is asking exactly compared to the normal log

[remote heron]

well log 1000 has no variables right

so its just a number

[charred musk]

ye

[remote heron]

i wonder what number it is

because if this were just

$10^n=?$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

that'd be a pretty easy problem

[charred musk]

what even is 10^n lol

[remote heron]

😔

[charred musk]

[remote heron]

here

the thing i told you to convince yourself is true

[charred musk]

n

[remote heron]

$\log (10^p) = p$

start here

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

oh yeah i know this

[remote heron]

you should know that if an equation is true, you can raise both sides as powers

yea?

[charred musk]

yes

[remote heron]

if 2 = 1+1

[charred musk]

well then

[remote heron]

then $10^2 = 10^{1+1}$

[charred musk]

its 1000

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

how could you use this fact

knowing the equation is true

[charred musk]

10^lg 1000=1000

[remote heron]

👀

think harder

[charred musk]

[remote heron]

or be more methodical

there is no reason to guess

[charred musk]

10^3

[remote heron]

you are just performing algebra

also you dont have to convince me lol just guessing until you get it right isnt gonna help

you should be able to start from knowing this is true

and get to the answer to your problem

in a way that you are convinced yourself

what is p in your problem

[charred musk]

1000

[remote heron]

😔

[charred musk]

unless it's just 1

or 10?

[remote heron]

stop guessing

[charred musk]

hmm i learn better that way, since if i understand why i got that answer

i can answer the others easliy

[remote heron]

say i know 2 = 3-1

[charred musk]

yeh

[remote heron]

use this fact to write me an equivalent expression to $10^{3-1}$

[charred musk]

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

10^3-1 = 10^2

[remote heron]

okay

you created an example problem

$\log (10) = 1$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

write for me an equivalent expression to 10^1 using this fact

[charred musk]

10^lg 1000= 10^3

[remote heron]

do you see why

[charred musk]

it's the same thing

[remote heron]

$\log (10 ^p) = p \longrightarrow 10^{\log(10^p)} = 10^p$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

ahh

so

e^ln1000

[remote heron]

this is not something you should need to memorize fyi

[charred musk]

[remote heron]

you should be able to get there very quickly from log(10^p) =p

just exponentiate each side

save space in your brain

[charred musk]

isen't ln

2.178?

[remote heron]

no

[charred musk]

or e

[remote heron]

youre thinking of e

[charred musk]

so what is the base of ln

[remote heron]

ln alone is a function

it has no value

[charred musk]

wtf

[remote heron]

it needs an argumenct

arg u ment

[charred musk]

e^ln1000

how do i use the rule

without 10 as the base

if it's =p

[remote heron]

squint

[charred musk]

the answer is in1000 but how do i rewrite it like i did with 10^3

e^ln1000=e^ln1000

[remote heron]

lets say e^a = 1000

for some known a

does this help

[charred musk]

so i have to do 2.179^a=1000?

[remote heron]

no

im trying to convince you to squint

$e^a = 1000$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

use this substitution in your problem

tell me why it doesnt matter if we know what a is or not in the end

[charred musk]

because a =1000

[remote heron]

😔

[charred musk]

so this log 10^p=p does not apply here

or what

[remote heron]

your problem is

$e^{ \ln 1000} = ?$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

im telling you to use the substitution $e^a = 1000$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

do the substitution on paper and try for a minute

[charred musk]

10^3

im dumb

[remote heron]

im not going to hold your hand on a problem i know you already know how to do

[charred musk]

but isen't 1000 technically correct?

[remote heron]

does it matter if its correct or not

[charred musk]

im just writing it in a different way

[remote heron]

you dont seem to believe it

what if it was wrong

would you know?

[charred musk]

i believed it

but u made it seem wrong

so i thought, what i learned was wrong

[remote heron]

you are not going to convince me its my fault

[charred musk]

10^lg2

[remote heron]

heres what you do my friend

solve this problem

[charred musk]

10^lg2=2^1

according to that rule

[remote heron]

if you believed it you wouldnt need to check every time you use it

what makes you think youve done something wrong

[charred musk]

well what im doubting right now is

10^2 is 100

so im abit confused

[remote heron]

here lemme try to convince

is it okay if stay really general

or should i use specific numbers

i think im gonna use letters

[charred musk]

uhh what will make me understand best

[remote heron]

ill mix and match

[charred musk]

[remote heron]

$b^a = 2$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

lets say it is known that this is true

for some fixed numbers b and a

this is not a problem, im telling you that if you take b, and raise it to the a power, it is 2

okay?

it doesnt matter what they are

but do you understand what i am saying

[charred musk]

uhh

ok i understand

😳

[remote heron]

okay

i want you to write $b^a = 2$ using logs instead of exponents

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

write an equivalent statement but use a log

[charred musk]

hmmmm

log 10^2=2

[remote heron]

you dont even have an equals sign

[charred musk]

[remote heron]

this is not equivalent

[charred musk]

what mean

[remote heron]

stop and think

[charred musk]

log 10^2= 10^2

[remote heron]

i never even used a 10

this makes me think you are not reading

what are referencing even as you make these guesses

[charred musk]

b^a= 2

[remote heron]

there is no reason to guess

yes

write this using a log

your answer should have a log with a base

an argument to the log

and an equals sign

and a 2

[charred musk]

log 10^100=2

[remote heron]

im leaving lol

[charred musk]

[remote heron]

because you arent trying

and its very frustrating

[charred musk]

im just confused

why isen't log 10^2 = 2 right

[remote heron]

for what

the question i asked you didnt even have a 10

i have no idea what you are talking about

[charred musk]

but 10 is b

[remote heron]

according to who

[charred musk]

me

[remote heron]

youd be wrong

okay here

$10^a = n$

how about this

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

this is our fact

this is true

for some fixed a and n

[charred musk]

hm ok

[remote heron]

write this using logs

[charred musk]

man idk tbh

i haven't practiced enough to remember what i've learnt

[remote heron]

then you should practice

start with things you know are true

remember 10^1 = 10

or sleep 🙂

[charred musk]

yes but

according to

10^a=n

N can not be the same as A

if we did a log

[remote heron]

[charred musk]

as in log10^2=2

[remote heron]

you should get sleep

what you are saying makes no sense

[charred musk]

idk man

[remote heron]

like even for someone who doesnt know logs

you are trying to learn everything in one go which is admirable but dumb on no sleep

and its a waste of time for everyone involved

[charred musk]

don't have time for sleep

just explain simply

[remote heron]

have you ever heard

the really long and boring story

about not having time to sleep

[charred musk]

i've heard 10^a=n

[remote heron]

but have you seen it with logs

[charred musk]

no i haven't

i just wanna understand what you want me to imply

that something with log and 10^a=n

[remote heron]

use this

alternatively google what is a log and this is one of the first images that comes up

[charred musk]

10^2=100

[remote heron]

i gave you the 10 damnit let me keep my a and n please 🙏

do i have to fight for every letter

[charred musk]

[remote heron]

somehow you are inserting a 2 and

idk what youre doing

[charred musk]

i have no idea what im doing ngl, i would learn faster if u told me the answer lol

[remote heron]

if you cant do this step then you dont know enough

you need to know the literal definition of a log

this is actually like

[charred musk]

log is basically

[remote heron]

the only thing you need to know

everything else comes from algebra and exponent properties

the only thing you need to be able to do is convert between logs and exponents

all other knowledge here comes from that

if you dont know that then this is what you need to know

not whatever extra shit im going to say

[charred musk]

the only thing i know of log is that special rule and that the base is 10 if not said otherwise

and e is ln

a natural logatithm

[charred musk]

can you show this in numbers

[remote heron]

no

[charred musk]

[remote heron]

there was a time someone showed you a 3 and you didnt know what it was

a letter instead of a number shouldnt be scary no offense

but thats the least of your issues here

you need sleep and to watch some lectures

[charred musk]

bruh, ill just keep on doing some questions i guess lol

ty for help

.close

[lone heart]

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[split sphinx]

How do we find the denominator here for the final fraction?
this is what my prof did but offered no justification for it so don't understand how he did it

<@&286206848099549185>

i think the channel closed because i deleted the original message?

[lone heart]

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[split sphinx]

How do we find the denominator here for the final fraction?
this is what my prof did but offered no justification for it so don't understand how he did it

[simple turtle]

teacher further reduced 5/100 = 1/20 and 4/80 = 1/20

so you got 400 for common denominator

[split sphinx]

no i meant how did he come up with this

I mean shouldn't it be P(MnT)= P((MnT)n S) + P((MnT) n Sbar) ?

[lone heart]

@split sphinx Has your question been resolved?

[split sphinx]

<@&286206848099549185>

[lone heart]

@split sphinx Has your question been resolved?

[remote heron]

actually this seems fine

i was afraid to comment since probably gonna be wrong

but this seems straightforward

assume there are two events S and S complement such that P(S) + P(barS) = 1

well wait

maybe wrong

[split sphinx]

i guess it is P((MnT)n S) + P((MnT) n Sbar)

and these two just reduce to the green stuff in the picture

by bayes

[remote heron]

well lemme think

[split sphinx]

P(B|A)=P(ANB)/(P(A))

[remote heron]

its just total probability right

[split sphinx]

yep seems like it

thank you!

[remote heron]

sorry idk if i helped

[split sphinx]

oh no worries

i sorta figured it out but you confirmed it

,close

.close

[lone heart]

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[spice kettle]

How do I make this into slope intercept form? It’s really confusing and I keep getting something impossible to graph

[gray isle]

subtract 8 from both sides

[spice kettle]

How do you subtract 8 from the parentheses? Do you not distribute?

[gray isle]

subtracting b from a:
a - b

the expression you start with doesn't really matter

[spice kettle]

Ah, okay

[gray isle]

you could subtract 8 from both sides immediately

or after distributing

and you already distributed

[spice kettle]

Yeah

But how the heck do you subtract 8 from -4/13

.close

[lone heart]

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[modern hemlock]

I am doing some linear algebra right now and I think I have the Gaussian Elimination problems down on the math side but figuring out the real-world questions has me confused. For example, what would the augmented matrix for this one look like?

[modern hemlock]

Is it something like this for the augmented matrix?

|1.50   4.00   5050|
|1      1      2200|

Or this?

|1      4.00   5050|
|1.50   1      2200|

I think the right side is somewhat clear, its what constitutes as the correlation matrix that I'm confused about

[lone heart]

@modern hemlock Has your question been resolved?

[lone heart]

@modern hemlock Has your question been resolved?

[livid jolt]

i think u can just do the matrix multiplication and see which is correct

$\begin{pmatrix} 1.5 & 4 \ 1 & 1\end{pmatrix}\begin{pmatrix} x \ y\end{pmatrix}=\begin{pmatrix} 5050 \ 2200\end{pmatrix}\\ \begin{pmatrix} 1.5x+4y \x+y\end{pmatrix} =\begin{pmatrix} 5050 \ 2200\end{pmatrix}$

[ocean seal]

AᵃᵏKₐₖ

[livid jolt]

so this one will be correct

[livid jolt]

where x is the number of children and y is the number of adults

[modern hemlock]

Actually now that I'm looking at it this makes sense

Because we can get an estimate of the money ($5050) by a calculation of adult and children prices, but we don't have any known parameters for how we got to 2200 people

Is my understanding correct?

[lone heart]

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[modern hemlock]

.reopen

[lone heart]

✅

[modern hemlock]

Just checking if my understanding of the setup is correct

[vale wigeon]

@proven fossil this channel is occupied. please read #❓how-to-get-help

[modern hemlock]

lol

Yeah guess my question doesnt matter

Just put it somewhere thats not occupied

I just read the rules

[proven fossil]

alr sorry

[modern hemlock]

np

My R solution and my hand-written solution dont seem to match

Oh I think I just realized why

I didnt make a pivot

So the R output and my calculations match now

I guess that solves the problem from what I can tell

Looks like it:

1.5(1500) + 4(700) = 5050
1(1500) + 1(700) = 2200

Still confused about if 1500 is adults or if 700 is adults

Oh im so dumb

If its 1.5 for children and 4 for adults...

That means there were 1500 children who paid $1.50 and 700 adults who paid $4.00, in total 2200 people paid $5050

Okay I got it, thanks guys

[livid jolt]

u literally cleared ur own doubts lol

[modern hemlock]

Lol sometimes my brain needs time to wake up

Im old after all

[livid jolt]

if u are done then u can close the channel

[modern hemlock]

Yeah i was curious on how you do that

Umm

.close

[lone heart]

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[modern hemlock]

There we go

Thanks @livid jolt

[lone heart]

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[scenic canopy]

help please

[scenic canopy]

please help

[lone heart]

@scenic canopy Has your question been resolved?

[lone heart]

@scenic canopy Has your question been resolved?

[scenic canopy]

:[

[lone heart]

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[warm cloud]

is there an analytical way to solve $\x_{n+1} = x^2_{n-1} -nx_n, x_0=3, x_1=4$?

[ocean seal]

Typo

[warm cloud]

someone i know doesn't like the solution that you can just guess x_n = n+3 and use induction to prove it

[lone heart]

@warm cloud Has your question been resolved?

[lone heart]

@warm cloud Has your question been resolved?

[lone heart]

@warm cloud Has your question been resolved?

[warm cloud]

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[warm vessel]

Calculate all Fourier polynomials of the 2π-periodic function
Also decide whether the corresponding Fourier series converges.

[warm vessel]

I believe the function is odd

so used

but how does (-pi affect it?

[near hollow]

Do you remember the formula for calculating fourier coefficients?

[warm vessel]

no

or yes

[near hollow]

Well L is the half period. So our total period is the difference between our lower bound and upper bound (2pi)

[warm vessel]

yeah

[near hollow]

So our half period is pi

[warm vessel]

but the lower period is not included

(-pi

does that make a diff

[near hollow]

So our formula for $b_n = 1/\pi\int_{-\pi}^{\pi}f(x)sin(n\pi x / \pi) dx$

[warm vessel]

yes

[ocean seal]

Max..

[warm vessel]

and we use this bc its odd right?

[near hollow]

Doesn't make a difference

[warm vessel]

functio

oh okay then I did something already

found this after 3 or 4 partial integrations that was so f long

[near hollow]

Think about it logically from an exam point of view, are they going to give you a problem that you havent been taught how to solve? Because you wouldve only learnt 1 way to find fourier coefficients (using these integrals) so if it isnt included it's probably not going to make a difference

[warm vessel]

yeah

[near hollow]

from a mathematical point of view a fourier series is an approximations that as n goes to infinity approximates almost perfectly.... except for at 2 points (in general) what are these two points?

[warm vessel]

not sure

maybe bounds?

[near hollow]

yeah nice, I won't check but you can check on a fourier series calculator online

[near hollow]

yes kinda, more precisely the endpoints (im guessing that's what u meant by bounds0

[warm vessel]

yeah yeah ofc

[warm vessel]

yep

[near hollow]

expansion via fourier series produces a strictly continuous function

[warm vessel]

okay

[near hollow]

but sometimes the function you want to express as a fourier series has a jump discontinuity

but yeah looks like u were doing the right thing, just werent confident enough in urself

[warm vessel]

eyy nice : D

but I got one more question

about the sum

what should I do when it starts from 1

It also asking for the convergence

[near hollow]

Well it has to start from one because the usual way of calculating a_0 gives 0 so a_0 is 0... for convergence you need to use summation convergence tests

do you know these?

[warm vessel]

I checked it online but dont know how to use it

[near hollow]

can you send what excatly they said btw

[warm vessel]

Also decide whether the corresponding Fourier series converges

this is what they said in question

[near hollow]

Converges on R?

[warm vessel]

ah yeah

[near hollow]

Well for this just check value at pi and -pi is the same

if its not then it definetly doesnt converge to the periodic function f(x) on R

If it does then you need to apply the root test

[warm vessel]

should I try this on the function or what Ive found?

[near hollow]

On the original

If the end points arent the same then it will be discontinuous (originally) but our fourier series is continuous

[warm vessel]

okay I didnt understand something

oh or i did

okay I try what you said

it is same

both 0

[near hollow]

you see the original function (the line in red) it jumps up to 1 from 0, we call this a jump discontinuity and if our function we want to express as a fourier series doesnt have the same start height as end height then itwill have one of these and as you can see by the approximations it will try to approximate it continuously

[near hollow]

oh nice so u could conclude that it does converge for all R

Im not sure how formally ur required to do it

[warm vessel]

but I didnt use root test?

[near hollow]

but you can use a convergence test to the actual series converges

[near hollow]

this is more formal idk if u will be required to use it

[warm vessel]

okay is this only when both 0

or is it bc they both equal

[near hollow]

it's because they are equal

If they weren't equal (going back to our original function before we did fourier) there will be a jump discontinuity

Because we are plotting a function where our segment in the bounds is repeated side by side infinitely

[warm vessel]

okay I think I got it, its bc after root test we find 0 and its less than 1 and therefore abs conv

and one more thing what is the difference between finding the convergence of these functions and (there is another topic they teaching) convergence of series of functions, pointiwse, uniform etc.

[near hollow]

yes nice work

[warm vessel]

I kinda learned how to do uniform and pointwise but dont really understand the concept

[near hollow]

Ah ic so what u proved is the convergence of the power series for all R u didnt prove it converges to another function

Weiestrauss M test will be good for this

[warm vessel]

hmm okay

[near hollow]

What this means is say I have a function $f_n(x)$ as n gets very large does it get closer and closer to f(x)

[ocean seal]

Max..

[warm vessel]

oh okay that was easier than I thought

[near hollow]

Btw what I find difficult about convergence of functions like this is the difference between pointwise and uniform

[warm vessel]

yeah I confuse them too

I didnt really understand that part too

like I try the x bounds or endpoint is the correct thing to sa

then check limit

[near hollow]

Generally pointwise is a given. (not always but mostly) for series it's super easy as we can just use Weiestrauss M test

But for non series questions you need to show that an epsilon (that DOESN'T depend on x) can be chosen and for all n > N our function differs by less than epsilon

And if we can show that value of epsilon converges to 0 as N gets big then we showed its unfiromly convergent

tbh its easier to disprove than prove

[warm vessel]

in most of the questions I always found for both points it is the same value I find so I say it is pointwise then I have to find a value which is mostly something like 1/n in order to make the

(0i1)

(0,1)

and then I find inf and say it doesnt converge uniformly

and even tho I tried many examples on a graph as I solved the questions I always forget what this really means

[warm vessel]

maybe : D

I actually got a question since we talked about it this might be an example too

[near hollow]

Haha yes I've done this question before

[warm vessel]

I tried to show this on a line

[near hollow]

Well first of all does it converge pointwise and what to?

[warm vessel]

I put -,+ 1/n

[warm vessel]

question says show that this converges pointwise but not uniformly

[near hollow]

yes it doesnt converge uniform and we'll prove this using a disproof

but to do this we need to find the function it converges to pointwise

as n gets VERY big

what does $f_n(x)$ roughly look like?

[ocean seal]

Max..

[warm vessel]

before I try may I ask which ones are the answers for fn

-1, nx, 1?

[near hollow]

Well as n gets very large that middle bound is going to disappear

[warm vessel]

yeah both will get closer to 0

[near hollow]

Excatly so if we take the lim as n goes to infinity then this part doesnt exist

[warm vessel]

yep

[near hollow]

and we're left with "when x is negative -1 and x is positive we get 1" or in other words the sign function (sgn(x))

[warm vessel]

okay but I dont know sign function is it literally sign function

okay

[near hollow]

To prove it converges uniformly we need to show for all x in R (this is a function on R) that as n goes to infinity $\abs{f_n(x)-sgn(x)}$ gets very small (we like to say that we can always choose an $\epsilon > 0$ such that an N exists with $n>N$ $\abs{f_n(x)-sgn(x)} < \epsilon$

[ocean seal]

Max..

[near hollow]

yeah kinda this but in our case at x=0 the function is -1

So what we do is examine $\abs{f_n(x)-sgn(x)}$

[ocean seal]

Max..

[near hollow]

We know that problems arise when x is near 0

[warm vessel]

how did we find -1

[near hollow]

look at the original $f_n$ it has $x\le -1/n$

[ocean seal]

Max..

[warm vessel]

okay we say its 0 when n inf

[near hollow]

because if you were to plot this graph or think about it as n goes to infinity there should in reality be a removable discontinouity as 0 where f(x) = infinity but we dont like writing that so we pretend it doesnt exist

So what we want to do is choose an x such that this function definitely doesn't converge

this x will always be in terms of n

For instance x = 1/2n (this tends towards 0 so we know it should cause problems as n gets large) we also know it's sign is strictly positive

So we get $\abs{f_n(x)-sgn(x)} = \abs{\frac{1}{2n} \cdot n-(1)}= 1/2$

[ocean seal]

Max..

[near hollow]

And well if we originally chose epsilon to be 1/4 we can now show that we infact can't find a big N such that the difference between these two function is less that 1/4 (at x=1/2n which is inside our bound)

Main thing: For disproving uniform continuity you want to strike the WEAKNESS of a function ie. where something is disappearing (in this case x=0). We then want to choose an x = g(n) such that when we put it into our difference of two functions, we are going to get out a value that is a constant, I chose 1/2n as I knew the n would cancel the 1/n to produce a constant, and choosing 1/n would mean it's not inside the correct bound

[warm vessel]

I dont understand choosing epsilon can we randomly choose an arbitary positive number for it?

[warm vessel]

so very basically we can say when you see something not going right go on it and find an x that will get out a constant?

[near hollow]

The epsilon part is basically saying for any positive number I can find a value of n to show that these functions are always within that distance of each other, so for epsilon=1/4 for every value of x we need to show that |fn(x) -f(x)| < 1/4

[near hollow]

Yes

[warm vessel]

but can I choose an epsilon randomly that will benefit my calculation

[near hollow]

So I chose the epsilon=1/4 just because it was less than 1/2

[warm vessel]

yeah thats why I find it difficult to understand

thats not random but you just choose a number

[near hollow]

It's the hardest bit to understand

[warm vessel]

: D

[near hollow]

It's just forming a contradiction

By definition of uniform convergence for all x in our domain I can show that for all epsilon >0 the difference between our two functions eventually gets below epsilon

Now if I choose epsilon =1/4 and it's true, for a large n the two functions differ by at most 1/4

It doesn't mean it converges uniformly

It's just a case we've proved it does for

But in our case we have shown actually if epsilon is 1/4 when x=1/2n the two functions differ by 1/2 which means I can't find for all epsilon >0 an n such that they differ by at most epsilon

Or in other words the function doesn't converge uniformly

[warm vessel]

okay that was a lot : D I will read this conversation again and again

doing the question is the easy part, it really is hard to understand the meaning : D

so it doesnt converge uniformly but to end the question

does it converge pointwise -1 if x<= 0 and 1 if x>0

[near hollow]

Yes it does

[warm vessel]

nice

[near hollow]

Generally a point wise convergence proof is too trivial to bother with but others here and ur course director might encourage you to lay one out

[warm vessel]

I mean if I can somehow explain the uniform convergence part with my words, he better give me points : D

but I really appreciate your help it really helped me to understand the logic better

[near hollow]

No worries, it took me ages to my head around this stuff, pretty it does the same for most people

It is really useful tho, especially in proving integrals and deriving integration in an analysis course

@warm vessel ur German right?

[warm vessel]

not really and thats the problem : D

[near hollow]

Ah how comes it's in German?

[warm vessel]

I study in germany with my half german

first year physics in tu bs

[near hollow]

Oh nice nice

My friend in Germany said half his courses are in English

[warm vessel]

well mine not but they accept english in hws and exams

so its a little adv for me

[near hollow]

Ah fair enough

Lots of YouTube videos in english

That are really good and helpful

[warm vessel]

yeah I watch more vids than my lectures

[near hollow]

googling any topic + the word pdf give tonnes of lecture notes, textbook exercises ext.

[warm vessel]

yeah but uni is such thing that you cant understand stuff easily without debate

so reading stuff on web is hard, not like high school

I will continue with my hw

thanks again and have a nice day

[near hollow]

You too

[near hollow]

True

That's the beauty of it tho

[warm vessel]

yep : D

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[alpine sable]

x³+9a+9 this was in someone else's question I saw on another help channel and I don't know how they solved it using quadratic formula pls help

[gray ingot]

solved a cubic with the quadratic?

[alpine sable]

I dunno mathway kinda does it

I'm not sure they used quadratic but they answer they got was what I got when mathway did it using quadratic or smthng

The*

Solve the rational  equation by combining expressions and isolating the variable xx.

x≈−0.91490784

[near hollow]

Is that 9a or 9x?

[alpine sable]

x I'm sorry

x³ + 9x+9

[gray ingot]

you'll have to figure out the first zero using trial and error

x³ + 9x+9 = 0 right?

[alpine sable]

Yeah

[alpine sable]

I wanted to understand this process maybe you could help..?

[lunar palm]

have you ever done polynomial division

[alpine sable]

Yeah

I have

[lunar palm]

oop, nevermind, misread the question

there is a bit of a longwinded way to do this more algebraically though

[alpine sable]

Oh

Just tell me

[lunar palm]

plug your values into the cubic equation

look for the 1 real solution (the other 2 will be complex conjugates)

[alpine sable]

Trial and error?

[lunar palm]

no

sorry, cubic formula*

its like the quadratic formula but for cubics

there's also one for quartics but don't look at that one

[alpine sable]

Okay

[alpine sable]

You just made me curious so

Anyway thanks for your help

.close

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[fallen rain]

What is a consecutive integer?

[worn fox]

integers that come one after another

e.g. 1,2,3

156,157,158

are examples of 3 consecutive integers

[fallen rain]

Am I on the right way?

[livid jolt]

u are supposed to take arbitrary numbers
bcz its a “proof”

[gray ingot]

aren't

[gray ingot]

you have to generally prove for any consecutive integers

try to assign the smallest one among them to a variable

like x

[slender gull]

You just verified it for some numbers. You have to PROVE it for all the integers which are consecutive like that.

[fallen rain]

okay thanks guys

.close

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[jovial saddle]

Hi' id love to get some help
I know M is (0,4) and 2 tangents are going out of it
The graph is f(x)=-x^2+bx
I need to express point A and point B with using b
and id love if you could explain to me how to do it (im practicing for a test)

[gray ingot]

can you express the y coordinate of A if the x coordinate is lets say t

[lone heart]

@jovial saddle Has your question been resolved?

[jovial saddle]

???

[jovial saddle]

<@&286206848099549185>

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@jovial saddle Has your question been resolved?

[lone heart]

@jovial saddle Has your question been resolved?

[lone heart]

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[alpine sable]

I'm just asking if this the right way to do this. I'm going over this and I'm teaching myself

And these change of variables is kinda confusing?

I'm kinda confused which route to go

I think my first way of doing it is right, IDK. If anyone can comment id appreciate it

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@alpine sable Has your question been resolved?

[alpine sable]

.close

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[smoky silo]

quick question! can anybody help me?

[smoky silo]

i am doing physics i think where i calculate the energy of a ball on top of a slope and at the bottom a slope

i just followed a video, but i need to understand how the guy in the video rewrote the equation

[remote heron]

what guy

[limpid spade]

conservation of energy

[smoky silo]

gh=1/2v^2, and he rewrote it to v=sqrt(2gh)

[limpid spade]

that's basic algebra

[remote heron]

looks like algebra to me friend

he multiplies the 2 across

this gives 2gh=v^2

[limpid spade]

arccos 👀

[remote heron]

he multiplies the two arccos

[limpid spade]

good

[smoky silo]

here its written to make it easier to understand

i

i understand, but what did he do next

ohh, nevermind i understand, he just flipped the equation and removed the exponent on the left, and then had to do the same on the right

thanks for the help!!

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[alpine sable]

Yo I have this discrete mathematics task without an answer so wanted to check if someone knows the answer: So I am suppose to write the graph from this table:

[alpine sable]

and then do a "Depth First Search Algorithm"
Which I did like this

[lone heart]

@alpine sable Has your question been resolved?

[oak perch]

I believe you forgot to connect CD

[alpine sable]

Oh yeh

@oak perch then I will have to go back to C

But if CD wasnt a requirement to be connected did I do it right

?

[oak perch]

Idk, I just noticed that the element in 4 th row 3rd column is x not empty

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[lone heart]

@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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[ocean prism]

Sup i have a proportional distribution problem and says:

3 athletes delegation’s made an agreement with an hotel to accomodate the athletes. The total amount of the bill was 1000$ .The first delegation had 22 athletes and they stayed there for 5 days, the second one had 18 athletes and stayed for 4 days and the third delegation had 20 athletes and stayed there for 6 days. How much each delegation must pay?

[prime badge]

so?

[ocean prism]

Idk how to do it

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[young finch]

Area of this figure

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@young finch Has your question been resolved?

[young finch]

<@&286206848099549185>

nvm figured it out

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[cosmic vapor]

so my friend sent me this problem but im not sure how to do it either i know the answers 50 but im not sure why or how

[cosmic vapor]

.close

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[haughty mist]

i'm not too sure on how the solution for 7b) was obtained. i know there's chain rule involved, but seeing this is giving me a bit of a headache

[placid zinc]

You'd need to go with the multivariable chain rule

Except z is f(x,y)

After that, sub in t = 1

[haughty mist]

i probably need sleep to get to the answer. but yeah, that makes sense

ty

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[placid zinc]

Hit it with a change of base. 3 would be a better base for everything here

[alpine sable]

Solution:

[placid zinc]

Why is there an x on both sides lol

[ocean prism]

Its 729

[pallid zealot]

i got 81

idk what im doing wrong

[alpine sable]

https://www.wolframalpha.com/input?i2d=true&i=log+9\(40)χ\(41)%2Blog+27+\(40)x\(41)+%3D+5

[alpine sable]

Dont think so

[placid zinc]

This is why we teach people how computers work before letting computers do the work for them haha

[alpine sable]

Wolfranalpha is smart iq than google and people.

[placid zinc]

log3(x)/log3(9) + log3(x)/log3(27) = 5

log3(x)/2 + log3(x)/3 = 5

That make sense so far @pallid zealot ?

[pallid zealot]

yup, that makes sense 👍

ohhh would i multiple both sides by 30?

[placid zinc]

Now this is a linear equation where log3(x) is the unknown

[pallid zealot]

ohhhh i see

[placid zinc]

I was going to suggest multiplying by 6 kek but 30 would also work

[pallid zealot]

ohh yeahh sorry
i'll multiply by 6

so 5log3(x) =30
log3(x)=6
ohh so x = 729?

omg okayy thank u so much!!

ur great at teaching, thank u!

[placid zinc]

Feel free to ask if you have anything else!

[pallid zealot]

okay, tysm! :D

would it be okay if i close the question?

.close

[lone heart]

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[alpine sable]

Help

[alpine sable]

This here man I need help

I feel like a garden gnome tryna get some soil

🙏🏼🙏🏼🙏🏼🙏🏼

hi

need

help over here

this

is making my friend go monke

Easy shit

[alpine sable]

Easy

Idk ma'am

[floral pawn]

use eyes theorem

[alpine sable]

he needs the steps

[gilded citrus]

its asking for the coordinates at which the curve and the line intersect

[alpine sable]

What?

1,2 and 7,6

?

Just assuming big momma

[gilded citrus]

not 7,6

[alpine sable]

6,7

[gilded citrus]

yup

[alpine sable]

If I had a nickel for every time you was a cutie @gilded citrus I would be a billion air

[gilded citrus]

😳

[alpine sable]

Praise to the white Jesus created you

Done

End

Stop

I finished question

[shy grail]

The solutions are points of intersection of the system graphs

[alpine sable]

I did it all Alr

The 10 problems

I just needed explaining

Scince I’m a jiggerboo