what do you mean?
#help-27
light quail
weak cove
you are tasked to identify the inner function u=g(x) and the outer function y=f(u)
what do you think those are?
light quail
.
light quail
f(u) = cos(u) g(x) = sin(x)
weak cove
looks good to me
weak cove
looks good to me
light quail
wow
f(u) = tan(u) g(x) = x^3 ?
f'(u) = sec^2(u) g'(x) = 3x^2
f'(g(x)) = sec^2(x^3) * 3x^2
can i do anything else?
main gull
Looks fine
light quail
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devout snowBOT
restive river
So from the small to the largest the factor would be 3.75
Find the area of the small one
Then use that factor
For the area of the small one, use pythagorean theorem
thorn flame
yeah but how does it lead to the area of 534
restive river
Oh
Oops
They already gave you the area for small one nvm
You got that answer from your teacher?
thorn flame
yeah 38
thorn flame
You got that answer from your teacher?
no from the mark scheme
restive river
..
thorn flame
sorry
gleaming socket
thorn flame
Oh i get it so (5.6/21)^2 /38= 0.071 and 38/0.071=534
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pastel bolt
How can I prove that if a matrix C is idempotent, then 2C - I is involutory
pastel bolt
note: a matrix is idempotent if C^2 = C
and a matrix is involutory if C^2 = I
I is the identity matrix
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pastel bolt
<@&286206848099549185>
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restive river
hello why does this bot shows the wrong answer?
devout snowBOT
hello why does this bot shows the wrong answer?
restive river
,w 15÷3*5 -10
topaz beacon
Order of operations
restive river
shouldn't it be 15
winter patrol
how are you getting 15
restive river
What is it called for you
BODMAS
topaz beacon
Ok
winter patrol
take a pic of the original expression
and show work
woven radishBOT
topaz beacon
So its technically implied that it goes B, O, DM (left to right), AS (left to right)
violet wind
because you multiplied by 5 instead of 3 now?
restive river
,w 15÷5*3 - 10
woven radishBOT
cosmic jacinth
Wait
restive river
did i?
restive river
wait nvm it was a typo
cosmic jacinth
15÷5*5 - 10
cosmic jacinth
Now after all, it wasn't machine error. It was a human error.
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rapid atlas
Hi, I'm not sure what to do here.
devout snowBOT
Hi, I'm not sure what to do here.
spiral geyser
Hi, I'm not sure what to do here.
let z = x + y i
and (presumably) solve for y in terms of x
rapid atlas
I should say what i've tried. I have tried that, and then squared both sides to get rid of the mod signs, but I still have conjugates etc
pseudo basin
rewrite |z-1|^2 = 3|z+3i|^2 in terms of x and y
rapid atlas
I'm just not sure, am I supposed to get rid of mod signs or just interpret them?
rapid atlas
RIGHHTTT okay ill try that
thanks
wat the
we got degree 2 y;s
y's
idk what to do
.close
nova whale
@acoustic vault how do i set up differential equation for the oblique throw
devout snowBOT
<@155680031673155594> how do i set up differential equation for the oblique thro...
nova whale
acoustic vault
sorry i dont know anything about physics
devout snowBOT
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nova whale
sorry i dont know anything about physics
what about differential equations
more specefic Eulers method
nova whale
How can I use Eulers method to solve an equation like the one below?
nova whale
or runge kutta doenst matter which 1
restive river
time step etc
nova whale
i've done these problems before but this time it is more physics related so i a bit lost
restive river
show the original question
nova whale
"Set up differential equations for the motion in the oblique throw with and without air resistance. Solve
the system of equations by numerical methods using the Euler/Runge-Kutta method"
nova whale
can it be any
if i know y(1)=0.9
that is fine
What i am trying to do
Is to get the program to approximate that curve for me
restive river
if i know y(1)=0.9
yes, that would be the initial condition
restive river
see this sec <https://en.wikipedia.org/wiki/Euler_method#First-order_process>
the step size is h in this
restive river
looks like the exact solution to me, but I'm not so sure
devout snowBOT
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nova whale
looks like the exact solution to me, but I'm not so sure
At a projctiles maximum height, the velocity is supposed to be 0 correct?
obsidian harbor
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obsidian harbor
How solve this differential equation??
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@obsidian harbor Has your question been resolved?
proud nimbus
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fierce heath
This for a hw assignment?
restive river
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restive river
How do I solve this?
sonic smelt
Break the sum up and reindex
sonic smelt
Should look like this $\sum_{k=1}^n(a_{k+1}-a_k)=\sum_{k=1}^na_{k+1} - \sum_{k=1}^na_k$
woven radishBOT
A Lonely Bean
sonic smelt
Does this make sense to you?
sonic smelt
Right, now let's consider the first sum
The index of a goes from 2 to n+1
So what we can do it let k go from 2 to n+1 as well
And have a_k there
Meaning $\sum_{k=1}^na_{k+1} = \sum_{k=2}^{n+1}a_k$
woven radishBOT
A Lonely Bean
restive river
is it latex form you are writing on?
sonic smelt
Yeah
sonic smelt
So we have $\sum_{k=1}^n(a_{k+1}-a_k) = \sum_{k=2}^{n+1}a_k - \sum_{k=1}^na_k$
woven radishBOT
A Lonely Bean
sonic smelt
fuck this lol
A little bit of rewriting and we are done
Firstly we can rewrite $\sum_{k=2}^{n+1}a_k$ as $a_{n+1} + \sum_{k=2}^na_k$, right?
woven radishBOT
A Lonely Bean
restive river
I have no clue
o show that $\sum_{k=1}^n (a_{k+1}-a_k) = a_{n+1} - a_1$, we can observe that the summand $a_{k+1}-a_k$ telescopes. Specifically, the $-a_k$ term in $a_{k+1}-a_k$ cancels with the $a_k$ term in $a_{k}-a_{k-1}$, leaving only the first term $a_{n+1}-a_1$ and the last term $-a_2+a_1$. All the other intermediate terms cancel. Thus, we have
\begin{align*}
\sum_{k=1}^n (a_{k+1}-a_k) &= (a_2-a_1) + (a_3-a_2) + \cdots + (a_{n+1}-a_n)
&= (a_2 - a_1) + (a_3 - a_2) + \cdots + (a_n - a_{n-1}) + (a_{n+1} - a_n)
&= -(a_1 - a_2) + (a_2 - a_3) + \cdots + (a_{n-1} - a_n) + (a_{n+1} - a_n)
&= a_{n+1} - a_1.
\end{align*}
woven radishBOT
Kristoffer_
sonic smelt
Ah, they went the simple way
Yeah, they just expressed the sum as it is and cancelled everything out
Which left them with a_{n + 1} - a_1
restive river
is it correct?
sonic smelt
Yes
restive river
hmm
sonic smelt
Did you actually use chatgpt?
restive river
ye
lol
b) We can write $\frac{1}{k} - \frac{1}{k+1}$ with a common denominator as $\frac{k+1-k}{k(k+1)}$, which simplifies to $\frac{1}{k(k+1)}$.
woven radishBOT
Kristoffer_
restive river
Is the b) correct?
c) Using our result from part b), we can write
\begin{align*}
\sum_{k=1}^n \frac{1}{k(k+1)} &= \sum_{k=1}^n \left(\frac{1}{k} - \frac{1}{k+1}\right)
&= \left(\frac{1}{1} - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + \cdots + \left(\frac{1}{n} - \frac{1}{n+1}\right)
&= 1 - \frac{1}{n+1}
&= \frac{n}{n+1}.
\end{align*}
Thus, we have the formula $\sum_{k=1}^n \frac{1}{k(k+1)} = \frac{n}{n+1}$.
woven radishBOT
Kristoffer_
restive river
is the c) correct?
sonic smelt
Yeah
restive river
isnt that crazy
restive river
devout snowBOT
restive river
how do we go from 3e^x * (e^2x -2) =0, to only the part within the bracket
fathom thicket
how do we go from 3e^x * (e^2x -2) =0, to only the part within the bracket
e^x
will never be 0
restive river
fathom thicket
usually
sonic smelt
Divide both sides by 3e^x
fathom thicket
you would consider
3e^x = 0
and
e^2x - 2 = 0
like you do with quadratics
but the 3e^x part is redundant
cosmic jacinth
do you mean this>?
It does not mean that the anything=0
$f(x)\cdot g(x) = 0$
\
Does not always imply that $f(x) \text{ or } g(x) = 0$
woven radishBOT
restive river
anything standing for the operators before the brackets
cosmic jacinth
However, one of them must be zero.
restive river
hmm
restive river
However, one of them must be zero.
yeah so either [anything ]( in your words f(x)) , or the[(...)](in your words g(x)) must be 0.
$f(x)\cdot g(x) = 0$
Did you mean:
$f(x)\cdot g(x) = 0$
Does not always imply that $f(x) \text{ AND } g(x) = 0$ but
$f(x)\cdot g(x) = 0$
DOES always imply that $f(x) \text{ or } g(x) = 0$
@cosmic jacinth
woven radishBOT
NurAlHuda
devout snowBOT
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cosmic jacinth
Yeah and you need to figure out which one can be zero and which one cannot
In your case...
You have
The exponential function
And another exponential function, however this time modified
Just note that
$a^{x} \neq 0,$ for all $a,x\in\bR$
woven radishBOT
granite glen
How is this incorect?
devout snowBOT
How is this incorect?
sonic smelt
Note that the range of inverse should have negative numbers, not positive ones
So it should be y = -sqrt(x)
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spark fiber
.reopen
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✅
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lilac fractal
if ada said no then she mustve got between 1 and 6
and if carlos wants at least 50% chance he could be 4+ and say yes
4-12 is 9 numbers
and u want equal to or less than
so isnt part a 5/9, yes?
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regal torrent
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regal torrent
I got 4^4/6^4
By the basic principle of counting thingy
By taking complement event
narrow plank
Ok then
regal torrent
Ohh shit
regal torrent
Ok then
Sorry i took the complementary event and did not subtract one to get actual thing
Thanks!!!
narrow plank
👍
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real estuary
devout snowBOT
real estuary
F^n , where n={1,2...n} is the set of all functions from n to F.
For example, { (1, X1), (2,X2),... (3,Xn) } , where X1..Xn are elements of F, is an element of F^n
On the other hand. F^n is the of lists or n-tuples of lenght n whose elements are in F
For example, (X1, X2, Xn) where X1..Xn are elements of F, is an element of F^n.
torn vessel
sure
real estuary
then the author claim:
In other words, claim F^n in both contexts can be tought as the same.
torn vessel
so every n-tuple has elements of F in an order. (x1, x2, x3, ..., xn)
So you've defined a function form {1,2,3,...,n} to F where
1 -> x1
2 -> x2
....
n -> xn
real estuary
as I think about it is : A function of F^n: { (1, X1), (2,X2),... (3,Xn) } = { X1, X2, Xn} obviating the first coordinates and then, {X1,X2,Xn} = (X1,X2,Xn) , an element of F^n, set of all n-tuples.
real estuary
so every n-tuple has elements of F in an order. (x1, x2, x3, ..., xn)
So you've ...
yes! but that function is a set of pairs of coordinates. That's not an n-tuple (x1,x2..xn)
real estuary
is this what Axler (first pic) mean by "F^n is a special case of F^s"
if so, why we can do that? ( eliminate the first coordinate of the functions and consider them n-tuples ) I mean, that has sense but, isn't it failing in the definitions?...
torn vessel
yes! but that function is a set of pairs of coordinates. That's not an n-tuple (...
yes. but they're equivalent. There's a one-to-one correspondence between functions from {1,2,...,n} to F and the ordered tuples of F^n
{(1,x1), (2,x2),... (n,xn)} <-> (x1, x2, ..., xn)
They aren't identically the same. But the idea is equivalent.
real estuary
it's more clear now. It's like because n-tuples are order elements, we can assign an index j={1,2,...,n} and express (x1,x2,...xn) = {for i in j , give me xj, but in order!} <- a function: {(1,x1), (2,x2),... (n,xn)}
real estuary
They aren't identically the same. But the idea is equivalent.
Thanks! I get it now
.close
jolly swan
Absolute maximum is y?
devout snowBOT
Absolute maximum is y?
restive river
Absolute maximum is y?
What do you mean by that? That the absolute maximum is the y-value?
As far as I know, there is ambiguity over whether the absolute maximum is the x-value, y-value, or point itself
It depends, really
But when in doubt it's better to give the point because then you give as much information as possible
Or is that not what you meant?
jolly swan
What do you mean by that? That the absolute maximum is the y-value?
yes for example
locals are 0 maximum and 4 minimum.
what are global
absolute*
absolute and locals are same?
restive river
locals are 0 maximum and 4 minimum.
Yes, that is one way to describe them
Sometimes they are described as their x-values
Sometimes they are described as their y-values
restive river
Absolute maximum is y?
Or, sometimes, like in this screenshot, they are described as the point itself
restive river
absolute and locals are same?
No
Absolute minimums/maximums are minimums/maximums over the whole function
But a local maximum/minimum is a maximum/minimum over a region surrounding a point
Take this image from Wikipedia, for example
You can see there is a local minimum on the right
Yet it is higher than the global minimum on the left
It is a local minimum because, no matter which direction you go, you'll be going higher than it
Local or global minimums or maximums all occur where the derivative of the function is 0
restive river
or second derivate
The second derivative helps you find whether it is a minimum or a maximum
But the second derivative being 0 doesn't tell you whether it is a minimum/maximum
jolly swan
does not exist if that case occurs?
restive river
Actually hold up, I just realised the derivative being 0 doesn't make it a minimum/maximum
Take y=x^3
Derivative at x=0 is 0
Yet at x=0 there is neither a minimum or a maximum, whether local or global
jolly swan
doest exist?
restive river
does not exist if that case occurs?
Well uh it's more complicated than that actually
If the second derivative is non-0 and the first derivative is 0, you know you have a maximum or a minimum
And the sign of the second derivative tells you whether it is a maximum or a minimum
But take y=c for example, where c is a constant
Every point of that function is technically a local and global minimum and maximum
Yet both first and second derivatives are 0
I feel like I'm making this way harder than it needs to be, sorry about that
jolly swan
dont worry
restive river
For most functions this isn't an issue
For polynomial functions of degree higher than 0 (a.k.a. non-constant polynomials), for example, you don't have to worry about that
The nice math breaks when you have a region where the function is constant though
But since most functions don't have any of those you don't really have to worry about it
All you need to remember is that global minimums and maximums are minimums and maximums over the whole function, and that local minimums and maximums are points where, in whichever direction you go, the function gets bigger (for minimums) or smaller (for maximums)
Another way to think about it is that if you zoom into the region surrounding a local minimum/maximum, it'll look like a global minimum/maximum
Take this again for example
If you zoom into the region of the local minimum, it'll look like the lowest point on the graph
But if you zoom into any other point (other than the global minimum) you will see that no matter how far you zoom it'll clearly not be a local minimum
jolly swan
It got a bit complicated, I'm sorry but is there any way to know 100% what are the local minimum, maximum and global points?
restive river
It got a bit complicated, I'm sorry but is there any way to know 100% what are t...
A global maximum/minimum is a maximum/minimum over the whole function, so far so good?
jolly swan
yes
restive river
A local minimum/maximum is a minimum/maximum over its immediate region
As you can see, if you zoom in, it becomes clear that it is a minimum
By the way, global minimums/maximums technically also qualify as local minimums/maximums
@jolly swan Is that clear as well?
jolly swan
yes
restive river
Good, now you understand global and local maximums and minimums
Back to your original question, as I said, it is ambiguous whether you should give the x-value, y-value, or the point itself
There is no agreed upon consensus
So when in doubt, just do what they do, or give the point itself because that has the most information (a point having both x-value and y-value)
jolly swan
okay
restive river
@jolly swan To find local minimums/maximums, find the first derivative, set it equal to 0 (to find points where the function is flat, which as you can see from the graph indicates there is a minimum/maximum), and solve for x. Then, check the second derivative at that point. If it is positive, that means the slope is going up, so you have found a minimum. If it is negative, that means the slope is going down, so you have found a maximum. If it is 0, you got trolled, that is neither a minimum nor a maximum (unless the function is constant around that point, but unless the function you were given is of the form y=c that is very very unlikely to happen)
jolly swan
yes critical points
restive river
👍
slender nimbus
can somebody help me, how do i factor this??
devout snowBOT
can somebody help me, how do i factor this??
lusty sapphire
If they want you to factor it, try random integers and see which make the polynomial zero
slender nimbus
ive seen this method everywhere but i dont understand how they do it
lusty sapphire
Say if x=1 made the polynomial zero (it does not), then one factor would be (x-1)
slender nimbus
ive seen this method everywhere but i dont understand how they do it
i think its easier if i do the method u explained but for curiositys sake do you know how they did this?
@lusty sapphire ?
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restive river
velocity is the change in distance over time
devout snowBOT
devout snowBOT
Available help channel!
red oak
Don't ping random people
ok, can u help pls
lusty sapphire
I don't do stats
lusty sapphire
lusty sapphire
which problem
red oak
5
red oak
total of all of them is 20
and
there is 4 red
so is it 4/20
1/5 is the simplest form
when
on question 5
do u do the same but there’s 3 answers
in one question
lusty sapphire
question 5 is asking the total probability of either getting a red, green, or yellow ball
1 of any of those colors is acceptable
So you you need to find out how many red, green, and yellow balls there are total
lusty sapphire
red 1/5 green 3/20 yellow 2/5
How did you get 2/5 for yellow?
devout snowBOT
@red oak Has your question been resolved?
red oak
How did you get 2/5 for yellow?
I fixed the stuff, I got the number 5
I’m on number 10
Currently
I got 5-9
10 and 11 doesn’t look easy
restive river
,rccw
woven radishBOT
red oak
,rccw
woven radishBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
red oak
,help cmd
woven radishBOT
You really shouldn't take it literally :upside_down:. Please type ,help ping, for example!
The full command list may be found using ,list.
red oak
,list
woven radishBOT
tame palm
What do you need help with?
red oak
I need help on question 10 letter b to d
red oak
What do you need help with?
tame palm
What did you find for the sample space?
restive river
Well first, what is the probability of getting a green marble?
red oak
Well first, what is the probability of getting a green marble?
3/20
wait
3/20 for green and 4/20 for blue
red*
red oak
do u have to do 1/3 or something
red oak
1 divided by 3
restive river
Just 1 / 3 works
This signifies that there is a 1 in 3 chance of us picking the green marble
red oak
and same goes to red
restive river
Yes
red oak
give me 1 minute
in the last problem
I divided by 8/20 and 4/20
got .2 and .4
I multiply them
do I do the same to 10 b
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Available help channel!
ionic dagger
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ionic dagger
help
weak cove
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
6
merry canopy
Ehhh wouldn't it be just 11? like 7+4 since all the angles are 90 degrees? / no sería simplemente 11? osea 7+4 porque todos son ángulos rectos?
devout snowBOT
Ehhh wouldn't it be just 11? like 7+4 since all the angles are 90 degrees? / no ...
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.
weak cove
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
ok
weak cove
!nosols
devout snowBOT
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.
merry canopy
I allready did more than necesary in the first one, just use the same concept with this one
I'll give you a hint, in this case use rest / te daré una pista, en este caso usa la resta
ionic dagger
I allready did more than necesary in the first one, just use the same concept wi...
que numero serian en este caso
merry canopy
que numero serian en este caso
I'll give you the answer in math if you want / te daré la respuesta en matemáticas si queires / but just realize that the line of 14cm measures the same as the 2 lines below it / la linea de 14 mide lo msimo que las 2 lineas debajo de ella
?= 2(2^2)
ionic dagger
mira se que sonara insistente esto pero necesito la repuesta ya que estoy un poco apurado
merry canopy
8
ionic dagger
ok
merry canopy
mira se que sonara insistente esto pero necesito la repuesta ya que estoy un poc...
14 = 6+? so/entonces 14-6=8 so/entonces ?=8
merry canopy
14 = 6+? so/entonces 14-6=8 so/entonces ?=8
replace this formula/remplaza esta formula /I'll make it easy for you / te lo pondré facil / 10 = 4+?
so/entonces ?=10-4
ionic dagger
todos?
merry canopy
ehhh it's in the rules • When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.
Plus if you're in a hurry bc you're in an exam it's considered cheating and you'd get banned
ionic dagger
ok
weak cove
is this for an exam?
merry canopy
is this for an exam?
not likely just said so that he takes his time
merry canopy
you can help me whith the process
ok the right side is 16ft which is exactly the sum of the 2 left sides 10 and 6
this is the same for the 14 below it
ionic dagger
ok
help please
ma sacaba malo pero era porque falta una medida es como el ejercicio anterior
ionic dagger
devout snowBOT
ionic dagger
help please
merry canopy
it's the same idea as in all the previous ones
I get that you might be young but listen it's just adding and sustracting small numbers
16 is 5 + 11 and 13 is 7 + ?
ionic dagger
pero el ejercicio dice que falta un angulo y como sacaria ese angulo faltante
merry canopy
pero el ejercicio dice que falta un angulo y como sacaria ese angulo faltante
no
al mencionar los angulos
solo es para que no tengas dudas en que 5 + 11 son 16
lo que te dice es que por los ángulos usados, la suma de los números de arriba 5 y 11 es igual al numero de abajo 16
es lo mismo con el 13 y el 7 más la incognita
13-7= 6
con eso ya sumas todos los números y ya está
ionic dagger
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ionic dagger
ayuda porfa
devout snowBOT
ayuda porfa
merry canopy
ayuda porfa
I just love how you just asked it in spanish hoping I saw it
ehhh it's still the same idea
perimetro is suming all of the numbers
for that you need to find the number not given
wait
merry canopy
it's the same one...
merry canopy
tomate tu tiempo
(why "take your time"??) I allready gave you the answer 
just sum the numbers plus the 6
if you can use discord you can open a calculator
ionic dagger
merry canopy
ok I'll give you a trick /te voy a dar un truco
merry canopy
<:sully:651816820122189834>
listen
the perimeter is equal to the sum of the 2 full sides by 2 / el perimetro es la suma de los 2 lados completos 2 veces
13+16= 29
ionic dagger
merry canopy
29x2=58
merry canopy
merry canopy
esque esta dificil
nope
ionic dagger
que no es solo hallar el perimetro
merry canopy
entendes esta?
ofc, they're really easy
merry canopy
que no es solo hallar el perimetro
mira es lo mismo de antes el lado de arriba mide lo mismo que los dos lados de abajo
11
mide lo mismo que 5 más x
ionic dagger
ok
merry canopy
y ni siquiera necesitas eso
ionic dagger
entonces sumo todos los numeros y le agrego 5 esi es verdad
merry canopy
si solo sumas 12 más 11 y tomas el resultado y lo multiplicas x 2
merry canopy
what are the 2 full sides / cuales son los dos lados completos?
ionic dagger
creo que tiene
._.
esta raro eso
creo que esta esta mas facil
help please
bro help
ionic dagger
😦
merry canopy
la geometria no la domino bien por eso necesito tu ayuda
ok, mira es que esto es muy pero que muy básico
solo tienes que pensar, es más facil mientras no estás escuchando reggaeton
ionic dagger
por?
merry canopy
porque así te concentras
ionic dagger
como asi?
merry canopy
yo suelo esuchar música mientras estudio, pero te sugiero darte un tiempo para entender bien
ionic dagger
escucho variado
merry canopy
escucho variado
no es sobre la música es sobre concentrarte
ionic dagger
pero necesito tu ayuda no la respuesta el procedimiento esto no me lo enseñaron
merry canopy
este disc esta hecho para ayudar a encontrar la solución no para dartela
14 = 9 + 5
si te das cuenta el número de arriba es igual a los de abajo (el 9 y el 5) sumados
merry canopy
para problemas así toma los dos lados grandes, 14 y 10, sumalos
=24 y multiplicalos por 2
=48
es el último que te resuelvo porque me tengo que ir, pero escucha te lo he explicado varias veces es tan simple como eso
no es que no puedas entenderlo es que tienes quque darte el tiempo
ionic dagger
ok
dense juniper
I am trying to prove proposition 4.2.10 from Lebl's Introduction to Analysis. In the end, the problem boils down to proving that g(x) = lim (y → x) f(y) is continuous (or at least it will be really easy to prove the proposition once this is proven). I have searched for this problem and came across 3 different responses in math.stackexchange but their working out is unclear or wrong. I would appreciate any help!
devout snowBOT
I am trying to prove proposition 4.2.10 from Lebl's Introduction to Analysis. In...
dense juniper
Here is a screen cap of proposition 4.2.10:
**TL;DR: Proove that g(x) = lim (y → x) f(y) is continuous **
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fast helm
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fast helm
how can i solve for x
woven radishBOT
Buddy
woven radishBOT
Buddy
weary holly
Can you mate?
fast helm
yes ik
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wooden veldt
. @fast helm it says show graphically I.e. plot the graphs of both functions and show they intersect in that interval
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mossy falcon
The picture next to this shows a square divided into 6 equal parts. Each part is a rectangle that has a circumference of 70 cm. The square area is equal to
devout snowBOT
The picture next to this shows a square divided into 6 equal parts. Each part is...
craggy dagger
what have you tried so far
winter patrol
where's the pic?
is this translated?
craggy dagger
chances are the picture is just 6 congruent rectangles forming a square
okay there is some ambiguity there tbh
mossy falcon
Yes The real question is Indonesian Languages
mossy falcon
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mossy falcon
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The picture next to this shows a square divided into 6 equal parts. Each part is a rectangle that has a circumference of 70 cm. The square area is equal to....... Please Answer!!!!
craggy dagger
picture?
mossy falcon
I cant take a picture because i use with PC
craggy dagger
draw the picture then
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heavy terrace
how do I simplify this further?
devout snowBOT
how do I simplify this further?
lost laurel
the denominator is of thr form sin(a+b)
finite briar
thats sin and cos of phi right
heavy terrace
the denominator is of thr form sin(a+b)
somehow it becomes this
and although I've studied everything to this point, I do not understand how this happened
lost laurel
what's the entire question
lost laurel
somehow it becomes this
missing info, I guess
heavy terrace
missing info, I guess
In triangle ABCD M is on AC and AM=18, MC= 2sqrt(3), if BAC = 30 degrees, then the tan of ABM = ?
I'm 100% confident nothing helps
but here it is I guess
it's just following the sinus theorem
and simplifying it
devout snowBOT
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heavy terrace
<@&286206848099549185>
restive river
In triangle ABCD M is on AC and AM=18, MC= 2sqrt(3), if BAC = 30 degrees, then t...
10ти клас ли си?
restive river
това е от приемният изпит за ФМИ,СУ предишната година
Опа, ясно 😂
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heavy terrace
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fluid night
Hey, anyone knows a good place to learn calculus w/o much knogledge(basic derivatives and limits) about it?
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Hey, anyone knows a good place to learn calculus w/o much knogledge(basic deriva...
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orchid axle
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lofty monolith
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lofty monolith
for part b the markscheme says u can split it into two partial fractions but when i did that im not getting their answer
they also split into 3 partial fractions but i dont see why/if thats the only way
fierce rune
you can show that (a) is true by the parametric integration formula which is on a level spec
fierce rune
oh lol
you sure you're doing partial fractions correctly?
=(at+b)/t^2 + c/t+2
you want to go one degree higher than the denominator
lofty monolith
at+b/t^2?
fierce rune
yeah
lofty monolith
i dont get that
fierce rune
because the denominator is a quadratic
so the numerator is one degree lower
thats just how partial fractions work
cursive thicket
I need help with understanding the proof of the Chinese Remainder Theorem. x ≡ (a₁M₁y₁ + a₂M₂y₂ + ... + aₙMₙyₙ) (mod M), I dont understand where does Mn and yn come from
devout snowBOT
I need help with understanding the proof of the Chinese Remainder Theorem. x ≡ ...
@cursive thicket Has your question been resolved?
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supple knot
I need help with understanding the proof of the Chinese Remainder Theorem. x ≡ ...
show the proof you're reading
cursive thicket
Okay i think I asked a bad question. Im not really reading much as I struggle to understand what's written. Ive been watching a youtube video https://www.youtube.com/watch?v=SU3vouq7lN4 however i loose him after 2:50
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autumn tulip
Hi so im doing question #7 and I cant figure out how I got it wrong or if im doing the wrong formula? Can someone please give me the correct formula or correct where I made a mistake?
devout snowBOT
Hi so im doing question #7 and I cant figure out how I got it wrong or if im doi...
autumn tulip
wait which 3?
supple knot
wait which 3?
The first term is 3. You didn't include that when you calculated 59049
59049 = 3^9
,calc 3^9
woven radishBOT
Result:
19683
Why is it 3/3?
quaint sequoia
Why is it 3/3?
3×1/3
autumn tulip
oh wait so u multiply it at the beginning?
woven radishBOT
AwitNamanSayoPar
quaint sequoia
$$3×\frac{1}{19683}$$
woven radishBOT
AwitNamanSayoPar
quaint sequoia
$$\frac{3}{6561}$$
woven radishBOT
AwitNamanSayoPar
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autumn tulip
i also did a similar question to it
and i got it wrong
so can someone explain how i got it wrong?
the quesiton is: find the 9th term of the geometric sequence whos common ratio is 1/2 and whos first term is 3
<@&286206848099549185>
supple knot
i also did a similar question to it
Same mistake as before
supple knot
Why do you keep multiplying the denominator by the first term
supple knot
**AwitNamanSayoPar**
This was the right answer to your previous problem
feral kayak
Find the unit tangent and unit normal vectors T(t) and N(t) of the vector function r(t)=(Sqrt(2)t,e^t,e^-t)
devout snowBOT
Find the unit tangent and unit normal vectors T(t) and N(t) of the vector functi...
pulsar dock
This is a pretty straight forward case of just applying the formula
feral kayak
Idk, when I applied it I just kept getting crazy functions
I guess I was just a little intimidated
pulsar dock
What do you have
feral kayak
Well for T(t) I have the answer and its right (I checked the book), but for N(t) I have something crazy
Idk If I can write it down
Just making sure N(t)=T'(t)/|T'(t)| right?
pulsar dock
That is one way yes. I haven't tried it to see if it would make your equation explode into a nightmare, but you will need the quotient rule and that is sort of painful
feral kayak
Yeah
pulsar dock
It is usually easier to calculate B(t) and then use N(t) = B(t) x T(t)
feral kayak
Wait but I thought the formula was B(t)=T(t) x N(t)
pulsar dock
That is something else
T(t) = N(t) x B(t), N(t) = B(t) x T(t) and B(t) = T(t) x N(t)
feral kayak
Wait but how is it easier?
pulsar dock
You already have T(t), so all you need is to find B(t) then take the cross product and B(t) is easy
analog trellis
B(t) seems very hard to get unless there's some trick I don't know. You might just have to do it the long way. I'm not sure there's many tricks since the parameter is not the arc length.
feral kayak
Well for the cross product of B(t), we need N(t) which is T'(t)/|T'(t)|, so I guess I'll have to take the derivative anyways
pulsar dock
analog trellis
They have that the parameter is the arc length s, sadly.
feral kayak
Oh I see now, I didn't know about that formula
analog trellis
Oh I see now, I didn't know about that formula
Your problem does not have |r'(t)| ≡ 1. You can't use this.
feral kayak
Oh
analog trellis
Note: alpha = T, beta = B and gamma is N in your notation.
I think you can write the numerator of beta as x' cross (x'' cross x') if it helps or not.
pulsar dock
To be honest, I am not really an expert on this subject and none of my Calculus textbooks are at home. Also I have absolutely zero interest in differential geometry. But I have worked with a differential geometer for about 10 years and I used his lecture notes on this topic when I taught it in the past and from my understanding there is nothing wrong with what I said.
feral kayak
I got the answer
analog trellis
To be honest, I am not really an expert on this subject and none of my Calculus ...
I crossed out my error earlier. The formula in your link is valid even if t is not the arc length. 🙂
feral kayak
This really helped thank you guys
feral kayak
Also this is differential geometry?
analog trellis
True. I remember now that these formula come from the arc length version using the chain rule and manipulation though. 🙂
analog trellis
Also this is differential geometry?
This is in the Differential Geometry chapter of my book. But that topic gets a lot more complicated than the stuff in my book from the stuff I've seen in #diff-geo-diff-top . 🙂
feral kayak
Interesting
analog trellis
I dug out my derivations of the equations (4).
I made many errors at the time as can be seen by me ending up using pencil and the erased stuff in the background.
feral kayak
Were you required to memorize this formula for your class (I'm "in" Calc 3)
pulsar dock
My current class covering this gets the freaking unit circle and I was vetoed on trying to not give it to them. They get this and a lot more. Their formula sheet is 20 something pages.
analog trellis
I do this for personal entertainment but I don't think I'd be able to remember that formula.
feral kayak
I see
analog trellis
If I sat there I could probably remember it as I covered it somewhat recently. I spent a lot of time trying to do that problem.
feral kayak
Alright
analog trellis
But in reality I'd probably misremember it. 🙂
feral kayak
Well thank you again for all your help
sage socket
Anyone see anything wrong with my math here?
devout snowBOT
Anyone see anything wrong with my math here?
restive river
Where did the + sign vanish from line 3 to line 4
sage socket
Omg
sage socket
Where did the + sign vanish from line 3 to line 4
I totally forgot to write it
That might be my problem
Ty for catching thay
.close
indigo zinc
devout snowBOT
nova idol
!show
devout snowBOT
Show your work, and if possible, explain where you are stuck.
nova idol
thats really hard to read
indigo zinc
alr
so the only part I am cofident in is that I cancel the same values
then, I am left with negative powers so y^-1/2 - x ^-1/2
outer jacinth
You are wrong with the powers
indigo zinc
indigo zinc
You are wrong with the powers
which part
outer jacinth
You first seperate out the terms
(x½ y-½)/(xy)½ - (x-½ y½)/(xy)½
Solving it, you should get (x^-1) - (y^-1)
indigo zinc
where did u get the subtraction sign from
like the way u multiplied both by (xy)1/2
and then you directly subtracted
outer jacinth
I didn't mutliply it, i seperated the terms and gave both the terms their denominator
stone apex
How do I prove that "If Lim(an+bn) exists and Lim(an-bn) exists then Lim(an) and Lim(bn) also exist"
devout snowBOT
How do I prove that "If Lim(an+bn) exists and Lim(an-bn) exists then Lim(an) and...
stone apex
I got no clue how to start
actually I did start by definition of Lim->
Lim(an+bn)=L1
-> exists N such that, |(aN+bN)-L1|<e
do I just do that for everything ?
its gonna be super long and I dont feel like it works out
or is the statement wrong lmao
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stone apex
is this disproof sound? I know im cringe for using chatgpt but its interesting
an oscillating sequence is not limited by definition right?
nova idol
is this disproof sound? I know im cringe for using chatgpt but its interesting
No
an-bn oscillates
And even in their wrong answer they said that it’s zero which is wrong
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stone apex
lmao
I am confused then how would I approach the statement
"If Lim(an+bn) exists and Lim(an-bn) exists then Lim(an) and Lim(bn) also exist"
nova idol
I am confused then how would I approach the statement
I don’t think it’s true
I just think that chatgpt messed up on the explanation
As usual
vast rain
hmm I think it's true
ignoring the cases where you say infinite limits "exist"
suppose the first sequence has limit L1 and the second sequence has L2
that means past some N1 and N2, you can ensure that each is different from L1 and L2 by epsilon/2
oh wait hmm
that doesn't work does it
maybe it does
yeah it does
so pick N3 = max(N1, N2)
now consider the sequence 2an = (an+bn) + (an-bn)
this thing has limit L1 + L2 by the triangle inequality
maybe I goofed the proof lol
stone apex
hmm
stone apex
now consider the sequence 2an = (an+bn) + (an-bn)
this part confused me a bit, why did u take the sum of these and equate it to 2an
I understand that u get 2an by adding them but why did u add them
vast rain
because we're going to recover a_n from the two
basically the fact that the two limits exist constrains the two sequences as N gets large
and therefore, since a_n is just a linear combination of them, a_n is also constrained
surely you don't have to go through this proof though, yeah?
are you not told that the sum of two sequences is convergent if the two sequences are convergent?
stone apex
but like in the statmenet it says; if Lim(an+bn) AND Lim(an-bn) then...
vast rain
but like in the statmenet it says; if Lim(an+bn) AND Lim(an-bn) then...
what about it
vast rain
im just confused on why we're adding them
because it leads to a useful result
stone apex
so 2an has a limit of L1+L2
therefore we can conclude that an also has a limit?
what about bn then
vast rain
similar argument
stone apex
except u minus them?
vast rain
in fact, the very same argument
you can literally even say something like because a_n - b_n is convergent, so is b_n - a_n
and by the first part
vast rain
damn chatgpt really disappointed me this time lmfao
stone apex
u can gaslight it into anything
vast rain
it's usually pretty good
stone apex
for any statement I can ask it to disprove it and prove it
it would do both
from what ive tried at least
stone apex
hehe
aight I think we can close this one out
it clicked for a second but I gotta reread the stuff thanks for the help
.close
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fluid night
How would you graph this? 5/2x^2 + 5x 6
devout snowBOT
How would you graph this? 5/2x^2 + 5x 6
sonic smelt
Using desmos 
polar chasm
is it 5/2x^2 + 5x + 6?
sonic smelt
Or 5/(2x^2 + 5x + 6)?
fluid night
Or 5/(2x^2 + 5x + 6)?
Like this
sonic smelt
I would first graph 2x^2 + 5x + 6
fluid night
Yeah, my intuition tells me that the x values of that function are the asymptotes of the rational function
sonic smelt
What happens when you take 1/(some function) is something similar to reflecting the points around y = 1 or y = -1 (depending on whether the point is above or below the x-axis)
Except
The smaller the number, the further it will get located from the horizontal line
And vice versa
Hard to explain in words
fluid night
This is another function of the same sort
But its diferent from the exact function ive described
So, why?
sonic smelt
Because 2x^2 + 5x + 6 is always positive
That also explains why the last graph has no vertical asymptotes
2x^2 + 5x + 6 is above the x-axis, meaning 2x^2 + 5x + 6 is never zero
Thus 1/(2x^2 + 5x + 6) will not have an asymptote
fluid night
Oh, and how do you calculate the asymptotes of the first one?, are they the x values of the cuadratic function?
sonic smelt
1/f(x) has a vertical asymptote whenever f(x) = 0
fluid night
Yea, i know that, so in this case it has two vertical asymptotes because of the x^2 right?
sonic smelt
Yeah
fluid night
Thanks
devout snowBOT
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