😭
#help-39
pearl pondBOT
pearl pondBOT
✅
toxic lichen
btw you should never write $\sum_{r=1}^r$
jolly parrotBOT
Ann
toxic lichen
"r goes from 1 to r" doesnt make sense
rigid mist
like any other
toxic lichen
the upper limit should be any letter except r yes
ruby otter
Necessity and uses of Probability Generating Function in layman's terms please
wet osprey
It’s a pretty technical concept why do you need it in layman’s terms?
pearl pondBOT
@ruby otter Has your question been resolved?
pearl pondBOT
pearl pondBOT
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tribal shale
pearl pondBOT
cursive fulcrum
<@&286206848099549185>
!15min
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
cursive fulcrum
guessing there is something more to this question
tribal shale
guessing there is something more to this question
A swimmer is in the sea at a point N, located 3 km from a straight beach, and just in front of a point S, located on the beach by the water; and wants to go to a point A, also located downstream and 6 km from point S, so that the triangle NSA is right-angled at the vertex S. The swimmer swims at a constant speed of 3 km/h and walks at a constant speed of 5 km/h.
cursive fulcrum
so you did miss crucial info
tribal shale
a) If P is a point between point S and point A that is a distance x from S, show that the time, in hours, required by the swimmer to swim from point N to point P and walk from point P to point A is determined by the expression
cursive fulcrum
the speeds
tribal shale
the speeds
3km/h and 5km/h?
cursive fulcrum
yes, you should have also mentioned which speed corresponds to which distance
this question is a little similar to the one you asked yesterday
cursive fulcrum
now, have you made any progress?
or do you have any ideas on how you should proceed from here?
tribal shale
i got √x^2+9=y
tribal shale
i need to use the formula of speed?
cursive fulcrum
can you find the time it will take?
cursive fulcrum
i need to use the formula of speed?
which formula to be exact?
tribal shale
Time=distance/speed
cursive fulcrum
yes thats good
tribal shale
so t=√x^2+)/3?
tribal shale
time taken to travel PN, yes
but i have x and t has a unknow quantic
cursive fulcrum
but i have x and t has a unknow quantic
... i dont undersatnd
tribal shale
i mean variable
tribal shale
so t=√x^2+)/3?
don't know how to solve this
cursive fulcrum
you dont have to, and there is nothing you could further do to this
what you are to do now is to find the expression of time taken to travel PA
and since the total time taken t(x) = time taken to travel PN + time taken to travel PA
you should be good to go
tribal shale
what you are to do now is to find the expression of time taken to travel PA
t=6-x/5?
cursive fulcrum
yes
tribal shale
what i should do now?
cursive fulcrum
and since the total time taken t(x) = time taken to travel PN + time taken to tr...
...
tribal shale
t(x)=√x^2+9/3 +6-x/5?
cursive fulcrum
yes, you mean √(x^2+9)/3 + (6-x)/5?
tribal shale
oh, so that it?
tribal shale
yes, you mean √(x^2+9)/3 + (6-x)/5?
yea
tribal shale
yes that would be it
I thought it was calculating the time it takes to go from N to P and from P to A, with just those given. I feel stupid for not reading the statements correctly. But thank you very much anyway!!
cursive fulcrum
I thought it was calculating the time it takes to go from N to P and from P to A...
its my pleasure. have an awesome day ahead:)
tribal shale
its my pleasure. have an awesome day ahead:)
you too, thanks for help me again
.close
pearl pondBOT
pearl pondBOT
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runic glacier
pearl pondBOT
runic glacier
Not sure what kind of argument or example i can give for part b)
in order to compare the speed at which the error at the kth iteration converges to zero
pearl pondBOT
@runic glacier Has your question been resolved?
pearl pondBOT
@runic glacier Has your question been resolved?
pearl pondBOT
@runic glacier Has your question been resolved?
runic glacier
<@&286206848099549185>
pearl pondBOT
@runic glacier Has your question been resolved?
pearl pondBOT
@runic glacier Has your question been resolved?
pearl pondBOT
@runic glacier Has your question been resolved?
heavy raven
hey guys
tropic saddle
geometric sum
tropic saddle
if x=2, yes
heavy raven
so it would be something like
tropic saddle
in general $\sum_{i=0}^n x^i = \frac{x^{n+1}-1}{x-1}$
jolly parrotBOT
Denascite
pearl pondBOT
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hollow pike
can someone help me understand the question
pearl pondBOT
can someone help me understand the question
scarlet mirage
by write a defenition for the nth term it means write a formula so that for any n you plug in it will give you f(n)
thats not dependant on knowing the value of any other function
hollow pike
by write a defenition for the nth term it means write a formula so that for any ...
so an explicit function?
scarlet mirage
For example 6n + 5 or whatever it may be
hollow pike
For example 6n + 5 or whatever it may be
wait but in this case its -4-2^n?
scarlet mirage
i just was giving an example
hollow pike
i just was giving an example
but am i right?
dreamy ibex
yup
scarlet mirage
if by ^ you mean *
dreamy ibex
how did you approach @scarlet mirage
scarlet mirage
i just wrote a table for the first 4 funcs
dreamy ibex
i just wrote a table for the first 4 funcs
and do you observe any sequence?
hollow pike
f(1)=f(0)-2
huh?
dreamy ibex
huh?
yes, according to the condition given, f(n)=f(n-1)-2 for all n greater than or equal to 1
scarlet mirage
and do you observe any sequence?
yeah its what T2 said but *n instead of ^n
hollow pike
yes, according to the condition given, f(n)=f(n-1)-2 for all n greater than or e...
it should be n equal or greater than or equal to 2
dreamy ibex
yeah its what T2 said but *n instead of ^n
could you show your work?
dreamy ibex
it should be n equal or greater than or equal to 2
scarlet mirage
T2 plug in 1 to all the ns and you will get f(1) = f(1-1) -2, which means f(1) = f(0) -2 and since we know f(0) = -4 we get f(1) = -4-2 = -6
hollow pike
so my explict def is going to be
f(1)=-4
f(n)=-4-2^n
n equal to or greater then 1?
scarlet mirage
T2 why ^n?
hollow pike
T2 why ^n?
ohhh yea
dreamy ibex
it wouldnt be ^n
dreamy ibex
are you aware of arithmetic sequences?
hollow pike
right?
dreamy ibex
yes
hollow pike
wait i have one question tho
dreamy ibex
yeah its what T2 said but *n instead of ^n
yep, your answer is correct
hollow pike
in this case is n greater or equal then 2, right?
dreamy ibex
you should open up another channel for your question
but now that youve already asked
in this case you observe that the numbers are increasing exponentially
hollow pike
in this case you observe that the numbers are increasing exponentially
im aware of that
dreamy ibex
so yes, itll be ^2
hollow pike
so yes, itll be ^2
huh?
scarlet mirage
what
scarlet mirage
yeah youre good
dreamy ibex
yes, n would be greater than equal to 2 in this case
hollow pike
yes, n would be greater than equal to 2 in this case
but in my previous question its 1?
dreamy ibex
but in my previous question its 1?
the one that @scarlet mirage asked?
scarlet mirage
n is just there to count it should just be 1 more than the function with a value
hollow pike
the one that <@741327936795181066> asked?
yea, the question i opened up my channel for
scarlet mirage
the one that <@741327936795181066> asked?
my guy i didnt ask any questions
hollow pike
lol
dreamy ibex
but in my previous question its 1?
since we started with the 'zeroth' term, we didnt have any information about the term before it, thats why we said that n>=1
hollow pike
laito didnt ask any question
hollow pike
since we started with the 'zeroth' term, we didnt have any information about the...
but i said f(1)=-4
scarlet mirage
can someone help me understand the question
.
scarlet mirage
this and the last one were
hollow pike
in this case is n greater or equal then 2, right?
and this also is, right?
hollow pike
both work lol
so im good, right?
scarlet mirage
One just starts counting from 1 and the other from 0
hollow pike
since all this time ive been thinking it was your question lmao mb
im good tho, right?
like it is n greater then or equal to 2 on my sec question
and n greater then or equal to 1 on my first ques?
dreamy ibex
is this the correct form?
in the first part, the lowest term we were given was C(0) and since the condition we were given made use of the previous term, that's why we said n>=1 so that when n=1, C(1)=C(0)-2
hollow pike
in the first part, the lowest term we were given was C(0) and since the conditio...
mhm
and how about my sec question?
dreamy ibex
in the second part, the lowest term we were given was C(1), and again, since the condition we were given made use of the previous term, we put n>=2, so that when n=2, we would get C(2)=C(1)*1/4
dreamy ibex
and how about my sec question?
yes, youre correct in both of the questions
the only difference was we started counting from 0 in the first part and from 1 in our second part
and the condition was given such that we couldnt go lower than our initial count, ie 0 in the first case and 1 in the second case
hollow pike
yes, youre correct in both of the questions
should i close thread?
hollow pike
and the condition was given such that we couldnt go lower than our initial count...
yh i get it
thx @scarlet mirage @dreamy ibex
dreamy ibex
yup, youre good then :>
hollow pike
.close
west bloom
pearl pondBOT
west bloom
Where have i made a mistake
pearl pondBOT
@west bloom Has your question been resolved?
west bloom
<@&286206848099549185>
pearl pondBOT
@west bloom Has your question been resolved?
pearl pondBOT
@west bloom Has your question been resolved?
sweet radish
pearl pondBOT
sweet radish
Im really confused ://
solid ivy
Hint: try to find two angles that inscribe the same arc
sweet radish
I don't get it ://
This whole inscribed angles and inscribed arc isn't making sense to me
solid ivy
ok well for starters
Can u recall the formula for central angles based on the arc they have?
Like from ur notes or something
A central angle would be one whose...I guess middle point would be the center of the circle
sweet radish
Theta/360 = sector area/circle area = arc length /circumference
solid ivy
Yeah. What about when the middle point is on the circle like X here?
sweet radish
I don't know :(
solid ivy
Hmm you kinda need to for this problem 
, Ill tell u ig
$\angle AXB = \frac{\theta}{2}$
jolly parrotBOT
992qqoloy
jolly parrotBOT
992qqoloy
solid ivy
What arc does that cover?
sweet radish
Yeah. What about when the middle point is on the circle like X here?
ABX?
solid ivy
In the diagram for your problem I mean
sweet radish
Arc abc..?
sweet radish
Two end points?
solid ivy
Well not end points but like
Eh ill just draw another example
What do you think the inscribed arc is here for both of these angles
sweet radish
Cdx..?
solid ivy
CDX would imply the arc starts at C and ends at X
sweet radish
CD?
solid ivy
ye
sweet radish
So inscribed is the one in between..?
solid ivy
Yeah
Well there's one caveat: CD could teeeeechnically refer to two arcs, the "minor" one and the "major" one. So by convention, it usually refers to the one with the smallest possible arc measure, I. E. The minor arc
If you wanted to refer to the major arc, you'd call it CXD (or some other point in between), to denote that while it starts at C and ends at D, X is in between
But u don't gotta worry bout that here
sweet radish
Ookay
solid ivy
so basically my hint is to find two angles that have the same arc in between
and as another hint, one of them is $\angle ACB$
jolly parrotBOT
992qqoloy
sweet radish
Could it be <acb and <apc?
solid ivy
$\angle APC$ has arc $AC$ in between
jolly parrotBOT
992qqoloy
sweet radish
What about apb
solid ivy
Yeah that works
solid ivy
$\angle AXB = \frac{\theta}{2}$
lastly, remember this formula (but here put in C instead of X)
sweet radish
34 = 1/2 (APB) ?
jolly parrotBOT
992qqoloy
solid ivy
But it makes up an angle in a triangle that contains x
solid ivy
Yeah
sweet radish
Thank uuuu so muchh for being patient with me
solid ivy
np
If ur curious here's the proof for the formula https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/inscribed-and-central-angles-proof
safe crescent
.help
pearl pondBOT
Commands:
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factoids: .tag
help: .help
Type .help <command name> for more info on a command.
safe crescent
just need help with similar shapes, dialations and things
pearl pondBOT
just need help with similar shapes, dialations and things
midnight haven
send question
safe crescent
oops
hold on sorry
here ypu gos
WAIT NEVERMIND THATS SO EASY LOL but i really dont understand this one
pearl pondBOT
@safe crescent Has your question been resolved?
pearl pondBOT
@safe crescent Has your question been resolved?
safe crescent
<@&286206848099549185>
spice hawk
Ok let’s see
So the equation to go from blue triangle to green triangle it is 8(Scale Factor)=4.6
Solve for Scale factor,
Then multiply the scale factor by 12 and u get ur Awnser @safe crescent
safe crescent
Then multiply the scale factor by 12 and u get ur Awnser <@758094816629489714>
HELLO
IM SOS ORRY I HAD TO MAKE DINNER
spice hawk
So the equation to go from blue triangle to green triangle it is 8(Scale Factor)...
This
The scale factor is 4.6/8
pearl pondBOT
@safe crescent Has your question been resolved?
pearl pondBOT
@safe crescent Has your question been resolved?
pearl pondBOT
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Available help channel!
soft mist
where does this x go to?
pearl pondBOT
where does this x go to?
dark ingot
du=xdx
wind lagoon
I don't understand this. A polynomial of degree at most $n-1$ with $n$ zeroes is the zero polynomial. Suppose we factor the polynomial of degree at most $n-1$, $$f(x) = c_{n-1} (x - a_1) \cdots (x - a_{n-1}).$$ How can this have $n$ zeroes?
jolly parrotBOT
sunside
wind lagoon
It seems to me we would need another factor (x-a_n).
pearl pondBOT
Available help channel!
outer echo
how do I simplify
$\frac{5}{n-1}-\frac{5}{n}+\frac{5}{n}-\frac{5}{n+1}$
jolly parrotBOT
Price
woven patrol
I don't understand what it wants me to do for B? What does expression mean?
queen osprey
it mean when x people come, how the price can splice with those people
and y mean price per people
woven patrol
But what would an expression look/be like?
warped violet
i think y = 500/x will do
!nosols
pearl pondBOT
i think y = 500/x will do
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.
warped violet
But what would an *expression* look/be like?
You want to figure out how the price per person (y) is affected by how many people there are
So you need to figure out how to calculate the price per person (y)
We can see the table tells us that the number of splicers evenly divide the price of $500
So how can we write an expression here
woven patrol
Well, if singular, then price pr person would be 500, so
y = 500
Is that right?
My issue was more of a language non-understanding, I don't understand what the definition of an expression would be in term of math, so I didn't understand what it specifically wanted me to do. Was it really as simple as to just.. Say that y = 500? Does it not require more?
warped violet
Well, if singular, then price pr person would be 500, so
> y = 500
Is that right...
That's incorrect. y = 500 means that y (the price per person) is $500. But if we have 2 people, then do they still each pay $500 if the total cost is $500?
woven patrol
Ah. No, we wouldn't.
warped violet
Well, if singular, then price pr person would be 500, so
> y = 500
Is that right...
Technically, this isn't an expression as expressions don't have an equals sign. An equals sign presents an equality, if there are variables inside, an equation.
woven patrol
Then it would be 250. ..What about y = x / y?
warped violet
Here we want to see how y (the price per person) is affected by how many people there are. This is called an equation.
warped violet
Then it would be 250. ..What about y = x / y?
You don't know what y is. You are trying to figure out the price per person which is y. If you don't know y you can't divide by y 😄
Let's try again
If there's 1 person
What's the price per person
woven patrol
500
warped violet
What if there are 2
woven patrol
250
warped violet
And 5 people?
woven patrol
100
warped violet
What are you doing to get this?
woven patrol
Dividing, so I'm partly right about the / symbol in it, right?
warped violet
It's about division, yes
But what are you dividing and what with
To get the price per person when there are 2 people
What did you divide?
woven patrol
If Y is the people and x is the number, do I use 500 or x in the expression?
warped violet
Both 😄
warped violet
What did you divide?
Try this
woven patrol
So, 500 / y OR x / y?
woven patrol
o h heck
warped violet
You can't divide by y if you don't know y
Just tell me this:
If there are 2 people
What'd you do to get that it costs $250 per person?
woven patrol
Wait hold on. Y is the price. X is the people.
500 / 2 = 250. 500 / x. Y / X?
Or am I still off base here
warped violet
Wait hold on. ***Y*** is the *price*. X is the people.
500 / 2 = 250. 500 / x. ...
You started well
You divided 500 by 2 (the number of people) to get 250, the price per person
We can switch words for variables
2 is what we picked (the amount of people, x) and we got 250 (y, the price per person)
So we divided 500 by x to get y
Writing this mathematically
woven patrol
Ooh..
warped violet
What do we get?
woven patrol
And y is what we need an expression for! So in essence I need to.. give it a word??
warped violet
Well, in math we use variables (letters like x, y, z, a, k ...)
You are perfectly fine to write price per person = 500 divided by the amount of people
Though that isn't very mathematical 😅
So we usually declare variables and say, look, the price per person will equal y and the amount of people will be x
And we get $y = \frac{500}{x}$
jolly parrotBOT
USS-Enterprise
jolly parrotBOT
USS-Enterprise
warped violet
These 2 are the same
woven patrol
Oooh.. Okay this also makes the later tasks look a little less daunting.
warped violet
But you'll probably learn about functions later on
Pretty much, y is the "dependant variable". It depends on the value of x. x is the "indepedent variable". We pick it
And we want to see how y is affected by our choice of x
So, how the price per person is affected by how many people there are
woven patrol
I see. It's a lot to take in, but having an example makes it a lot easier to understand what it means/wants me to do even if the numbers are different. Thank you for being so patient with me!
warped violet
We can see the effect of x on y easily on a graph. This isn't something you need to know yet though
The green curve is the graph of the function $f(x) = \frac{500}{x}$
jolly parrotBOT
USS-Enterprise
warped violet
You see how if we pick that there are 10 people (so x = 10 (the yellow dotted line)), the y value is 50
Which means if there are 10 people the price is $50 per person
You can see the trend where the bigger the x (the more people there are) the lower the y (lower price per person)
woven patrol
This might come up later this year, so I'm thankful that you're broaching the subject for me
warped violet
This might come up later this year, so I'm thankful that you're broaching the su...
No problem 🙂 Have you done functions yet at all?
woven patrol
Not that I can recall, it's been over ten years since I was last at school, and I recently picked up my studies anew, specifically math, to get a better education, so there has been a lot to take in all at once; percentage calculations, equations, fractions, squared numbers, calculating diluted ratio, etc etc. Most of this just this week, really.
warped violet
Not that I can recall, it's been over ten years since I was last at school, and ...
Oh damn, that seems like a lot
But anyway, you've created your first function 🙂
woven patrol
Oh damn, that seems like a lot
It really has been 
warped violet
It really has been <:NekoSweat:1155603796244844654>
Hehe
woven patrol
But anyway, you've created your first function 🙂
With your amazing help 
warped violet
I wish the best of luck to you 🙃
And don't hesitate to ask if you need help with something else as well!
woven patrol
Thank you! You'll probably see me in here tomorrow, as it's almost 8pm here and the buildings alarm is soon armed, so I have to leave now. But truly, thank you 
.close
pearl pondBOT
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midnight haven
"It can be shown that if $E$ is a separable Banach space and $\mu$ is a locally finite Borel measure on $E$ that is quasi-invariant under all translations by elements of $E$, then either $\dim(E) < +\infty$ or
$\mu$ is the trivial measure $\mu \equiv 0$"
jolly parrotBOT
pearl pondBOT
pearl pondBOT
Available help channel!
wintry mirage
pearl pondBOT
toxic lichen
that's correct, though the automatic 4dp rounding is a bit sus
what's impeding your progress?
wintry mirage
what's impeding your progress?
ans not correct
toxic lichen
oh
wait hold on
i misread your thing
these 4Ck should be 8Ck instead
there's 8 questions
8 trials
wintry mirage
these 4Ck should be **8**Ck instead
may i know why in this case p = 3/4 ?
toxic lichen
it's the probability of getting a question wrong
wintry mirage
it's the probability of getting a question wrong
then part (c) p = 1/4 again
pearl pondBOT
@wintry mirage Has your question been resolved?
true eagle
https://www.youtube.com/watch?v=4hG3yQBVFwg&t=546s This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1". Converts to a regular inequality and then does this } -1 + 7 < x -1 + 7 < 1 + 7 \text{ Next he does something vert very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
jolly parrotBOT
Nerdy_Coder
https://www.youtube.com/watch?v=4hG3yQBVFwg&t=546s This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1". Converts to a regular inequality and then does this } -1 + 7 < x -1 + 7 < 1 + 7 \text{ Next he does something vert very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
```Compilation error:```! Misplaced alignment tab character &.
l.57 https://www.youtube.com/watch?v=4hG3yQBVFwg&
t=546s This video is provin...
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.```
rigid mist
here @true eagle
true eagle
oh
This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1".} $$. $$\text{ Converts to a regular inequality and then does this }$$ $$-1 + 7 < x -1 + 7 < 1 + 7 $$ $$\text{ Next he does something very very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
what
jolly parrotBOT
Nerdy_Coder
This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1".} $$. $$\text{ Converts to a regular inequality and then does this }$$ $$ $$-1 + 7 < x -1 + 7 < 1 + 7 $$ $$\text{ Next he does something very very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.57 ...newline 6 < x + 6 < 8 \text{ now } \lvert
x + 6 \rvert = 8 \text{ t...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
true eagle
yes it works uhh what?!
go to hell!
This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1".} $$. $$\text{ Converts to a regular inequality and then does this }$$ $$ $$-1 + 7 < x -1 + 7 < 1 + 7 $$ $$\text{ Next he does something very very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
jolly parrotBOT
Nerdy_Coder
This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1".} $$. $$\text{ Converts to a regular inequality and then does this }$$ $$ $$-1 + 7 < x -1 + 7 < 1 + 7 $$ $$\text{ Next he does something very very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.57 ...newline 6 < x + 6 < 8 \text{ now } \lvert
x + 6 \rvert = 8 \text{ t...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
true eagle
This video is proving this limit $$ \lim_{x\to1} x^2 + 5x + 6 = 12 \hspace{5pt} \text{The author at 7:34 says "Say delta is 1".} $$. $$\text{ Converts to a regular inequality and then does this }$$ $$-1 + 7 < x -1 + 7 < 1 + 7 $$ $$\text{ Next he does something very very confusing. } \newline 6 < x + 6 < 8 \text{ now } \lvert x + 6 \rvert = 8 \text{ therefore } 8\lvert x - 6 \rvert < \epsilon $$
jolly parrotBOT
Nerdy_Coder
brazen vector
why is what
true eagle
Why can you just convert from |x + 6| to 8
brazen vector
why did he take |x-1|<1?
true eagle
unclear
brazen vector
so you want x to be within a close distance from 1 am i right
true eagle
the video says
brazen vector
you want a reasonably close distance
true eagle
now again he makes this equation
from the delta modification
you can see it in the code
brazen vector
no it isnt delta modification
true eagle
| x + 6| |x - 6| < 8|x - 6|
brazen vector
he didnt let delta=1
true eagle
he didn't?
brazen vector
no
true eagle
In the video?
brazen vector
what he did is the following
he said that |x-1|<delta
now delta is a very small positive number
why because we want x to be very close to 1 is this right
true eagle
idk
brazen vector
we want it to be within distance delta
thats what epsilon delta def means
it is definition of the limit
brazen vector
limit of f as x approaches a is the same as checking which number does f approach as x appraoches a
jolly parrotBOT
Nerdy_Coder
brazen vector
yes it is for all delta but we want to delta to be small
true eagle
limit of f as x approaches a is the same as checking which number does f approac...
Well obviously.
brazen vector
if it is large then we arent talking about a limit
ok x is approaching 1 so its distance from 1 is approaching 0
so we want its distance from 1 to be small
let this small distance be delta
now delta should be small
so it will be <1
thats for sure
bc we are trying to let the distance between x and 1 approach 0
true eagle
if it is large then we arent talking about a limit
We can be though
brazen vector
1 isnt small enough
ok even if it can be 1
we didnt say that delta is 1
we said that if distance between x and 1 is delta
then it is safe to assume that it is less than 1
bc as i said before we want delta to be small
otherwise this wont a definition of limit
true eagle
we said that if distance between x and 1 is delta
*Less than delta
true eagle
then it is safe to assume that it is less than 1
Sure just keep in mind a limit can be a “large” distance away from delta.
brazen vector
??
true eagle
Episilon can be say 200 away from the limit
brazen vector
i am not talking abt epsilon
true eagle
Then delta would be “large”
brazen vector
no thats not necessary
true eagle
Sure but you act as if it breaks a rule
brazen vector
sometimes you get limits as x approach a number and the value of the limit explodes to infinit
this is the case with vertical asymptotes for example
true eagle
That doesn’t disprove my point
brazen vector
maybe i didnt get what you mean can you explain what you mean
brazen vector
Sure just keep in mind a limit can be a “large” distance away from delta.
what did you mean by this
i understood this as : the distance between x and the number it is approaching maybe large
brazen vector
delta shouldnt be large
true eagle
Because to us that tends to be small
brazen vector
it should be reasonably small
true eagle
delta shouldnt be large
Yes but it can be
brazen vector
ok now if i tell you |x-1|<1000 how is x near 1
getting the limit as x approaches 1 means that we want x to be close to 1 in tems of distance
do you disagree with this
true eagle
No
Near is relative
Anyway how did we get 8 |x - 6|
Put upper bound on delta
Then add 7 to all sides
brazen vector
Near is relative
wdym by this
true eagle
The delta inequality is now 6 < |x + 6| < 8 somehow this means |x + 6 | = 8
brazen vector
what does fa stand for
brazen vector
The delta inequality is now 6 < |x + 6| < 8 somehow this means |x + 6 | = 8
no they arent equal
true eagle
So why does this happen? 8|x - 6| < episilon
Uhh from my pov this is a different equation entirely
brazen vector
you want a number k such that $|x+6|<k$ so that you make $k|x-1|<\epsilon$ by taking $|x-1|<\frac{\epsilon}{k}=\delta$
jolly parrotBOT
calculus is fun
brazen vector
now we got this number k which we got as 8
true eagle
and why is that not changing f(x)?
jolly parrotBOT
calculus is fun
brazen vector
i dont see any change in f
true eagle
Okay
Fine this makes sense
As to how they found episilon
However delta is less than one
brazen vector
ok now what did you mean by defintion of nearness
idk what you mean by that but it is clear that x is near 1 here is "defined" as x being too close to 1 so that |x-1|<delta where it is near 0
i mean we are interested in numbers close to 1 thats what taking limit as x approaches 1 is
since we want numbers close to 1 it is safe to take the distance as 1
true eagle
For all epsilon > 0 there is a delta so that the distance from x and the limit is less then delta. Also, the distance from f(x) and the limit is less than epsilon
Value that f(x) approaches = L Limit = For all epsilon > 0 there is a delta so that the distance from x and the L is less then delta. Also, the distance from f(x) and the L is less than epsilon
This is a limit
brazen vector
yes we want small numbers delta and epsilon
brazen vector
you cant say x is near 1 if the distance between them is within delta =100 can you
does this seem near to you
true eagle
You can
brazen vector
ok at this point you arent taking limit anymore
if you use this then you cant substitute when evaluating limit
true eagle
.0000000000000000000000000000000001 is less than hundred
brazen vector
ok but then you are giving chances of delta =99 or 98 or 98.777777777 or large numbers which will definitely not be close distance between x and 1
you are talking about any delta <100 it can be any number <100 but not all of these satisfy "near 1"
true eagle
Yes human intuition is more like delta [5, 0)
brazen vector
you just want sufficiently small delta
brazen vector
Yes human intuition is more like delta [5, 0)
you meant (0,5]?
true eagle
you are talking about any delta <100 it can be any number <100 but not all of th...
But this definition is more rigorious then intuition
true eagle
you meant (0,5]?
Yea my bad
brazen vector
But this definition is more rigorious then intuition
I don't see rigor in there
I see unaccepted numbers appearing
Numbers which don't satisfy our condition of x being close to 1
Sorry but I gtg sleep now it's late in my time cyaaa
Nice to meet you , this was a nice conversation and have a nice day/night
true eagle
.close
drowsy flare
pearl pondBOT
grizzled raft
whats the translation
drowsy flare
The ^2 of the imaginary unitn= -1
drowsy flare
whats the translation
ixi = -1 thats what it saya
grizzled raft
whats ixi
grizzled raft
The ^2 of the imaginary unitn= -1
thats impossible
a square of any real number will always be positive
o hwait
imaginary unit
idk
drowsy flare
<@&286206848099549185>
pearl pondBOT
@drowsy flare Has your question been resolved?
pearl pondBOT
@drowsy flare Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
How should one go about solving this? The explanation did not make much sense on khan academy (ignore my answer, I just put something down randomly)
surreal coral
jolly parrotBOT
taro
midnight haven
I see
ok so pairing this with the KA explanation it makes more sense
if this discriminant is <0 then no real roots cause you cant sqrt a negative?
pearl pondBOT
@midnight haven Has your question been resolved?
worldly glacier
pearl pondBOT
worldly glacier
so I was able to prove the case where you just had column vectors in R^n
but uh
a little confused on how to approach this
so what I have proven so far
let $ b_oI_n + b_1A + .... + b_kA^{k} = 0_{nxn} = C \in R^{n x n}$
I proven that for a column vector i in C, it is equal to $\sum_{n=0}^{k}b_n(A^{n}e_n)$
<@&286206848099549185>
jolly parrotBOT
nosqldb
worldly glacier
.close
shell moat
hi, is possible to write for extension the next set?
pearl pondBOT
hi, is possible to write for extension the next set?
shell moat
and if it can, is it correct?
jolly parrotBOT
ℝam()n()v
light helm
your values would need to satisfy both conditions
shell moat
your values would need to satisfy both conditions
so is this incorrect? C = {3, -3, 8} because the 8 don't satify the first condition
and the correct answer would be C = ∅ or C = {}
light helm
yeh
pearl pondBOT
pearl pondBOT
Available help channel!
opal forge
pearl pondBOT
opal forge
How to solve this?
pearl pondBOT
@opal forge Has your question been resolved?
opal forge
https://www.youtube.com/watch?v=QmvORSJUHXY&ab_channel=Doubtnut
I know every question is available on doubnut topper
opal forge
.close
pearl pondBOT
pearl pondBOT
Available help channel!
untold cloud
Is this correct?
pearl pondBOT
Is this correct?
untold cloud
hollow condor
especially when it doesn't even have a file extension
untold cloud
hollow condor
which part do you need help with
untold cloud
which part do you need help with
All six questions
Need to make sure I got all of them right
hollow condor
if you don't need help with the question itself and just want to verify the answers, you're better off using an online calculator
untold cloud
if you don't need help with the question itself and just want to verify the answ...
Alr will do
Thanks for helping me out
languid coyote
junior pawn
I'm trying to calculate the double sum below
pearl pondBOT
I'm trying to calculate the double sum below
half vapor
I'm trying to calculate the double sum below
first to second line is wrong
you don't have p terms
you sum goes from 1 to infinite
pearl pondBOT
@junior pawn Has your question been resolved?
pearl pondBOT
@junior pawn Has your question been resolved?
willow laurel
pearl pondBOT
willow laurel
Someone please help i have been trying to solve it’s not the right answer
old marsh
$\sqrt {8x} - 1 = \sqrt {6x + 13}$
jolly parrotBOT
Stephen
old marsh
Is the whole 8x under the square root? Or just the 8
willow laurel
**Stephen**
this is correct
jolly parrotBOT
Stephen
old marsh
Now what after this
old marsh
Good and then it becomes
cedar scarab
Quick interjection, $(\sqrt(8)x)^2$ isn't 8x.
jolly parrotBOT
Narutoes
old marsh
$-2\sqrt {8x} = -2x + 12$
willow laurel
it isnt?
cedar scarab
You have to square the x too.
jolly parrotBOT
Stephen
willow laurel
so 8x^2
cedar scarab
Oh I though you said that only the 8 was squared.
There was many things said, apologies.
old marsh
Yea I think both the 8 and the x are under the radical
old marsh
**Stephen**
Ok so back to this
willow laurel
we divide -2?
willow laurel
8+6
old marsh
$\sqrt {8x} = x - 6$
jolly parrotBOT
Stephen
old marsh
Yes?
willow laurel
my bad x-6
old marsh
Now what from here
willow laurel
then squared
willow laurel
x^2 + 49x + 36
old marsh
49?
jolly parrotBOT
Stephen
old marsh
It’s aight
willow laurel
-20x + 36
old marsh
18 and 2 or -18 and -2
willow laurel
positivbe 18 and 2
old marsh
But it’s -20x+36
willow laurel
-18 and -2
willow laurel
18 and 2?
old marsh
Ye
willow laurel
stepehen may you watch throguh one more of my thing
old marsh
Now plug back into original equations
willow laurel
i want to see if i get it correctly
willow laurel
Now plug back into original equations
only 18 works
ok i will do this
give me a min to complete
may i ping?
old marsh
What’d u get
pearl pondBOT
@willow laurel Has your question been resolved?
willow laurel
pearl pondBOT
pearl pondBOT
@willow laurel Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
frosty vale
HELP!
toxic lichen
!status
pearl pondBOT
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
why the dot-dot-dot?
frosty vale
bad habit
toxic lichen
right, anyway.
frosty vale
...
toxic lichen
i'd begin by finding the value of p here
frosty vale
sorry
frosty vale
i'd begin by finding the value of p here
its 0.15
toxic lichen
there was zero point in concealing your progress
so you know the probability of rolling a four is 0.15
find the probability of this happening either 0 or 1 times in 3 rolls
the number of fours in 3 rolls of this die follows a Binomial(3, 0.15) distribution
toxic lichen
???
frosty vale
i mean 0.15
toxic lichen
so whenever you mean 4, i must read it as 0.15?
frosty vale
no
i get it now
yes please carry on
what i don't know is the steps
in some the solutions i saw to this
toxic lichen
the number of fours in 3 rolls of this die follows a Binomial(3, 0.15) distribution
do you know what this means
toxic lichen
the score is 4 on not more than 1 of the 3 throws
literally says so in the problem!
frosty vale
...
latent dragon
Hi and thank you! I need to calculate the limit. I have x1 and xn+1 of series, but idk how to get xn(((
pearl pondBOT
Hi and thank you! I need to calculate the limit. I have x1 and xn+1 of series, b...
@latent dragon Has your question been resolved?
pearl pondBOT
@latent dragon Has your question been resolved?
pearl pondBOT
@latent dragon Has your question been resolved?
woven matrix
lim x_n is 0 as a consequence of Banach fixed point theorem
by the same theorem, you can have some results about lim x_n/x_n+1
pearl pondBOT
@latent dragon Has your question been resolved?
gusty prism
pearl pondBOT
gusty prism
hello
I am currently struggling finding the x intercept 😭
like i cant factor it out
autumn topaz
just set y=0
autumn topaz
no
pearl pondBOT
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.
@gusty prism Has your question been resolved?
tepid panther
Is this right?
pearl pondBOT
Is this right?
tepid panther
@vocal grail (could you come back and take a look? 
)
Could you help me after you're done with them?
midnight haven
They chose the only weeb they knew
pearl pondBOT
@tepid panther Has your question been resolved?
midnight haven
$$A = { 1 , 2, .. n }$$
$$B = {x | x \subseteq \mathbb{P}(A), \abs{x} = i , i \in \mathbb{Z}}$$
$$\forall i, \abs{B} = ?$$
jolly parrotBOT
help me
midnight haven
?
wild fable
I'm finding the solid generated from $y=\sqrt{x}\left{0\le x\le4\right}$, when rotated about the x-axis. is this the right integral? $V=\pi\int_{0}^{4}\left(\sqrt{x}\right)^{2}dx$
jolly parrotBOT
water beam
toxic lichen
yeah seems fine to me
wild fable
okey
and another one, the region bounded by the line y = 3-x and the x and y axis, rotated about the x-axis. I would be finding this area rotated about the x axis right?
(same problem)
and that would make like a pyramid i think
when I use disk for this
do I just use y = 3 - x
as my f(x)
oh yeahh
thats right
$V=\pi\int_{0}^{3}\left(3-x\right)^{2}dx$
jolly parrotBOT
water beam
silent shadow
Im stuck on Q17, ive tried using a table but unsute where to go from there
silent shadow
can you show the table you made
Srry had to do something
Its a bit messy but here
toxic lichen
ok great
that table looks correct
now look which of the middle 4 boxes fit into the event A ∪ B'
silent shadow
Yeah i tried that thats where i made the mistake of picking 0.2
I feel like the answers might be wrong on this one
lunar rain
could someone explain how to solve these? simply. thanks!
pearl pondBOT
could someone explain how to solve these? simply. thanks!
@lunar rain Has your question been resolved?
lunar rain
<@&286206848099549185>
lunar rain
<@&286206848099549185>
old geyser
could someone explain how to solve these? simply. thanks!
What have you tried
pearl pondBOT
@lunar rain Has your question been resolved?
noble scaffold
could someone explain how to solve these? simply. thanks!
What's the level of knowledge? Do you know what Asymptotes are? @lunar rain
unreal flume
pearl pondBOT
unreal flume
Not sure how to start
strange quiver
,rotate
jolly parrotBOT
unreal flume
strange quiver
then we get n*pi/6=2pi
strange quiver
$1=e^{2\pi i n}$
jolly parrotBOT
WhereWolf(ping if needed)
unreal flume
But how?
strange quiver
for a complex number $re^{i\theta}$ theta represent the angle
jolly parrotBOT
WhereWolf(ping if needed)
strange quiver
and $\theta+2\pi n=\theta$
jolly parrotBOT
WhereWolf(ping if needed)
strange quiver
so $1=e^{0*i}=e^{2\pi i}$
jolly parrotBOT
WhereWolf(ping if needed)
tribal badger
What am I doing wrong here? the site It still says something is wrong
tribal badger
Need help asap my assignment is due in like 5 mins 😭 <@&286206848099549185>
glad galleon
Did you just guess
strange quiver
just draw the angles out
tribal badger
I did and thats what i came up with
I took theta as 60 degrees
A and b are x and y coordinates btw
tribal badger
60 - 180 is -130 so its in quadrant 3 so -a and -b
180 - 60 is 120 its in quadrant 2 so -a and +b
pearl pondBOT
pearl pondBOT
Available help channel!
uneven canopy
I'm told to find all taylor polynominals for f(x)=x^4 - 3x^3 + x^2 + 2x - 4 centered in x = 2.
So am I just supposed to set a to 2 in the taylor series formula and that's it? Doesn't that solve the exercise? It just seems too simple... Am I missing something?
frigid horizon
That's just it.
heady oak
pearl pondBOT
heady oak
how would i do this
pearl pondBOT
@heady oak Has your question been resolved?
heady oak
<@&286206848099549185>
shy stratus
if x+2 is factor of $x^3-2kx^2+6x-4$,
jolly parrotBOT
A_Note
shy stratus
$(-2)^3-2k(-2)^2+6(-2)-4 = 0$
jolly parrotBOT
A_Note
shy stratus
because $x^3-2kx^2+6x-4$ = (x+2)Q(x)
jolly parrotBOT
A_Note
twin glacier
HELP
winter agate
How do I do this?
pearl pondBOT
How do I do this?