0.78, 0.708, 0.7008 etc
#help-33
unreal oxide
marsh citrusBOT
Available help channel!
crimson perch
marsh citrusBOT
crimson perch
,rotate
elfin berryBOT
crimson perch
why the f am i getting the negative of the answer
wait
im stupid
i have to change boundds
oops
lol
.close
uneven vector
marsh citrusBOT
uneven vector
so i was able to do A)
but im completelyy stuck on b
so i think P is the starting point?
and 2g(-x) is the translation
.close
long cape
marsh citrusBOT
long cape
Anybody else feel like a pirate when they use the Quotient Rule?
worn nimbus
half rampart
I'm trying to get the eccentricity of an orbit inside lua code, but it just isn't working right.
It should have an eccentricity close to 0 (I set the velocity to a near circular orbit's velocity) but instead, it has an eccentricity very close to 1. I feel like it's the Specific Angular Momentum, but I really don't know. (by the way, all the vectors are aligned always)
marsh citrusBOT
I'm trying to get the eccentricity of an orbit inside lua code, but it just isn'...
north sparrow
I'm trying to get the eccentricity of an orbit inside lua code, but it just isn'...
how did you get that denominator?
Also, is this eccentricity formula not under one big square root?
marsh citrusBOT
@half rampart Has your question been resolved?
half rampart
how did you get that denominator?
Also, is this eccentricity formula not under o...
sorry I'm back
I found it on a website with formulas for eccentricity
because all the other formulas I got the same answer
so I don't really know whats going on any more
north sparrow
this is the closed I can find to yours
half rampart
this is the closed I can find to yours
yeah that's the formula I'm pretty sure
north sparrow
gonna be hard getting anything close to 0 with this right
half rampart
gonna be hard getting anything close to 0 with this right
I'd think so
I'm a 9th grader trying to understand this stuff lol
north sparrow
the right part stays posetive, and you have 1+..., so root
half rampart
the right part stays posetive, and you have 1+..., so root
so square root it?
north sparrow
I think
half rampart
oh yeah wait I'm blind hold on
north sparrow
they also don't seem to square gravitational constant
half rampart
they also don't seem to square gravitational constant
This is what it returned
before and after removing the exponet on the gravitational constant
which is really wierd
north sparrow
is the magnitute of your velocity zero?
half rampart
is the magnitute of your velocity zero?
no I know the velocity isn't zero
lemme actually make it show me every value rq
north sparrow
yeah, check if that right part alone gives 0
marsh citrusBOT
north sparrow
.reopem
half rampart
.reopen
marsh citrusBOT
✅
half rampart
whats the result of the eccentricity formula without the root and 1+ ?
lemme see
this number
which is definitely wrong
half rampart
well I mean it's relative to the earth
north sparrow
ofc, its comparative to the total energy
half rampart
yeah
north sparrow
this number
this funny value here should be less than 1 and more than -1
half rampart
this funny value here should be less than 1 and more than -1
yeah
wait how would you have negative eccentricity?
north sparrow
isn't that just the right part?
half rampart
isn't that just the right part?
well an eccentricity of 0 is a circlular orbit
then 0 - 1 is elliptical
- eccentricity isn't a thing
or shouldn't be at least
north sparrow
well an eccentricity of 0 is a circlular orbit
no, I mean, isn't that just the right term of the equation
so 1 gets added afterwards
north sparrow
right, it should be between 0 and -1
half rampart
yeah I forgor
north sparrow
the 4k mass is the satelite?
what is earth compared to that
north sparrow
how are we dividing by 10^48 and still get a high number
half rampart
I have no idea
half rampart
I'm just very confused
elfin berryBOT
Jigglyproff
north sparrow
like, sus small
half rampart
it's not that close to parabolic*
half rampart
I feel like it has something to do with one of the terms in the problem tbh
which is common sense right
north sparrow
but u doing this right
half rampart
but u doing this right
yes
north sparrow
kekw
half rampart
????
marsh citrusBOT
@half rampart Has your question been resolved?
marsh citrusBOT
@half rampart Has your question been resolved?
marsh citrusBOT
@half rampart Has your question been resolved?
half rampart
no kind sir it hasn't
half rampart
<@&286206848099549185>
marsh citrusBOT
@half rampart Has your question been resolved?
marsh citrusBOT
@half rampart Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
burnt abyss
marsh citrusBOT
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
Model the growth with an exponential function. The initial value is 800.
a) The stock is shrinking by 8% every day.
b) The stock grows monthly by 13%.
c) After one year the stock is 768.
d) After three weeks the stock is 409.6
Im at 2
This is my work
elfin berryBOT
marsh citrusBOT
@burnt abyss Has your question been resolved?
burnt abyss
<@&286206848099549185>
marsh citrusBOT
@burnt abyss Has your question been resolved?
marsh citrusBOT
@burnt abyss Has your question been resolved?
burnt abyss
<@&286206848099549185>
spark siren
$f(t)=800\cdot 0,92^t$
elfin berryBOT
ThM
burnt abyss
why
spark siren
it shrinks by 8% per day.
burnt abyss
ok and
spark siren
and what?
burnt abyss
and how do you get to 0.92
spark siren
100 percent minus 8 percent are how many percent?
spark siren
if it would neither grow nor shrink it would stay constant.
burnt abyss
so 800?
spark siren
yes
burnt abyss
ok
now at b)
a) The stock is shrinking by 8% every day.
b) The stock grows monthly by 13%.
c) After one year the stock is 768.
d) After three weeks the stock is 409.6
800*(100+13)%^t?
spark siren
if it would grow we would add.
this
burnt abyss
,calc 113/100
elfin berryBOT
Result:
1.13
yes, but why 900?
burnt abyss
typo
spark siren
ok
elfin berryBOT
Result:
0.96
burnt abyss
800*0.8^t
spark siren
yes. but: be aware you have different periods. in a) f(1) is one day later, in b) one month, in c) one year .... you are maybe asked to have always days odr always month ...
burnt abyss
im not
i also checked the answer
with the back of the book
and it's correct
can you help me with another one?
it's the next exercise
spark siren
i can try it.
burnt abyss
thx
1 sec to get my phone and take a picture
500 pasque flowers are blooming in a meadow. 32% of the remaining flowers wither every day. After how many days does only one pasque flower bloom?
so
our a is 500
the initial number of flowers
f(0)=500
and we need to do
500*(100-32)%^t
,w (100-32)/100
elfin berryBOT
burnt abyss
500*0.68^t
spark siren
ok so far.
spark siren
yes
burnt abyss
,w 500*0.68^t=1
elfin berryBOT
spark siren
just to test: what is f(16)?
burnt abyss
,w 500*0.68^16
elfin berryBOT
burnt abyss
👍
spark siren
and f(15)?
burnt abyss
,w 500*0.68^15
elfin berryBOT
spark siren
is your answer still 16?
burnt abyss
yes
spark siren
why?
burnt abyss
1 flower needs to remain
at 15, 1.5 flowers remain
at 16, 1.04 remain
so basically 1
spark siren
its your example. you can count partial flowers as blooming, then you have 1.04 after 16 day which is more then 1. or you can say, we wouldnt count partial flowers so you are some days earlier below 2. so my answer wouldnt be 16. maybe 17 something earlier. but its your example. and your answer.
elfin berryBOT
elfin berryBOT
burnt abyss
so we could say the answer is 16.11
or close to 16 days
@spark siren do you agree?
spark siren
i just said all what i wanted to say some minutes before.
spark siren
number 8?
burnt abyss
no that;s easy
number 16
1 sec
During thyroid scintigraphy, a patient is injected with radioactive iodine 123. It has a half-life of 13.22 hours.
a) What proportion of the sprayed 1123 is still present after 5 hours?
b) After what time has 99% of the 1123 decayed?
Half-life basically means it halfens after 13.22 hours
so i know a^half time=1/2
,w a^13.22=1/2
hm
a is 0.94
spark siren
it is like the "easy" number 8. you have two points (0,1) and (13.22,0.5)
burnt abyss
why
spark siren
can you be more detailed in your question?
burnt abyss
i dont understand how you got to that conclusion
you have two points (0,1) and (13.22,0.5)
spark siren
it is just the written words. At start (t = 0) you have 100% (=1). After 13.22 hours (t=13.22) you have te half left.(=0.5).
burnt abyss
yes
spark siren
so you have a function y = c a^t with 2 points (0,1) and (13.22,0.5), just as in Number 8.
burnt abyss
y=a*x^t
spark siren
if you like, in this notation, it is ok for me.
spark siren
when a function $y = a\cdot x ^t$ has a point (0,1) then a = 1.
elfin berryBOT
ThM
spark siren
maybe we should do number 8 first - seems it is not so easy.
spark siren
then what is your question? you know haow to make 8. 16a is just the same as 8.
spark siren
I would use more decimal places.
elfin berryBOT
burnt abyss
0.77
so after 5 hours there is 77% left
that's what they got too
now b)
when will 1% remain
spark siren
it is just the same as the flower example.
spark siren
the same at the flower example. you have a function and you search for a x-value which results in a given y-value.
spark siren
how much is it after 13.22 hours?
spark siren
half what?
burnt abyss
?
oh shit
a is 1
yes
so half of 1
after 13.22 hours
meaning that
1% times 1 is 0.01
,w 0.949^t=0.01
elfin berryBOT
burnt abyss
88 hours
meaning almost 4 days
thanks so much @spark siren
i love you
.close
static kernel
got the answer for part a, but how would you evaluate a 1 line answer for part 2?
marsh citrusBOT
got the answer for part a, but how would you evaluate a 1 line answer for part 2...
static kernel
part a limit = -1/24
desert dirge
the expression for (ii) (ignoring the limits) is the expression of (i)-1
so its the result of (i) - lim(1)
@static kernel
static kernel
why is it -1?
desert dirge
its the same as the first expression - (x-2)/(x-2)
you can see if you look at the ends of the numerators
static kernel
right right
i see
so you get
but how do you know that the bit before -1 is equal to the original equation?
desert dirge
by just looking at it? idk what you mean, you can see they are the same expression
btw you forgot the -4
which might be the source of your confusion
static kernel
so I applied summation properties of limits rule to ii
and took limt of x-2/x-2
=1
and i got that -1 for ii
but in the first equation i) there is a -4 so I dont see how they are the same
desert dirge
-4 - (-2) = -2
the -4 is still there
when you subtract 1 from the expression it becomes -2
static kernel
wait
desert dirge
in this image, the -4 should be in the numerator still
desert dirge
i know, so am i
desert dirge
static kernel
I dont get why there would be 4
desert dirge
,rotate
elfin berryBOT
static kernel
im a little confused how you got the first step
wouldnt the first step be the answer
and im a little confused what I did then
was I not supposed to break the limit up in ii)?
desert dirge
i did it in reverse to show you the -4 is still supposed to be there
static kernel
oh I see
desert dirge
the first line is what you use to find the answer of ii
its just the answer of (i) -1
static kernel
so I see how
working backwards
from that
you can get it
actually im just not sure how your getting the -4
desert dirge
the -4 is just in the question in the first place from (i)??
static kernel
to me it looks like the -4 just spawned in the numerator and your subtracting 1 in the form (x-2/x-2)
right but I dont get that ii) = i-1 still
i get that
if you know that
it makes sense
you can just sub the original equation
desert dirge
the question said its a one line thing - i just recognised that the numerator of ii = the numerator of i - (x-2). By that logic the entire expression of (ii)= the expression of (i)-1
since the denominator is x-2
static kernel
the question said its a one line thing - i just recognised that the numerator of...
what about the -4 in i)
wouldnt it be i) +4 - (x-2)
static kernel
youd have to plus 4 to take it out and then do -x-2 no
elfin berryBOT
desert dirge
you do not +4 - that doesnt happen anywhere
youre just adding two fractions
im not sure how i can really make it clearer
theres not much to show
desert dirge
like this
static kernel
like whats happening to the 4
desert dirge
the 4 is not disappearing or anything
at the end of the numerator after adding you have -4-(x-2)
that is why it becomes -4-x+2=-x-2
im not removing the 4, im just adding the fractions
desert dirge
like in the second line
desert dirge
Yeah
vestal pilot
$\lim_{x \to 0} \frac{\sqrt{1+x}+1}{x}$
marsh citrusBOT
$\lim_{x \to 0} \frac{\sqrt{1+x}+1}{x}$
proud ice
elfin berryBOT
afeAlway
vestal pilot
I tried using L'Hopitals rule and got 0
because the derivative of the nominator is $\frac1{2\sqrt{1+x}}$ and the derivative of x is 1. So we can ignore the denominator. And just put in 0 in the nominator instead of x which will be.
.close
elfin berryBOT
afeAlway
marsh citrusBOT
marsh citrusBOT
Available help channel!
vestal pilot
You can't use hospital here btw
I closed it, while writing my question, I realised where I made the mistake so it is all fine now about that.
marsh citrusBOT
I closed it, while writing my question, I realised where I made the mistake so i...
vestal pilot
Find all the asymptotes of $f(x) = x − \arctan(x) + \frac1{x−1}$
elfin berryBOT
afeAlway
vestal pilot
I found one vertical asymptote and it is x=1 since the limits of it goes to infinity at that point.
I also thought -pi/2 and pi/2 would be vertical asymptotes since they are not defined for arctan and the closer it comes to +/- pi/2 the function as a whole goes to positive and negative infinity according to me but apparently I was wrong. Why?
proud ice
You're thinking of tan
vestal pilot
You're thinking of tan
shit you're right arctanx can take in all x's right?
Okay then I tried seeing if it has horizontal asymptotes
As x goes to infinity, I get $\lim_{x \to 0} \infty + 0= \infty$
elfin berryBOT
afeAlway
vestal pilot
You're thinking of tan
So it doesn't have horizontal aymptote. Is my explanation right?
proud ice
That explanation works for me, yeah
vestal pilot
Ok then we can move to slant asymptote. That is where I am kinda facing a problem
This is the formula I used $\lim_{x \to \infty} \frac{f(x)}{x}$ but for some reason it is not working for me?
elfin berryBOT
afeAlway
vestal pilot
That explanation works for me, yeah
I should be able to get the a in y=ax+b using this right?
proud ice
I do not knot what you mean
vestal pilot
I do not knot what you mean
where?
proud ice
Where did y=ax+b come from
vestal pilot
Where did y=ax+b come from
it is the formula for a slope and the there $a=\lim_{x \to \infty} \frac{f(x)}{x}$
elfin berryBOT
afeAlway
proud ice
Oh you're trying to find the line asymptote of the function
Have you learned derivatives yet
vestal pilot
Have you learned derivatives yet
yes
proud ice
Derivative at x will give you slope at x
vestal pilot
Derivative at x will give you slope at x
huh?
but I want the slope of the asymptote
proud ice
Stands to reason the limit of derivative as x approaches infinity will give you your asymptotic slope
vestal pilot
the derivative has different slope depending on x
vestal pilot
Stands to reason the limit of derivative as x approaches infinity will give you ...
that could work but in order to do that I still need to know if the funciton has a slope asymptote tho so how do I do that?
vestal pilot
Take the limit of the derivative
but I feel like that is kinda what I was doing techinically?
$a= f'(a) =\lim_{x \to \infty} \frac{y-f(a)}{x-a}$
proud ice
$a= f'(a) =\lim_{x \to \infty} \frac{y-f(a)}{x-a}$
This is incorrect definition of derivative
That's why it does not work
elfin berryBOT
afeAlway
proud ice
Still incorrect
vestal pilot
Still incorrect
I know that the derivative is $f'(a) = \frac{y-f(a)}{x-a}$ but I need it when a goes to 0?
elfin berryBOT
afeAlway
proud ice
I know that the derivative is $f'(a) = \frac{y-f(a)}{x-a}$ but I need it when a...
This is not true
marsh citrusBOT
@vestal pilot Has your question been resolved?
vestal pilot
Draw the graph of $f(x)=xe^{-x^2}$
marsh citrusBOT
Draw the graph of $f(x)=xe^{-x^2}$
elfin berryBOT
afeAlway
vestal pilot
I was trying to see if it had an asymptote. It doesn't have a vertical asymptote since all x's are defined for it. Then we come to horizontal asymptote. There I have a problem since I get $a=\lim_{x \to \infty} \infty e^{-\infty} = \infty * 0$. But this is not defined tho so what I should I do?
elfin berryBOT
afeAlway
glass silo
Exponentials beat powers - that limit is zero
vestal pilot
Exponentials beat powers - that limit is zero
wdym?
river trench
If you want to work it out, use L'Hopital's rule
proper zodiac
other advice look for calculate extrema and intervals of increase/decrease
vestal pilot
If you want to work it out, use L'Hopital's rule
That is what I was implying but how do I make it look like infinity/infinty or something like that so I can use L'Hopital?
river trench
The negative exponent can be written as a fraction
vestal pilot
The negative exponent can be written as a fraction
you're right!!
glass silo
wdym?
$e^{x^{2}}$ grows much faster than $x$, so $\frac{x}{e^{x^{2}}} = x e^{-x^{2}}$ goes to zero as $x\to\infty$
elfin berryBOT
chartbit
vestal pilot
**chartbit**
Now the only thing left to do it to check if it has slant asymptote
I was thinking of doing $a=\lim_{x \to \infty} \frac{f(x)}{x}$ where a is in y=ax+b
elfin berryBOT
afeAlway
vestal pilot
it doesn't have a slant asymptote
river trench
The function has a horizontal asymptote, so it can't have a slant asymptote
vestal pilot
right?
river trench
yes
vestal pilot
yeah true!
proper zodiac
other advice ~~look for~~ calculate extrema and intervals of increase/decrease
finding extrema now should give you enough info to sketch
vestal pilot
finding extrema now should give you enough info to sketch
yeah exactly!
wait guys so
f'(x) =0, I got x=+/- (1/sqrt(2))
vestal pilot
finding extrema now should give you enough info to sketch
According to the second derivative I got for 1/sqrt(2), I get a max. For -1/sqrt(2) I get min.
proper zodiac
yep sounds good
vestal pilot
But how do I find f(1/2^0.5) without a calculator?
proper zodiac
er you dont really
but you're just drawing a graph it doesnt matter what the exact value is
vestal pilot
er you dont really
why? How do I know where the max/ min value of x are then?
proper zodiac
just approximate it, as long as the graph roughly looks the right shape no one is going to chastise you for it
vestal pilot
$e^{x^{2}}$ grows much faster than $x$, so $\frac{x}{e^{x^{2}}} = x e^{-x^{2}}$ ...
Also I checked answer and they don't seem to have any type of asymptote in the graph
vestal pilot
just approximate it, as long as the graph roughly looks the right shape no one i...
I did but the graph I got looks nothing like the answer or geogebra
proper zodiac
what did you draw
vestal pilot
what did you draw
Mine has a horizontal asymptote in y=0.
proper zodiac
as it should
vestal pilot
It looks so wrong I don even think it is worth mentioning it
proper zodiac
you should send a picture of your graph
proper zodiac
a horizontal or slant asymptote yes
vestal pilot
you should send a picture of your graph
In that case then mine looks right too now that I have connected the graphs but when do I know if a graph crosses it's asymptote?
proper zodiac
well you can just draw it and look like you did
vestal pilot
But my inital thought was draw a concave and convex functions that never meet. As in one under the x axis and one above x axis. The closer both come to y=0 the function goes to infinty was my thought?
vestal pilot
well you can just draw it and look like you did
So how do I not make the same mistake again?
proper zodiac
i have no idea what mistake you made bc i havent seen a single graph you've produced
vestal pilot
i have no idea what mistake you made bc i havent seen a single graph you've prod...
ok here is a quick grpah I drew that looks like mine
proper zodiac
right well your mistake there was you didn't even draw a function
vertical line test..
vestal pilot
vertical line test..
Shit you're right! Is that the only reason tho?
Lets say I instead didn't draw x>0 for the bottom function and x<0 for the above
Why wouldn't it be okay?
vestal pilot
still not right
Yeah of course so bottom line is that I need to check if it crosses x and y axis before drawing a function like this?
It is not enough to just find the min/ max and asymptotes?
proper zodiac
yeah you should probably always check for axis intercepts additionally
vestal pilot
If you don't mind I've one last question I am stuck at
Does the function have a min and max value $f(x) = \arctan x− \frac1{1+x^2}$?
elfin berryBOT
afeAlway
vestal pilot
So I differentiated and got $f'(x)= \frac1{x^2+1} + \frac{2x}{(1+x^2)^2}$. Then what I did is $f'(x)=0 <=> x^4+2x^3+2x^2+2x+1=0$. But there is no way I can solve that without a calculator is there?
elfin berryBOT
afeAlway
proper zodiac
where did you get that quartic from?
vestal pilot
by moving 2x/(1+x^2)^2 to the other side and then simplifying
proper zodiac
yeah that gonna make your life harder
vestal pilot
yeah that gonna make your life harder
But wouldn't it be the same, I need to make their denominators the same so the nominators will get as complicated as this right?
proper zodiac
one of the denimoninators is just the other one squared
so the numerators dont get that complicated
way less complicated than a 4th degree poly
vestal pilot
one of the denimoninators is just the other one squared
you're right. (How come I keep missing these simple details lol)
so x^2+2x+1=0
right?
proper zodiac
yes
vestal pilot
x=-1
vestal pilot
yes
Anyways isn't the domian of this function all real numbers?
The answer says [-pi/2, pi/2]
proper zodiac
you are being told the domain of the function is [-pi/2,pi/2]? are you sure?
vestal pilot
you are being told the domain of the function is [-pi/2,pi/2]? are you sure?
Yes at first I thought it was because of the def tan. But arctan can take in all x's right?
proper zodiac
yes
marsh citrusBOT
@vestal pilot Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
heady kernel
Not sure how to do part b. I've tried doing the 2-path test but all the paths i've gotten are the same yet wolfram alpha is telling me the limit doesn't exist
marsh citrusBOT
Not sure how to do part b. I've tried doing the 2-path test but all the paths i'...
@heady kernel Has your question been resolved?
flat raft
if you graph it
you might be able to find paths that result in different values
in particular, I think you get different values if you take a path on that tear
my guess would be if you look at the difference between approaching on something slightly below y = x and something slightly above y = x
heady kernel
thanks i was able to find a different path
do have any recommendations on how best to solve this without graphing it tho lol
or is it kinda just guess and check
heady kernel
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
I am unsure how to write conjectures and converses, can anyone help?
bleak reef
marsh citrusBOT
@still temple Has your question been resolved?
still temple
.close
harsh pumice
How do I solve this equation? I do not know how to start.
marsh citrusBOT
How do I solve this equation? I do not know how to start.
open shale
marsh citrusBOT
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
warped wind
Guys complex numbers aren't useless
Everything is useless if you're dumb enough
Which I am
fathom ridge
I said I didn't know where to start..
Well what did you try
fathom ridge
Write it as a complex number and multiply by *i*
This is as fast as it gets
Have you learnt about complex numbers btw?
harsh pumice
No
harsh pumice
is there another way I can do it
fathom ridge
What you can do is find the line passing through (5, 4) and the origin, and then find a line perpendicular to it (passing through the origin as well), then find a point on that line a distance of √(5^2 + 4^2) from the origin (logically in the second quadrant because counter-clockwise)
You should get (-4, 5) after doing all that
warped wind
Generally a point (x, y) is rotated 90° counterclockwise by doing (-y, x).
I don't really know how to show it without complex numbers, but you could think of it as taking the axes and rotating them 90° counterclockwise such that the positive numbers on the y-axis "goes to" the negative numbers on the x-axis, the negative numbers on the x-axis "goes to" the negative numbers on the y-axis and so forth for all 4 directions in the plane ℝ²
And such will the points follow the same rotation around as the axes
marsh citrusBOT
Available help channel!
wraith trench
hello, how can I solve this problem?
marsh citrusBOT
hello, how can I solve this problem?
late geode
marsh citrusBOT
@wraith trench Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
barren lance
I know this is a p serie which converge but do u also know where it converges to?
marsh citrusBOT
I know this is a p serie which converge but do u also know where it converges to...
main idol
I know this is a p serie which converge but do u also know where it converges to...
pretty sure that's an open question
barren lance
what is a open question
main idol
,w sum n=1 to inf n^(-3/2)
elfin berryBOT
proper zodiac
wow wolfies first open problem solve
barren lance
what I don't understnad
main idol
it's approximately 2.6124, but nobody knows if it's expressible in algebraic terms. or if it is, it's probably beyond the scope of your class
main idol
complicated
barren lance
oh my question is more general
say for example this
do I know what it converges to
I know it converges cuz p = 2
elfin berryBOT
riemann
main idol
,w sum n=1 to inf n^(-2)
elfin berryBOT
barren lance
ye but I need to know how u do it
main idol
ye but I need to know how u do it
do you?
main idol
and why can't i use integral test?
integral test doesn't ever tell you the value of a series or integral
main idol
barren lance
ahh
civic blade
divergence test also not?
none of the tests give u the value of the sum
it just gives u info on whether or not it may converge or diverge
barren lance
well so I can't calculate the value which it converges to?
civic blade
you can, just not with those tests
barren lance
but how did riemann knew the answer
civic blade
it's a popular one
barren lance
oh
main idol
ye but even with calculator I still don't see how to get this
if you don't need to, don't bother
civic blade
ask euler, he did it first
civic blade
I onlyt know how to calculate geomtric series
that's okay, series and sums can be hard
main idol
skim these if you want, but again, you absolutely don't need to
https://math.stackexchange.com/questions/187295/a-geometric-proof-of-zeta2-frac-pi26-and-other-integer-inputs-for-the
https://math.stackexchange.com/questions/8337/the-basel-problem
barren lance
ye I guess I skip that
barren lance
skim these if you want, but again, you absolutely don't need to
https://math.st...
btw did you finish all of calculus?
proper zodiac
yeah he completed calculus a couple years ago
civic blade
most people finish calc pretty early on
barren lance
and linear algebra?
civic blade
mhm depends, but lin alg is like 2nd year in college course
well it depends
I took it my 2nd semester
barren lance
linear algebra a modern introduction that one
civic blade
wym
civic blade
uhh
I don't think so?
I can check the textbook we used
one sec
we used this
barren lance
oh I but I could ask those questions too?
civic blade
Yeah sure, i just don't respond to them lol
others here are good at stats so they can help you instead !
civic blade
oh this is calc
civic blade
less than
so it's clearly divergence for all positive p
and at p=0 its also divergent since it's the sum of n to infinity
so then we have negative values that it can be
barren lance
oh so p has to be below -0.5
civic blade
mmm no, that was an asumption made to use the integral test
but the actual value is p < - 1
bc when u do the integral test u will get that this
is gonna get u to...
one sec lemme write it out
barren lance
wait so I gotta assume p < -0,5
because
then the n^2 is like n^-1 maximal
and I can bassically ignore the 1
and the p below -0.5 means a smaller number
right?
civic blade
not quite
barren lance
oh so why choose -0.5
civic blade
to get this
civic blade
barren lance
and then I am at this step
civic blade
I wrote the test out in a way that is easier to understand
notice that if the exponent (p+1) is greater than or equal to 0 then it would be divergent
civic blade
so we need to solve for p in the exponent such that it's less than 0 aka
p+ 1 < 0 which gets us p < -1
civic blade
yes
barren lance
ah got it
barren lance
I feel like this wasn't a easy one
civic blade
it's not, no
the asumption to make the function able to be used for the integral test was key
but it's not obvious
barren lance
but why couldn't u instantly assume p < -1
civic blade
u could have but u still have to show the test being done
barren lance
but it's not obvious
ye that was the hard part
but guessing p < -0.5
does that have to di with this
n^2 has to be below n^1
so it compensate for the n
civic blade
tbh u can pick like p < -40 or something and then after doing the test you can get p < -1
civic blade
so it compensate for the n
nah, just a random but reasonable guess
barren lance
huh
civic blade
we just need any p so that the function can be decreasing, continuous, and positive
barren lance
but like
barren lance
any p above -0.5 is divergent obviously no cuz then the n here wouldn't be compensated
if p = -0.5
n^2 will become n^-1
civic blade
yeah
barren lance
and then the n and n^-1 would be comepnsated
civic blade
yeah
barren lance
so that's why u choose below -0.5?
barren lance
what u mean
civic blade
barren lance
but I won'
civic blade
barren lance
get a graph on test prob
civic blade
I know, but just is just to add to what ur saying
like this is basically what's going on
choosing p =- 1
barren lance
wait can u explain the graph
civic blade
I'm trying to say, that as long as it's negative enough u can pick any other negative and it's the same
bc they behave the same
similar*
barren lance
oh always decreasing cts and postivie?
civic blade
yup
barren lance
oh at a = 0 it's not decreasing
barren lance
uh I can see it graphically
civic blade
any p above -0.5 is divergent obviously no cuz then the n here wouldn't be compe...
it's as u were saying
yes
civic blade
let's choose something a bit easier like -.25
so that's x(1+x^2)^(-1/4)
which is
,w x(1+x^2)^(-1/4)
elfin berryBOT
civic blade
this thing at best is not enough
barren lance
wait to check if it's decreasing u gotta get the derivative no?
barren lance
this thing at best is not enough
how can usee it's never decreasing
civic blade
wait to check if it's decreasing u gotta get the derivative no?
true, but u can also just think about how this behaves
barren lance
oh wait the number above is always increasing faster?
right
so it's always increasing?
civic blade
essentailly
barren lance
what u mean by essentially
civic blade
this is just for getting a general idea of what it might be behaving like
but if u have things like
x^2 or somehting then u just know it's claer
barren lance
oh wait so basically everything higher then -0.5 is always increasing? can u say that too
civic blade
oh wait so basically everything higher then -0.5 is always increasing? can u say...
not always
but in our case yea
civic blade
np
barren lance
and ln is undefined if b < 0
so that's also the reason right?
civic blade
yuh
idk why it isn't b >= 0 tho uh
bc ln(0) = 1
anyways, I gotta go to my class so cya
barren lance
ah okay bye
@main idol are u still here?
I can't understand this one
<@&286206848099549185>
main idol
add the fractions
barren lance
add the fractions
wiat but is that not the harmonic series
so 1/ (n+1) goes to 0
so u are left with
and I thought taht 1/i is the harmonic series and that diverges already no?
main idol
you're unjustifiably simplifying
barren lance
oh wait
I did smth wrong?
can u explain it a bit
I feel like I am not getting it
main idol
$\sum(a_n + b_n) = \sum a_n + \sum b_n$ only if each individual sum converges
elfin berryBOT
riemann
main idol
wiat but is that not the harmonic series
as you stated, the harmonic series doesn't, so you can't split the sum
barren lance
at this part
elfin berryBOT
riemann
barren lance
cuz it originates from this
barren lance
$-\frac{a}{b} = (-1) \times \frac{a}{b}$
or am I missing smth?
btw is ur name riemann as in the real riemann sum?
main idol
shouldn't this be in bracket
type what you think should be the correct equation
main idol
or draw brackets over the image
barren lance
oh ye I can do that
so u start with this
this is what I think should be correct
oh wait
barren lance
or draw brackets over the image
what u think?
main idol
no
barren lance
huh
elfin berryBOT
riemann
barren lance
oh wait
main idol
$\frac{a}{b}\left[ - \frac{c}{d}\right ]$ is multiplication
elfin berryBOT
riemann
barren lance
so it's alreaedy outside the summation?
main idol
yes
barren lance
buyt then i can just delete taht as n goes to infinity no?
main idol
if you want it more clear, you add brackets around the summation and summand
$\left(\sum_{i=2}^\y \frac{1}{i}\right) - \frac{1}{n+1}$
elfin berryBOT
riemann
barren lance
$\left(\sum_{i=2}^\y \frac{1}{i}\right) - \frac{1}{n+1}$
ye lim n goes infinity
so right side is 0
right
main idol
yes
main idol
$\frac{1}{n+1} \ra 0$ as $n \ra \y$
elfin berryBOT
riemann
barren lance
so only c = 1 can compensate that
then it's 0 times infinity but how do I know that will be convergent
so c = 1 is the answer I understand cuz then harmonic series times 0
but
how do I know 0 times infinity will converge?
l'hospital?
main idol
the finite sum is not infinity
main idol
nope
main idol
$\sum(a b_n) = a \sum b_n$ only if the sum converges
elfin berryBOT
riemann
main idol
barren lance
ye basically if it's convergent I can take it out
so if c = 1 then it converges to 1 right?
barren lance
yes
in the second point
what if summation bn is alternating divergent then an could be bigger then bn but not alternating and then it converges no?
barren lance
yes
u understand what I mean?
so if there is a summation bn which diverges because it alternates between 2 and 4 idk the function but there probaly exist one. and there is a function an which converges to a finite number and is always bigger then 4 an > bn? could this exist?
anyone?
<@&286206848099549185>
marsh citrusBOT
@barren lance Has your question been resolved?
marsh citrusBOT
@barren lance Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
bright badge
Can someone help me with a task that ist relatet to electical eng. ?!
knotty trellis
just ask, if it will be related to math someone might help
bright badge
What is the value of two ohmic resistors connected in series with the equivalent resistance 18 ohm and have the equivalent resistance 4 ohm in parallel?
thats the question
spark berry
What is the value of two ohmic resistors connected in series with the equivalent...
AH ur asking about the value of each resistor. You will use the resistors in two instances so that u know what is the resistance of both resistor. One is in a series and one is in a parallel
unreal oxide
What is the value of two ohmic resistors connected in series with the equivalent...
Consider their resistances to be r1 and r2
And set up a system of equations
spark berry
Ok I got it
spark berry
And set up a system of equations
Yeah that's what I did
unreal oxide
I got it but i cant figure out the equetions
If r1 and r2 are in series what must be their equivalent resistance
In terms of r1 and r2
spark berry
But @unreal oxide I'm not yet good at matrices and I notice that this one requires system of equation, can we create a matrix for this
?
unreal oxide
But <@811501664367673354> I'm not yet good at matrices and I notice that this on...
We can come up with a matrix yes
spark berry
If r1 and r2 are in series what must be their equivalent resistance
Yeah, then create for the parallel
spark berry
We can come up with a matrix yes
I wasn't really satisfied the way I answered this
unreal oxide
So we can't have a matrix
bright badge
yes
spark berry
But I remember on a jacobian integration video that he used matrices for sin functions?
Can we really not use matrices if it is linear?
bright badge
spark berry
Uhm no
unreal oxide
This is quite unclear