sin? i have not learnt that yet
#help-10
dense tinsel
lone echo
hmmm
dense tinsel
can we do some other version
lone echo
lemme think a bit harder then
dense tinsel
maybe 8 + x = 5 + x
lone echo
no, you're saying that 8=5 there
lone echo
im gonna need a pen for this
dense tinsel
@cursive pagoda ?
cursive pagoda
yes
dense tinsel
oh and by the way e4 buddy
dense tinsel
i just wanted to ask which grade you're studying in
10
dense tinsel
oh and by the way e4 buddy
?
dense tinsel
and you don't know sin yet?
no 💀
cursive pagoda
wow,
dense tinsel
we did it in 8th grade but teacher was a bitch and i memorized nothing
cursive pagoda
lol
dense tinsel
e4
cursive pagoda
oh
lone echo
okay
dense tinsel
?
lone echo
so you got two similar triangles
dense tinsel
YES CHEF
dense tinsel
ight
lone echo
you got the triangle ADE, which have an angle A on A (obviously), an angle of 86º on D, and an unknown angle that we dont care about on E
dense tinsel
sir yes sir
lone echo
you got the triangle ABC which has the same angle A on A (again, obviously), the angle of 86º on B, and an unknown angle that we still dont care about on C
dense tinsel
YES CHEF
lone echo
the length from A to D divided by the length of A to E has the same ratio as the length from A to B divided by the length from A to C, because they are similar triangles
that means that you have:
$\frac{x}{x+2}=\frac{x+5}{x+8}$
warm shaleBOT
LordFelix
lone echo
first try, wohoo!!
dense tinsel
where did u get x+ 5 from
lone echo
(x+2) + 3
dense tinsel
goodjob but hwere did u get x+ 8 from
lone echo
x+5 is the length from A to B
x+8 is the length from A to C
(actually i should put the cm there on the 2, 5 and 8, but i was lazy)
lone echo
that's cheating
dense tinsel
*that's cheating*
it;s not teacher tells us to check it after every assignment
dude that's actually sick you are a fucking elgend
lone echo
hm, you should not have a need to check if you are sure that your procedures are correct
dense tinsel
but what subtopic of maths is this?
similar figures
cursive pagoda
oohhhhh alright
dense tinsel
hm, you should not have a need to check if you are sure that your procedures are...
im never sure, it's math
dense tinsel
oohhhhh alright
once again
lone echo
then you havent studied it properly
dense tinsel
your move, lets play in dms
cursive pagoda
okay
lone echo
if you studied it properly enough to fully understand it, you know that the procedure you're doing is correct
an that's your goal
cursive pagoda
so what level of maths are you studying, felix?
and what does it take to become a maths help?
lone echo
i believe it's just activity measured by bot
cursive pagoda
and then you're upgraded to maths help?
lone echo
dont know, and dont really care tbh. There are many white names that know a fuckton more than me
lone echo
go to #odes-and-pdes and pretty much every white name there knows more
cursive pagoda
alright thakns
lone echo
and in many other channels too
dense tinsel
.close
orchid wolf
im stuck with parts b and c
obtuse pebbleBOT
im stuck with parts b and c
orchid wolf
.close
dense tinsel
#6. Do not understand
obtuse pebbleBOT
#6. Do not understand
dense tinsel
How to solve
lone echo
Does this help?
dense tinsel
yeah
yeah it really fucking does holy shit
right so
i can't tell which fractions to make
irdk what to do
im probably mentally impaired
@lone echo
lone echo
does this help more?
lone echo
you should be able to get y by similarity of triangles
dense tinsel
can u tell me the fractions for that
it's 10 PM here, my brain aint braining
i got it
i got it
i got it
i got it
i made a breakthrough
new issue
We lookin for x
How
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spice chasm
why does Fs decrease and not increase
obtuse pebbleBOT
why does Fs decrease and not increase
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
pine barn
Well Fn is increasing
And (mu_s)(Fn)=Ffriction=Fparallel
so as F parallel increases, Fn has to increase so it can still be on the board but since that's the variable increases mu_s has to stay the same (?)
obtuse pebbleBOT
Available help channel!
flat wharf
why is an integral an anti derivative
obtuse pebbleBOT
why is an integral an anti derivative
severe igloo
obtuse pebbleBOT
obtuse pebbleBOT
<@&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.
latent walrus
youre doing good
keep it up
graph looks a bit off so far, but idk if youve started it
obtuse pebbleBOT
@severe igloo Has your question been resolved?
severe igloo
graph looks a bit off so far, but idk if youve started it
Alright but I got a question on the last one
What am I supposed to do for that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
distant seal
obtuse pebbleBOT
warm shaleBOT
puckmyseen
distant seal
i have no idea after
subtle sinew
Similar triangles/shapes
distant seal
i don't understand how you thought of that
inland bay
You are trying to find AB in this
and since DEC is similar to ABC
you can do EC/EC+BE=DE/AB
subtle sinew
i don't understand how you thought of that
If you recall, area of a triangle is (1/2) * b * h, finding the hypotenuse (DC) is useless since you have the base, you just need the height of the triangle, AB
inland bay
yeah, that's the point of finding AB in this scenario
so you have to set up equivalent ratios
distant seal
ohhh ok i see it now
inland bay
glad to help
shut geode
Hello
azure anchor
partial fraction decomposition
azure anchor
no, its a way of breaking a fraction into a sum of fractions
shut geode
in class were doing solving for rational equations
wdym?
like breaking left side
into a sum of fractions
OH
I think i understand
like split the lf into 2 fractions with same denominators as right side
azure anchor
its a bit involved, i suggest looking at a video or two on youtube. explaining it here completely would be quite tedious
gray pulsar
Hello
warm shaleBOT
Umbe
gray pulsar
basically (S) means seed
or a infinite number of decimals
and n is the number and x is the place of that number
so for instance, seed = 596166825
we take 8 from 596166825 and n = 8. since 8 is in the 7th place, so x = 7
so that means we take 8 minus the first n which is 5
so 8-5 = 3
so the next seed (x) is 3
not the next seed but the next 7th place seed
therefore
$S = n_{x}-n_{1}$
warm shaleBOT
Umbe
gray pulsar
and if $n_{1} > n_{x} $ then, $n_{1} - |n_{x}|$
warm shaleBOT
Umbe
gray pulsar
for example, take $π, 3.14159265$
we want to know the outcome or the number after 5, so to do that, we plug x in
and remember, x cannot be 1
so we instead take 4 in this case of 3.1415~
so 4 - 1 = 3
so the next digit of this "seed" is 3
which is correct.
does this make sense?
<@&286206848099549185>
warm shaleBOT
Umbe
gray pulsar
Positive: $S^+ = n_{x}+n_{1}$ if not, then Negative: $S^- = n_{x}-n_{1}$
warm shaleBOT
Umbe
gray pulsar
<@&286206848099549185> Do y'all think makes sense
I think bc it follows the decimals
for irrational numbers
obtuse pebbleBOT
@gray pulsar Has your question been resolved?
gray pulsar
.close
tepid sedge
obtuse pebbleBOT
tepid sedge
How do I do this?
outer siren
tepid sedge
I don't get it
obtuse pebbleBOT
@tepid sedge Has your question been resolved?
tepid sedge
<@&286206848099549185>
obtuse pebbleBOT
@tepid sedge Has your question been resolved?
hexed basalt
neon finch
Is it right?
obtuse pebbleBOT
Is it right?
tepid sedge
Is it right?
not the IXL bru
latent walrus
12,5,1, nope
neon finch
not the IXL bru
🥲
tepid sedge
where did bro get 28?
merry canopy
my computer is saying the answer is D and I am very confused
obtuse pebbleBOT
my computer is saying the answer is D and I am very confused
obtuse pebbleBOT
my computer is saying the answer is D and I am very confused
Show your work, and if possible, explain where you are stuck.
violet sentinel
my computer is saying the answer is D and I am very confused
Can you show your work and where you're confused?
merry canopy
yes
tight patio
Can you show your work and where you're confused?
Just said that 
violet sentinel
Just said that <:sully:651816820122189834>
congrats on being first!
tight patio
congrats on being first!
I hate sarcastic people so much especially on a math homework night 
merry canopy
what I'm mainly confused on is because I got B as the answer but is there anyway for D to be the answer??
elfin burrow
No, you are correct
merry canopy
so it must be an error 🤔
cold thistle
Yeah your answer is right, the book is wrong
molten ether
partial derivative ∂D/∂P when D = Y/2P
obtuse pebbleBOT
partial derivative ∂D/∂P when D = Y/2P
molten ether
im just confused how you do the partial deriv of this when its a fraction but P only appears in denominator
violet sentinel
you just treat anything not P as a constant
so look at it like $D = \frac{Y}{2} \cdot \frac{1}{P}$
warm shaleBOT
MellowDramaLlama
violet sentinel
the derivative of 1/P should be straightforward
molten ether
deriv of 1/p is lnp correct?
warm shaleBOT
MellowDramaLlama
violet sentinel
then just use the power rule
molten ether
ohhh so it would be -p^-2 ?
but you still have to include the Y/2 right, so the answer would be -((Y/2p^2))?
violet sentinel
yep nice work!
molten ether
thank you!!
violet sentinel
yep np
molten ether
.close
hazy saddle
obtuse pebbleBOT
obtuse pebbleBOT
@hazy saddle Has your question been resolved?
obtuse pebbleBOT
@hazy saddle Has your question been resolved?
timid silo
This is a problem i have never seen before, does anyone know how to calculate instantaneous rate of chance, when square roots are involved? I can't stretch my mind to grasp how anyone could remove the denominator.
obtuse pebbleBOT
This is a problem i have never seen before, does anyone know how to calculate in...
green epoch
Do you know about rationalization
timid silo
it sounds familiar, I am unbelievably rusty.
timid silo
Do you know about rationalization
how would it work with two square roots? im trying to do mental math, but it doesnt compute
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
oh hey what the heck rationalizing does work
timid silo
Do you know about rationalization
how did you know to rationalize?
green epoch
how did you know to rationalize?
I just do it everytime I see root in limits 
timid silo
I just do it everytime I see root in limits <:joeyoufine:804738730501865502>
my hero 
.close
honest flicker
What is the range of f
obtuse pebbleBOT
What is the range of f
uneven palm
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
safe haven
When proving a statement in the form of A or B implies C, do I have to show the case where A and B implies C? Or is showing the cases A but not B and B but not A sufficient?
obtuse pebbleBOT
When proving a statement in the form of A or B implies C, do I have to show the ...
safe haven
do you explicitly use the "not B" or "not A" assumptions?
can you clarify a little?
i dont really get what you mean by "explicitly use"
candid yarrow
i dont really get what you mean by "explicitly use"
If you assume both not B and A and prove C, then if you use the assumption that not B, then it's not enough
Same but with A and B switched
kind hawk
do you actually use "B and not A" or does your proof actually only use "B"
safe haven
i assumed A and not B
then assumed B and not A
and i do use the assumption "not A" in my proof
kind hawk
then its not enough
safe haven
So then is this a false statement then?
First I changed to a contrapositive statement, "If a or b is odd, then a^2 - 3b is odd"
Then assumed a odd b even and a even b odd
in both of those cases a^2 - 3b is odd, however when I let a and b be odd it gives me that a^2 - 3b is even
or maybe i should use a proof by contradiction instead? but idk how to start with that
kind hawk
yes the statement is false
bright geyser
obtuse pebbleBOT
bright geyser
I've found a pattern
1 -> 1/2
2 -> 5/6
3 -> 23/24
...
but the indctuin part im not sure
so the pattern would be
((n+1)! - 1) / (n+1)!
induction
n(1) is true because n(1) = 1/2! = ((2)! - 1) / (2)!
=
((1 + 1)! - 1) / (1 + 1)!
where n = 1
coolio
suppose n(k) = ((k+1)! - 1) / (k+1)!
then I have to show n(k+1) is true right
but how
n(k+1) = ((k+2)! - 1) / (k+2)!
like how
n(k + 1) = (((k+1) +1)! - 1) / ((k+1) + 1)!
idek
jagged falcon
Do you see how n(k) and n(k+1) are related?
bright geyser
Do you see how n(k) and n(k+1) are related?
how do u mean related
jagged falcon
Like what do you need to add to n(k) to make it equal to n(k+1)?
bright geyser
uhh
jagged falcon
n(k)=1/2!+2/3!+...+(k-1)/k!+k/(k+1)!
bright geyser
i need to add (k+1) / (k+2)!
bright geyser
mhm
jagged falcon
i need to add (k+1) / (k+2)!
So add this to the n(k) above, and see if you can get it to be equal to n(k+1)
bright geyser
ahhhhhhhhhhhhhhhhhhhhhhhh i get you
bright geyser
So add this to the n(k) above, and see if you can get it to be equal to n(k+1)
i did it 🙂 awesome tysm
.close
bright geyser
obtuse pebbleBOT
bright geyser
wtf is wrong with this
jagged falcon
To determine if everything in the set has same color, you'll have to make comparisons, and to make comparisons, you need atleast 2 objects. So the base case should've been P(2) instead of P(1), and in P(2), the induction hypothesis fails
bright geyser
To determine if everything in the set has same color, you'll have to make compar...
ty
i have another inudction question i think im kinda struggling with these
this time its just wiht the algebra though
i've gotten to
(k+2)^2 * (k^2 + k + 1) / 2^2
and im tryna get the top to be square
but idk how
jagged falcon
Do you mean $(k+1)^3+(\frac{k(k+1)}{2})^2$?
bright geyser
yee
i tried to doa bit of simplifying and facotring
like i ran the power of 2 through the second + term
and then took out a common factor of (k+1)^2
not sure how to finish it
warm shaleBOT
Tardis
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
jagged falcon
Ah, you get what I mean though
bright geyser
yee i do
jagged falcon
It's just some algebra here. You take (k+1)^2 common to get (k+1)^2×(4(k+1)+k^2)/4 which is (k+1)^2×(k+2)^2/4, which is exactly what you require
bright geyser
It's just some algebra here. You take (k+1)^2 common to get (k+1)^2×(4(k+1)+k^2)...
how did u simplyify
jagged falcon
k^2+4k+4 is (k+2)^2
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
hello what is
obtuse pebbleBOT
hello what is
timid silo
-7+4c=7c+6
(sorry im in middleschool i find this hella hard im 14)
i basically
got
3c=13
but if i divide it
its 4.33333333...
royal basin
you screwed up the signs
should be 3c = -13
also you can and should leave it as a fraction
-13/3 is just fine as -13/3, you don't need to make it into a decimal
obtuse pebbleBOT
timid silo
.reopen
obtuse pebbleBOT
✅
timid silo
ye so i tried the working out again
i basically got
like
7c - 4c = -7+6
is there something im doing wrong...
gray turtle
it has to be +7
timid silo
ahhh ok icic
timid silo
-7+4c=7c+6
this is the question
gray turtle
it has to be -6
gray turtle
yes
timid silo
is that -13
gray turtle
-7-6= -13
gray turtle
3c= -13 not 3c=13
gray turtle
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
light vortex
obtuse pebbleBOT
light vortex
how do i do part bn
static marten
what'd you get from a
copper badge
So we know that 1-2i is a 0
That means 1+2i is a zero as well
If that is the case, there should be only one rational zero for P(x)
in order to find b
You should expand (x-(1-2i))*(x-(1+2i))
and you will get the polynomial at b
then you should do polynomial division to find c
Is it clear
obtuse pebbleBOT
@light vortex Has your question been resolved?
dusky tree
All I need is this question answered so I can go through the rest myself
dusky tree
Thanks for helping me!
So how would how would the table look?
Not sure if I'm correct so far
obtuse pebbleBOT
@dusky tree Has your question been resolved?
dusky tree
do you know how logic gates work?
I don’t remember 
copper badge
ok so not reverses the value
that should be easy
firstly fill the not A column
and please write your answer here so I can check
obtuse pebbleBOT
dusky tree
.reopen
obtuse pebbleBOT
✅
dusky tree
and please write your answer here so I can check
Done
copper badge
and operator works the same as multiplication
if one of the inputs is 0 then the output is 0
if both of the inputs are 1 then the output is 1
crude coral
also the bar shouldnt be over A.B , it should only be over A
copper badge
do not forget that you should find (not A) and B
dusky tree
Correct?
tacit scarab
last row wrong
dusky tree
last row wrong
What do I do?
copper badge
in the last row B is equal to 0
if even one of them is 0, the result of an AND operation is 0
so last row should be 0 as well
obtuse pebbleBOT
@dusky tree Has your question been resolved?
hexed timber
how do i use the root test to check whether this series is convergent or divergent
obtuse pebbleBOT
how do i use the root test to check whether this series is convergent or diverge...
@hexed timber Has your question been resolved?
candid yarrow
how do i use the root test to check whether this series is convergent or diverge...
do you know the root test?
errant crane
How do I solve this?
obtuse pebbleBOT
How do I solve this?
lean glen
i'm willing to know how this fraction thing works
royal basin
i'm willing to know how this fraction thing works
!occupied
obtuse pebbleBOT
i'm willing to know how this fraction thing works
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
candid yarrow
How do I solve this?
You know the period, so you can get the wavelength
obtuse pebbleBOT
@errant crane Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ocean night
any practice sheets for functions
obtuse pebbleBOT
any practice sheets for functions
ocean night
like indentifying domain range continuity equations transformations and opperating f(x)+-*/g(x)
obtuse pebbleBOT
@ocean night Has your question been resolved?
heavy bobcat
obtuse pebbleBOT
heavy bobcat
Need serious help with this
copper badge
You just substitute everything that has been given to you
and then take the integral
you could take the A0 constant outside the integral
you would be left with x*e^x
take the integral and take the boundaries from 0 to L
then multiply with the given constants
copper badge
Need serious help with this
Can you do these
heavy bobcat
so plug in everything and then what
copper badge
First of all take the integral of x*e^x
heavy bobcat
yes
copper badge
what do you find
copper badge
no need for + c
since we will take the boundaries
the boundaries are from 0 to L
L is 0.11
so first 0.11 and then 0
copper badge
you should have found 0.11e^x
then multiply with the remaining constants
which are 2400, 9.81 and 0.014
and that is your answer
copper badge
so its (0.11-1)e^0.11
this should be 0.11e^0.11
heavy bobcat
thanks a lot man
can u double check my answer?
40.47
?
@copper badge
hello?
obtuse pebbleBOT
@heavy bobcat Has your question been resolved?
pseudo minnow
I need help with this, how do I prove that its not injektive nor surjective
dark stirrup
Send screenshots, not weird files.
dark stirrup
No PRTSC button?
pseudo minnow
its a macbook
median dome
f：R -> R，f(x) = x^4 - x^2
to prove it isn't injective, you can give two x values which give the same value for f(x)
pseudo minnow
it keeps making it into a file
oh okay
and to prove its not surjective
how do i do that
median dome
to prove it isn't surjective, you need to prove that there exists some value of y such that f(x) is not equal to y for any real x
the easiest way is to find the minimum of your function and say that a value of y below that minimum is part of the codomain but it cannot be achieved, hence the function is not surjective
pseudo minnow
ohh right
so not injective because when x = -1, 0 or 1, then y has the same value right
median dome
yeah you can say that
more generally, f(x)=f(-x), hence it isn't injective
but your explanation is fine
pseudo minnow
and not surjective cause when y is below -0,25 there are no solutions
pseudo minnow
more generally, f(x)=f(-x), hence it isn't injective
right
pseudo minnow
perfect
median dome
but you need to make sure that
pseudo minnow
thank you so much
median dome
those values of y are in the codomain
for example if the function was defined as f: R -> [-1/4, inf) then it would be surjective
as every value of the codomain can be achieved by the function
i.e codomain = range
median dome
yeah, I was just giving an example
dry egret
While trying to work out this DE, im getting this constant 8/5 at the end, shouldnt my particular solution be Ax+Be^{-x}? Where does the constant come from?
obtuse pebbleBOT
While trying to work out this DE, im getting this constant 8/5 at the end, shoul...
dark stirrup
While trying to work out this DE, im getting this constant 8/5 at the end, shoul...
!show
obtuse pebbleBOT
While trying to work out this DE, im getting this constant 8/5 at the end, shoul...
Show your work, and if possible, explain where you are stuck.
dark stirrup
While trying to work out this DE, im getting this constant 8/5 at the end, shoul...
There could be a remaining constant. Plugging back in to check is always a good idea.
obtuse pebbleBOT
@dry egret Has your question been resolved?
dry egret
There could be a remaining constant. Plugging back in to check is always a good ...
shouldnt I be able to know that there is a constant in the first place?
dark stirrup
shouldnt I be able to know that there is a constant in the first place?
wdym?
obsidian shadow
hi guys
tough tusk
what is Xi ( Z?
brazen gorge
what is Xi ( Z?
x_i is an integer
quiet wadi
I would try to solve this without the x_2\leq 4 first, then filter out those sols. later
tough tusk
then you can base it on X2 condition
make it scenario where x 2 = 2, 3, and 4
and solve it
quiet wadi
or that, I suppose
tough tusk
when x2 = 2
a = 2, c = 2, d = 2, e = 3
a = 2, c = 2, d = 3, e = 2
a = 2, c = 3, d = 2, e = 2
a = 3, c = 2, d = 2, e = 2
x2 = 3
a = 2, c = 2, d = 2, e = 2
x2 = 4
not possible
where x1 = a , x3 = c, x4 = d, and x5= e sorry if it is confusing
quiet wadi
why are there 1s in that?
regal tundra
If you put all x_i =2 sum is 10
So only way to get 11 is that one those should be 3 and others should be 2
tough tusk
why are there 1s in that?
opps yea my bad
quiet wadi
:^)
regal tundra
If you put all x_i =2 sum is 10
So only way to get 11 is that one those should b...
So only 5 ways
Like x1=x2=x3=x4=2 and x5=3
And just rotate the 3 among all xi
obtuse pebbleBOT
@obsidian shadow Has your question been resolved?
obsidian shadow
i've solved this problem here already
i just needed to exclude case 2
tysm everyone
obtuse pebbleBOT
@prisma dome Has your question been resolved?
obtuse pebbleBOT
@prisma dome Has your question been resolved?
prisma dome
obtuse pebbleBOT
obtuse pebbleBOT
@prisma dome Has your question been resolved?
obtuse pebbleBOT
@prisma dome Has your question been resolved?
royal moat
Hey, Don, could you show me an example of a function that has a derivative of 0 almost everywhere, but not constant
obtuse pebbleBOT
Hey, Don, could you show me an example of a function that has a derivative of 0 ...
fathom flicker
Who is Don?
cold thistle
I guess x/x^2 has a derivative of almost zero over most of its domain
royal moat
I need a derivative of exactly 0 almost everywhere, not a derivative of almost 0
grizzled shore
The step function
Its derivative is 0 almost everywhere except for a countable set of discontinuities
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dusk widget
what is the "quick proof" I'm looking for?
obtuse pebbleBOT
what is the "quick proof" I'm looking for?
dusk widget
I have that lim(x_n) = x* and I want to show that (x*)^2 = a
by problem 3, I have that lim(x_n)^2 = (lim(x_n))^2
I need to show that lim(x_n) = sqrt(a), and Q3 gives me that lim(x_n)^2 = (lim(x_n))^2
so if I can show that lim(x_n)^2 = a, then I've shown that lim(x_n) = sqrt(a) = x* , so (x*)^2 = a
but that doesn't seem quick nor easy
so I don't understand what the "quick" proof is supposed to be
pseudo swift
well the only thing you really know is x_n
and the only equation you have is the recursive case of x_n
you could try working w/ that recursion equation (and limits)
@dusk widget
dusk widget
you could try working w/ that recursion equation (and limits)
Hm
pseudo swift
to be a bit more precise, if you have two sequences u_n and v_n such that u_n = v_n for pretty much all n, can you say anything about their limits ?
dusk widget
Limits are the same
obtuse pebbleBOT
@dusk widget Has your question been resolved?
pseudo swift
want more hints ? @dusk widget
dusk widget
want more hints ? <@456913063300431934>
I feel like I'm close, lemme try for a bit more
pseudo swift
aight
pseudo swift
$$\lim_{n\to\infty}x_{n+1} = \lim_{n\to\infty} \frac12\left(x_n + \frac{a}{x_n}\right)$$
warm shaleBOT
aPlatypus
pseudo swift
taking the recursion equation, and looking at the limits
@dusk widget
that's what I was suggesting
(it's the place where our x* starts to shine)
dusk widget
**aPlatypus**
does lim(x_n+1) = x* also?
dusk widget
why?
pseudo swift
if n goes to infty, then n+1 also goes to infty when you think about it
dusk widget
i mean, i guess?
the terms in the sequence are offset by 1, but would that change the final value of x*?
pseudo swift
if x_n converges to L, then any subsequence of x_n also converges to L if we wanna be formal
and x_n+1 is one of those subsequences
pseudo swift
yes
dusk widget
does lim(x_n+1) = x* also?
what i did hinged on this fact
but I have a result that says that (x*)^2 = a
so I think I did it properly
pseudo swift
mélo writing a 3 page rebuttal on why I shouldn't be trusted with analysis
dusk widget
😆
wispy wadi
you can also see it as a consequence of Banach's fixed point theorem
since x_(n+1) = f(x_n) with f continuous on the given interval for the sequence, it converges to a fixed point, if it converges
so it converges to -sqrt(a) or sqrt(a) which are the two fixed points
wispy wadi
mélo writing a 3 page rebuttal on why I shouldn't be trusted with analysis
why would I do something like that lmao
I swear I've never eaten a kid in my whole life
dusk widget
you can also see it as a consequence of Banach's fixed point theorem
since x_(n+...
ah, I haven't gotten to any "proper" real analysis yet
no metric spaces and such
I'm a freshman
wispy wadi
what platypus said essentially leads to the same reasoning, since you'll have x* = 1/2 (x* + a/x*)
you're solving for a fixed point
dusk widget
by problem 3, I have that lim(x_n)^2 = (lim(x_n))^2
hm, I don't really think I used this assumption did I?
wispy wadi
you're using it when you're looking for x*
bc x* = lim x_n
so (x*)² = (lim x_n)² = lim (x_n)²
it's something you use when calculating the limit but it's so usual that the product of limits is the limit of the product that you don't really mention it
dusk widget
bc x* = lim x_n
so (x*)² = (lim x_n)² = lim (x_n)²
I dont have this anywhere though..
wispy wadi
yeah because in math when something is applied in a such obvious manner you don't mention that you use it, but you're using it when you're doing the calculations
when you write x* = 1/2 (x* + a/x*) so (x*)² = a
the fact that you could just multiply by x* (and write this in the first place)
is exactly because lim(x_n)^2 = (lim(x_n))^2 (and lim x_n+a/x_n = lim x_n + a/lim x_n)
and x* = lim x_n
you're just not writing it but you're using it
dusk widget
I dont have this anywhere though..
nvm i've found where I implicitly used this
mb
lemme write it
so i dont lose marks lol
.close
drifting sandal
obtuse pebbleBOT
drifting sandal
ive done the ratio test
i got lim n->inf (n+2)(x-5) < 1
inf < 1
and it equals inf when x > 5
so the interval is [-inf, 5]???
obtuse pebbleBOT
@drifting sandal Has your question been resolved?
drifting sandal
does it look like its resolved??
brave bramble
You are forgetting the absolute value
You care about
lim |(n + 2)(x - 5)|
@drifting sandal
brave bramble
Yeah that's it
drifting sandal
so how i find interval of converge?
brave bramble
Which values does 1/(1 - x) converge for?
drifting sandal
depends on x
drifting sandal
when 1/(1-x) < 1
so 1000 also works
which is not between -1 and 1
@brave bramble
brave bramble
This is one worth memorizing, it's -1 < x < 1
I gave the answer here
drifting sandal
idc about the answer i want the path to get there
obtuse pebbleBOT
@drifting sandal Has your question been resolved?
obtuse pebbleBOT
@drifting sandal Has your question been resolved?
drifting sandal
surely the programmers of this bot can see if i previously answered no and there is no messages after that, the answer is still no
obtuse pebbleBOT
@drifting sandal Has your question been resolved?
obtuse pebbleBOT
@drifting sandal Has your question been resolved?
warm dome
surely the programmers of this bot can see if i previously answered no and there...
Sometimes people solve it by themselves. Sometimes they just leave so them still having a channel blocks that channel unnecessarily
timid silo
Would I not use the shell method for this?
obtuse pebbleBOT
Would I not use the shell method for this?
royal basin
why wouldn't you
timid silo
Because I did and got a negative number
-45
But I don't see what's wrong with my setup
Oh I see an error in my factoring, -x cubed times -x, but that doesn't solve anything
past sand
What's the goal here? Compute the integral of h(x) from 0 to 3?
timid silo
The goal is to find the volume of the given enclosed area between the two y functions revolving around x=3
I don't see what's wrong with my setup using the shell method
But the resulting output is now -5
past sand
I mean... (3x^2-x^3)(1-x) does not equal (3x^2-3x^3-x^3+x^2)
timid silo
Or -10π I mean
past sand
Oh that's the error you saw?
past sand
You have the expected solution?
timid silo
From my professors review answer key, the result should be 81π over 5
past sand
Ok, what's weirding me out now is that your graph of x^3 is ok but that of 3x^2 is not
high lily
your radius is wrong
timid silo
Oh is it 3-x?
high lily
also graph is wrong, but 3x^2 >= x^3, so that component didn't affect the calculations
yes, that's what you should be using for the radius
,w 2pi * integral of (3x^2-x^3)(3-x) from x=0 to 3
warm shaleBOT
timid silo
Ahh, that's my bad, I don't know why I put 1, I know it's supposed to be the distance between the axis of rev and the rectangle
God bless 🙏
.close
austere violet
Hello, I’m having a problem solving (c). I understand I should use the information above, but I’m confused as to how I should proceed with the calculations.
obtuse pebbleBOT
Hello, I’m having a problem solving (c). I understand I should use the informati...
timid silo
$$x^2 + y^2 + z^2 = \frac{3}{4}$$
Given that:
$$x^2 + y^2 + z^2 + 2xyz = k$$
How many possible values of k can exist where k is a positive integer
obtuse pebbleBOT
$$x^2 + y^2 + z^2 = \frac{3}{4}$$
Given that:
$$x^2 + y^2 + z^2 + 2xyz = k$$
How...
warm shaleBOT
AgentSpiely
timid silo
I have no idea how I am supposed to approach this question
timber island
Hmm okay
timid silo
Any clue on how I could approach this?
timber island
I am thinking
AM-GM doesn't seem to help
Well 4|(3+8xyz) or u can say 2xyz = 1/4 + w for some positive integer w
timid silo
right
timber island
And that w is a multiple of 4
spice citrus
are x, y and z integers or reals?
kind hawk
would be pretty boring if they are integers
spice citrus
oh, true
But xyz has a minimum and maximum, since x, y, z are on a sphere
You can use AM-GM to get an upper bound on (xyz)^2
timid silo
are x, y and z integers or reals?
Reals
timid silo
You can use AM-GM to get an upper bound on (xyz)^2
What’s am-gm? 😭
spice citrus
a + b + c >= 3cbrt(abc), for all nonnegative real a, b, c
kind hawk
arithmetic mean vs geometric mean. very classic inequality
timid silo
I have absolutely no idea what it is but I will surely look it up.
Tysm for your help guys
timid silo
would be pretty boring if they are integers
Btw if they were integers…then there would be no positive integer values of k right?
median dome
Btw if they were integers…then there would be **no** positive integer values of ...
there would be no values of x,y,z itself
timid silo
Btw if they were integers…then there would be **no** positive integer values of ...
Cause then:
$$\frac{3}{4} = k - 2xyz$$
warm shaleBOT
AgentSpiely
timid silo
And obviously by subtracting an int from an int, we cannot create a fraction
median dome
integer + integer + integer cannot equal a fraction.
twin peak
i am super confused by the image
obtuse pebbleBOT
i am super confused by the image
late stump
the grey dashed lines is the original plane
the stretched parallelogram is the new transformed space relative to the original
twin peak
how do you find the matrix from this tho
like this is in R^2 right
so im assuming you have some standard basis right
twin sapphire
a matrix of a linear transformation is just the action of the transformation on a basis on the columns
like column 1 is A(e1)
expressed in e1,e2
column 2 is A(e2) expressed in e1,e2
twin peak
so like first i should find the x ,y of the transformation right
twin sapphire
wdym the x y
you need to find A(e1) and A(e2)
and then write the result inside a matrix
twin peak
and then write the result inside a matrix
can i try then show you my work
twin sapphire
go
twin peak
obtuse pebbleBOT
@twin peak Has your question been resolved?
twin peak
@twin sapphire
twin sapphire
re
so thats a way
but you dont need to "solve"
a is always going to be the first cordinate of A(e1)
etc
twin sapphire
its how we define it
twin peak
0
1
mapped to
2
1
if that makes sense
how do you know which standard basis maps to which coordinate
twin sapphire
wdym they give you a basis
you dont know if its the standard
and it doesnt matter
e1 = 1 e1 + 0 e2
twin peak
twin peak
oh like of the gray region?
twin sapphire
no
but you sent me vectors
as if they were in R^2
but they're not necessarily
e1 e2 might be something else
twin peak
wait so itis all wrong?
twin sapphire
no
the calculations are the same its conceptual
you dont and shouldnt always think in terms of R^2
we want the matrix representation of A inside the e1,e2 basis
twin peak
but was it goot to use a letter matrix
twin sapphire
its not false but unnecessary
if you have something aloing the lines of "matrix representation of a linear transformation" inside your class material go re read that
obtuse pebbleBOT
@twin peak Has your question been resolved?
white oar
obtuse pebbleBOT
timber island
Split the fraction into two fractions
$\lim_{n -> \infty} \frac{3^{n+1}}{3^{n-1} + 1}$ + $\lim_{n -> \infty} \frac{2^{n}}{3^{n-1} + 1}$
warm shaleBOT
ItzKraken
royal basin
\to not ->
timber island
Ah thanks
obtuse pebbleBOT
@white oar Has your question been resolved?
keen bobcat
anyone got any idea?
