using the distance formula
#help-13
vital pumice
bold hinge
Which is?
vital pumice
what
bold hinge
Can you tell me what the distance formula is
vital pumice
oh √(x_2-x_1)^2+(y_2-y_1)^2
vital pumice
okei, so i solve that separately?
bold hinge
Not quite
bold hinge
Can you find the distance from (x,y) to (-2,0)?
vital pumice
yes
vital pumice
Can you find the distance from (x,y) to (-2,0)?
x^2+y^2+4x+4
cedar kilnBOT
@vital pumice Has your question been resolved?
vital pumice
<@&286206848099549185>
sonic robin
<@&286206848099549185>
assume the point to be (h,k)
and then just do what the question says
after simplifying replace h and k with x and y
vital pumice
then what?
sonic robin
after simplifying replace h and k with x and y
thisi
this is your last step
this is your answer
vital pumice
okaayy
candid coyote
The continious function f(x) is defined on interval [a,b] the task is to prove that g(x) is continious on interval [a,b] where g(x) = min value of f(x) on interval [a,x]
bleak harbor
so g(x) = a constant?
candid coyote
No
It depends on interval
For example g(1) = min value of f(x) on interval [a,1]
cedar kilnBOT
@candid coyote Has your question been resolved?
grim yacht
Have you tried using the epsilon delta definition and see if you can form the inequality in such a way that |g(x) - g(y)| \leq |f(x) - f(y)| ?
That's the trick at least
If you can I some way show that then that means g(x) is continuous too
Doesn't have to be exactly like this tho
candid coyote
Have you tried using the epsilon delta definition and see if you can form the in...
This is the hardest part
candid coyote
I try if x2>x1 then g(x2) is g(x1) or
min value f on interval (x1,x2]
Let define min value f on interval (x1,x2] g(x1,x2)
Then g(x2) - g(x1) = 0 or
g(x1,x2) - g(x2)
But can we find bound on it?
candid coyote
I observe that it monotonic decreasing function
grim yacht
Yeah this method does not work here sorry
Guess you have to investigate the neighborhood of where f(x) attains its minimum on the specified interval
Start with a fixed point in other words
candid coyote
@grim yacht lets go on channel real analysis
I think it is right place for question
.close
keen nova
cedar kilnBOT
keen nova
two questions: 1) am i right to assume they mixed up proof a and b here and 2) I don't rly understand proof a (which i assume is for b). Why is t neither in A or B but has to be in both A^c and B^c?
ok fuck i realize A^c is the complement of A not A to the power of c lmao
still anyhow are they mixed up? am i still right to try to prove the first law?
muted bear
Think so
keen nova
thanks
complement are basically inverses i see now
i already kinda saw that but now i see it with proof and reasoning too
. close
.close
quartz cove
Hi I'm here to drop the level of math because I'm dumb
Solve this dumb question for me plss
9/24,10/24,11/24,12/24,13/24,14/24 It can also written as 3/8,40/96,22/48,13/24,7/12.
Why and how it can be written like that?
sinful geyser
You can not ask for answers here
ocean flame
3/8
ocean flame
You can not ask for answers here
?
cedar kilnBOT
Hi I'm here to drop the level of math because I'm dumb
Solve this dumb questio...
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
crimson sedge
Solve this dumb question for me plss
Why and how it can be written like that?
I can't tell if this breaks the guidelines or not
quartz cove
The purpose of this server is to help you learn, not to hand out answers. Do not...
Ok
quartz cove
ex: 9/24 is divided with 3
What 40/96 is coming from
crimson sedge
Okay, image you have 2 friends (very sad) and one of them is male
solid juniper
breaks the unspoken guidelines
ocean flame
What 40/96 is coming from
multiplication by 4
crimson sedge
Okay, image you have 2 friends (very sad) and one of them is male
That means half of your friends is male
ocean flame
quartz cove
multiplication by 4
Wait a sec
crimson sedge
Or, in other words, 1/2 of your friends is male
ocean flame
Wait a sec
shall i DM?
crimson sedge
Now, imagine you have 4 friends and 2 of them is male
quartz cove
shall i DM?
No
crimson sedge
That still means half of your friends are male
quartz cove
.close
cedar kilnBOT
crimson sedge
oh
solid juniper
cedar kilnBOT
Available help channel!
bleak peak
why does squaring a random variable retain the probability distribution before it was squared
bleak peak
In otherwords, why does X^2 have the same PMF as X?
Because the way I see it, given a geometric distribution:
If you have X= 1,2,3,4 and p = .9 q = .1, then P(X=1) = .9, P(X=2) = 09, P(X=3) = .009, P(X=4) = .0009
Suppose I square X
X^2 = 1,4,9,16
Well, to get P(X=1), its .9
BUT to get P(X=4) its .0009
cedar kilnBOT
@bleak peak Has your question been resolved?
cedar kilnBOT
@bleak peak Has your question been resolved?
dire geode
X^2 = 1,4,9,16
Find P(X^2 = k)
cedar kilnBOT
@bleak peak Has your question been resolved?
bleak peak
Find P(X^2 = k)
Cant
dire geode
In otherwords, why does X^2 have the same PMF as X?
Then you can't conclude this
oblique prawn
cedar kilnBOT
scenic brook
crimson sedge
i have to prove it using epsilon and N
cedar kilnBOT
i have to prove it using epsilon and N
crimson sedge
i did this but is it correct tho
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
fervent monolith
i did this but is it correct tho
the handwriting is annoying to read 
but yeah, i was able to follow the steps. as long as you write in the right order and not in MSPaint, it should be good 
also as long as you bracket (sqrt(4n + 1) / n - 2) after the second equality
crimson sedge
the handwriting is annoying to read <:KEKW:625351342432583720> but yeah, i was a...
in the official solution its 1/4epsilon <= N
mine is 1/2epsilon <= N 😦
that means im wrong?
fervent monolith
well 1/2\epsilon > 1/4\epsilon, so if you pick N bigger than 1/2\epsilon, it will be larger than 1/4\epsilon as well and whatever the official solution did will work also
fervent monolith
if i had to guess, maybe the official solution assumed n >= 2 so they could say that $$\sqrt{\frac{4n + 1}{2}} = \sqrt{2n + 1/2} > \sqrt{2*2 + 1/2} > 2$$ to get 2 + 2 instead of 0 + 2 under the denominator
wraith daggerBOT
ves
fervent monolith
its not 1/2/epsilon doe
that's okay. you just need to show that given any epsilon, you can pick SOME N such that (blah blah blah...)
you showed that, its just a different N than the """official solution"""
(the official solution gets a tighter bound than you did, they only have to go half as far out to find N, but its okay if you go twice as far out as they did to find your N)
crimson sedge
yeah i mean after all for every epsilon
i gotta find and N
doesnt matter if its 1/2e or 1/4e
right?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
drifting isle
I know these triangles are similar, that there proportion is equal in terms of a fraction but 7/10 is 70% and 8x+6 is not 70% of 77
arctic scaffold
I know these triangles are similar, that there proportion is equal in terms of a...
77 needs to be 70% of 8x+6
AB = EF, not DE
drifting isle
But how when it’s similar angle is 10/7
I’m comparing the 77 and 10 over the 7 and variable equation
arctic scaffold
no, the triangles are fliped
it’d be easier to compare 7 to 77, as its multiplying by 11
drifting isle
Ohhh shit…. How did you realise the proper alignment
arctic scaffold
then 11 . 10 = 8x +6
arctic scaffold
Ohhh shit…. How did you realise the proper alignment
the length of the lines are different
drifting isle
Ohh gosh
arctic scaffold
do you understand the issue?
drifting isle
Yeah , I’ll just have to work out the cross multiplication
I always get confused wether to go straight across or diagonally
arctic scaffold
I always get confused wether to go straight across or diagonally
when there’s an equal sign between, it’s diagonal
when is a multiplication, it’s straight
cedar kilnBOT
cedar kilnBOT
Available help channel!
gloomy bough
Given today is Tuesday, what day of the week was it 200 days ago?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
E. Saturday
split pike
use odd days concept
plain dock
is it friday
split pike
idk
plain dock
the last tuesday in that week was 196 days ago
4 days behind tuesday: monday(1) sunday(2) saturday(3) and friday(4)
split pike
what is the first day of your week?
plain dock
sunday
plain dock
you can also just count 200 days 
split pike
@gloomy bough
jaunty pumice
Use cyclicity
gloomy bough
<@619925522826133515>
Yes?
woven idol
yh its mod
gloomy bough
🗿 what are yall saying 💀
jaunty pumice
for example let tha day be x then after 200 days fay will be x+4
gloomy bough
I don't understand anything
jaunty pumice
I don't understand anything
See days will repeat after every 7k type days
200 = 7k+4
gloomy bough
See days will repeat after every 7k type days
yes'
jaunty pumice
for example let tha day be x then after 200 days fay will be x+4
So see this msg
cedar kilnBOT
woven idol
let x be the day
x + 200 is congruent to 1 mod 7
so x is congruent to -199 mod 7
so x is congruent 4 mod 7
friday is teh 4th day
smthn like that
with 0 -> monday, 1 -> tuesday etc
@gloomy bough
gloomy bough
<@619925522826133515>
thanks but don't understand 💀
cedar kilnBOT
Available help channel!
crimson sedge
What am I doing wrong when I'm trying to find the sector area for this?
-
$\theta = 90$ degrees, $r = 10$cm
-
Convert to radians $\frac{90\pi}{180}$ or $\frac{1\pi}{2}$
-
Plug it in the formula $\frac{\frac{1\pi}{2}}{2}*10^2$
-
$\frac{2\pi}{2}*10^2
-
=314.159265359 cm
wraith daggerBOT
Matt
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crimson sedge
says it has an error but it gets the gist across
livid hound
careful with the order of division
crimson sedge
on #3?
minor crystal
yep
livid hound
note that you're supposed to be dividing $\frac{\pi}{2}$ by 2 which would be
$$\frac{\br{\frac{\pi}{2}}}{2}$$
which isn't the same as
$$\frac{\pi}{\br{\frac 22}}$$
wraith daggerBOT
ℝαμΩℕωⅤ
crimson sedge
Doesnt $\frac{\br{\frac{\pi}{2}}}{2} = \frac{\pi}{2} * \frac{2}{1}$
wraith daggerBOT
Matt
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
crimson sedge
oh
livid hound
$\frac{\br{\frac{\pi}{2}}}{2}$ can be viewed as the product:
$$\frac{\pi}{2} \cdot \frac 12$$
crimson sedge
so would i literally just divide pi by 2 and then by 2 again
wraith daggerBOT
ℝαμΩℕωⅤ
raven smelt
If
sin( ) > 0, and tan( ) = 5/3 ,0 < or = < or =360
, then ,correct to the nearest whole angle, must be _____.
raven smelt
idk how to solve this the answer was 239 on the snwer sheet
i just tan-1 and got 59...
dire geode
If
sin( ) > 0, and tan( ) = 5/3 ,0 < or = < or =360
, then ,correct to th...
Find the quadrant the angle must be in first
Sine and tangent are both positive in what quadrant
raven smelt
Find the quadrant the angle must be in first
using CAST it would be in 1st quad
right?
then tan = opp/hyp
dire geode
,calc tan(59 deg)
wraith daggerBOT
Result:
1.6642794823505
Close to 5/3
raven smelt
Close to 5/3
so 59 is correct??
dire geode
Should be close yea
opal zodiac
cedar kilnBOT
opal zodiac
How do you get the max angular velocity at 45 degrees?
All I was able to get out of what was shown was the moment of inertia of the plate at its centre.
The question didn’t even give velocity, so I was wondering where do I even begin…
drifting fable
opal zodiac
K, I’ll try doing that.
I ended up with 2 variables: the final linear and angular velocity.
Did I do this right? I ended up with 2 variables when all I’m looking for is the angular velocity…
Is there a way to relate the angular and linear velocity so that I could solve this equation?
cedar kilnBOT
@opal zodiac Has your question been resolved?
opal zodiac
Hmm…
I tried using v=wr, with radius being .919, but I don’t think it would be that simple.
Well, I’ll keep on it.
sharp pollen
opal zodiac
Integration for me is just finding the anti derivative of a given function. Also, shouldn’t you post this on an open question chat?
opal zodiac
Ok…?
<@&286206848099549185>
I tried exchanging the v using equation v=wr, but it didn’t work in the end.
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
lilac island
I'm trying to solve if this is either convergent or divergent .¿What would be the right criteria ?
raw gulch
I'm trying to solve if this is either convergent or divergent .¿What would be th...
I suggest a comparative criterion in the limes version
notice that :
$\lim_{n \to \infty}\left( \frac{n+3}{n+1} \right)^{n}=\lim_{n \to \infty}\left( 1+\frac{2}{n+1} \right)^{n}=_{\cdots }=e^{2}$
wraith daggerBOT
Joanna Angel
raw gulch
that helps you, how to find the general term of the other series, to be compared to yours
another approach is to apply the classical comparative criterion using this inequality:
$\ln\left( 1+\frac{1}{n} \right)<\frac{1}{n}$
wraith daggerBOT
Joanna Angel
cedar kilnBOT
@lilac island Has your question been resolved?
lilac island
thank you for your help.I tried using that approach but I it wasnt conclusive, maybe my calculations are wrong
I know that it is convergent but I dont really know how to solve the question
raw gulch
I know that it is convergent but I dont really know how to solve the question
look at such , very alike example:
$0<\frac{1}{n}\ln\left( \frac{\sqrt{n}+1}{\sqrt{n}} \right)=\frac{1}{n}\ln\left( 1+\frac{1}{\sqrt{n}} \right)<\\<\frac{1}{n}\cdot \frac{1}{\sqrt{n}}=\frac{1}{n^{\frac{3}{2}}}$
wraith daggerBOT
Joanna Angel
raw gulch
and now think, how to behave analogously, with your series
lilac island
okay I think i understand
could you give advice about wich serie(I don't know if it is like that in english) should I compare it with?
raw gulch
what you compare with always depends on the form of the series, there is no wonderful rule that always uses the same thing, for example:
$\sum_{n=1}^{\infty}\sin\frac{1}{n\sqrt{n}}\text{ is a convergent series because}\\0<\sin\frac{1}{n\sqrt{n}}<\frac{1}{n\sqrt{n}}=\frac{1}{n^{\frac{3}{2}}}$
wraith daggerBOT
Joanna Angel
raw gulch
but:
$\sum_{n=1}^{\infty}\sin\frac{1}{\sqrt{n}}\text{ is a divergent series because}\\0<\frac{2}{\pi}\cdot \frac{1}{\sqrt{n}}<\sin\frac{1}{\sqrt{n}}\text{ }\text{ since}\\\forall_{x\in \left( 0,\frac{\pi}{2} \right)}\text{ }\text{ }0<\frac{2}{\pi}x<\sin\text{}x$
wraith daggerBOT
Joanna Angel
raw gulch
we have to remember that:
that is, we very often strive to compare it with this harmonic series of the order p
Another very popular series for comparison is the school geometric series
$\sum_{n=0}^{\infty}q^{n}\text{ }\text{ is a convergent series if and only if }\text{ }\left| q \right|<1$
wraith daggerBOT
Joanna Angel
raw gulch
could you give advice about wich serie(I don't know if it is like that in englis...
I hope you can understand this, I have a lesson in 15 minutes, I have to get ready now, Good luck!
runic ingot
∀a∀b((∀x(x is prime)) -> ∀c, ac=bc))
cedar kilnBOT
∀a∀b((∀x(x is prime)) -> ∀c, ac=bc))
prisma gull
what are you implying here?
cedar kilnBOT
@runic ingot Has your question been resolved?
runic ingot
what are you implying here?
i just gave myself tricky nosense implication that is mathematically legal
i want to show this odd statement is true, can i just negate and show it's false?
prisma gull
i just gave myself tricky nosense implication that is mathematically legal
remove the quantifiers and explain in words what the statement is about?
prisma gull
i just gave myself tricky nosense implication that is mathematically legal
also what makes you think it’s mathematically legal?
maybe it’s a statment but what makes you think it’s correct
runic ingot
also what makes you think it’s mathematically legal?
that it's vacously true
prisma gull
ie, the antecedent is always false?
runic ingot
∀a∀b( (∀x(x is prime)) -> ∀c, ac=bc) )
this is different then looking at this like ∀a∀b∀x(((x is prime)) -> ∀c, ac=bc))
runic ingot
ie, the antecedent is always false?
let's define it other way so it will be clearer for you to see:
P(a,b) = ∀x(x is prime))
q(a,b) = ∀c(ac=bc)
∀a∀b( P(a,b) -> q(a,b))
cedar kilnBOT
runic ingot
.reopen
cedar kilnBOT
✅
prisma gull
let's define it other way so it will be clearer for you to see:
P(a,b) = ∀x(x is...
The statement P(a,b) says any choice of a number is a prime?
runic ingot
The statement P(a,b) says any choice of a number is a prime?
yes without matter of a,b values
prisma gull
which is a false statement within our standard definitions
runic ingot
which is a false statement within our standard definitions
yes so that makes the sentence vacously true aint it
prisma gull
Sure
but this remainds me ex falso quodlibet
if 1=2 then unicorns are real
this is a true statement
Essentially from falsehood you can prove anything
runic ingot
Essentially from falsehood you can prove anything
yes
thats what i wanted to make sure
ty
prisma gull
Refer law of explosion
runic ingot
if 1=2 then unicorns are real
i can look at negation of this, 1=2 and unicorns are not real, so 1=2 is false, therefore the negation is false thus original is true?
prisma gull
Yes, the negation is 1=2 AND unicorns are not real, you could also say that negation is false forcing us to say that the implication is true
this notion of vaccously true is not bad
certain cases we can use them usefully
If you have taken some analysis, you may know null set is both open and closed
runic ingot
If you have taken some analysis, you may know null set is both open and closed
ah, i was asking this because i could decide wether this is true or false. it's over naturals(including 0)
cedar kilnBOT
@runic ingot Has your question been resolved?
cedar kilnBOT
@runic ingot Has your question been resolved?
tropic oxide
i must have misremembered the value
nothing else to it
i remembered it was somewhere just under 2, but i didn't remember exactly how much.
wraith daggerBOT
tropic oxide
,w InverseCDF[NormalDistribution[0,1],0.975]
wraith daggerBOT
tropic oxide
yeah, it's 1.96 alright
tropic oxide
last step is screwed up
did you mean to divide both sides by 2.1609?
2.1609n - 2.1609 won't simplify to just n
yes. this is not even about stats
just algebra
trail dock
suppose that we have an R-algebra A of dimension n such that every non-zero element of A admits an inverse. show that A is isomorphic to a subalgebra of Mn(R).
cedar kilnBOT
suppose that we have an R-algebra A of dimension n such that every non-zero elem...
@trail dock Has your question been resolved?
cedar kilnBOT
@trail dock Has your question been resolved?
cedar kilnBOT
@trail dock Has your question been resolved?
cedar kilnBOT
@trail dock Has your question been resolved?
cedar kilnBOT
@trail dock Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
azure marsh
cedar kilnBOT
azure marsh
my first line is
mod(z)+4/mod(z)>= 2
but it yeilds no solution
so what is wrong with it
shy widget
careful its - not +
shy widget
no i mean mod(z)-4/mod(z)>= 2
azure marsh
all g
crimson sedge
cedar kilnBOT
dry latch
hi
crimson sedge
make equations for the lenthg and width constraints
I got 15>x and 20>x
I know x can't be 0
crimson dune
well try putting it in the general equation of volume
(40-2x)(30-2x) <----- this is always greater than zero
crimson sedge
(40-2x)(30-2x) <----- this is always greater than zero
What about x for the depth of the tray?
Do we not need to include that also?
crimson dune
yes
so the equation will be x(40-2x)(30-2x) >0
now you can just find the solution by number line method
crimson sedge
That becomes 1200x -140x^2 +4x^3>0
crimson dune
That becomes 1200x -140x^2 +4x^3>0
you dont have to expand it
crimson sedge
now you can just find the solution by number line method
How do I use this method?
crimson dune
wait ill send you the screenshot lemme write it out for you
crimson sedge
wait ill send you the screenshot lemme write it out for you
Thanks
velvet hemlock
Given a number N that is natural (N>=1) it is necessary to prove that any number N can be represented using a different powers of 2
I need to prove this using induction!
vagrant elbow
what do you mean by different powers of 2
idle tusk
what do you mean by different powers of 2
he means distinct
velvet hemlock
If N is even, then :
N=2k for some k .k can be represented as a sum of different powers of 2.
Therefore, N=2k can also be represented as a sum of different powers of 2 (just one power higher for each term in k's representation)
@tropic oxide
this is a part just part
I Assumed that for some arbitrary natural number k, where 1≤k<N, the statement is true.
tropic oxide
i said not to ping me, but ok
velvet hemlock
Im sorry for being rude btw
tropic oxide
it's whatever
velvet hemlock
I would be happy to know what u think and ty
lyric narwhal
Given a number N that is natural (N>=1) it is necessary to prove that any number...
Doesn’t this directly come from the fact that every positive integer has a unique binary equivalent?
velvet hemlock
ye i think so
crimson sedge
How did k = -1 and k = 1/10 come?
cedar kilnBOT
How did k = -1 and k = 1/10 come?
vague rapids
k+1=0 or 10k-1=0
opaque root
When you multiply two things and that’s equal to 0, either one is zero, the other is zero or both are zero. AB = 0, either A=0, B=0 or (A and B) =0
cedar kilnBOT
@crimson sedge Has your question been resolved?
fringe pollen
\frac{x}{a}+\frac{y}{b}=8
cedar kilnBOT
\frac{x}{a}+\frac{y}{b}=8
fringe pollen
/frac{x}{a}+\frac{y}{b}=8
lyric narwhal
surround the initial expression in $$
lyric narwhal
$\frac{x}{a}+\frac{y}{b}=8$
wraith daggerBOT
kheerii
atomic saddle
thats possible
lyric narwhal
jus need to know the steps
what would you do first?
atomic saddle
- on side is - on the other'
fringe pollen
transform the equation 4x + y = 8 to
$\frac{x}{a}+\frac{y}{b}=1$
wraith daggerBOT
skrr
lyric narwhal
yeah
fringe pollen
yeah so what do I do when its 4x divided by 8
is it just going to be
$\frac{x}{2}+\frac{y}{8}=1$
wraith daggerBOT
skrr
lyric narwhal
yeah looks good
fringe pollen
is that it
cedar kilnBOT
@fringe pollen Has your question been resolved?
fringe pollen
a=2 and b=8
thank you, ive forgotten a lot of things bout this topic can you help me with another one if you dont mind? I just need to recall
" Given the gradient of straight line is -2. "
Find the x-intercept
so the coords r ( 3 , 1 )
I know that in order to get the x-intercept, you need to make the y value equals to 0 but is that it? I think im missing some steps
cedar kilnBOT
@fringe pollen Has your question been resolved?
fringe pollen
nobody cares
paper gull
I think i'm missing something here
cedar kilnBOT
I think i'm missing something here
paper gull
i need to find the area encased between 2 curves sin(2x) and 2sinx
1 of their areas
so i need to find 2 consecutive intersections, so i equated sin(2x) = 2sinx
=> 2sinxcosx = 2sinx
cosx = 1 ; x cannot equal k(pi), where k is a natural number
so what are the solutions???? i'm a bit confused
mighty shuttle
0 and pi is one set
wraith reef
cosx = 1 ; x cannot equal k(pi), where k is a natural number
why can it not equal kpi?
mighty shuttle
paper gull
why can it not equal kpi?
because we just divided by sinx, so we would be dividing by 0, no?
so we need to restrict it for those values
wraith reef
because we just divided by sinx, so we would be dividing by 0, no?
ah ye true
paper gull
(i think, at least)
mighty shuttle
because we just divided by sinx, so we would be dividing by 0, no?
well, the limit is 0, so it roughly holds true
it would be an open interval
the end points have no significant contribution to the area, whether inclusive or exclusive, so just integrate between those bounds
paper gull
well, the limit is 0, so it roughly holds true
ok, but cos(pi) = 1 isn't true either
cos pi is -1
paper gull
well, the limit is 0, so it roughly holds true
i knowwwwww... intuitively at least it feels like that, but the fact that this is before taking any integral there are no limits involved here, it's just realllly uncomfortable to do that
mighty shuttle
i knowwwwww... intuitively at least it feels like that, but the fact that this i...
in the integral calculus, atleast afaik, there's no real way to differentiate(pun not intended) between a close interval [a,b] and an open one (a,b) so the integral will be the same
paper gull
ok, but cos(pi) = 1 isn't true either
but what about this?
paper gull
'tis, i see
paper gull
2sin(pi)cos(pi)=2sin(pi)
that value is negated because for that value (pi), this relation doesn't hold true
mighty shuttle
that value is negated because for that value (pi), this relation doesn't hold tr...
why not?
0=0
paper gull
yes but if we proceed to the next step, we would be dividing by 0
so it's negated by the time we come to cosx=1
mighty shuttle
in that case solve by simply substituting values
opaque root
|sin(2x) - 2sin(x)| between 0 and pi
mighty shuttle
so it's negated by the time we come to cosx=1
or sin(x)=0; 2sin(x)(cos(x)-1)=0
ah, I see what you mean, yes, again find the limit at x=pi
paper gull
limit?
mighty shuttle
the limit at x=pi is 0, is it not?
crimson sedge
hi! i'm having a problem with this exercise
cedar kilnBOT
hi! i'm having a problem with this exercise
distant wyvern
its an isoceles triangle so those two angles will be equal. also they have the same area (rpq and spq) + ros is similar to pos. how do i proceed?
cedar kilnBOT
its an isoceles triangle so those two angles will be equal. also they have the ...
@distant wyvern Has your question been resolved?
crimson sedge
!status
cedar kilnBOT
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
Is S just a random point on the line?
distant wyvern
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
2
distant wyvern
Is S just a random point on the line?
yep, according to the q. it does look very perpendicular tho
distant wyvern
ook..?
crimson sedge
1st one: If S is a random point on the line the answer shouldnt depend on where S lays exactly. So imagine S is very far to the right. Then what will happen to PS and QS?
crimson sedge
Wait what
cedar kilnBOT
crimson sedge
Oh yeah you are right
distant wyvern
thats what the answer key says as well
crimson sedge
I thought the bottom left option was B
distant wyvern
Oh yeah you are right
ahh happens
cedar kilnBOT
Available help channel!
rare solstice
Let’s say I wanna buy 6 fishes, but I don’t know the gender.
What’s the probability/chance of me getting at least one female and one male fish?
opaque root
You can get the probability all of them are male and add the probability all of them are female
So when that doesn’t happen u get at least one of each
tribal kite
Let’s say I wanna buy 6 fishes, but I don’t know the gender.
What’s the probabi...
What's the options to not get at least one female and male
All male or all female right
so just take 1- that
rare solstice
Guys do you not understand
I wanna have the chance of me getting at least one female and at least one male
Fish
So it can be that all of them are 6 males or 6 all are females
Can y’all find the chance?
opaque root
If you say 1 male ANd 1 female at least that means they can’t be 6 males
AND means both
idle tusk
So it can be that all of them are 6 males or 6 all are females
does that satisfy your condition?
FFFFFF - 6 female fish
MMMMMM - 6 male fish
MFFFMF - 2 male fish and 4 female fish
do all of these examples count? or only 2 male fish and 4 male fish?
cedar kilnBOT
@rare solstice Has your question been resolved?
rare solstice
do all of these examples count? or only 2 male fish and 4 male fish?
I wanna have chances in %
idle tusk
yes i know
rare solstice
<@&286206848099549185> someone else help cause they don’t understand anything
idle tusk
I'm just trying to understand what do you mean by "at least one female and one male fish"
if FFFFFF and MMMMMM don't satisfy that, then the probability is 1-(probability of getting all male + probability of getting all female)
crimson sedge
2 ways to solve this:
1)Use bayes theorem here
Or
2) use PNC to calculate the number of possibilities then use basic probability
opaque root
<@&286206848099549185> someone else help cause they don’t understand anything
You are rude and you are the one who doesn’t understand what’s going on here
Listen to the people is helping you or explain yourself better
odd verge
whats the number of male and female fish(es) present
cedar kilnBOT
@rare solstice Has your question been resolved?
rare solstice
this is the probability
No?
rare solstice
<@&286206848099549185>
lyric latch
No?
do you know sum rule of probability?
If you don't, you have no right to say that the helpers "don't understand anything"
dry latch
<@&286206848099549185>
you need to have a basic underdtanding of the topic before asking for help its not the helpers fault
the probability of getting at least one female and one male fish out of 6 fishes is 31/32.
crimson sedge
<@&286206848099549185>
do you even know what baye's theorem application is or how to impliment PnC in probability?
cedar kilnBOT
@rare solstice Has your question been resolved?
winged flint
anyone please help me with this question-Consider that a, b, c, d are positive real numbers satisfying (a + c)(b + d) = ac + bd.
Find the smallest possible value of S=a/b+b/c+c/d+d/a
cedar kilnBOT
cedar kilnBOT
Available help channel!
lament kelp
log8 2
fallen moat
in case you really don't wanna use latex, you can try to use _ for subscript
e.g.
log_8 2
and for longer expression, you may have to use 
lament kelp
log_8 2
fallen moat
yes
lament kelp
I’m not sure how to do it
primal socket
Do what?
fallen moat
use the change of base property that we recalled earlier
lament kelp
to ln?
lament kelp
I don’t see a reason to
fallen moat
since, you know, 8 and 2 both powers of 2
lament kelp
Right
fallen moat
usually, when we are simplifying log with "special" bases, we tends to use the "change of base property"
lament kelp
Log_2/log_8
fallen moat
$\log_82=\frac{\log_22}{\log_28}$
wraith daggerBOT
Biscuity
fallen moat
lament kelp
So the two logarithm can be chosen?
fallen moat
the two log need to be of the same base
fallen moat
So the two logarithm can be chosen?
which we choose 2 in this case
lament kelp
Right
Okay
Hmm
1/2?
No
I meant 1/3
i need to read more about this property
Thank you
.close
cedar kilnBOT
fallen moat
i need to read more about this property
cedar kilnBOT
Available help channel!
royal dock
cedar kilnBOT
royal dock
I need help for solve this limit
my idea was to use the principle of substitution of infinitesimals
but i think is wrong my idea
rugged palm
It may work, what did you try?
royal dock
the solution should be** f(x) lower order than g(x)**
vast pike
use taylor expaion of ln and exp
royal dock
It may work, what did you try?
my idea was just -2x/3x but is probably wrong
rugged palm
Something is a bit off, are you sure about that denominator?
royal dock
this is the exercise from the book
rugged palm
And you are supposed to do f(x)/g(x), right?
What I meant before is, are you sure you applied the rule correctly in the denominator? Are you also sure that you didn't leave anything behind?
royal dock
yeah i should f(x)/g(x) and from this understand after some calcolous what infinitesimals order is
rugged palm
Are you italian by any chance?
royal dock
yes
rugged palm
Bene! Allora, io gli infinitesimi me li immagino un po' come se una funzione "arrivasse a 0 (oppure qualsiasi altro valore a cui tende limite) più velocemente di un'altra"
royal dock
okk
rugged palm
Nel denominatore hai un'esponenziale, una funzione che notoriamente cresce "velocemente", e nel numeratore un logaritmo, una funzione che notoriamente cresce "lentamente". Però devi vedere quello che fanno in un intorno abbastanza piccolo di x = 0, che è il valore a cui tende il limite
Il limite puoi risolverlo per sostituzione come hai fatto tu, però hai sbagliato dei passaggi nel denominatore, perchè hai (spoilers) || lasciato indietro la x || e || applicato male un asintotico, che per ottenere devi prima cambiare di segno ||
In alternativa se le hai già fatte puoi usare le espansioni di taylor come ti ha consigliato everg
(Translation: otherwise, you can do what everg recommendend and use taylor expansions)
royal dock
no, ancore no le ho fatte le espansioni di taylor
rugged palm
Ah ok, riprova con il metodo che stavi usando, fai bene le sostituzioni però
royal dock
si una cosa sola, mi spieghi dove ho applicato male l'asintotico?
al denominatore dovrei fare -3x?
wraith daggerBOT
Nonna
rugged palm
È questo l'asintotico, tu lì ce l'hai del segno opposto
quindi prima ti conviene raccogliere un -
wraith daggerBOT
Nonna
rugged palm
ed ora puoi usare l'asintotico, però la x che hai lì al denominatore fuori dall'esponenziale non scompare nel nulla, rimane lì
rugged palm
si
royal dock
però in questo caso diventerebbe (-2x)/(-3x^2) giusto?
rugged palm
Si
royal dock
aspe una cosa che ora non mi ricordo, l/0=inf?
l inteso come numero reale
perchè se il procedimento è giusto potrei semplificare ed ottenere -2/-3x
a questo punto l'unca cosa che posso fare è sostituire x con 0
rugged palm
l/0 è indefinito, qualunque sia l.
Se c'è il limite (!) invece devi vedere da dove arriva quello 0 nel denominatore, dovresti vedere se ti viene lo stesso limite da sinistra e da destra, e allora hai il risultato del limite
royal dock
perchè se il procedimento è giusto potrei semplificare ed ottenere -2/-3x
fino a qui il procedimento è corretto si?
ora io non saprei come procedere, prechè se sotituisco x con 0 non risolvo niente perchè sarebbe un risultato indefinito, come dovrei fare?
rugged palm
È una forma di limite che dovresti conoscere, però prova a separalo in limite destro e sinistro e vedi se ti viene la stessa cosa
Prova proprio a calcolare il valore della funzione per valori piccoli di x, prima da destra di 0, poi a sinistra
e così ne vedi l'andamento
royal dock
scusa, forse mi sbaglio, ma per il limite del quoziente l/0 non è uguale a |infinito|? (metto il modulo perchè può essere sia +inf che -inf in base sia ad l che a 0)
rugged palm
Si, ti viene o +inf o -inf, però devi sapere se ti viene lo stesso infinito da entrambi i lati
In soldoni, sti limiti di -2/3x da sinistra e destra hanno lo stesso valore?
royal dock
avremo dei valori leggermente diversi perché da sinistra tenderà ad un valore leggermente più piccolo di 0, da destra leggermente più grande
rugged palm
?? Come leggermente più piccoli o più grandi, abbiamo detto che o è +inf o è -inf
puoi spiegarmi bene il ragionamento che hai fatto?
royal dock
no vabbè ho sbagliato perchè ho ragionato in modo più che altro generico, in questo caso da sx tende a +inf e da dx a -inf
.close
cedar kilnBOT
rugged palm
no vabbè ho sbagliato perchè ho ragionato in modo più che altro generico, in que...
È il contrario
cedar kilnBOT
Available help channel!
crimson sedge
i need help to solve the rendering equation in terms of the integral using the monte carlo method in psuedocode, which i can easily translate to programming
crimson sedge
im not sure how you add all the values together to solve the integral
more so as more samples are taken
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
viscid wolf
hey guys, i tried u-sub and it didn't work, i guess integration by parts will not work also, so how can i solve it
viscid wolf
how can i simpilify those exponents
mighty shuttle
The hard way would be to expand it using the binomial theorem
viscid wolf
the easy way?
mighty shuttle
Let me think, just a minute
Take 1/X outside try subbing 7+ 1/x=t
Or something similar to that
tropic oxide
why not factor x^3 out of the parenthesis
viscid wolf
i guess i found it, there is an amazing exponent rule i found
tropic oxide
you will get $\int \frac{(7x^2+8)^7}{x^{16}} \dd{x}$
wraith daggerBOT
Ann
viscid wolf
but is it true or not idk
viscid wolf
i guess i found it, there is an amazing exponent rule i found
is that true, like can i solve it using that way? @tropic oxide
tropic oxide
i guess i found it, there is an amazing exponent rule i found
this is badly written
viscid wolf
i guess i found it, there is an amazing exponent rule i found
we will just use this rule, then we will get (7x-7)^5 then we will use u-sub and the final answer will be 1/42 (7x-7)^6 + C
$\frac{1}{42}(7x-7)^6 + C
$\frac{1}{42}(7x-7)^6 + C$
wraith daggerBOT
just be ok
cedar kilnBOT
@viscid wolf Has your question been resolved?
cedar kilnBOT
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Available help channel!
dry dirge
cedar kilnBOT
dry dirge
find maclaurin series of $sin^2(x)$
wraith daggerBOT
Filga
fallen moat
consider what will happen in your final answer when n=0
dry dirge
if n=0 then sin^2x = 0
fallen moat
nah, not x=0, i mean the case for n=0
what is the expression inside the sum when n=0
dry dirge
-1/2
dry dirge
will it cancel out anything?
1/2-1/2=0 that was what i said first
dry dirge
if n=0 then sin^2x = 0
here
tropic oxide
hold up
tropic oxide
correct unswer is the same only without 1/2
are you sure about this
your formula gives f(0) = 0 just as it should be
dry dirge
yes i checked the unswer even in wolfram
tropic oxide
answer* ?
dry dirge
yes
tropic oxide
,w sum[n=0, infty] (-1)^(n+1) * 2^(2n-1)/(2n)! * x^(2n)
wraith daggerBOT
tropic oxide
,w 1/2 + sum[n=0, infty] (-1)^(n+1) * 2^(2n-1)/(2n)! * x^(2n)
dry dirge
yes
wraith daggerBOT
tropic oxide
your answer is correct
tropic oxide
1/2 - 1/2 cos(2x) is sin^2(x)
fallen moat
well, if i google for Maclaurin series for sin²(x), we will have the starting n=1 instead of 0, if that's what you mean
tropic oxide
,w sum[n=0, infty] (-1)^(n+1) * 2^(2n-1)/(2n)! * x^(2n)
this is "same as yours but without the 1/2"
dry dirge
tropic oxide
yeah, it starts from k=1 and not from k=0 like yours!
so you were wrong to say that the correct answer was the same as yours minus the 1/2 !
dry dirge
this is the same as my answer without 1/2
dry dirge
are you tripping or am i tripping?
fallen moat
latter
tropic oxide
it starts from k=1 and not from k=0 like yours!
tropic oxide
are you tripping or am i tripping?
it's you.
dry dirge
ah
when k =1 the result will be x^2/2 right ?
ok ok i get this my first therm is 0 and then comes x^2/2
tnx boys
.close
wild belfry
So I got the answer, but I still kinda dont understand the question
wild belfry
I just found the extreme point, it was obvious what I had to do
But what does it mean by x>0?
royal loom
It’s just clarifying like
When you go to solve 1/x-6=0
You only have to care about x>0 because ln(x) in your original function only takes on positive values of x anyways
Which is weird that it says this because 1/x-6=0 only has a positive solution anyways but like if it was something else like x^2=9 then it’d matter and you’d only take x=3 (and not x=-3)
wild belfry
Ahh I think I get you
Cause the answer can only be positive
Makes sense
Oke thats all I was wondering haha
Thank you!
❤️
.close
honest moon
Just need to make sure it's right, I'm not sure because I asked two people and they said different things
honest moon
I have more tasks to ask if it's right or wrong 😅
tropic oxide
,calc sqrt(4.3^2 + 5.7^2)
wraith daggerBOT
Result:
7.1400280111495
The task said, first make the calculations and then draw the construction
Is beta right? I saw on a page for calculating that I swapped beta and alpha
tropic oxide
oh yes, you did mix them up
side b is opposite to angle β
not side a
this would not happen if you made a crude sketch that tells you what is where
honest moon
I made that but I'm not the best in this theme xD
tropic oxide
can you show
honest moon
Like this now?
honest moon
can you show
It was a piece of paper that I threw away after I finished all the tasks
Can I show u a, b, c and d also?
When this isn't right, maybe I made more mistakes
tropic oxide
sure
but i would also like to see the original problems, for reference
tropic oxide
ok
i strongly recommend that you don't try to do these problems blind
like you showed
tropic oxide
brb
im gonna assume all your arithmetic is correct as written
under that assumption everything seems correct
cedar kilnBOT
@honest moon Has your question been resolved?
honest moon
Thank you for your help!! I appreciate it
celest apex
why does (1 2) and the 3-cycles generate S6?
cedar kilnBOT
why does (1 2) and the 3-cycles generate S6?
tropic oxide
is this a "i don't know what's going on" or a "i think this is false" type of question from you?
celest apex
Sn is generated by the transpositions (1, 2), (1, 3), . . . ,(1, n)
or (1 2) and (1 2 ... n)
tropic oxide
ok right
so heres the idea
given a subset S of a group G,
if we have another set S' for which it's known that S' generates G,
and we show that every element of S' can be generated from S,
then we'll know that S generates G too
do you agree with this idea?
celest apex
yes
tropic oxide
ok right
so from this
im gonna show you how to generate (1 i) for any i ∈ {3,4,5,6} using (1 2) and the 3-cycles
(1 i) = (2 i j) (1 2) (2 j i)
where j is a number distinct from 1, 2 and i
verify for yourself that this works (unless we run into a left-right miscommunication...)
near aurora
Can someone help me i forgot how to do modul equations beed help with 13
south tundra
Can you recall the definition of a module?
cedar kilnBOT
@near aurora Has your question been resolved?
south tundra
Right, so for simplifying expressions we just need to figure out whether the number inside the module is positive or negative
What's the sign of $2 - \sqrt3$?
wraith daggerBOT
A Lonely Bean
cedar kilnBOT
south tundra
.reopen
cedar kilnBOT
✅
south tundra
**A Lonely Bean**
@near aurora
near aurora
Its positive
south tundra
Right, so $\abs{2 - \sqrt3}$ is just $2 - \sqrt3$
wraith daggerBOT
A Lonely Bean
south tundra
What about $1 - 2\sqrt3$?
wraith daggerBOT
A Lonely Bean
near aurora
That’s negative
south tundra
Can you simplify that?
near aurora
So a number in a modul can’t be negative right
south tundra
A module can't be negative, yeah
If the number inside is negative, you just put - in front of it
To make it nonnegative
near aurora
Is the answer 3 ?
south tundra
Yes
near aurora
Ok thanks
cedar kilnBOT
@near aurora Has your question been resolved?
carmine kernel
Let $K$ be a closed curve. Prove that $\oint_K(\phi\nabla\psi,\Vec{t})ds=-\oint_K(\psi\nabla\phi,\Vec{t})ds$
How can I prove this?
wraith daggerBOT
Jordi
carmine kernel
I know that if the left item of the inner product is conservative, that the cyclic integral is equal to 0, but I can't find a proof that this is conservative.
.close
sharp sequoia
I love chicken nuggets please help me find a formula that gives me the volume of a chicken nugget
sharp sequoia
never mind its too late my little brother ate my chicken nuggets like usual another time
.clse
.close
cedar kilnBOT
crimson sedge
everyone laughed
dense locust
mighty shuttle
I love chicken nuggets please help me find a formula that gives me the volume of...
Find it's approximate dimensions and treat it as a cuboid
Its
cedar kilnBOT
Available help channel!
halcyon granite
Hi folks 🙂
Can someone please help me how to proceed?
\begin{align*}
&\lim_{x\to\infty} x^\frac{5}{4} \left( \sqrt[3]{x+1}+\sqrt[3]{x-1}{\color{orange}-2\sqrt[3]{x}} \right) = \lim_{x\to\infty} x^\frac{5}{4} \left( \sqrt[3]{x+1} {\color{orange}- \sqrt[3]{x}} + \sqrt[3]{x-1} {\color{orange}- \sqrt[3]{x}} \right) \
&= \lim_{x\to\infty} x^\frac{5}{4} \left( \frac{x+1-x}{(x+1)^\frac{2}{3}+[(x+1)x]^\frac{1}{3}+x^{\frac{2}{3}}} + \frac{x-1-x}{(x-1)^\frac{2}{3} + [(x-1)x]^{\frac{1}{3}} + x^\frac{1}{3}} \right) && \text{difference of cubes} \
&= \lim_{x\to\infty} \left( \frac{
x^{\cancelto{\frac{7}{12}}{\frac{5}{4}}}
}{ x^{\cancel{\frac{2}{3}}} \left[ (1+\frac{1}{x})^\frac{2}{3} + (1+\frac{1}{x})^\frac{1}{3} + 1 \right] } - \frac{ x^{\cancelto{\frac{7}{12}}{\frac{5}{4}}} }{ x^{\cancel{\frac{2}{3}}} \left[ (1-\frac{1}{x})^\frac{2}{3}+(1-\frac{1}{x})^\frac{1}{3}+1 \right] } \right) && \text{factor the } x \text{'s} \
&= \lim_{x \to\infty} x^{\frac{7}{12}} \cdot \left( \frac{1}{ (1+\frac{1}{x})^\frac{2}{3} + (1+\frac{1}{x})^\frac{1}{3} + 1 } - \frac{ 1 }{ (1-\frac{1}{x})^\frac{2}{3}+(1-\frac{1}{x})^\frac{1}{3}+1 } \right)
\end{align*}
wraith daggerBOT
Sweet Tea 🧋
halcyon granite
I've got here $[\infty \cdot 0]$, but I don't see right away what else could be done
wraith daggerBOT
Sweet Tea 🧋
long arrow
carmine kernel
How did you get that $\frac{x^{5/4}}{x^{2/3}}=x?$
wraith daggerBOT
Jordi
halcyon granite
daaaamnnn, used sympy cause wanted to do it faster xDD 😂
lemme correct it, one moment
\begin{align*}
&\lim_{x\to\infty} x^\frac{5}{4} \left( \sqrt[3]{x+1}+\sqrt[3]{x-1}{\color{orange}-2\sqrt[3]{x}} \right) = \lim_{x\to\infty} x^\frac{5}{4} \left( \sqrt[3]{x+1} {\color{orange}- \sqrt[3]{x}} + \sqrt[3]{x-1} {\color{orange}- \sqrt[3]{x}} \right) \
&= \lim_{x\to\infty} x^\frac{5}{4} \left( \frac{x+1-x}{(x+1)^\frac{2}{3}+[(x+1)x]^\frac{1}{3}+x^{\frac{2}{3}}} + \frac{x-1-x}{(x-1)^\frac{2}{3} + [(x-1)x]^{\frac{1}{3}} + x^\frac{1}{3}} \right) && \text{difference of cubes} \
&= \lim_{x\to\infty} \left( \frac{
x^{\cancelto{\frac{7}{12}}{\frac{5}{4}}}
}{ x^{\cancel{\frac{2}{3}}} \left[ (1+\frac{1}{x})^\frac{2}{3} + (1+\frac{1}{x})^\frac{1}{3} + 1 \right] } - \frac{ x^{\cancelto{\frac{7}{12}}{\frac{5}{4}}} }{ x^{\cancel{\frac{2}{3}}} \left[ (1-\frac{1}{x})^\frac{2}{3}+(1-\frac{1}{x})^\frac{1}{3}+1 \right] } \right) && \text{factor the } x \text{'s} \
&= \lim_{x \to\infty} x^\frac{7}{12}\cdot \left( \frac{1}{ (1+\frac{1}{x})^\frac{2}{3} + (1+\frac{1}{x})^\frac{1}{3} + 1 } - \frac{ 1 }{ (1-\frac{1}{x})^\frac{2}{3}+(1-\frac{1}{x})^\frac{1}{3}+1 } \right)
\end{align*}
wraith daggerBOT
Sweet Tea 🧋
halcyon granite
still, no idea what to do next
I mean, I could possibly try to subtract two fractions, but I'm not sure anything fruitful will appear from that
<@&286206848099549185>
cedar kilnBOT
@halcyon granite Has your question been resolved?
cedar kilnBOT
@halcyon granite Has your question been resolved?
fallen moat
<@&286206848099549185>
hello! do you still need help with your question? @halcyon granite
halcyon granite
hello! do you still need help with your question? <@1181333984081367151>
hi!
yep
fallen moat
**Sweet Tea 🧋**
ok, lemme check your steps first, it'll take a bit of time
looks good except a small typo, anyways
halcyon granite
looks good except a small typo, anyways
well, maybe the steps are correct, but they lead nowhere 😆
fallen moat
yea, that's what I'm struggling with too right now😆
fallen moat
I mean, I could possibly try to subtract two fractions, but I'm not sure anythin...
but this seems to be working ig
halcyon granite
but this seems to be working ig
huh?
fallen moat
if writing the whole thing is tedious, just try to write the numerator out and see what happens
halcyon granite
in the numerator we'll maaaybe get something decent, but the denominator will be just a mess
fallen moat
but things will be cancelled out since tou made some nice 1/x 's
I'll work on it right now, let's see if i can something
hmmm
still thinking if there's any other way
do you know if the answer is infinity or 0?
halcyon granite
do you know if the answer is infinity or 0?
nope, but I can ask wolfram
,w lim_(x -> +infty) x^(5/4) ( (x+1)^(1/3) + (x-1)^(1/3) - 2 * x^(1/3) )
wraith daggerBOT
fallen moat
hmmm
halcyon granite
hmmm
I mean, maybe the whole idea of separating $-2\sqrt[3]{x}$ as two $\sqrt[3]{x}$ was in the wrong direction..
wraith daggerBOT
Sweet Tea 🧋
fallen moat
hmmm
i remember i have done similar stuff before
i kinda get it now
lemme type it out, it'll be tedious
Let $a=\sqrt[3]{x+1}$, $b=\sqrt[3]{x}$, and $c=\sqrt[3]{x-1}$.
Then $\sqrt[3]{x+1}+\sqrt[3]{x-1}-2\sqrt[3]{x}$ becomes $a-2b+c$.
wraith daggerBOT
Biscuity
fallen moat
let's start with these
fallen moat
**Sweet Tea 🧋**
from the 2nd line of this we have,$$a-2b+c$$
$=\frac1{a^2+ab+b^2}-\frac1{b^2+bc+c^2}$
wraith daggerBOT
Biscuity
fallen moat
please don't mind the format, I'm lazy 😆
halcyon granite
hmm, and the denominator looks like a part of $(a^3-b^3)$
wraith daggerBOT
Sweet Tea 🧋
halcyon granite
and $(b^3-c^3)$ accordingly
wraith daggerBOT
Sweet Tea 🧋
fallen moat
by finding common factors, we have,
$$\frac{c^2+bc-a^2-ab}{(a^2+ab+b^2)(b^2+bc+c^2)}$$
which is equal to
$$\frac{(c-a)(a+b+c)}{(a^2+ab+b^2)(b^2+bc+c^2)}$$
wraith daggerBOT
Biscuity
fallen moat
now, we break this $c-a$ into
$$\frac{c^3-a^3}{c^2+ca+a^2}$$
which is just
$$\frac{-2}{c^2+ca+a^2}$$
wraith daggerBOT
Biscuity
fallen moat
now we have $a-2b+c$ equals to $$\frac{(a+b+c)}{(a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2)}$$
wraith daggerBOT
Biscuity
