This is a more general question than a specific example...
#help-13
wild belfry
tropic oxide
if you're familiar with card games you can ask yourself like "is this more like cards in hand or cards arranged on a table"
wild belfry
if you're familiar with card games you can ask yourself like "is this more like ...
In which one is order important and repetition allowed?
tropic oxide
this one's about order specifically
and order is important in the "arranged on a table" scenario
with cards in your hand you can rearrange them any way you like -- what matters is not which card is the leftmost in your hand but what cards you have and don't
wild belfry
and order is important in the "arranged on a table" scenario
As in arranged face up in order from lowest to highest?
tropic oxide
no
think more like poker
it kinda matters for gameplay purposes which card ends up as the turn and which as the river
vs. the same cards being known already at the flop
wild belfry
Hmmm I dont know poker haha
But for an example
This is like cards in the hand because it doesnt matter about which friend gets which icecream, right?
Oh wait i just checked it says order is important...
tropic oxide
This is like cards in the hand because it doesnt matter about which friend gets ...
it DOES matter who gets what flavor
wild belfry
with cards in your hand you can rearrange them any way you like -- what matters ...
Ok I dont really understand then haha
tropic oxide
some ppl might have preferences for or against some of these
if you just order "2 vanilla, 4 chocolate" it does matter which of your friends get the vanillas
wild belfry
Ohhhhh
I see
Ok 1 sec another example
So order isnt important right? Cause were just checking all the different combinations?
So its like cards in hand?
tropic oxide
order is important in the sense of it matters who's the chair, who's the treasurer and who's the admin -- those positions are not interchangeable
but among the rest of the committee members it doesnt
... maybe this was a bad idea all along to give the cards analogy
wild belfry
Ah sry i didnt post the full thing
wild belfry
order is important in the sense of it matters who's the chair, who's the treasur...
So order is still important?
tropic oxide
yeah ok i think i dont know how to explain this without just giving out the answer as is
definitely drop the cards analogy
wild belfry
Im just trying to figure out about order and repetition first before I actually attempt these questions
gonna go watch some more videos on this topic
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cedar kilnBOT
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muted cedar
no idea what to do after finding the gradient vector
cedar kilnBOT
no idea what to do after finding the gradient vector
ancient lodge
no idea what to do after finding the gradient vector
The gradient vector needs to point in the same direction as (1,1)
aka they have to be (positive) scalar multples of each other
muted cedar
The gradient vector needs to point in the same direction as (1,1)
ye so
< 2xy + y^2, x^2 + 2xy > = c * < 1, 1 >
where c is some scalar positive constant
ancient lodge
ye so
< 2xy + y^2, x^2 + 2xy > = c * < 1, 1 >
where c is some scalar positive c...
correct
muted cedar
after that i equate them to each other ?
ancient lodge
mhm
muted cedar
i get y = x, -x
muted cedar
yep
ancient lodge
so check if those two cases (y=x and y=-x) give you a c is positive
ancient lodge
alr thank u so much
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onyx girder
Can anyone help me out on this?
cedar kilnBOT
Can anyone help me out on this?
dire geode
plug x=-3 into g(x)
then use that number in red, suppose it's some number c. then repeat with x=c plugged into f(x)
onyx girder
Would it be g(-3)=2 ?
onyx girder
This was like the only problem I was lost on. I've always struggled with graphs.
f(2)=2???
dire geode
f(2) = 2 is correct, but you were wrong about g(-3)=2
dire geode
g(-3) is the y value on the line g(x) when x = -3
read this and try again
onyx girder
follow the vertical line up to the red point?
Wait
I think I get it
You just go up to the blue line from the -3 point
I think
OHHHHH it was 4!!!!
Thanks for the help
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cedar kilnBOT
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dire storm
How does one come up with these repeating bit patterns? I assume you'd use a geometric series or such? It's been a while since I've done any analysis or calculus whatsoever and I'm just trying to revise for my computer systems midterm tomorrow and even if we don't have this on the exam (we will have stuff with 2^k, which isn't too bad) I just want to understand it for my own sake
surreal cave
geometric series
for the first note that:
[\sum_{n=1}^{\infty}\left(\frac14\right)^n=\frac{\frac14}{1-\frac14}=\frac13]
wraith daggerBOT
PajamaMamaLlama
dire storm
oooooh I see
surreal cave
then of course, this is 1/4^n so we're missing out on 1/2, 1/8, 1/32 etc. so that's why we alternative 0.01010... for 1/3
similar things occur for 1/5 and 1/10
dire storm
Right, that makes sense
thank you :)
I'm a little embarrassed that I missed such a simple sum š
surreal cave
I'm a little embarrassed that I missed such a simple sum š
no worries, more embarrassing things have been said/asked 
dire storm
no worries, more embarrassing things have been said/asked <:KEK:5862408773583503...
Understandable, nevertheless, thank you very much again for your help
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cedar kilnBOT
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smoky owl
Historical question: What was the first time someone wrote down a proof of the Pythagorean theorem? (Not pythagorean triples, not the statement, I'm looking for a proof)
upper abyss
As far as I understand, we don't know
cedar kilnBOT
@smoky owl Has your question been resolved?
smoky owl
Do we know of any that predates Euclid's elements?
hollow trail
from this, there appears to be an older proof for the special case of 3-4-5 triangles (could be easily generalized), but the first extant fully general proof appears to be in the elements
cedar kilnBOT
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void sand
I'm honestly not sure where to start on this problem 
I know that a simple group has no strict normal subgroups other than {e} by definition, but I don't see why that's important here, or what to do with the abelian assumption
void sand
could somebody lend me a suggestion?
hm, maybe contrapositive is easier here 
if A is not isomorphic to Z/p, then A is not generated by a single element a 
and maybe I can construct a normal subgroup of A like this
okay, I think this will be the plan after all 
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broken talon
How do I solve this
cedar kilnBOT
How do I solve this
broken talon
(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^{k}
avec
\binom{n}{k} = \frac{n!}{k!(n-k)!}
(x+2)^4 = x^4 + 8x^3 + 24x^2 + 32x + 16
How do I solve this
slender ginkgo
[(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^{k}]
avec
[\binom{n}{k} = \frac{n!}{k!(n-k)!}]
[(x+2)^4 = x^4 + 8x^3 + 24x^2 + 32x + 16]
wraith daggerBOT
k
slender ginkgo
What are u tryna solve here
hot cipher
Probably hes trying to prove that this is true, or at least how would one come to the last polynomial expression based on the first identity.
cedar kilnBOT
@broken talon Has your question been resolved?
torn marsh
I need some help with 4
cedar kilnBOT
I need some help with 4
livid hound
what have you tried
torn marsh
To be honest, we were never learnt finding derivatives of trig yet
so idk why they gave us this question
livid hound
that should've all be taught in calc 1 before integrals
torn marsh
we will learn trig sooon however
livid hound
course structure sounds a little dodgy,
try looking up derivatives and integrals of trig functions
fossil dawn
wait, then why are you expected to solve this before learning about trig derivs and integrals?
stiff brook
do u know the derivative of sinx
sudden cairn
do u know the derivative of sinx
uhh
livid hound
the csc, sec and stuff?
those are reciprocal trig functions
sudden cairn
It's cos
stiff brook
your lecturer is cooking you
sudden cairn
Bruh moment
Yeah you need to learn trig functions in calculus before you try integrating them
torn marsh
I mean
sudden cairn
Don't know how that would work
livid hound
course structure sounds a little dodgy,
try looking up derivatives and integrals of trig functions
sudden cairn
After you were given a question involving calc with trig functions?
livid hound
usually you'd be taught most derivatives before being introduced to integrals
sudden cairn
They're expecting you to do something that you haven't been taught
You might as well reinvent calculus at that point
livid hound
if you've done stuff with first principles you could get the derivatives yourself
sudden cairn
That's quite difficult if you haven't seen the derivation before
torn marsh
if you've done stuff with first principles you could get the derivatives yoursel...
i done the first principle
sudden cairn
You need to use geometry and the squeeze theorem to find lim[x->0]{sin(x)/x}
livid hound
do you know compound angle identifed and common limits involving trig functions
torn marsh
I dont think so
sudden cairn
Biggest bruh moment I swear
livid hound
probably best to just look up the result for now
sudden cairn
Has to integrate tan(x) without being taught derivatives of trig functions
Like what
torn marsh
thats weird fr
livid hound
if you want to do the question
or just wait for your class
stiff brook
erm akshually cotx
sudden cairn
Might as well skip it
livid hound
so you've never seen stuff like\ \
$\dv{x} \sin(x), [\sin(x)]'$?
wraith daggerBOT
ĻĪ±Ī¼Omeganato5
livid hound
course structure sounds a little dodgy,
try looking up derivatives and integrals of trig functions
sudden cairn
Try differentiating yourself
livid hound
that snapshot is enough to complete the question
sudden cairn
I love how a chemistry channel is teaching calculus š¤£
livid hound
if you had no issues with Q1 to 3
sudden cairn
Yeah just use u-substitution
torn marsh
I was never taught u sub as well
livid hound
u-sub isn't explicitly needed
it helps some people but the integrals in this set have a similar form
recognising the derivatives in that vid, you can apply the same idea
torn marsh
so its [ln(sinx)], upper bound: pi/2, lower bound: pi/4
livid hound
yes
sudden cairn
Your class is doing you dirty bro
stiff brook
so its [ln(sinx)], upper bound: pi/2, lower bound: pi/4
congrats!!
livid hound
no
you're not applying log and trig laws properly
and try not to do an excessive amount of things at once
i recommend to ALWAYS (even if its just a single character) put () around the argument of your logs
torn marsh
oh wait
livid hound
firstly i wouldn't apply that log law here
when you could do a lot of simplification evaluating directly
ln**(** sin(pi/2) ) - ln ( sin(pi/4) )
but if you really wanted to apply the difference to quotient law, that gets you something different to what you wrote down
livid hound
i recommend to ALWAYS (even if its just a single character) put () around the ar...
without those (), you treated lnsin as a log function
and in the subsequent step that sin also vanished
so its a mess
wraith daggerBOT
torn marsh
I got ln(2) again
livid hound
i recommend to ALWAYS (even if its just a single character) put () around the argument of your logs
this extends to ALL functions
it should've been clear that you can't extract that /2 from the sin(pi/2)
tropic oxide
i mean tbh, isn't this a manifestation of "op has no good grasp of what a function is bc he's not yet done that thorough algebra review he's in dire need of"?
livid hound
also the attempt at manipulation is excessive,
just because you see "something" doesn't mean you must apply some law to get rid of that
torn marsh
> i recommend to ALWAYS (even if its just a single character) put () around the ...
Didnāt I do it
livid hound
livid hound
the red part is invalid, and you dropped () around the pi/4
the whole point of having those ()
is that they're a hard indicator that you can't freely move stuff in/out of those parentheses
$\sin(kx) \redneq k \sin(x)$
wraith daggerBOT
ĻĪ±Ī¼Omeganato5
torn marsh
I see
torn marsh
just because you see "something" doesn't mean you must apply some law to get rid...
What do u mean
livid hound
well i'm assuming you applied difference to quotient log law
because
you saw you had a difference of logs
and you attempted to manipulate the multiple fractions because you saw multiple fractions present and didn't like that
in some cases it would be really helpful, but that doesn't mean that you should or have to do it every time
like the situation yesterday with the ln(1)
similar thing here, why not try evaluating directly
torn marsh
Yep ^
tropic oxide
is that how u evaluate
if you do not already know that log_a(1)=0 or need a reminder for yourself, then sure
livid hound
you could use that inverse relationship to justify the value of ln(1),
but there is no real need for that work and you can just assert that ln(1) = 0
evaluate: ln(1)
answer: 0,
(nothing else needed)
torn marsh
any log to 1 is equal to 0
livid hound
to is the wrong word
torn marsh
any log of 1 is equal to 0
livid hound
yes, assuming the base is valid
wraith daggerBOT
fox(x, y); ā(fox)/āx (Flower)
fossil dawn
likewise, $\sin(\frac{\pi}{4}) \neq \frac{\sin(\pi)}{4}$
wraith daggerBOT
fox(x, y); ā(fox)/āx (Flower)
fossil dawn
it has been pointed out to you already
fossil dawn
sin(pi/2) is nowhere near sin(pi)/2
^
torn marsh
I thought that was only for ln or log functions
tropic oxide
with FUNCTIONS IN GENERAL you CAN'T pull factors out like that.
UNLESS you explicitly know FOR A FACT that you can do that IN A SPECIFIC CONTEXT
livid hound
didn't i just say this
tropic oxide
let's try to forget about logs
just forget about logs for a bit
what is sin(pi/2)?
torn marsh
sin(1.57079ā¦)
tropic oxide
no, you should be able to tell me the exact value of it
fossil dawn
the value, please
tropic oxide
big nope
you definitely used a calculator and you definitely had it in degree mode
both of which were wrong
ok so basically you also need to review trigonometry a lot
cause right now you're kinda in a state where, as sad as it is to declare, you don't know squat
the ability to recall a trig value such as sin(pi/2) unassisted by a calculator is about as important as being able to multiply 3*4 without a calculator
torn marsh
To be honest, itās best to skip this question and come back to it later. I havnt learnt calculus of trig functions yet
fossil dawn
though if you want a basic example of why that doesn't hold generally
torn marsh
as stated earlier
fossil dawn
no need to even consider trig functions
just consider f(x) = x + 1
f(4/2) = f(2) = 2+1 = 3
but f(4)/2 = (4+1)/2 = 5/2
see the issue?
torn marsh
Yes
fossil dawn
we have rules in algebra for a reason, good sir
torn marsh
If we had f(x)= 10+x + 3 + 2
and had to evaluate f(x)/2, would it (10+x+3+2)/2
tropic oxide
To be honest, itās best to skip this question and come back to it later. I havnt...
you haven't learned TRIG FUNCTIONS THEMSELVES yet!
or you have but you forgor it all
fossil dawn
If we had f(x)= 10+x + 3 + 2
and had to evaluate f(x)/2, would it (10+x+3+2)/2
this would be correct as per the bracketing given
cedar kilnBOT
@torn marsh Has your question been resolved?
calm compass
Hey I am trying to prove that if n squared is dividable by 3 then so is n.
I just started my calculus course so syntax might be off.
The official courses solution is trying to proof by denying then show contradiction.
I am trying to proof by assuming then proving and I got to section 5.
I canāt find a way to prove that section and if I do find a way will this be a viable solution to the question?
Thanks in advance!
calm compass
chrome elk
Look at how elements of ā/3 behave when squared
chrome elk
In particular, when do they stay in ā/3
calm compass
Not sure I get u. Do u have any way of drawing it? From what I understood u want me to try and square the numbers in the set for instance the first number 1/3 squared is 1/9 meaning it is out of the set. The only numbers that stay in the set are when OOOOO
I got it mid sentence wait
chrome elk
Good
calm compass
How to prove that there isnāt any number down the line where they both exist when p isnāt natural?
chrome elk
Every element in ā/3 is one of three forms
n +(1/3)
n+ (2/3)
n
Show what happens for each form
calm compass
while n is in N right?
chrome elk
Also this is overcomplicating the problem. Sometimes just doing it by contradiction is fine
Yes
calm compass
Also this is overcomplicating the problem. Sometimes just doing it by contradict...
Ik itās also the official solution I just wanted to check if there was a way to prove it like this if I get stuck in an exam or something
Thank u so much tho
How do I close the channel?
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past wave
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cedar kilnBOT
calm compass
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chrome elk
Smh let OP do it
past wave
Lol
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rancid prairie
Need help with this problem
cedar kilnBOT
Need help with this problem
rancid prairie
So confused on where to start
tropic oxide
have you solved problems of this kind before?
"given sin(x)=[number] and some other info, find cos(x)"
restive glade
So confused on where to start
you can solve for this in a couple of ways
either you solve for x itself
or you use the pythagorean identity
restive glade
^
tropic oxide
let's let @rancid prairie answer the question i asked him, though.
rotund bloom
Need help with this problem
make a triangle and use pythagoras theorem
rancid prairie
what is happening lol
rancid prairie
"given sin(x)=[number] and some other info, find cos(x)"
not really
rotund bloom
I probably have just don't remember it
first make a triangle with the values ur given for sinx, cosx or tanx
rancid prairie
ye ye
tropic oxide
sin^2(x) + cos^2(x) = 1.
rotund bloom
u know that sinx = perpendicular/hypotenuse etc... right?
past wave
first make a triangle with the values ur given for sinx, cosx or tanx
Let ann help first
restive glade
tbh i think the triangle method is intended given how clean the values are
tropic oxide
u know that sinx = perpendicular/hypotenuse etc... right?
this is either poorly worded or incorrect or both
past wave
You can share your method afterwards
rotund bloom
this is either poorly worded or incorrect or both
i was thinking about tanx and sinx at the same time and mixed up
tropic oxide
and i would rather handle this on my own without interruption by anybody else
restive glade
š
rancid prairie
I'm listening Ann
tropic oxide
so starting with this
can you use the identity sin^2(x) + cos^2(x) = 1 and the known value of sin(x) to solve for cos(x)?
ignore the interval thing for the moment
we won't be done yet, but i want you to do this one step yourself.
tropic oxide
pothecary?
tropic oxide
py-tha-go-ras
rancid prairie
LOL
tropic oxide
anyway, go and do what i asked you.
rancid prairie
its translating it lol
tropic oxide
preferably don't jump ahead.
rancid prairie
so starting with this
can you use the identity **sin^2(x) + cos^2(x) = 1** and ...
Ok so it would be (3/5)^2 + cos^2(x) = 1?
tropic oxide
yes, keep going.
tropic oxide
cos = 4/5
ah no
cos^2(x) = (4/5)^2
at this point you should have stopped because the next step would be cos(x) = **Ā±**4/5
and now is where the interval thing comes in
[pi/2, pi] is the second quadrant; is cos(x) positive or negative here?
tropic oxide
yes, cos(x) = -4/5
rancid prairie
ik ik
ikik
I'm just fast typing it
I think I could figure it out from here
I get it now
thanks!
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rancid thorn
Can someone help me with this equation.
the task is "solve the following equation"
i tried back and forth, the furtherst i came was -xĀ² + x = -0,5 (it might include calculation mistakes)
wicked mantle
Can someone help me with this equation.
the task is "solve the following equatio...
That's decent
iron wren
$\frac{3x+1}{x}=2x+1$
wraith daggerBOT
ImOakley
iron wren
$3x+1=2x^2+x$
wraith daggerBOT
ImOakley
iron wren
i was going to ask if they got here because he says he got -x^2+x
sacred iron
i was going to ask if they got here because he says he got -x^2+x
Well it looked like you were about to give them the answer
iron wren
Well it looked like you were about to give them the answer
alr sorry
wraith daggerBOT
šøšššššššĀ³
sacred iron
You would multiply by š„ on both sides to get rid of the denominator
Which would be
wraith daggerBOT
šøšššššššĀ³
sacred iron
which you can distribute the š„
wraith daggerBOT
šøšššššššĀ³
sacred iron
Herro? 
you still there?
cedar kilnBOT
@rancid thorn Has your question been resolved?
sacred iron
š where did he go 
crimson sedge
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clever hazel
cedar kilnBOT
chrome elk
All the triangles that are created have two of their sides being equal
Could probably use herons formula in some way
The semiperimeter is r+k/2
clever hazel
i do not know this formula sadly
pastel vault
i do not know this formula sadly
consider the case where you have a triangle
each of the 3 triangles has area 1/2 r^2 sin(theta)
implying the central angles $\theta_1 = \theta_2 = \theta_3$
wraith daggerBOT
south
chrome elk
each of the 3 triangles has area 1/2 r^2 sin(theta)
Missing the sin
pastel vault
gah I was thinking about a circular sector
chrome elk
I realized
pastel vault
the key is to thus glue together congruent isosceles triangles
this is TMUA 2022 p2 by the way
wait, doesn't the figure in the solution assume that the circle centre can be on the boundary
cedar kilnBOT
@clever hazel Has your question been resolved?
grizzled shard
In lesson, we were asked to solve for x, where 4^(2x+1) = 8^(2x-1). The teacher only wanted the real solution, which I believe to be x= 5/2. However, I wondered if there were any other solutions, and lo and behold, wolfram alpha comes up with infinitely many. How do you solve for these solutions, & why are there infinitely many? How can you generally solve for all solutions of an exponential equation?
Thank you in advance.
grizzled shard
could you please explain what that is?
iron wren
have you done complex numbers
iron wren
it would involve the e^ix formula ig
pastel vault
do you understand how $\ln 4 = \ln(4 \cdot 1) = \ln(4 \cdot e^{2 \pi i})$?
sacred iron
what would that extent be? Do you know what the complex logarithm is, and the difference between the real logarithm?
wraith daggerBOT
south
grizzled shard
it would involve the e^ix formula ig
Yep ,I'm fine with that
grizzled shard
what would that extent be? Do you know what the complex logarithm is, and the di...
never heard of a complex log
pastel vault
e^(2 pi i) = 1
tropic oxide
yeah so the crux of it is that the function $e^z$ is periodic in the imaginary direction.
wraith daggerBOT
Ann
grizzled shard
e^(2 pi i) = 1
makes sense
tropic oxide
precisely because $e^{2\pi i} = 1$. the exponential is $2\pi i$-periodic!
wraith daggerBOT
Ann
grizzled shard
snazzy
pastel vault
e^(2 pi i) = 1
squaring both sides, you get e^(4 pi i) = 1
then e^(6 pi i) = 1 and e^(8 pi i) = 1 etc
so actually it's not just plusminus 2pi i, but 4pi i, 6pi i etc
so +2k pi i where k is an integer
wraith daggerBOT
MineNinja77777
grizzled shard
in order to get all solutions, I mean
pastel vault
in order to get all solutions, I mean
you can just do $\pm 2k \pi i$ to one of the sides
wraith daggerBOT
south
grizzled shard
how so?
tropic oxide
uhhhhhh hm
pastel vault
so $(2x + 1) \ln 4 = (2x - 1) \ln 8$
$x (2 \ln 4 - 2 \ln 8) = -\ln 4 - \ln 8$
$x (\ln(1/4)) = \ln(1/32)$
wraith daggerBOT
south
grizzled shard
yup
pastel vault
then for some reason I can't figure out, it suffices to do $x = \frac{\ln(1/32) + 2k i \pi}{\ln(1/4)}$
wraith daggerBOT
south
pastel vault
you don't need $x = \frac{\ln(1/32) + 2k i \pi}{\ln(1/4) + 2m i \pi}$
wraith daggerBOT
south
grizzled shard
okay
grizzled shard
yup
grizzled shard
what would that extent be? Do you know what the complex logarithm is, and the di...
what was this idea of a complex log?
sacred iron
Forget it I was probably wrong
grizzled shard
you sure?
sacred iron
most likely, unless another helper has something to say on it 
pastel vault
what was this idea of a complex log?
there's proper definitions for the complex log that are important
and that I am implicitly using
grizzled shard
could you explain these please?
pastel vault
so this is how the logarithm is defined when z is a complex number
not directly relevant, but it's for your understanding
grizzled shard
what does it mean by $Arg(z)$?
wraith daggerBOT
MineNinja77777
pastel vault
what does it mean by $Arg(z)$?
the angle that z makes with the positive real axis, on the complex plane
the complex plane is basically like the xy plane, but where the real axis = x-axis and the imaginary axis = y-axis
grizzled shard
yup
pastel vault
you can think about the complex number (a + bi) as the point (a, b)
cedar kilnBOT
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smoky topaz
I need help with my excerice 10 I just dont get it how u are able to calculate y to draw the graph
smoky topaz
Could anyone help me?
cedar kilnBOT
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smoky topaz
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buoyant python
Can someone help me verify this limit?
cedar kilnBOT
Can someone help me verify this limit?
buoyant python
Idk how to proceed
bright river
are you trying to proceed using the epsilon-delta definition of the limit ?
buoyant python
are you trying to proceed using the epsilon-delta definition of the limit ?
Yup.
I removed the abs value bc x is greater than 0
Itās between 0 and epsilon
bright river
Okay, then what you want to do is basically set an arbitrary epsilon
Then find some other quantity delta which is small enough to have x + sqrt(x) smaller than epsilon
(do you follow until here ?)
buoyant python
Yup
bright river
So basically you can't choose epsilon cause it's arbitrary. But once you've fixed that epsilon, you may choose delta
By delta, I mean that
it should satisfy
whenever $|x| < \delta$, then necessarily $|x + \sqrt x | < \epsilon$
wraith daggerBOT
Twenty
bright river
As you said, you can remove the | | here because x>0
buoyant python
**Twenty**
So i have to prove that
bright river
A hint I can give you: try to find a good $\delta$ such that, for all $x < \delta$ you have both $x < \varepsilon / 2$ and $\sqrt x < \varepsilon / 2$ for example. So that when you sum them up it's still smaller than $\varepsilon / 2 + \varepsilon / 2 = \varepsilon$
wraith daggerBOT
Twenty
bright river
Yep, tell me if you can find it :)
buoyant python
Let me write
It
Although my book says smth different
On how to prove that
It says
Wait lemme translate it
Its not english
Write and solve the inequality |f(x) - l| < epsilon, with epsilon > 0.
Observe that, for arbitrarily small values of x, the inequality is satisfied in a complete neighborhood of 0 and, in particular, in a right-hand neighborhood.
I guess i donāt have to use delta?
buoyant python
Yep, tell me if you can find it :)
My textbook is confusing me
cedar kilnBOT
@buoyant python Has your question been resolved?
buoyant python
what seems to be the issue sir
I canāt figure this exercise
summer aurora
this?
summer aurora
idk how youd do it without using delta
you still gotta use delta i think
whats the book saying
buoyant python
Write and solve the inequality |f(x) - l| < epsilon, with epsilon > 0.
Observe...
.
This is what its saying
buoyant python
not yet bc i was trying to figure this out
summer aurora
try that
buoyant python
**Twenty**
Wait how do i do text like this
buoyant python
cant i
summer aurora
you can
buoyant python
you can
ok i canāt do it
I thought i could but i canr
I feel dumb
@summer aurora can u help me please?
summer aurora
<@764891391640731690> can u help me please?
sorry idk how to solve it either lol
did your textbook not do smth like that previously
buoyant python
No it never solves then like that
cedar kilnBOT
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@buoyant python Has your question been resolved?
cedar kilnBOT
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Available help channel!
torn marsh
cedar kilnBOT
torn marsh
Is dP/dt referring to derivative of P
Respect to time
If yes, please show the proof
dusk goblet
dawg itās notation
torn marsh
Ok whatās p0 im confused
void glen
p0 is the initial population or the population at t=0
just a constant of integration that pops out really
open stream
cedar kilnBOT
open stream
Can someone help me on this question please?
prisma pike
Without knowing what f(x) and g(x) are this question is not solvable
sacred iron
!original
cedar kilnBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@open stream Has your question been resolved?
cedar kilnBOT
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warped venture
cedar kilnBOT
whole nexus
Well let's start with the second one
For continuity the limit just below and the limit just above 1 must be equal, and x becomes 1
What would that look like?
Is there something wrong?
warped venture
What would that look like?
e^b+1=2/(b^2-ln1)
warped venture
Alright, where would I go from there?
whole nexus
It's basically a piecewise function where x<1 = x>=1, that's how we show continuity at x=1, or am I missing something big
whole nexus
Alright, where would I go from there?
Okay so e^b + 1 = 2/b^2
maybe expand e^b?
1 + b + b^2/2 + 1 = 2/b^2
4b^2 + 2b^3 + b^4 = 2
And I guess it's solvable after that
oh god or maybe it's not
Like how deep do you reckon we should simplify, would you say just 1 + b instead of 1 + b + b^2/2! would work?
Also are you permitted to use a graphing calculator perchance?
warped venture
Yeah I am, and Iāve already figured out the other problem, Iām just struggling on how to find the answers for the one youāve been trying to help me with, which are -1.246 and 0.79, Iām just not sure how to get there
whole nexus
I mean if you are permitted then it's great for us
We could be as accurate as you want (like b^3/6 sounds good enough)
So e^b + 1 = 2/b^2
e^b = 2/b^2 - 1
1 + b + b^2/2 + b^3/6 = 2/b^2 - 1
2b^2 + b^3 + b^4/2 + b^5/6 = 2
12b^2 + 6b^3 + 3b^4 + b^5 = 12
Let's check that on the graphing calculator
warped venture
For me itās only given -1.246 and 0.792
whole nexus
12b^2 + 6b^3 + 3b^4 + b^5 = 12
What, like the equation here?
warped venture
From making it a function a graphing it, like y=e^x+1-2/x^2
whole nexus
Ahhh yeah
Dude I forgot we don't even need to expand e^b if you have graphing calculator
warped venture
Yeah lol, thanks for the help though I really did not know how to get started
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
warped venture
.close
dire radish
cedar kilnBOT
dire radish
Can someone explain to me
why p(x,y) = ky
i am having a little trouble understanding it
restive oriole
density is dependent on distance from x axis
restive oriole
try finding the distance from (x,0) to (x,y) using the distance between two points formula
I'm assuming they mean shortest distance between the point and the x-axis
cedar kilnBOT
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Available help channel!
marble solstice
cedar kilnBOT
marble solstice
I am unsure how to solve for the variables
marble solstice
X=-(y+2)/3
then I plug it in
and get
(-y+2/3)^2+9y^2-10(-y+2/3)+36y=20
how do I do it after that
gritty viper
that's not the right way to isolate x
cedar kilnBOT
viral narwhal
would it be x/3=(y+2)/3
That's not right
cedar kilnBOT
Available help channel!
timber mauve
cedar kilnBOT
timber mauve
Could anyone help to check my steps for this question, it dont seem to have any answers....
Or do i need to times the 4/5 /10 into the vector? Is it correct to do so?
neon egret
actually wait let me recheck
timber mauve
whats wrong in that btw
im not sure if i can just mulitiply into it or no
carmine bronze
Yes.
neon egret
im not sure if i can just mulitiply into it or no
you can
carmine bronze
You found the unit vector of the opposite direction. Multiplying by 8 will give the 8 unit long vector in the opposite direction vector GH.
neon egret
alrgith, is it because they re both vector?
you can multiply a vector by a scalar, it will only change its magnitude in the direction
carmine bronze
Although intuitively, you did not need to do all of that work.
GH points straight down and the opposite direction points straight up.
neon egret
alrgith, is it because they re both vector?
here it was a scalar multiplied by vector so it worked, but if it were a vector then you have to take a cross product
timber mauve
Can anyone help question 11 please?
cedar kilnBOT
Can anyone help question 11 please?
timber mauve
Im confused about what it means by move along two straight lines... Where the T suppose to be?
cedar kilnBOT
@timber mauve Has your question been resolved?
timber mauve
<@&286206848099549185>
dense bridge
Help
dense bridge
Can someone just show me the work to simplify this
I donāt really understand how to show the work when splitting the negative radicals
Radicands *
Like is it -8^2 ā¢ 2
Or are there brackets
Like -(8)^2 or (-8)^2
smoky idol
When there are no brackets, assume the negative sign is outside the square. Otherwise itās just poor notation
also 8^2 is not 16 :p
dense bridge
also 8^2 is not 16 :p
My bad
I meant this
Is that correct?
Notation
Especially?
smoky idol
Yeah thatās fine
dense bridge
Yeah thatās fine
Thx
smoky idol
.close
solar isle
I need to show that the gray triangles have the same area. I know that the middle triangle have a angle of 90.
pastel vault
I need to show that the gray triangles have the same area. I know that the middl...
you can do this with the formula area = 1/2 ab sin C
solar isle
Do I need to know what C is?
wise quail
No.
floral arrow
You can do some nice geometric construction here
solar isle
I see the sides that it shares two sides with the middle one but they have different angles and I donāt know how to go forward.
pastel vault
Do I need to know what C is?
that's the point
it's a good idea to label one of the angles in the middle right triangle as theta
so then the other angle is 90 - theta
you can find the two obtuse angles in terms of theta
wise quail
Is it allowed to be used the Pythagoras Theorem?
ancient nova
Is it allowed to be used the Pythagoras Theorem?
Pythagoras seems no use in this ngl
pastel vault
I think you eventually need to use it
hidden mural
u could label stuff and brute force it
like label the sides/angles and find areas explicitly
pastel vault
you can do this with the formula area = 1/2 ab sin C
yeah that's my idea here
floral arrow
hidden mural
but this picture screams pythagoras' theorem š¤
hidden mural
lol
crystal linden
looks beautiful ngl
mighty shuttle
this is a standard pictorial representation of PT
floral arrow
? Not really
The triangle + the three squares, sure
But I'm not using Pythagoras here
wise quail
this is a standard pictorial representation of PT
what
hidden mural
oh i see, all the green triangles are congruent.
wise quail
A standard pictorial representation would be like this.
pastel vault
the clever bit is justifying why the heights of the right and obtuse triangles are the same, of course
floral arrow
Right, which is just some angle calculation
pastel vault
Right, which is just some angle calculation
well, I thought of it as ||being half of a parallelogram||
floral arrow
Can do that too, yeah
cedar kilnBOT
@solar isle Has your question been resolved?
prisma pike
A standard pictorial representation would be like this.
Nasa always coming in clutch
Except when it comes to sending objects to space first
solar isle
So what exactly is the method here?
pastel vault
pray such a diagram appears in your dreams
or practice enough Euclidean geometry to make seeing this easier
hidden mural
So what exactly is the method here?
there are a few methods
pastel vault
you can do this with the formula area = 1/2 ab sin C
I don't know why this brute-force way isn't working for me
oh wait yeah, okay I figured out how the two obtuse ones are equal
floral arrow
When looking for the area of a triangle, you can always try to find an adequate base-height pair; then you can try to reshape the triangle into having a right angle, with the same base and height. That's how I came up with that diagram
pastel vault
you start from tan theta = a/b and then a cos theta = b sin theta follows
so then a sin(theta + pi/2) = b sin(pi - theta) and that's the right form
prisma pike
Yea with (1/2)ab sin is the most straightforward way to get it
pastel vault
like in maths, there's usually a clever way, but you have to spend some time thinking creatively to get there
cedar kilnBOT
cedar kilnBOT
ā Original question: #help-13 message
pastel vault
and then there's a brute force way, which can be messy and long
but all the steps are relatively simple, if you know your stuff
solar isle
Any tips on what to search to understand the concepts?
hidden mural
no
solar isle
š¢
floral arrow
When looking for the area of a triangle, you can always try to find an adequate ...
This is basically the only tip I can give
Well, since the question is to show that the triangles have the same area, you can think of it as given while you are coming up with the proof
Like, don't just try to calculate the areas individually; you know they are equal, so find a way to relate them
(and then check that the relations you found are actually correct)
hushed slate
Any one can help how to solve it step by step provided only these formulas....I know we have to do u substittution but I get stuck after that, thanks in advance.
pastel vault
Any one can help how to solve it step by step provided only these formulas....I ...
!help
cedar kilnBOT
Any one can help how to solve it step by step provided only these formulas....I ...
To ask for mathematics help on this server, please open your own help channel or help thread. See #āhow-to-get-help for instructions.
hushed slate
I went to Cannels and roles and from there I customized it to help in maths, if that's what you meant I already did it.
pastel vault
I went to Cannels and roles and from there I customized it to help in maths, if ...
go ask in #help-36
hushed slate
Thanks
cedar kilnBOT
@solar isle Has your question been resolved?
torn marsh
cedar kilnBOT
torn marsh
do u guys know why its looking like a straight line?
I am attemping e
the graph is not supposed to be straight
lofty topaz
I think it is because you chose the x-variables too close.
torn marsh
the intervals?
sacred iron
did your teacher chose to expand sinh for a reason?
lofty topaz
I mean instead of choosinf x from {-2, -1, 0, 1, 2}, I think it would be better to choose from like {-10, -5, 0, 5, 10}
wraith daggerBOT
Erebus
torn marsh
we never been taught
this
just pure calculus of exponentials
idk how this function supposed to look like
lofty topaz
just pure calculus of exponentials
I see.
torn marsh
yea its pretty weird
torn marsh
I seee
what am i supposed to do? let my teacher now
or
idk what to do at this point
lofty topaz
Idk, it depends
If you want to draw the graph
Just draw it
If you want to learn more about these functions
You should probably go watch some videos related to them
torn marsh
could u suggest me few if its possible
lofty topaz
dry fossil
$y[n]=\sum_{m=-2}^{2}(3-|m|),\text{sgn}(n-m)
=\text{sgn}(n+2)+2,\text{sgn}(n+1)+3,\text{sgn}(n)+2,\text{sgn}(n-1)+\text{sgn}(n-2).$
tropic oxide
where's the actual question
dry fossil
where's the actual question
wait
wraith daggerBOT
alee
dry fossil
$h[n]=\begin{cases}3-|n|,& |n|\le 2 \ 0,& |n|>2\end{cases}$
tropic oxide
maybe you could just send a screenshot
wraith daggerBOT
alee
dry fossil
maybe you could just send a screenshot
im writing the problem , so i have h[n] (above)
and x[n] = sgn(n)
where sgn(n) = 1 when n >0 , 0 when n = 0 and -1 when n < 0
i have to calculate:
$y[n]=(x*h)[n]=\sum_{m=-2}^{2}(3-|m|)\mathrm{sgn}(n-m).$
wraith daggerBOT
alee
dry fossil
I tried to use the max and min indexes, but it's a mechanical process and too long
so for now i just entered all m inside
and ive got
tropic oxide
dry fossil
why n is from -5 to 5 only ?
tropic oxide
you could extend it further
but for any values of n outside the range [-3, 3] the convolution will be constant Ā±9 anyway
after all, all the sgn() terms will be -1 for n ā¤ -3, and they're all +1 for n ā„ 3...
if you want, i can, specifically for you, extend the table until n = Ā±9
dry fossil
I ask myself the question, how can I think about this thing, that is, how did you realize it?
tropic oxide
realize what exactly?
dry fossil
after all, all the sgn() terms will be -1 for n ā¤ -3, and they're all +1 for n ā„...
.
tropic oxide
all i did was basically just add up your sgn() terms, the only interesting thing being that i did it in Excel rather than by hand.
sgn(n) has "interesting" (i.e. not constant) behavior near n=-1,0,1 only.
dry fossil
ok so here what i need to do is put n = 0,1,2,3,... etc and see what happened ?
tropic oxide
looking only at positive values of n is not quite enough (unless you can convince yourself that the signal is an odd function of n)
dry fossil
so basically in this case there a change at m>n and m< n ?
$y[n]=\sum_{m<n}h[m]-\sum_{m>n}h[m]$
wraith daggerBOT
alee
dry fossil
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
runic merlin
cedar kilnBOT
runic merlin
can someone guide me through this solution
tropic oxide
i did not wish to know anything about your opinion on the looks of any of your friends and i wish to un-know that particular bit of info
anyway i would not expect this to have anywhere near a nice solution
ember heath
ur friend is probably trolling u
tropic oxide
ok, so what else did your friend say to do w/ this
ember heath
,w solve (x^4-6x^3+11x^2-6x+2)/sqrt(x+1) +ln(x^2+1) = e^(x/2)
wraith daggerBOT
sacred iron
wolfram aināt being helpful here
runic merlin
<:bruh:637677132671221810> wolfram aināt being helpful here
hi again
jade blaze
x = 1?
mighty shuttle
pls tell me X is a variable here and not a Random Var
sacred iron
Iām not even sure there are great ways of cleanly solving this.
jade blaze
dosent work
its like a 0.3 difference
ancient nova
,w (x^4-6x^3+11x^2-6x+2)/sqrt(x+1) +ln(x^2+1) = e^(x/2)
jade blaze
lets assume that space ate that difference yay
wraith daggerBOT
runic merlin
pls tell me X is a variable here and not a Random Var
itās a variable (I hope)
potent echo
Hello
sacred iron
ancient nova
Is 2 a solution, at least it close lol 
potent echo
Can i help or its late ?
sacred iron
Can i help or its late ?
well it looked like it just got answered by wolfram
ancient nova
Can i help or its late ?
Go ahead sheldon
tropic oxide
i would be incredibly surprised if this had anything like an algebraic solution
so yes i think a graphical or numerical method is your only option
you've not told us what your friend actually wants you to do though
I canāt start to solve this and neither am I supposed to
you're on record as having said you are, and i quote, "not supposed to" solve this equation
the question remains: what ARE you supposed to do?
runic merlin
He said me to do the equation
tropic oxide
"do"?
livid hound
polynomial mixed with log or exponential is already bad enough.
here you have all of them and a radical chucked in as well
just skip imo
potent echo
It's not very simple
ember heath
+from what OP has told us till now its not even a real question its just an ugly expression made up by their friend
runic merlin
I am just curious to know how to solve it in a algebraic manner (of course if thereās a way)
flint cape
He said me to do the equation
Simply being given a question from a friend typically isn't grounds for that question a) being good, b) being solvable, c) being well within your means to attempt to begin with
tropic oxide
is this a language barrier
ancient nova
"Jarvis, generates something crazy to make my friend go nut"
flint cape
It's "Jarvis"*
runic merlin
if thereās no way itās just better to close it out I guess
flint cape
(Also, "Jarvis, generate* something..." )
runic merlin
.close
cedar kilnBOT
tacit girder
cedar kilnBOT
Available help channel!
sonic fossil
cedar kilnBOT
sonic fossil
!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
- I don't know where to begin
frank ice
Hey
We have a uniform cylinder of radius
spun with an initial angular velocity.
( \omega_0 )
wraith daggerBOT
YZYBlueBoy22
frank ice
The cylinder is placed in a corner where it experiences friction from the two walls.
@sonic fossil
sonic fossil
Yes i understood setup
cedar kilnBOT
@sonic fossil Has your question been resolved?
bright river
No it never solves then like that
Hey sry yesterday idk why but I didnt got the notification. Do you still need help ? (If yes letsgo in another channel)
buoyant python
Hey sry yesterday idk why but I didnt got the notification. Do you still need he...
Yes please
bright river
1. I don't know where to begin
Do you know Coulomb law for solild friction ? I think that's what you're looking for