There aren't going to be many price curves that have sharp changes like that.
#help-13
opaque harbor
well, yes, but you have a continuous function that when evaluated at whole numbers gives you the price, and you're being told (really asked to assume) for h=1 the approximation above is close enough
yes
f(x+1)-f(x) is the slope between the points on f when x is 10 and 11
kindred storm
What do you mean when you say we aren't taking a derivative?
The question is asking you to. What Edward II said had a derivative in it.
Who is for what question?
opaque harbor
we are finding the rate of change by approximating it with the derivative
opaque harbor
we're saying 'this isn't the exact value, but it will be close enough'
kindred storm
An approximation is a value that's close to the actual value.
opaque harbor
the derivative is the slope at 10, and we're saying it will be close to the slope between 10 and 11
kindred storm
I'm sorry, what problem are you solving?
Your original problem had a derivative in it to get an approximate answer.
The increase in cost.
kindred storm
Not with a derivative, which it's asking you to use.
It doesn't matter what it would be.
Your question is directing you to take a derivative.
So, you should take the derivative.
What does it say there?
opaque harbor
you're being asked to assume the cost function is continuous (I agree it's slightly dumb when you're at 10 but if e.g. you were producing 10000 radiators then moving one either way would essentially be the same as a continuous change)
then I may have slightly confused things with notation, but the h on the right here is 1, and is not the same as the h in the limit hidden inside the derivative on the left (which is just a variable we send to 0 that we could have used any letter for) under that continuous assumption
we can approximate whatever we're taking the limit of with the limit itself, assuming we've gotten close enough (again, within 1 should be close enough in this situation) which is where what I sent there comes from
kindred storm
It's an approximation. Just because you'd only use integers as inputs does not at all prove that taking the derivative is a bad approximation.
opaque harbor
for being an approximation, yes
kindred storm
Because it's cheaper to calculate the estimate.
They don't need exact answers.
They need something that's close enough.
So, they take the path that requires less work.
opaque harbor
yes
kindred storm
No, you're using it because it's a decent approximation.
opaque harbor
in real life, there would be examples where you don't know the function
e.g. you might know the speed of a car at a certain point using radar, but not whether the driver is accelerating or braking or whatever, so you wouldn't actually know where it is even half a second later
opaque harbor
e.g. you might know the speed of a car at a certain point using radar, but not w...
but you could guess that it would be roughly speed * time away
(where speed is derivative of position)
yes
cedar kilnBOT
kindred storm
No problem.
cedar kilnBOT
Available help channel!
crimson sedge
need to work this out:
cedar kilnBOT
need to work this out:
crimson sedge
$4sinxtanx-3tanx+20sinx=15$
wraith daggerBOT
mj
wraith daggerBOT
mj
crimson sedge
problem is, I'm not too sure how to get the cos out of the denominator
dire geode
problem is, I'm not too sure how to get the cos out of the denominator
Multiply both sides by cos(x)
crimson sedge
$\frac{cosx(4sin^2x-3sinx)}{cos^2x}+20sinx-15=0$
wraith daggerBOT
mj
odd kayak
Can someone give me the steps?
crimson sedge
hmm
dire geode
Can someone give me the steps?
!1c
cedar kilnBOT
Can someone give me the steps?
Please stick to your channel.
crimson sedge
maybe turning cos^2x into 1-sin^2x would help?
crimson sedge
oh you meant
wheat ocean
and you get 2 cases
crimson sedge
the entire thing
$\frac{cosx}{1}(\frac{4sin^2x-3sinx}{cosx}+20sinx-15)=0\cdot cosx$
wraith daggerBOT
mj
crimson sedge
would the cosx's just cancel?
idk it feels wrong to me
but I guess that's just the zero property
wheat ocean
4sinx(tanx+5)-3(tanx+5)=0 <=> (tan(x)+5)(4sinx-3)=0
try this
i think that is what you were expected to do
crimson sedge
4sinx(tanx+5)-3(tanx+5)=0 <=> (tan(x)+5)(4sinx-3)=0
how does this work
$4sinx(tanx+5)-3(tanx+5)=0$
$(tan(x)+5)(4sinx-3)=0 $
wraith daggerBOT
mj
crimson sedge
$(tan(x)+5)(4sinx-3)=0$
wraith daggerBOT
mj
crimson sedge
I'm confused how you got here
wheat ocean
that's factoring
wheat ocean
i factored out 4sinx from terms 4sin(x)tan(x) and 20sin(x), and -3 from terms -3tan(x) and -15
crimson sedge
makes sense
wheat ocean
you don't need that
wheat ocean
you got 2 cases: tan(x)=-5 and sin(x)=3/4, solve them
crimson sedge
wait what
crimson sedge
**mj**
when I kept going through with this
ended up with
3/4 aswell
got -5
but for sinx
which is invalid obviously
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
north thistle
The picture is about improper usage of AM-GM but I don't really understand how it is wrong. I think the inequality on the left will be equal when a=b=c=1 so substitude in should give 3/2. From the picture, I think there's a way to make a/2b + b/2c + c/2a >= (a+b+c)^2 /2(a+b+c).
Can someone tell me where I'm wrong please?
cedar kilnBOT
The picture is about improper usage of AM-GM but I don't really understand how i...
@north thistle Has your question been resolved?
dire geode
The picture is about improper usage of AM-GM but I don't really understand how i...
What are you even supposed to prove
wheat ocean
The picture is about improper usage of AM-GM but I don't really understand how i...
can you tell what you need to prove and what you're trying to do?
north thistle
This is what I need to prove and the blog tells me to use inverse sign AM-GM technique. The blog already has the correct way to do it, but I don't know what's wrong with the usual one.
wheat ocean
also, you might be talking about this: if you have A>=B and A>=C, then you can't tell if B>=C or B<=C
north thistle
also, you might be talking about this: if you have A>=B and A>=C, then you can't...
Well I don't understand how a/2b + b/2c + c/2a >= 3/2. Can you explain please?
wheat ocean
$\frac{a}{2b}+\frac{b}{2c}+\frac{c}{2a}\ge 3\sqrt[3]{\frac{abc}{8abc}}=\frac{3}{2}$
wraith daggerBOT
Alisia
wheat ocean
do you agree?
north thistle
I think that to get the equal sign here a=b=c=1 so it would make 3/2 if I continue right?
I don't know why it's >= 3/2 instead of = 3/2
wheat ocean
this sign means that LHS is less or equal to RHS
if i understand your question right
sour jetty
hi can someone explain to me the reason behind this note. This is a chapter talking about vectors
tropic oxide
the set of all possible values of ha is a straight line through the origin parallel to a
likewise the set of all possible values of kb is a straight line through the origin parallel to b
since a and b are not parallel, these lines don't coincide and only intersect at the origin, a.k.a. 0
subtle raven
I think I can also rephrase this as "if a and b are not parallel then there is no constant K such that a = Kb"
cedar kilnBOT
@sour jetty Has your question been resolved?
tropic oxide
@sour jetty did my explanation answer your question?
if not, tell me what you still don't understand.
sour jetty
im still trying to understand it
tropic oxide
ok
cedar kilnBOT
cedar kilnBOT
Available help channel!
ripe ermine
How to derive this geometrically?
cedar kilnBOT
How to derive this geometrically?
tropic oxide
,rccw
wraith daggerBOT
soft umbra
cedar kilnBOT
soft umbra
So, you can simplify this because it is a perfect square and the squares cancel, but I'm a bit unsure on why when you evaluate 1- sqrt3, I get a negative, even though it should be positive
wraith daggerBOT
Joanna Angel
tropic oxide
$\sqrt{a^2} = |a|$ not just $a$
wraith daggerBOT
Ann
soft umbra
Oh
How can I identify when it is the principle root?
Because I wouldn't know to include both answers or not
raw gulch
you do not need to consider more than one square root in your case, because you calcualte a real arithmetic sqaure root, not complex one
raw gulch
Because I wouldn't know to include both answers or not
look:
$\sqrt{17-12\sqrt{2}}=\sqrt{\left( 3-2\sqrt{2} \right)^{2}}=3-2\sqrt{2}\\\text{but you can also write this way:}\\\sqrt{17-12\sqrt{2}}=\sqrt{\left( 2\sqrt{2}-3 \right)^{2}}=\left| 2\sqrt{2}-3 \right|=\\=-\left( 2\sqrt{2}-3 \right)=3-2\sqrt{2}$
wraith daggerBOT
Joanna Angel
soft umbra
Oh okay thanks
raw gulch
yw
slow jewel
Can you help me with this one too?
Have you factorised it?
slow jewel
What did you get
soft umbra
You could write that as a square as you did for the previous one
How?
slow jewel
Didn't you do the same for the previous question?
soft umbra
Yeah but idk how I would factorise this one
slow jewel
I see
Let's say $\sqrt{28 + 16\sqrt{3}} = \sqrt{x} + \sqrt{y}$ for some $x,y \in R$
$$28 + 16\sqrt{3} = x+y+\sqrt{4xy}, x+y= 28, 4xy=256\cdot 3$$
wraith daggerBOT
Lorentz
slow jewel
You can find x and y from solving the two equations
soft umbra
I think that this may be overcomplicating it a bit
slow jewel
It is one of the methods to simplify forms like sqrt(a± sqrtb)
Since sometimes it's difficult to hit and try
You just introduce two variables x and y and then write it in the form of sqrtx + sqrty and square both sides
soft umbra
Can you go through it with me?
slow jewel
Alright, the reason I wrote it like that is coz sometimes the number might be big, ik it's not in this case but I just wrote the general thing
soft umbra
Okay
slow jewel
**Lorentz**
So, did you understand the first line here
soft umbra
Yeah
slow jewel
Alright, now just square both sides
soft umbra
Yep
slow jewel
$28+16\sqrt{3} = x+y+2\sqrt{xy}$
wraith daggerBOT
Lorentz
slow jewel
You'd get this
soft umbra
Yeah I understand that
slow jewel
Ok now if you compare both sides, x+y is the part that's not under the sqrt
So x+y=28
Just by comparing terms from both sides
soft umbra
Ohh that makes sense
slow jewel
so sqrt 4xy is 16 sqrt3
Yes that too
Now you have two equations in terms of x and y:
$$x+y=28$$
$$\sqrt{4xy}= 16\sqrt{3}$$
wraith daggerBOT
Lorentz
slow jewel
I think you'll be able to solve em
slow jewel
Precisely
soft umbra
Okay thanks
slow jewel
Is that for sqrt(28 +16sqrt3)?
soft umbra
No
slow jewel
Oh
slow jewel
Oh you meant the final ans?
soft umbra
soft umbra
Oh you meant the final ans?
Yeah
soft umbra
I got that from sqrtx + sqrty to give me 4 + 2 sqrt3 then put the extra square root back to get sqrt (4+ 2sqrt(3)) then to sqrt(1+ 2sqrt3 + 3) then sqrt((1+sqrt3)^2) it cancels then I got that
soft umbra
Ye seems right
Okay thanks
slow jewel
I got that from sqrtx + sqrty to give me 4 + 2 sqrt3 then put the extra square r...
Right
Np
soft umbra
.close
night karma
can someone help me understand this?
I don't know how I can fill in the values because I don't understand the difference between the two expressions
night karma
maybe the lower one has these values?:
1 a b c
a b c 1
b c 1 a
c 1 a b
would say it's the usual group but the upper one hmm not sure
night karma
oh because it has no neutral element
south tundra
Yeah
night karma
can you explain to me how i can know which values i should write in there?
because this is my main problem
south tundra
And the second one is not determined uniquely
Usually for filling Cayley tables you can use the latin square rule (if that doesn't help, perhaps associativity and some consideration of orders of elements)
night karma
i read it like that, the upper one: "for all y in set M there is at least one x in set M that is x with y = y with x = y"
sth like this
south tundra
I.e., in each row/column each element should appear exactly one (if you've played sudoku, this should be familiar)
night karma
okay I see, so b with b would be c?
south tundra
i read it like that, the upper one: "for all y in set M there is at least one x ...
Yeah that's correct interpretation
night karma
or why is a with 1 = 1?
south tundra
okay I see, so b with b would be c?
Why is that?
night karma
Why is that?
´m not sure lmao
south tundra
night karma
was a guess
or is it even possible to fill the table (only the top one) with the given definition?
south tundra
Are you actually supposed to fill the second table? There are two different groups that satisfy the answer
south tundra
or is it even possible to fill the table (only the top one) with the given defin...
No
night karma
oooh okay
yea maybe then it´s only about differentiate whether it is a group or not
tyty
.close
gritty prairie
cedar kilnBOT
gritty prairie
Is ADC 180-(168/2) because D is not subtending the same arc
tropic oxide
right answer wrong reason/wording
gritty prairie
right answer wrong reason/wording
What’s the correct reasoning can you tell me please
I can see cyclic quadrilateral
That’s the reasoning?
tropic oxide
OACD isn't cyclic
gritty prairie
No but BACD is right
tropic oxide
ABCD
gritty prairie
😅
tropic oxide
angle ADC subtends arc ABC, which is complementary to arc ADC, whose measure is 168°
"not subtending the same arc" isn't a reason for anything
gritty prairie
angle ADC subtends arc ABC, which is **complementary** to arc ADC, whose measure...
Oh
vapid whale
i have a question about why limit sinx/x = 1
cedar kilnBOT
i have a question about why limit sinx/x = 1
vapid whale
but in this proof, we can see that there is a (0 x ∞) form
like in the expansion of sin x
isnt (0 x ∞) an indeterminate form, making the proof invalid
vapid whale
expansion of sin x at 0
paper vigil
$1-\frac{0}{3!}+\frac{0}{5!}-\frac{0}{7!}+....$
wraith daggerBOT
Combustion
vapid whale
ok i was thinking of it as (1 - ((0 x ∞))
because its repeating the 0 infinite times
twin panther
For the permutation of the set (1, 2, 3, ..., 12) (a1, a2, a3, ..., a12) a1 > a2 > a3 > a4 > a5 > a6 and a6 < a7 < a8 < a9 < a10 < a11 < a12 is paid. We can show (6, 5, 4, 3, 2, 1, 7, 8, 9, 10, 11, 12) as an example of such a permutation. Find the number of all such permutations.
cedar kilnBOT
For the permutation of the set (1, 2, 3, ..., 12) (a1, a2, a3, ..., a12) a1 > a2...
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
1
twin panther
6
opal basin
No look at the example, try to understand why a6 is always the same
why would a6 = 6 give problems
kindred storm
6
a1 is the first number listed there, a2 is the second number, and so on.
So, a6 is the sixth number there, which is 1.
Does that make sense?
twin panther
so first number will be in the middle ?
kindred storm
No, 1 will be in the middle.
The first number means the number that it starts off with, so like (6, 5, 4, 3, 2, 1, 7, 8, 9, 10, 11, 12).
twin panther
(1, 2, 3, ..., 12) (a1, a2, a3, ..., a12) when it is like a1 is 1
kindred storm
Right, in that case, a1 is 1.
twin panther
i mean like that
kindred storm
But with (6, 5, 4, 3, 2, 1, 7, 8, 9, 10, 11, 12), a1 is 6.
Because 6 is the first number listed.
twin panther
so how can we find all numbers of permutation
kindred storm
OK, so we notice things about it first.
For example, a6, the sixth number listed, is 1.
Does it always have to be 1?
twin panther
no
kindred storm
OK, try to find a way of rearranging the numbers so that something other than 1 is there. Remember that you have to have a1 > a2 > a3 > a4 > a5 > a6 and a6 < a7 < a8 < a9 < a10 < a11 < a12.
kindred storm
Where is the 1?
kindred storm
Well, permutations mean you keep the same numbers, but rearrange them.
So, you still need 1 through 12.
You can't remove a number or add one, because it's just rearranging the numbers, not changing them.
twin panther
oh i got it know in that case yes a6 must be 1
kindred storm
OK, so let's look at the two different sides of a6.
If I pick 5 numbers that aren't 1 and put them on the left side of a6, how many ways are there to rearrange those exact 5 numbers? Like, if I choose 2, 10, 5, 7, 3.
kindred storm
OK. Good.
Let's say I choose 10, 7, 5, 3, and 2 and those are used on the left. How many different ways are there to pick numbers for the right side? Remember that we already used 1 for the middle.
twin panther
4 < 6 < 8 < 9 < 11 < 12
kindred storm
OK, so once you pick the left side numbers, the right side numbers are automatically going to be the remaining numbers with only one arrangement possible, right?
twin panther
yes
kindred storm
OK, so basically, we just have to choose 5 numbers for the left numbers and then the permutation is fully decided on.
So, how many numbers are there to choose from for the left side?
Sorry, have to go, but the main idea is that once you choose the five numbers for the left side, that decides for you which numbers are available for the right side and then there's only one arrangement for the left numbers and one arrangement for the right numbers.
So, however many ways there are to choose the five left side numbers is equal to how many permutations work with your question's restrictions, so however many ways there are to choose the left numbers is the answer.
Oh, wait. I don't have to go.
cedar kilnBOT
@twin panther Has your question been resolved?
twin panther
@kindred storm should i count it one by one or is there any formula
kindred storm
Oh, there's the binomial coefficient.
It can be written like n C r.
And you can read it as "with a set of n items, choose r of them".
So, if you had 6 items and you wanted to find out how many ways there are to choose 5 of them, you'd write 6C5.
Does that make sense?
twin panther
6!/5!
kindred storm
Not exactly.
twin panther
(6-5)!
wraith daggerBOT
Chai T. Rex
twin panther
i was trying to write this
kindred storm
n!/r! is for when you care about ordering.
Oh, wait n!/(n - r)! counts the ways to permute r items chosen from n items.
So, it's like (a, b, c, d, e) and (a, b, d, e, c) and so forth.
That's written n P r.
n C r doesn't give ordered tuples like that.
It counts sets, like {a, b, c, d, e}, where order doesn't matter ({a, b, c, d, e} is the same as {a, b, d, e, c}).
And that's what we want.
Once we get the set, the arrangement of them is handled already by the a1 > a2 etc.
So, we don't need all the possible rearrangements, just the sets of r elements.
So, the question is: what is n and what is r here?
twin panther
if i am honest i could not find n or r
just cus i do not know nCr very well
<@&286206848099549185>
kindred storm
OK, so once you place the 1, how many numbers are left over for when you pick the left side numbers?
twin panther
5
kindred storm
No, think about it. You start with {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, right?
If we remove 1 from that, how many are left over for use on the left side?
twin panther
11 ?\
kindred storm
Right, so we have 11 elements to choose from. How many elements are we choosing?
twin panther
for left or right
kindred storm
For left.
twin panther
5
kindred storm
OK, so it's 11C5.
From 11 elements, you're choosing 5 of them.
Does that make sense?
twin panther
11C5 =462
kindred storm
Right.
twin panther
so there is 462 permutations ?
kindred storm
Yes, 462 that fulfill the requirements.
twin panther
Thank you so much
kindred storm
You're welcome.
twin panther
.close
crimson sedge
hi can i get help on a
cedar kilnBOT
hi can i get help on a
slow jewel
Where's the table
crimson sedge
Where's the table
which table?
kindred storm
"Table 1.1"
slow jewel
Sure
kindred storm
are you there
I'm back.
crimson sedge
oh thank you so much
kindred storm
OK, so finish filling out the factors.
crimson sedge
so i don’t get it
kindred storm
There's 15 and 432 to go.
crimson sedge
i have finished all the factors
kindred storm
Oh, what did you get for 15 and 432?
crimson sedge
@kindred storm actually my question is really simple
like here in this image
i don’t know the answer for 2A
kindred storm
I'm not sure exactly what it's asking, but it might want a list of numbers.
You're right about prime and composite, though.
For A, look at the lists of factors.
Which number has only one factor?
crimson sedge
I don’t seem to figure out
dense cargo
1
kindred storm
Well, let's go down the list.
How many factors does 1 have?
Then, how many factors does 2 have?
And so on.
Find which numbers have 1 factor.
crimson sedge
one just has one factor
kindred storm
OK, so that's in group A because it has exactly 1 factor.
dense cargo
That's the answer
crimson sedge
Then, how many factors does 2 have?
two factors
kindred storm
OK, so that doesn't have exactly 1 factor, so it's not in group A.
crimson sedge
so what number we will say has got one factor
kindred storm
Well, look past 2.
crimson sedge
like composite
kindred storm
What about 4, 6, 7, 13, and so on? Do any of those have exactly 1 factor?
crimson sedge
They don’t have one factor
kindred storm
OK, so it looks like group A just has 1 in it.
crimson sedge
So what do we call it
kindred storm
Oh, just 1.
You can tell that 1 is the only number like that because every higher number has 1 and itself as factors at least, so 2 factors at least.
crimson sedge
So the answer will be just one?
kindred storm
Yes, that's right.
kindred storm
You're welcome.
hollow storm
Hi guys is this correct? I have to verify the limit using the definition
hollow storm
I don't have the solution
atomic valley
!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.
cedar kilnBOT
@hollow storm Has your question been resolved?
cedar kilnBOT
@hollow storm Has your question been resolved?
cedar kilnBOT
@hollow storm Has your question been resolved?
cedar kilnBOT
@hollow storm Has your question been resolved?
twilit tendon
Something seems off about the last step where you take the abs value
twilit tendon
$4(2^{-\epsilon}-1)<x-4<4(2^{\epsilon}-1)$ is actually implied by $|x-4|< \text{min}(|4(2^{-\epsilon}-1)|, |4(2^{\epsilon}-1)|)$
you want to first show $|4(2^{-\epsilon}-1)| \leq |4(2^{\epsilon}-1)|$, which you can use to show $\delta = |4(2^{-\epsilon}-1)|$
wraith daggerBOT
Corpuscular Crow
cedar kilnBOT
@hollow storm Has your question been resolved?
tropic oxide
this is the harmonic series and it is quite famous
blazing zephyr
yes
tropic oxide
in that it diverges DESPITE its terms approaching 0
i guess...
i don't understand what you're trying to say
there's at least two ways
one is via the integral test
the other is via comparison with a specially constructed series whose sum equals an infinite number of 1/2's
dreamy sleet
Consider 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16 + …
tropic oxide
... yeah, that
dreamy sleet
which is the sum she’s talking about
tropic oxide
"aur"?
dreamy sleet
Each individual term is smaller than the corresponding term in the harmonic series
which is
1 + 1/2 + 1/3 + 1/4 + 1/5 + …
subtle harbor
1+(1/2)+(1/3+1/4)+(1/5+1/6+1/7+1/8)+...
crimson sedge
Each individual term is smaller than the corresponding term in the harmonic seri...
dont you mean bigger? 1/4+1/4+1/4+1/4 is obviously bigger than 1/4+1/5+1/6+1/7
dreamy sleet
dont you mean bigger? 1/4+1/4+1/4+1/4 is obviously bigger than 1/4+1/5+1/6+1/7
I think I did the wrong series
let me edit it
crimson sedge
huh
tropic oxide
so your modus operandi is to first say some utter BULLSHIT
and then to distract from it by asking to explain something different
got it
to apply the integral test you look at the integral $$\int_1^{\infty} \frac{1}{x}\dd{x}$$
wraith daggerBOT
Ann
tropic oxide
which is easy to see that it diverges
what are you talking about now
good lord
every time i try to explain something to you, you slap me in the face with some more bullshit
crimson sedge
is English your native language
tropic oxide
not in the slightest
crimson sedge
what is
tropic oxide
HOLY FUCKING SHIT!!!!!!
WHY didn't you begin with the original question????????????
all of this bullshit has been for NOTHING!
crimson sedge
dire geode
every time i try to explain something to you, you slap me in the face with some ...
This seems apt
crimson sedge
you gotta be trolling
tropic oxide
(n+1)/n is very different from 1/n !!!!!
and just ignored the other part
the 1
for $\sum_{n=1}^{\infty} \frac{n+1}{n}$, the terms approach 1. the terms fail to approach 0, therefore the series diverges. full stop, end of story, nothing else to see here.
wraith daggerBOT
Ann
crimson sedge
For the sake of your knowledge, yes:[
\lim_{t \to \infty} \int_1^t \f1x\dd x = \lim_{t\to\infty} \eval[\bigg]{\m\log{\abs x}}_{1}^t
]
wraith daggerBOT
tropic oxide
for $\sum_{n=1}^{\infty} \frac{n+1}{n}$, the terms approach 1. the terms fail to...
reread this like 20 times
until you get it
and then 10 more
by the way
you always always
ALWAYS
have to START your channel with the ORIGINAL question
no exception zero exception
no you didn't.
the series $\sum \frac{n+1}{n}$ and $\sum \frac{1}{n}$ don't differ by 1, they differ by an infinite sum of 1's !!!!!
wraith daggerBOT
Ann
minor crystal
Could someone explain why \lambda_a - \lambda_b can't be 0?
cedar kilnBOT
Could someone explain why \lambda_a - \lambda_b can't be 0?
crimson sedge
context?
minor crystal
context?
The context is that the two vectors are being acted on the same hermitian operator and then rearranging got to that result
and then it just stated that the eigen values can't be the same
didn't really explain why
is it because eigenvalues don't have to be unique for a set of eigenvectors? I'm not sure at least that's what i got from some research
solid juniper
this might need some more context
minor crystal
its because they dont change direction
i don't follow the implication here
minor crystal
this might need some more context
okay so basically there's no question 
. I was trying to derive the inner product of b and a is zerowhen acted by the same operator
I'm confused by the final step when it is concluded that lambd_a - lambda_b can't be zero
crimson sedge
if lambd_a - lambda_b is equal to 0 it implies that lambd(a-b) = 0 , for this to be true either lambd or (a-b) must be 0
minor crystal
it's lambda_a not lambda * a
crimson sedge
yes
abstract laurel
I'm confused by the final step when it is concluded that lambd_a - lambda_b can'...
if the two eigenvalues are distinct then the eigenspaces are orthogonal
cedar kilnBOT
@minor crystal Has your question been resolved?
minor crystal
thank you sn 
vital sphinx
What does the [x] mean in this notation:
cedar kilnBOT
What does the [x] mean in this notation:
vital sphinx
Its in field theory
ornate lake
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
stoic gale
looks okay apart from the last line with the two dx's on either side of equality
although i wouldnt distribute minus n all, it can lead to errors if not careful sometimes
stoic gale
once integrating you get 'rid' of dx
dire geode
well, surely i could w irte it as -1/(x^2+1)dx
Yes 1 * anything = anything
summer lintel
so why is he saying no
royal finch
Mainly because your notation is ambiguous
wary sinew
Can u ask here or do you have to wait?
royal finch
-dx/(x^2+1) is not the same as -1/((x^2+1)dx) and it's not clear if you meant to write that but were lazy about parenthesis
wary sinew
I’m new and don’t really understand how it works lol
plucky merlin
$\frac{-1}{x^2+1}dx$
wraith daggerBOT
dragonbreath
plucky merlin
yes whether it is in the top or to the side it all means the same thing
plucky merlin
$\frac{-dx}{x^2+1}=\frac{-1}{x^2+1}dx$
wraith daggerBOT
dragonbreath
summer lintel
yes
plucky merlin
how do i get rid of -dx
also, what aman is saying on this is
summer lintel
so why was i wrong
plucky merlin
$\int \frac{-dx}{x^2+1} = -arctan(x)$
vague vigil
I’m new and don’t really understand how it works lol
Ask in any "MATH HELP (AVAILABLE)" chat
plucky merlin
yes, sorry
wraith daggerBOT
dragonbreath
plucky merlin
integrating gets rid of the dx
it's like the end of the parenthesis
int = (
dx = )
shows what it is and isn't contained inside of the integral
@summer lintel do you understand now?
summer lintel
well
my question was why was i wrong
but i wasnt so idk if i really understood anything new
plucky merlin
I mean you're not wrong dx is technically treated as a number and can replace the one, it's just easier if you put it at the end of the equation to see what is and isn't inside the integral
summer lintel
yh yh like normal notation
but i am just saying dx/x^2+1 is the same as 1/x^2+1 dx
plucky merlin
my question is what was your first step?
summer lintel
to what
plucky merlin
$\frac{dy}{dx} = -\frac{y^{2}+1}{x^{2}+1}$
summer lintel
can tou express arctan as =cos/sin
wraith daggerBOT
dragonbreath
plucky merlin
arctan isn't 0 it's 2
plucky merlin
$arctan(y) = -arctan(x)$
wraith daggerBOT
dragonbreath
plucky merlin
is this what you mean?
plucky merlin
so, after integrating you always add C, as there could be an undefined constant (the derivative of a constant is 0, so there always has to be room to define a constant in an anti-derivative
so technically it is
$arctan(y) + c = -arctan(x) + c$
wraith daggerBOT
dragonbreath
plucky merlin
solve for y, which pay attention to c as it is not exactly treated like a variable
@summer lintel what is your basis of understanding integrating? after reviewing this entire discussion it seems that it is very beginner level but I want/need to know how beginner is beginner to you?
summer lintel
i have to go
but i dont think you understnad my question
ofc there is a + C on one of the sides lol
cloud venture
Hi
summer lintel
thansk for hlep tho
plucky merlin
can tou express arctan as =cos/sin
also nvm on this no, that's cotangent (cot) that is cos/sin
cedar kilnBOT
@summer lintel Has your question been resolved?
cedar kilnBOT
rugged tusk
.close
cedar kilnBOT
Available help channel!
lone moss
E
lone moss
.close
cedar kilnBOT
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✅
lone moss
.close
cedar kilnBOT
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Available help channel!
flint sapphire
How to solve
cedar kilnBOT
How to solve
flint sapphire
Is this even elementary
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
crimson sedge
no this is not integrable
iron sapphire
i can help you
tame stag
Hi, im new here.
tame stag
does anyone know how to make a net for a 3d star
iron sapphire
yes
crimson sedge
you get the integral [
\int \f{e^u}u \dd u
]
with a few substitutions and algebraic manipulations
wraith daggerBOT
crimson sedge
!occupied
cedar kilnBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
crimson sedge
!redir
cedar kilnBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
iron sapphire
the integral should have a few substitutions
crimson sedge
@iron sapphire @tame stag both of you
iron sapphire
i’m here to help
crimson sedge
you get the integral \[
\int \f{e^u}u \dd u
\]
with a few substitutions and alge...
this integral is not elementary.
flint sapphire
How
flint sapphire
this integral is not elementary.
How
crimson sedge
you cant do that
flint sapphire
Y
crimson sedge
[
\m{\ln^2}x = \p{\m\ln x}^2
]
tropic oxide
show your work and we will tell you exactly which step is illegal
wraith daggerBOT
flint sapphire
Yes
crimson sedge
thats not the same as $\m\ln{x^2}$
wraith daggerBOT
flint sapphire
show your work and we will tell you exactly which step is illegal
Ok
crimson sedge
where the product rule of logarithims apply
wraith daggerBOT
tropic oxide
it sounds as if you're trying to do calculus without having a good grasp of the algebra that comes before it...
flint sapphire
What
Well
I kind of don’t but do
I’m an 8th grader so yeah
Still got a learn to learn ig
tropic oxide
yes definitely
cedar kilnBOT
Available help channel!
short blade
let (u = u(t,x)), (u(t,0) = \phi(t)). is
[
\pdv{u}{t}\Big\vert_{x=0} = \pdv{\phi}{t} ?
]
wraith daggerBOT
maximo
short blade
if so, is a boundary value problem such as
[
\begin{cases}
u_{xx} - u_{tt} = 0\
u(t,0) = \cos t,\ u(0,x) = 1
\end{cases}
]
not well defined?
wraith daggerBOT
maximo
short blade
**maximo**
here im asking if the order of plugging in/differentiating matters
cedar kilnBOT
@short blade Has your question been resolved?
cedar kilnBOT
@short blade Has your question been resolved?
dull oxide
**maximo**
Technically, it would be $\frac{d\phi}{dt}$, but this should be correct yes.
I haven't done multivar in years, so I may be wrong, but my bet is on yes.
wraith daggerBOT
SWR
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.
short blade
**SWR**
are you saying this because phi is only a function of t?
isn't pdv still defined here, and it just means d/dt
cursive nacelle
what's the difference between those two?
short blade
Why would this be not well-defined?
because u(t,0) does not satisfy the pde
though this may be some techincality about requiring u to satisfy the pde only in the interior of the domain or something
which also makes me wonder if that kind of requirement makes it extend to the boundary as well by continuity/differentiability, but that's beside the point
short blade
what's the difference between those two?
one is a partial derivative, the other is a total derivative
cursive nacelle
ohh, no idea what the difference but can't wait to learn it in my classes. very interesting
cedar kilnBOT
short blade
.reopen
cedar kilnBOT
✅
cedar kilnBOT
@short blade Has your question been resolved?
short blade
i specifically just want to know if the partial wrt x_1 after plugging in a constant for x_2 is the same as differentiating before plugging in
short blade
**maximo**
^
ok i see that it should be equal from the definition of the partial derivative, i think
.close
crimson sedge
what do you do if you're trying to find the intersection of your oblique asymptote, you find the x-value, plug it back into the equation to find the coordinate and it comes back as undefined?
crimson sedge
would you have no intersection at that point?
civic eagle
if its an asymptote how would there be an intersection?
crimson sedge
if its an asymptote how would there be an intersection?
well in some instances there can be
short blade
,w plot xe^{-x^2} from -5 to 5
wraith daggerBOT
civic eagle
civic eagle
horizontal != oblique
wraith daggerBOT
short blade
this has a slant asymptote of y = x, but it still intersects
short blade
what do you do if you're trying to find the intersection of your oblique asympto...
do you have the original problem?
wraith daggerBOT
mj
crimson sedge
figured out the oblique asymptote was at x+2 through long division
set that equal to this
and determined that x=3
plugged 3 back in, gave me undefined
short blade
how did you determine x = 3
crimson sedge
through solving for x
short blade
what did you equate
crimson sedge
$x+2=\frac{x^3-9x}{x^2-2x-3}$
wraith daggerBOT
mj
short blade
assuming you did that correctly, identify what kind of discontinuity x = 3 is in your original function
crimson sedge
$x+2(x^2-2x-3)=x^3-9x$
wraith daggerBOT
mj
crimson sedge
,w (x+2)(x^2-2x-3)=x^3-9x
short blade
parentheses around the x+2
crimson sedge
probably did it wrong then
wraith daggerBOT
crimson sedge
nevermind
crimson sedge
assuming you did that correctly, identify what kind of discontinuity x = 3 is in...
what are you asking here
short blade
identify what kind of discontinuity x = 3 is in your original function
crimson sedge
oh
short blade
there's jump discontinuities, asymptotes, holes, ...
crimson sedge
there is a hole
short blade
yes
now if they are asking for the point of intersection, you dont have one
because the function is undefined at x=3, so the asymptote does not actually intersect the function
crimson sedge
so you can't have a hole and a point of intersection in the same place?
short blade
however, they may just want you to give the hole as the point of intersection
short blade
so you can't have a hole and a point of intersection in the same place?
the function is undefined at a hole
so that point is not part of the graph
so there is no intersection
crimson sedge
I assumed it was undefined at the coordinate, and not at all x values
crimson sedge
,w plot (x^3-9x)/(x^2-2x-3)
wraith daggerBOT
crimson sedge
can't really see the holes on this can you
short blade
it doesn't show it no
but it should be clear
that if you plug in x = 3
the function is undefined
so y = f(3) is not defined
so it is not part of the graph
crimson sedge
okay, so there is no intersection th en
then*
this is the first I've dealt with this
but if this were to happen again
it being undefined means that there is no intersections
?
short blade
it being undefined means that specific x value is not in the domain
but say you found that the solutions to the equation are x = 2 and x = 3
if x = 3 is undefined, x = 2 could still possibly be the x-coordinate of a point of intersection
so you'd need to check both
crimson sedge
but say you found that the solutions to the equation are x = 2 and x = 3
how are you able to have two solutions
are you talking about when it's something like
$a(a-3)(a-4)=0$
wraith daggerBOT
mj
crimson sedge
for example?
short blade
sure
crimson sedge
there can only be a maximum of two oblique asymptotes
short blade
im saying if you equate the oblique asymptote to the original function
and you get 2 possible x values, you need to check both
molten fern
what does it mean to be "setwise fixed"?
cedar kilnBOT
what does it mean to be "setwise fixed"?
granite knoll
context?
molten fern
for example, let D be a set and g be some action. g fixes D setwise.
we know that g acts on D
solid juniper
i don’t think this has much meaning here in your example. kinda just says the image of the action is a subset of D?
but that’s just part of the definition of action
lament yoke
Is it true that the biggest subspace is the space itself?
cedar kilnBOT
Is it true that the biggest subspace is the space itself?
lament yoke
Just assume there's a bigger subspace
so I would take a subspace X and another bigger subspace Y
lament yoke
Just assume there's a bigger subspace
and then ,what?
proving that it doesn't belong to that subspace
would I arbitrarily assign some variables?
dull oxide
If X is your space, and Y is bigger than X, how can Y be a subspace of X?
lament yoke
If X is your space, and Y is bigger than X, how can Y be a subspace of X?
makes sense,but was my approach wrong?
dull oxide
Not really, no
lament yoke
If X is your space, and Y is bigger than X, how can Y be a subspace of X?
and I would go on to define it arbitrarily ,just to show that can't be the case?
dull oxide
Ya
lament yoke
okay
subtle wadi
I'm trying to prove the formula $\sin^3t=\frac34\sin t-\frac14\sin3t$. This is on a section treating the complex exponential, so I'd expect to use it somehow. Any hints?
wraith daggerBOT
Philip
jagged oyster
I'm trying to prove the formula $\sin^3t=\frac34\sin t-\frac14\sin3t$. This is o...
Since e^ix = cosx + i sinx, e^iax = cos(ax) + i sin(ax) But also (cosx + i sin x)^a
Those are the same thing
subtle wadi
right
foggy merlin
sin t = (exp(it) - exp(-it))/2i
subtle wadi
ok, so sin^3 t=((exp(it)-exp(-it))/2i)^3, is that correct?
foggy merlin
yes
jagged oyster
You still get some "i" so depending on what you want u need to take the real or complex part
subtle wadi
ok, so sin^3 t=((exp(it)-exp(-it))/2i)^3, is that correct?
ok, I will try to write this out and see what I get
looks like a lot of work though
foggy merlin
it is
subtle wadi
that sucks, ok, well, I'll get to it
cedar kilnBOT
@subtle wadi Has your question been resolved?
subtle wadi
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
half zinc
Hello, I am not sure how to go about solving this problem. I am looking for someone who can explain it to me.
velvet mortar
Basically what is 10 degrees Celsius in Fahrenheit
The conversation formula is given so you just have to plug in
half zinc
50?
velvet mortar
Yeah
quick cipher
Think of it this way:
°F, which represents Fahrenheit, is directly proportional to °C, which represents Celsius.
The problem mentions an increase of 10°C, which can mean +10 on the number line.
Using the conversion equation given within the lesson, which is °F = 32 + 1.8(°C)
Using substitution, we can replace °C to 10°C.
Doing the math, it equates the following:
°F = 32 + 1.8(10)
°F = 32 + 18
°F = 50
So yeah, you are correct.
Get it now?
half zinc
ohh I see now. It's really quite simple I suppose, I just wasn't engaging my brain. Thank you Diesel and Math Guy
quick cipher
Welcome!
drifting isle
How do you solve
cedar kilnBOT
How do you solve
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 can solve when I know Both equations for each angle but missing one is throwing me off
plucky owl
You have equations for each angle
Do you know what vertical angles are and how it can help you solve this question?
plucky owl
No it says vertical angles
drifting isle
No it says vertical angles
This
plucky owl
Do you know what supplementary angles means?
plucky owl
Can you form the equation for that problem?
drifting isle
plucky owl
Good and that ? is <BOC, correct?
plucky owl
The problem is asking for the compliment of <BOC
drifting isle
Yea I know what it wants but I don’t know how to do that
plucky owl
Compliment meaning the complimentary angle with <BOC
So that equation you wrote down, solve for <BOC, aka the question mark
plucky owl
You are solving for <BOC, the question mark is <BOC
You have x - 15 + <BOC = 180, set that equation equal to <BOC
drifting isle
plucky owl
You still haven't set it equal to <BOC
drifting isle
What do you mean
plucky owl
Set equal to <BOC means <BOC = ...
drifting isle
So no x?
plucky owl
The x stays
drifting isle
So what am@I missing
plucky owl
If you had x - 15 + y = 180 and I said to set it equal to y, could you do it?
plucky owl
Now that's what <BOC is suppose to be equal to. As mentioned, the problem wants the compliment of that, and as I said too, compliment meaning complimentary angles
Do you know what complimentary angles are?
drifting isle
Complimentary angles are angles the add up to 180
plucky owl
Don't use AOB because that's not compliement with BOC
You can use a random variable instead
drifting isle
X plus boc = 180
plucky owl
Not 180
plucky owl
You want to find the compliemnt of BOC
drifting isle
Yeah so that plus aob =180 yeah