well factor that
#help-38
marble wharf
if you factor (2-lambda) out from this you obviously get the same
factoring is how you find the algebraic multiplicity
gaunt temple
if you factor (2-lambda) out from this you obviously get the same
okay and that becomes (2-lambda)^2 * (4-lambda)
but sorry for the stupid question
what if we dont know from the beginning that lambda=2 is an eigenvalue
how do we know which term we have to factor out
trim joltBOT
@gaunt temple Has your question been resolved?
gaunt temple
.close
trim joltBOT
trim joltBOT
Available help channel!
marsh forum
could someone explain the concept of span to me like I'm 5? so If I have two basis vectors, it's just the set of points I can reach, by multiplying each basis vector by a constant ?
pseudo grotto
a1v1 + ... + amvm
pseudo grotto
you can add the vectors as well
you're taking sums as well
marsh forum
got it, thanks!
yeah, how do I prove that
say the vectors are i+j
and i
how would I prove that the span of these vectors is $\R^2$
solid kilnBOT
ƒ(Why am. I here)=I don't know
pseudo grotto
show that for any vector (a,b) in R^2, you have (a,b) = xi + yj
where x,y are scalars
marsh forum
okay, so I have to prove any point can be expressed as $av+bu$
solid kilnBOT
ƒ(Why am. I here)=I don't know
pseudo grotto
yes
solid kilnBOT
ƒ(Why am. I here)=I don't know
pseudo grotto
it can
marsh forum
no $ai+bi+cj$ =$(a+b)i +c j$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
which is similar to ti+qj
pseudo grotto
span{(1,0), (1/2,0), (0,1)} is still R^2
solid kilnBOT
..,,
solid kilnBOT
Requested by physicsrocks
marsh forum
no
matrices haven't even been mentioned in axler yet
sort of
only upto 3 by 3
consistant
infinite solutions
yes
rigth
*right
solid kilnBOT
..,,
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
yeah, makes sense, thanks
ooh
okay
so for instance i and j are linearly independent
got it
thank you
thanks so much !
.close
trim joltBOT
trim joltBOT
Available help channel!
fresh wren
trim joltBOT
wraith hinge
Yes
solid kilnBOT
ƒ(Why am. I here)=I don't know
fresh wren
is it going to help?
solid kilnBOT
ƒ(Why am. I here)=I don't know
wraith hinge
I thought the term "common" was commonly used
fresh wren
i have to choose different variable
marsh forum
i have to choose different variable
you mean a u-sub?
marsh forum
no
marsh forum
re-write this as
fresh wren
can you write it down then please?
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
$\frac{1}{x}=u$
solid kilnBOT
ƒ(Why am. I here)=I don't know
fresh wren
but the derivative wil be log
marsh forum
no
fresh wren
that is going to fuck it up
marsh forum
thats the integral you're thinking about
marsh forum
**ƒ(Why am. I here)=I don't know**
differentiate this wrt x
fresh wren
what next
marsh forum
no
marsh forum
**ƒ(Why am. I here)=I don't know**
what's the differential of this
marsh forum
uh, the x^2 should disappear
marsh forum
complete the square and solve
marsh forum
yes
frozen plover
,w integrate 1/sqrt(1 + x^2)
solid kilnBOT
frozen plover
yeah you're good
marsh forum
pretty sure there are other ways to integrate that in terms of logs too imo
frozen plover
there's the logarithmic definition of arsinh
frozen plover
bro speaks in latin
trim joltBOT
@fresh wren Has your question been resolved?
wraith hinge
Alas!
trim joltBOT
frozen plover
.reopen
trim joltBOT
✅
frozen plover
@fresh wren no x outside the square root
or you messed up the sub somewhere in between
frozen plover
this should evaluate to an arsinh
trim joltBOT
trim joltBOT
Available help channel!
marsh forum
could I get an explaination of this
trim joltBOT
could I get an explaination of this
maiden hare
What part?
marsh forum
from thus we have written 0 as a linear combination...
marsh forum
okay
maiden hare
If d_n must equal 0 for all n, then the v_n are linearly independent
marsh forum
isn't that always the case
maiden hare
No let me think of an example
v1 = (1,0), v2 = (0,1), v3 = (1,1)
a1 = 1, a2 = 1, a3 = -1
c1 = 2, c2 = 2, c3 = -2
marsh forum
hmm
maiden hare
Well ok bad example since I took v = (0,0)
boreal harbor
isn't that always the case
basically think about when can you write two or more nonzero vectors that sum to the 0 vector? only when you can express one vector as a scalar multiple of the others right
maiden hare
a1 = 1, a2 = 1, a3 = 2
c1 = 2, c2 = 2, c3 = 1
v = 1(1,0) + 1(0,1) + 2(1,1) = (3,3)
v = 2(1,0) + 2(0,1) + 1(1,1) = (3,3)
marsh forum
hmm
maiden hare
So then you have
(0,0) = (-1)(1,0) + (-1)(0,1) + 1(1,1)
marsh forum
So then you have
(0,0) = (-1)(1,0) + (-1)(0,1) + 1(1,1)
so essentially these vectors aren't linearly indpendent because?
maiden hare
Because d_n =/= 0
marsh forum
ah
maiden hare
Yet d_n*v_n + ... = 0
maiden hare
Yea, d_1 = -1, d_2 = -1, d_3 = 1
supple copper
could I get an explaination of this
What does he say for the definition of linear independence?
supple copper
Finite dimensional 
You can extend the definition to a subset B of V is linearly independent if for any finite subset of B…
Anyhow, probably won’t encounter it often here
.close
trim joltBOT
supple copper
Actually you might, if you ever want to define a basis for function spaces that are often infinite dimensional
trim joltBOT
Available help channel!
severe stump
Is this not the definition of a limit but substituting M for k? Or is this some type of extension thing
digital bison
not exactly the definition, no
severe stump
I'm guessing I'd use the definition to prove this then?
digital bison
it's not saying x_n is close to x after M
It's saying x_n is positive after M, could still be miles away from x
severe stump
For $\epsilon>0$, there exists a $k\in\mathbb{N}$ such that, for all $n\in\mathbb{N}$, $n\geq k$. Then $|x_n-x|<\epsilon$?
solid kilnBOT
Narutoes
digital bison
that is the definition, yes.
severe stump
So if we're saying that x_n is positive, then there is an M that is less than n?
Is that not the definition of how numbers work?
Or does this not work if x_n is negative?
digital bison
x is positive, not x_n
severe stump
I'm not quite understanding what it's asking then.
digital bison
you're trying to show that if the limit of the sequence is positive, then eventually the terms of the sequence must be positive (and stay positive)
severe stump
It says x_n>0 for all n
Wouldn't that mean every term in the sequence has to be positive?
digital bison
read the rest of the sentence
severe stump
Oh
So once I hit this point where n goes higher than M, every other term is positive?
digital bison
not sure what you mean.
severe stump
Like negative log function starts super negative then comes up over the x-axis and zooms way out.
You don't need to know what I mean, I know what I mean.
Do I use the definition? Since it's the only thing given
digital bison
yes, you know the limit exists and it's positive, so you'll want to use the definition somewhere.
severe stump
So we know that for |x_n-x|<epsilon, there's gotta be a k in there
digital bison
yep
severe stump
So if I work backwards from my conclusion, I'm trying to reach the step that says x_n>0 implies n => M
What's the step before that?
digital bison
thats not really true though. x_n can be positive at any time, it may alternate +,-,+,-,.... but eventually x_n is positive for good. So x_n being positive doesn't imply n> M
severe stump
I'm trying to get to an easier step to reach
Cuz I'm not quite understanding the implications of the conclusion
hallow kite
well you know that if the limit of x_n is x and x > 0, then you can always find some natural number M such that for n beyond that so that your sequence is within some distance epsilon of x
severe stump
Right.
hallow kite
so if you know that beyond a certain point, you'll always be within some distance epsilon of x for any positive epsilon, and x > 0, then consider something like epsilon = x / 2
you know x / 2 > 0
and you know you'll be able to find some M so that you're within x/2 of x
which means beyond a certain point, as long as you choose epsilon < x, you can always find M so that x_n > 0 for all n >= M
severe stump
Gotcha
trim joltBOT
@severe stump Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
wraith hinge
Could anyone go over the antiderivative of this function for me?
maiden hare
Can you figure out the antiderivative of 1/sqrt(x) ?
earnest relic
Could anyone go over the antiderivative of this function for me?
Sure, what seems to be stumping you? I'd love to go through it step-by-step if you want
wraith hinge
Can you figure out the antiderivative of 1/sqrt(x) ?
Would it be -x to the negative 1?
maiden hare
$-x^{-1}$ is just $\frac{-1}{x}$
solid kilnBOT
Nel
maiden hare
What's 1/sqrt(x) written with an exponent?
wraith hinge
x^-2
maiden hare
No that would be 1/x²
earnest relic
You can think of √x as the same thing as x^(1/2)
trim joltBOT
@wraith hinge Has your question been resolved?
wraith hinge
No that would be 1/x²
Having a negative exponent with its reciprocal is an alternative way to denote the thing that you wrote. So mine isn’t wrong?
Thank you for the help though. I just figured it out!!
trim joltBOT
trim joltBOT
Available help channel!
hexed thunder
I have another coding question dealing with python.
I have "combined" the two previous questions, but it is not spitting out a single output. I have not gotten to the mean or square root of the question, I simply am trying to figure out this part first.
hexed thunder
I am able to create a random integer "n", but once it goes into my for-loop, it does not process correctly
smoky snow
I am able to create a random integer "n", but once it goes into my for-loop, it ...
Don’t we need the question 2 and 3 ?
hexed thunder
That is the two questons, but question 4 outlines what is needed for the code that I need to write
This is what I am getting after playing around with it more, but from here I want to have that final number be a piece of data that I can then find the sqrt and mean of
trim joltBOT
@hexed thunder Has your question been resolved?
slender shard
This is what I am getting after playing around with it more, but from here I wan...
Rather than print the output, store the output into a variable, and then print that variable.
hexed thunder
So it states that "store" is not defined
slender shard
In Python, you do not have to explicitly create a variable. You can just use a variable name and assign a value to it using the equal(=) sign.
It's usually a good idea to assign a default value to a variable, such as 0 for an integer variable, before actually using it.
You could do something like
output = 0
hexed thunder
Alright, so prior to your last statement, I thought I would be able to write this:
slender shard
And then in the if...else statements, assign the result of the multiply() function to the variable output.
slender shard
Yes. The idea behind this is to familiarize yourself with how to use a particular programming language, in this case Python. Your teacher should have taught you about using variables to store data but that apparently didn't happen. 🙂
On that note, you should learn about variable naming. Use meaningful variable names instead of names such as k. It helps to make the code self-explanatory for someone else who may read your code. Variable names such as input and output would make their purpose much more clear.
acoustic flint
On that note, you should learn about variable naming. Use meaningful variable n...
input is a keyword already
slender shard
I was just using an example.
I haven't used Python in years so I'm winging it a bit here.
hexed thunder
On that note, you should learn about variable naming. Use meaningful variable n...
We only really learned about the "print" for if-else statements. As well as for for-loops. So placing a variable to it will be helpful in the future! Thank you! I was able to get the code working how I needed it to!
slender shard
And on shsgd's note, you should familiarize yourself with Python's reserved keywords to avoid potential name collisions.
hexed thunder
Thank you! I take "programming part 2" starting next week, so I am sure the next professor wll dive into all ofthis a bit further.
.close
trim joltBOT
trim joltBOT
Available help channel!
marsh forum
Find all values of x, for which $ln(1+x) \leq x$
trim joltBOT
Find all values of x, for which $ln(1+x) \leq x$
solid kilnBOT
ƒ(Why am. I here)=I don't know
fair bison
marsh forum
yup
main drift
you could show that x increases faster than ln(1+x)
trim joltBOT
trim joltBOT
Available help channel!
torn shale
Ehm ehm
torn shale
So if you have (function)^-1
You cant use product rule twice to derive it
Right?
For example
1/(x^3 +5)
left oriole
torn shale
In order to use product rule you need the derivative of “1/(x^3+5) which you cant do using product rule again
Product rule
Not power rule
My bad
torn shale
In order to use product rule you need the derivative of “1/(x^3+5) which you can...
In order to derive this we either use quotient or chain, yes?
But we cant use product rule to derive it
trim joltBOT
@torn shale Has your question been resolved?
torn shale
Gimmie a sec
trim joltBOT
trim joltBOT
Available help channel!
limpid shoal
can anyone teach me how to draw the structural formula in chemistry?
trim joltBOT
can anyone teach me how to draw the structural formula in chemistry?
@limpid shoal Has your question been resolved?
marsh forum
- addition of water across the double bond
marsh forum
can anyone teach me how to draw the structural formula in chemistry?
I think this should be the answer?
I may be wrong though
and there;s no double bond anymore
limpid shoal
like this?
marsh forum
Yeah
limpid shoal
why’s there a plus one tho?
marsh forum
where
marsh forum
why’s there a plus one tho?
?
marsh forum
why’s there a plus one tho?
that's supposed to be a H
limpid shoal
that's supposed to be a H
oh ok
marsh forum
I MAY BE wrong though
limpid shoal
did I draw it right?
torn shale
1) addition of water across the double bond
Can they ask chem questions in this server?
Just wondering
marsh forum
Now that it's summer the demand for channels will be lower, so it's fine I guess?
marsh forum
did I draw it right?
it's supposed to be an alcohol
limpid shoal
it's supposed to be an alcohol
methanol I suppose
limpid shoal
then what is it
limpid shoal
It should be pentan-3-ol IMO
yo why’s chemistry so hard
marsh forum
don't ask me, I'm bad at chem
limpid shoal
don't ask me, I'm bad at chem
at least you can do it with no help
marsh forum
next up is chlorination
can you do that?
I have some resources on org chem that may help yoou
do you want them
they're all legal
limpid shoal
do you want them
sure
limpid shoal
chapters 1 though 5 may help
is it the one on haloalkanes?
marsh forum
is it the one on haloalkanes?
chapter 1 is
limpid shoal
For hydrogen is it like this?
marsh forum
yes
marsh forum
no
limpid shoal
where did I go wrong?
marsh forum
there should be one Cl on each atom that had a double bond
limpid shoal
like this?
limpid shoal
am I supposed to replace the hydrogen atoms with the chlorine atoms?
marsh forum
no, I'll send a remix of what it should look like
marsh forum
can anyone teach me how to draw the structural formula in chemistry?
and no double bond inbetween
I'm not too sure of the first answer though
marsh forum
this
limpid shoal
What about the third answer?
marsh forum
I'm sure it's right
trim joltBOT
@limpid shoal Has your question been resolved?
marsh forum
trim joltBOT
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
and f(0)=1
this implies it cuts the x-axis at some point in (0, π/3)
so $f(x)=3cos(3x)$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
at some point
could I have a hint
like how would i justify this
or is this just straight out wrong?
like am I overcomplicating this?
limpid dawn
**ƒ(Why am. I here)=I don't know**
how can this be if f(0) = 1
solid kilnBOT
ƒ(Why am. I here)=I don't know
limpid dawn
**ƒ(Why am. I here)=I don't know**
if this was f(x) then f(0) = 3
marsh forum
that's not alwys true
they're asking is this true for some $x \in [0 , \frac{\pi}{3}]$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
in other words, does the graph of f(x) intersect 3cos(3x) in this interval
limpid dawn
**ƒ(Why am. I here)=I don't know**
with this
marsh forum
sorry
so how would I formally argue this to be true
<@&286206848099549185>
I mean does staement 1 have to be true
just a hint please
oh
ooo
thanks for the hint
daamn
marsh forum
the integral is just 1
main sigil
are you sure?
marsh forum
$\int_0^{\frac{\pi}{3}} f(x) -3cos(3x)$
solid kilnBOT
ƒ(Why am. I here)=I don't know
main sigil
the first part is 1?
main sigil
yep
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
I can use the same logic for B I think
main sigil
nope
main sigil
correct
marsh forum
so this statement is correct too
marsh forum
,calc 6/π
solid kilnBOT
The following error occured while calculating:
Error: Undefined symbol π
main sigil
f(0) - 3sin(3*0) = 1
marsh forum
that's less than -2
main sigil
yep
marsh forum
it is yes
main sigil
but you can break it to a product of limits first
the second one is sinx / x * the other limit
marsh forum
so C is right too, right?
marsh forum
the second one is sinx / x * the other limit
yup
thanks
I don't think D is correct though
main sigil
so C is right too, right?
Hmm why?
marsh forum
Using LH
just a min
let me TeX it
$\lim_{x\ \rightarrow0}\left(\frac{\left(\int_0^xf\left(x\right)+xf\left(x\right)\right)}{-2xe^{x^2}}\right)$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
the second part is $\frac{-1}{2}$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
for the first part I use LH again
marsh forum
$\frac{f\left(x\right)}{-2e^{x^2}-4x^2e^{x^{2\ }}}$
solid kilnBOT
ƒ(Why am. I here)=I don't know
marsh forum
I think I'm doing something wrong here
main sigil
mhm
marsh forum
I forgot that
main sigil
so it's -1/2
marsh forum
.close
trim joltBOT
trim joltBOT
Available help channel!
rose sail
find the sum of the last 15 terms of the sequence -14, 5, 24, 43, 62..., 328
vague citrus
guangdong
rose sail
f(x) = a + (n-1)d
328 = -14 + (n -1)19
328 = -14 + 19n - 19
328 = 19n - 33
361 = 19n
361/19 = 19n/19
19 = n
19 terms
rose sail
guangdong
yeah
so would i set the 4th term as a for the purpose of finding the sum of the last 15 terms?
vague citrus
there's a formula for sum of last terms as well
rose sail
(19-4)+1 is 16 terms
whyd you add one at the end tho
vague citrus
whyd you add one at the end tho
because the 4th and 19th term are inclusive
count through 2 to 8
that'll be 7 numbers
rose sail
2, 3 , 4, 5, 6, 7, 8
vague citrus
there are (8-2)+1 and not (8-2) numbers
trim joltBOT
rose sail
ty
trim joltBOT
Available help channel!
cold crystal
Can someone tell me why a cross product of two vectors is perpendicular to both vectors or we just define it that way?
stiff aurora
You can make computation to check it is the case, but it is defined in order to be perpendicular
cold crystal
so, it is defined to be perpendicular?
stiff aurora
I do not know what is the definition of the cross product that you have seen
But in some definition of the cross product, it is asked, yes
cold crystal
In what definitions is it not defined as perpendicular?
stiff aurora
You may define it explicitly (with the explicit formula), and then you have to check if it is indeed perpendicular
cold crystal
.close
trim joltBOT
trim joltBOT
Available help channel!
little tide
trim joltBOT
little tide
So, what I have done so far is
1 job/4000 men-days = 1 job/3000 men-days + 1 job/5x men-days
I'm not sure if it's the right setup though...
The correct answer is supposed to be 200, but I want to understand how and why the answer is 200...
dusk light
So, what I have done so far is
1 job/4000 men-days = 1 job/3000 men-days + 1 jo...
where did u get this setup from?
400 men took 10 days to do the job
So that means 1 man would take 10 x 400 days to do the job
little tide
Because I thought it was a work problem
dusk light
Yeah thats right but still doesn't explain ur logic
oh waitt
no no I get what ur saying
you need 4000 men days
and so far
cold crystal
So, what I have done so far is
1 job/4000 men-days = 1 job/3000 men-days + 1 jo...
this is incorrect
4000men-days/1job = 3000 men-days/1job + 5x men-days/1job
little tide
1000?
little tide
200 🙂
little tide
But how come the men-days were above though?
dusk light
above what
little tide
like 4000 men-days/1 job instead of 1 job/4000 men-days
dusk light
I wouldn't think about it as a fraction
Think of it more as like the price of a job
the job costs 4000 men days
if you want to get 4000 men days done in 1 day, you need to have 4000 men
if you want to get 4000 men days done in 20 days, you need 4000/20 = 200 men
you get what I'm saying?
little tide
Yup 🙂
dusk light
yeah alr
little tide
Any tips though for future problems like that?
dusk light
hmm
just always work out the cost of the job first
and just format everything in a way which u understand
like for example for this q
I would first start with
the job costs 400 x 10 = 4000 men-days
since paul had 600 men on for 5 days, that means we have already gone through 3000 men-days
so what remains is 4000 - 3000 = 1000 men-days
So, we have 5 days left and I'm trying to work out how many men I need to reach 1000 men days
i.e. 5n = 1000, where n is the number of men
n = 1000/5 = 200
therefore, Paul needs 200 men to finish the job on time
this is a lot longer cause I've explained everything but this is basically what I'd so
just break the q up
little tide
I got it. Thank you so much for helping me 🙂
dusk light
if u want just send another q like this if u want to practise
little tide
I have yet to encounter a similar problem, but I will keep in mind what you said for future ones!
Really, thank you so, so much 🙂
dusk light
yeah no worries
little tide
.close
gusty plank
I don't understand why multiplying both sides by xy changes the derivative.
wet dragon
wdym
gusty plank
Just that, I can put x and y under a common denominator without changing the derivative, but when i multiply both sides by xy to get rid of it, it changes the derivative. I don't understand why.
wet dragon
Just that, I can put x and y under a common denominator without changing the der...
because x^2+y^2 is strictly nonnegative
but 5xy is not always nonnegative
split chasm
the expression just looks different due to the form / technique you're starting with
using the given relation, you can convert from one form to another
trim joltBOT
trim joltBOT
Available help channel!
smoky marsh
trim joltBOT
trim joltBOT
@smoky marsh Has your question been resolved?
trim joltBOT
@smoky marsh Has your question been resolved?
trim joltBOT
@smoky marsh Has your question been resolved?
trim joltBOT
@smoky marsh Has your question been resolved?
trim joltBOT
@smoky marsh Has your question been resolved?
cyan oxide
do you know the formula to get the volume of the revolution shape?
trim joltBOT
@smoky marsh Has your question been resolved?
tulip vector
trim joltBOT
tulip vector
Is anyone able to help with part 2 of this question
fleet bear
It is implied that the solutions to $x^2 - 4(2^x) = 0$ are also the solutions to $2 log_{\frac{1}{2}}{x} = m x + c$
solid kilnBOT
StrangeQuarkAL
fleet bear
One way you could find that line is by simply making $2 log_{\frac{1}{2}} {x}$ the subject of the equation: $x^2 - 4(2^x) = 0$
solid kilnBOT
StrangeQuarkAL
trim joltBOT
@tulip vector Has your question been resolved?
tulip vector
It is implied that the solutions to $x^2 - 4(2^x) = 0$ are also the solutions to...
AHH I didn't see this thanks so much
.close
latent axle
Question 11 I have no idea how to start, it’s an integral
latent axle
The area of the cross sections is 1/2 bh but idk how to implement that
marsh forum
is this multivariable calc?
marsh forum
hmm
maybe find the relationship between the height and length
take triangular cross-sections
marsh forum
Question 11 I have no idea how to start, it’s an integral
like so
you know that if we're x m from the vertex towards you
and the base of the red traingle is y
$\frac{y}{x}= \frac{4}{5}$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
@latent axle
similarly find a relationship between y and height
from that find an expression for area in terms of x alone
and then integrate
does that make any sense
trim joltBOT
@latent axle Has your question been resolved?
smoky marsh
find the volume of the solid under the surface z=y cos((x^3)-1) and above the region enclosed by the curves y=0 y=2 x=1 x=y/2
trim joltBOT
find the volume of the solid under the surface z=y cos((x^3)-1) and above the re...
smoky marsh
how do i go on about doing this
trim joltBOT
@smoky marsh Has your question been resolved?
placid radish
find the volume of the solid under the surface z=y cos((x^3)-1) and above the re...
can you write down the integral?
smoky marsh
i dont think i can
placid radish
i dont think i can
how much of multivariable claculus do you know?
smoky marsh
i know double integrals
placid radish
i know double integrals
do you know whats the area of cross section of the solid when y is fixed and x goes from 1 to y/2?
smoky marsh
i dont think so
placid radish
i dont think so
well its just the integral of the z value when x changes
and you can imagine when x changes, the height z is going through the cross section
smoky marsh
ok
placid radish
ok
with this do you have some idea of how to calculated the area?
maybe its helpful to draw a sketch of the 3d graph
using some online graphing tool
here is a sample problem: calculate the volume under the surface of f(x,y)=xy enclosed by y=0, y=2 and x=0, x=2
trim joltBOT
@smoky marsh Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
mint cave
need help with part a
trim joltBOT
need help with part a
mint cave
@pliant seal
trim joltBOT
@mint cave Has your question been resolved?
trim joltBOT
@mint cave Has your question been resolved?
old tiger
need help with part a
!status
trim joltBOT
need help with part a
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
- $y=2-mx\$
- $y=2-\frac{2}{5}x$
trim joltBOT
old tiger
need help with part a
the 2 equations always intersect
trim joltBOT
Available help channel!
marsh forum
$\cos\left(\frac{\pi}{11}\right)+\cos\left(\frac{3\pi}{11}\right)+\cos\left(\frac{5\pi}{11}\right)+\cos\left(\frac{7\pi}{11}\right)+\cos\left(\frac{9\pi}{11}\right)$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
which is a GP
marsh forum
what other method exists ?
wraith hinge
You want the value right?
marsh forum
yeah
wraith hinge
Lemme think
marsh forum
I've come until here:
smoky flax
Sounds like a job for the calculator 👍
marsh forum
$\frac{e^{\frac{i\pi}{11}}\left(e^{\frac{8\pi}{11}}-1\right)}{e^{\frac{2i\pi}{11}}-1}$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
Sounds like a job for the calculator 👍
no calculators in this exam
*the exam I'm preparing for
This is practice material
full dock
no calculators in this exam
jeeee adv
smoky flax
use estimations 😭
marsh forum
BITSAT
full dock
wats that
wraith hinge
Lmao
full dock
harder than jee?
marsh forum
**ƒ(Why am. I here)=I don't Know**
can someone verify this
smoky flax
Harder than the chinese gaokao?
marsh forum
but easier ones
smoky flax
marsh forum
Harder than the chinese gaokao?
no, idts
marsh forum
**ƒ(Why am. I here)=I don't Know**
so please verify this someone
wraith hinge
entrance exam for the best private engineering college in India
Ik ik
If it's from bitsat
There has to be something without Euler too
marsh forum
but I'd rather not use them
tepid rock
@marsh forum
marsh forum
yes
marsh forum
I know one exists
yes
but I don't know the formula for the same
I could derive it though
full dock
no and no and no and no and no and no 💀
oooh....
tepid rock
I could derive it though
Not for an exam with 130 questions in 180 minutes.
marsh forum
now I meant
tepid rock
Oh.
unborn bone
**ƒ(Why am. I here)=I don't Know**
you want this simplified?
marsh forum
want to know If I've made any mistake until there
unborn bone
ok so this model of thing is actually pretty common when you have exp(i.a) +- 1
what you basically do is turn thhe exp(i.a) into exp(i.a/2 + i.a/2) = exp(i.a/2).exp(i.a/2)
solid kilnBOT
ƒ(Why am. I here)=I don't Know
cosmic carbon
it's the sum of the first 5 terms, not 4
unborn bone
and since 1 is like the neutral element of multiplication in C (if i'm not wrong) you do 1 = exp(i.a/2).exp(-i.a/2)
hang on i need to pull out my drawing tablet it'll explain things better
typing math is so painful
livid thunder
why are u using a GP sum for an AP?
unborn bone
what do GP and AP stand for?
livid thunder
what do GP and AP stand for?
geometric and arithmetic progression
unborn bone
ok
livid thunder
like a series
tepid rock
why are u using a GP sum for an AP?
The angles are in AP but when cos(x) is written is Re(e^{ix}), that's a GP.
So you could do either.
marsh forum
It's from a prep book
unborn bone
**ƒ(Why am. I here)=I don't Know**
btw did you forget to add the imaginary number in the top exponential or is that intentional?
marsh forum
btw did you forget to add the imaginary number in the top exponential or is that...
my bad
livid thunder
I have done a question similar to this but with less terms
marsh forum
typo
unborn bone
kk
tepid rock
Fok I don't think this is bitsat
I just told you about the existence of a formula. I guess any exam could use a formula and ask you to use it for different values.
It's not even a tough formula to derive in the first place.
marsh forum
$\frac{e^{\frac{i\pi}{11}}\left(e^{\frac{8\pi i}{11}}-1\right)}{e^{\frac{2i\pi}{11}}-1}$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
yes, but we're starting from $e^{\frac{i \pi}{11}}$
so we add zero to the power first
solid kilnBOT
ƒ(Why am. I here)=I don't Know
marsh forum
so I now need to find $Re\left(e^{\frac{i\pi}{11}}\left(e^{\frac{i4\pi}{11}}+1\right)\left(e^{\frac{i\pi}{11}\ }-1\right)\right)$
solid kilnBOT
ƒ(Why am. I here)=I don't Know
covert thistle
$e^\frac{2i\pi}{11}-1=e^\frac{i\pi}{11}\left(e^\frac{i\pi}{11}-e^{-\frac{i\pi}{11}}\right)$
solid kilnBOT
BoiledAnchovies
marsh forum
**ƒ(Why am. I here)=I don't Know**
I'm here right now
covert thistle
oh ok
livid thunder
look u probably wouldnt have the foresight to see this but I believe this is a question using trig compount angles
covert thistle
?
livid thunder
had a question similar to this
marsh forum
could you give a hint please
livid thunder
if u multiply everything by 2sin(pi/11) then divide by it, it becomes easier
amber python
no
[2\textwidth] calculate
[ \map [\Big] \cos {\f \pi {11}} + \map [\Big] \cos {-\f \pi {11}} + \map [\Big] \cos {\f {3\pi} {11}} + \map [\Big] \cos {-\f {3\pi} {11}} + \dots + \map [\Big] \cos {\f {9\pi} {11}} + \map [\Big] \cos {-\f {9\pi} {11}} + \map [\Big] \cos {\f {11\pi} {11}} ]
solid kilnBOT
wraith hinge
How
amber python
well luckily this calculation is trivial
marsh forum
ah
wraith hinge
2sinAcosB= sin(A+B)+sin(A-B)
marsh forum
ooh
amber python
so you get a pretty clear way of getting the sum you want
marsh forum
so it;s -1/2
amber python
quite
amber python
well actually
marsh forum
thanks
livid thunder
i think its a half?
amber python
you got a sign error in there
marsh forum
oh right
cos(pi)=-1
got it
thanks a ton!
that was suprisingly elegant
.close
trim joltBOT
wraith hinge
2sinAcosB= sin(A+B)+sin(A-B)
trim joltBOT
Available help channel!
rapid horizon
Integration of [2sinx] limit 0 to 2π
trim joltBOT
Integration of [2sinx] limit 0 to 2π
rapid horizon
marsh forum
Is that floor (2sin(x))?
rapid horizon
Is that floor (2sin(x))?
Yeah
wraith hinge
Area of boxes
rapid horizon
wraith hinge
You got it , didn't checked the limits
trim joltBOT
trim joltBOT
Available help channel!
maiden hinge
are closures and interiors of conneted sets connected??
trim joltBOT
are closures and interiors of conneted sets connected??
ebon kite
the closures are always connected
the interiors are not always though, consider two tangent circles only connected at a single point
maiden hinge
the interiors are not always though, consider two tangent circles only connected...
i figured the interiors weren't always connected
maiden hinge
the closures are always connected
and this also makes sense, but im having a bit of trouble proving this
ebon kite
i think a natural way of doing it is by contradiction
maiden hinge
so suppose a set E is connected but its closure isnt
then cl(E) is the union of two separated sets
white spruce
my answer is yes because the l-norm, squared l-norm and constant functions are convex and the sum of convex functions is convex? I'm not too sure if that reasoning is valid or if I'm missing something or it's completely wrong
trim joltBOT
my answer is yes because the l-norm, squared l-norm and constant functions are c...
@white spruce Has your question been resolved?
white spruce
<@&286206848099549185>
trim joltBOT
@white spruce Has your question been resolved?
white spruce
<@&286206848099549185> no one?
fast dove
Yes
novel kernel
my answer is yes because the l-norm, squared l-norm and constant functions are c...
Does l norm means that the power is 1/l
trim joltBOT
@white spruce Has your question been resolved?
rapid horizon
trim joltBOT
rapid horizon
Hints please
hallow kite
consider this as a tree diagram, where either you draw a white or black ball from A, and then consider the possibilities of selecting from B
you have a 3/5 chance of adding a white ball to B and a 2/5 chance of adding a black ball
trim joltBOT
@rapid horizon Has your question been resolved?
rapid horizon
.close
tepid pewter
Hey would I be correct here
Doing fourrier transformation
trim joltBOT
Hey would I be correct here
Doing fourrier transformation
@tepid pewter Has your question been resolved?
tepid pewter
.close
trim joltBOT
trim joltBOT
Available help channel!
hollow field
Can someone explain to me how to approach graphing autonomous differential equations such as the one above? I understand how to determine if a critical point is stable/unstable but have no idea how to graph it
trim joltBOT
Can someone explain to me how to approach graphing autonomous differential equat...
@hollow field Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
solar void
trim joltBOT
sly pewter
struggling to get the inverse
Can you show your work
Oh wait
Do you need to use the inverse to find the slope or is there another way?
solar void
inverse to find the slope
inland forge
For the inverse just switch x and y which in this case is f(x) and then isolate y and set x to be 0 which is a
sly pewter
Do you know if there’s a relationship between the slope of the function and the inverse function
sly pewter
For the inverse just switch x and y which in this case is f(x) and then isolate ...
It’s a cubic function tho
inland forge
So
Squareroot or even root would make sense because of restrictions but cuberoot works for negatives and positives
solar void
y=x^3+2x+3 -> x=y^3+2y+3 -> x-3=y(y^2+2) -> (x-3)/(y^2+2)=y did all this when i switched x and y but i dont know how to get y by itself
sly pewter
the derivative of a functions inverse is 1/dx/dy with the input being y or something
sly pewter
y=x^3+2x+3 -> x=y^3+2y+3 -> x-3=y(y^2+2) -> (x-3)/(y^2+2)=y did all this when i ...
Did you learn any other strategies than that for finding the derivative
solar void
thats the main one but i also know about leibniz way, just dont use it much
ill try it but im not sure how to do it for inverse derivatives
sly pewter
thats the main one but i also know about leibniz way, just dont use it much
Use the leibinz way
sly pewter
Technically
But it’s the derivative of the original function with the input of Y
sly pewter
Isn't 1/dx/dy just dy/dx
Also not sure if you can do that
Dy and dx don’t act as numbers iirc
inland forge
But they can be treated as such
In topics like differential equations
Also, isn't taking the derivative with respect to y already the inverse, so having a reciprocal would just undo it right?
sly pewter
ok well if it worked that way then leibinz would have done it that way 😭
But it isn’t so it doesn’t work
sly pewter
idk they had a specific notation that was created by leibinz
solar void
its 1/5 but ill check again
jade shard
sure
sly pewter
just do leibinz it’s so much easier
inland forge
What do you mean by do leibniz
sly pewter
that’s just how I reference it 😭 srry
inland forge
It's fine
sly pewter
I don’t know the name but they know it so it’s ok
I’ll show it to you when I am at my computer
inland forge
Are you talking about dy/dx notation
sly pewter
ok
solar void
i dont know how to do leibniz for inverse derivatives
but if i do learn it or figure out ill use it if its much easier
inland forge
What do you guys mean by liebniz
inland forge
So is the issue separating y?