Fair enough, I happened to see that there was some struggling so I thought I'd give some additional help
#help-10
topaz zealot
steel night
We only plug in if they are in a determinate form right
viscid bronze
We only plug in if they are in a determinate form right
yes
that's where your table earlier comes in
because there was division of 0 giving undefined
steel night
Ohhh right
proud geyser
also, I recognize that text you showed earlier. who gave you that image, if I may ask?
proud geyser
oh, alright.
steel night
So when we’re not told where the discountuiny is, we just look at where the function changes definition
And that point will be where we test it
proud geyser
boundary points are always prime suspects for discontinuities.
steel night
When u say boundary point I thought it was the end points of the interval
proud geyser
I rarely use boundary point to mean endpoint.
if I do I will explicitly say what point I'm referring to.
and you can question me if I don't. that is fine.
viscid bronze
yes if both functions are continuous separately, the only possibility for a break to occur is the boundary point
steel night
Could we just say point where the function changes definition to avoid confusion or is there any other name for it
viscid bronze
you can say that
proud geyser
there is another name for it. it's called boundary point lol.
but I prefer not to type a bunch if it is understood what boundary points are.
steel night
I’ll just say boundary point alright 👍
viscid bronze
i say breakpoint but it doesn't rlly matter ig
as long as you get the point
pun unintended
steel night
The limit are not equal to each other which means there won’t be a max min in the interval
As the max min states that it should be a closed interval and be a continuous function within the interval
Wait
I’m confusing my self
Actually yeah
proud geyser
if the function is not continuous, then the EVT (which is what your theorem is actually called, if I read the statement correctly) does not apply.
steel night
Min max thereoum
proud geyser
most people refer to it as the EVT.
steel night
Oh ok
proud geyser
just to confirm, your theorem statement is this:
If f is continuous in a closed interval [a, b], there exists points c, d in [a, b] such that f(c) \leq f(x) \leq f(d) for all x in [a, b].
correct?
or equivalently,
If f is continuous in a closed interval, f attains a maximum and a minimum in the interval.
steel night
Yea
proud geyser
then yes, it is more commonly known as the extreme value theorem (EVT).
steel night
Ah, I see
So after the limits are not equal to each other at x approaches 2 , there won’t be a max min?
It’s not going to be a continuous function from the start of the interval to the end of the interval
topaz zealot
The limit as x->2 simply doesn’t exist
proud geyser
well then the theorem doesn't even apply to begin with.
it may happen that there is a max or min, but the conditions required for the EVT to apply are false, so it is not guaranteed.
proud geyser
we cannot guarantee their existence.
steel night
What does that mean
proud geyser
it may *happen* that there is a max or min, but the conditions required for the ...
^
steel night
Like we’re unsure
proud geyser
yes.
is your native language not English? I can try to see if I speak your native language.
deep kraken
Do you speak Viet
obtuse pebbleBOT
@steel night Has your question been resolved?
restive saffron
what does the degree sign on top of A mean on the second equation?
obtuse pebbleBOT
what does the degree sign on top of A mean on the second equation?
ionic oar
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
versed stratus
obtuse pebbleBOT
versed stratus
Let $Q$ be a refinment of $P$. Then $L(g,P)≤L(g,Q)≤U(g,Q)≤U(g,P)$. But $U(g,P)=L(g,P)$. So $U(g,Q)=L(g,P)=U(g,P)$. Similarly $U(g,Q)=U(g,P)$. Thus as there exist a sequence of partitions such that $U(g,P_{\varepsilon})-L(g,P_{\varepsilon})<\varepsilon$ for all $\varepsilon>0$, $g$ is integrable
warm shaleBOT
Wai
latent quiver
Let $Q$ be a refinment of $P$. Then $L(g,P)≤L(g,Q)≤U(g,Q)≤U(g,P)$. But $U(g,P)=L...
I think this is fine
But I dont think you even needed to define a refinement Q
You can do it directly with P
versed stratus
You can do it directly with P
huh
I mean fair
consider the constant seqeunce of partitions P,P...
and we're done
.close
obtuse pebbleBOT
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wooden surge
Can someone help? For some reason i just cannot get my marginal profit to work as expected
obtuse pebbleBOT
Can someone help? For some reason i just cannot get my marginal profit to work a...
wooden surge
I set revenue to be 2300u, because u is in thousands and we naturally want them all to be in similar units, and so i then set profit P(x) = 2300u minus the original given function C(u), which after some simplifying turns out to -0.0022u^2 + 2299.87u - 330
I then take the derivative of the profit and go from there
hollow grail
I set revenue to be 2300u, because u is in thousands and we naturally want them ...
yeah but you need not multiply it by thousand as all units are givem in thousands already.
wooden surge
Did i misread it
hollow grail
Marginal profit of 307 thousand batteries
wooden surge
hmm ok
i suppose that the "the manufacturer plans to charge wholesalers $2.30 per battery" maybe was what got me
but thanks!!!! :)
.close
obtuse pebbleBOT
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final radish
Guys I don't have a clue how to do this
obtuse pebbleBOT
Guys I don't have a clue how to do this
final radish
tardy epoch
how come the right side doesn't have an n
obtuse pebbleBOT
@final radish Has your question been resolved?
obtuse pebbleBOT
@final radish Has your question been resolved?
analog cape
you are in the right way just seprate equations the constes alone, the x alone and the x^2 alone
I hope tha helped @final radish
obtuse pebbleBOT
@final radish Has your question been resolved?
tender condor
You made a careless mistake when expanding (ax)^2
and also after what you've done so far, just group all the terms by constant, x, and x^2 and compare coefficients of these between LHS and RHS
you also have quite a number of presentation issues but i think you should get the right answer before addressing these
round island
Can I grab another set of eyes to help me find my mistake?
obtuse pebbleBOT
Can I grab another set of eyes to help me find my mistake?
polar fossil
,rccw
warm shaleBOT
round island
Just to clarify the answer is…. 16/sqrt 377
short crescent
is that not what you got
polar fossil
also like.... what's the question?
short crescent
also like.... what's the question?
assuming given sinA = 5/sqrt(29) and cosB = 3/sqrt(13) find cos(A-B). assuming this is the question based on what questions he did before
round island
is that not what you got
That is- I just wanted to make it more obvious
The system said it wasn’t
round island
also like.... what's the question?
polar fossil
why are we taking the sin of 5/√29?
do you mean something like: sinA = 5/√29?
if so, write that. you have two angles flying around here
round island
It’s a whole big thing
short crescent
@polar fossil read my last message in #serious-discussion thatll explain
round island
I don’t even….
She would rather me separate and write it all by triangle and- idk it’s weird
polar fossil
that's fair enough, triangles are helpful, but like.... can you write something like a table then? or like
A
sin: 5/√29
cos: 2/√29
tan: 5/2
idk
it's just really hard to figure out what you've done
we've got
cos(A - B) = cosA cosB + sinA sinB
round island
Yes
polar fossil
oh maybe it wants you to rationalise the denominator
round island
Maybe
short crescent
rationalizing marked you wrong on the last question, i was gonna say yeah your work is right though
short crescent
multiply it by the square root on top and bottom
polar fossil
you just multiply by √377 / √377
round island
Wait nvm I know what you mean now
short crescent
Wait nvm I know what you mean now
was it marked correct by the system?
obtuse pebbleBOT
@round island Has your question been resolved?
round island
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
heyyyy how shoudl i go abt practicing loops for python
obtuse pebbleBOT
heyyyy how shoudl i go abt practicing loops for python
vale pelican
write loops of your own if I had to guess
like just make up your own examples of functions/operations whose computation likely involves a loop
tardy epoch
heyyyy how shoudl i go abt practicing loops for python
Can you not abuse math help channels with non math questions
timid silo
Can you not abuse math help channels with non math questions
oops im so sorry i ddint mean to "abuse" them
timid silo
write loops of your own if I had to guess
thank uuuuuuu
viscid bronze
heyyyy how shoudl i go abt practicing loops for python
do coding practices
compact star
little projects can be nice, i remember one of the first thing I did with loops was to verify the Collatz conjecture up to n=1000000, with that you get a while and a for loop for sure. A lot of thing could be good practice Fibonacci, matrix multiplication etc…
timid silo
do coding practices
any useful websites or resources?
timid silo
thank uuuuuu
timid silo
little projects can be nice, i remember one of the first thing I did with loops ...
got u
vale pelican
what about a function that prints the first n rows of pascal's triangle?
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
etc.
if that's the level you're looking for
proud geyser
if you want something that uses while or do-while loops as well, maybe you can try implementing Newton's method for finding square roots with a set precision goal as the condition, if you want to challenge yourself a little bit.
restive gorge
Can you not abuse math help channels with non math questions
loops are sums 
vale pelican
sums are loops you mean
proud geyser
loops are sums <a:nerdge:875193493293760534>
$\prod$
warm shaleBOT
Yukari
viscid bronze
print("1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
etc.")
proud geyser
ah yes, the YanSim method when all else fails.
viscid bronze
yansim 😭😭😭😭
proud geyser
you have a point.
restive gorge
sums are loops you mean
I was making a point in terms of functionality
vale pelican
I took my first c++ course before taking calc 2
viscid bronze
it can go both ways tbf
quiet condor
can i get help with this [
obtuse pebbleBOT
can i get help with this [
viscid bronze
for part a you can start by finding the critical points in the triangle
quiet condor
for part a you can start by finding the critical points in the triangle
xy-x-3y is what shape
viscid bronze
hyperbolic paraboloid
quiet condor
hyperbolic paraboloid
im just lost bruh
on what the extrema thing is in this regard
i mean last thing i did was finding critical points on curves
but this is totally different
so idk how what i did earlier relates to any of this
viscid bronze
for a triangle, the extreme points are usually on the boundary OR inside the region where gradient=0 (or derivative doesn't exist)
so you should check both cases
viscid bronze
for part a you can start by finding the critical points in the triangle
this is to find possible extreme points IN the region (when you set gradient to 0)
quiet condor
for a triangle, the extreme points are usually on the boundary OR inside the reg...
can we start from the terms, so when they say find the absolute extreme, whats that supposed to mean here
like intuitively i mean
viscid bronze
you can probably just think of a 2d graph, with a curve
find the extreme points of it while the x value is bounded
kinda same thing here
here you're finding the highest/lowest value that f reaches over the triangle
quiet condor
here you're finding the highest/lowest value that f reaches over the triangle
what does this mean exactly
obtuse pebbleBOT
@quiet condor Has your question been resolved?
quiet condor
highest/lowest value
i dont understand
viscid bronze
what do you not understand about it
quiet condor
what do you not understand about it
im just not understanding what we want here
viscid bronze
you can probably just think of a 2d graph, with a curve
it is similar to this where you plug every possible (x,y) in this curve into your f(x) and find the extremes
in the triangle case, your bounds are
x=0 for 0≤y≤4
y=0 for 0≤x≤5 and
y=4-(4/5)x for 0≤x≤5 (hypotenuse with line through (0,4) and (5,0))
so you take every possible point in this bounded triangle and plug it into f(x) and find the largest/smallest value f produces
obtuse pebbleBOT
@quiet condor Has your question been resolved?
obtuse pebbleBOT
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Available help channel!
zealous haven
$$ \int_0^{infinity} e^(-x^2) dx $$ I want to prove that with Laplace method
trim portal
\int
warm shaleBOT
William James Moriarty
deep kraken
If power is using ^{}
trim portal
and infinity is \infty iirc
zealous haven
$$ \int_0^{\infty} e^{-x^2} dx $$
warm shaleBOT
William James Moriarty
zealous haven
If power is using ^{}
I just started learning latex that's why
deep kraken
Np bro
zealous haven
$$I=\int_0^{\infty} e^{-x^2} dx $$
We square I
$$ I^2=\int_0^{\infty} e^{-x^2} dx \int_0^{\infty} e^{-y^2} dy$$
warm shaleBOT
William James Moriarty
zealous haven
$$I^2=\int_0^{\infty}\int_0^{\infty} e^{-(x^2+y^2)} dxdy $$
warm shaleBOT
William James Moriarty
zealous haven
Here I want help to get the right substitution
shut lagoon
What do you think you should use?
zealous haven
Arctan I think
shut lagoon
You need to subtitute something for x and y as functions of some other two variables.
x^2 + y^2 is a certain value with a specific meaning
zealous haven
I know this you want to say polar coordinates
zealous haven
But there are another way
shut lagoon
Okok well yeah polar coordinates is the usual way there's probably some other way
zealous haven
I think y=tx
dy=xdt
e^(-(x^2+y^2))=e^(-x²(1+t²))
Okay that's will be easy
@shut lagoon thank you
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stiff citrus
how would i start with this prove? im not too sure where to begin...
obtuse pebbleBOT
how would i start with this prove? im not too sure where to begin...
shut lagoon
What is Q_n?
stiff citrus
n-dimentional hypercube
shut lagoon
Investigate Q_4 first, and then you should be able to argue about the other ones from how they're constructed inductively.
stiff citrus
would i do induction on the number of vertices?
shut lagoon
If you show that Q_4 is non planar, then it has a k_3,3 minor and from the construction of Q_n from Q_{n-1}, you should be able to argue that Q_5 does as well and so on
stiff citrus
im having a hard time seeing Q_4 having any edges crossing xD
wait nevermind im looking at a 3d Q_4 not 2d
.close
halcyon shuttle
obtuse pebbleBOT
halcyon shuttle
so for this, do i find the value of signum for every quadrant?
oh nvm got it
.close
brittle trail
I'm reading something on field theory right now and the author casually remarked, that if $K$ is a field with $\text{char} K = p$, we know that $K$ has $q := p^n$ elements for some $n \in \mathbb{N}$. Thus the multiplicative group has order $q - 1 = p^n - 1$ and every element in it satisfies $a^{q-1} = 1$. I got all that, but I didn't get the next part:
``Thus the polynomial $f = X^p - X \in \mathbb{F}p[X]$ has exactly $q$ distinct roots. We obtain $f = \prod{a \in K} (X - a)$ and $K$ is the splitting field of $f$ over $\mathbb{F}_p.$.''
(To be more percise, I don't get why the polynomial has exactly $q$ \textit{distinct} roots and why the other identity for $f$ holds.)
obtuse pebbleBOT
I'm reading something on field theory right now and the author casually remarked...
warm shaleBOT
Ruby
brittle trail
.close
meager trench
Let ABC be a triangle and let D be some point on the line segment AB which is neither B nor C. The circle of ABD intersects AC at an interior point E. The cricle ACD intersects AB at an interior point F. A' is the reflect of A about the line BC, such that the rays of A'C and DE meet at P and the rays of A'B and DF meet at Q. Prove that AD, BP and CQ are either concurrent or all parallel.
really lost but heres what i got: AD is the radical axis of the two circles,
since ABDE and ACDF are cyclic quadrilaterals, ∠CDE = ∠BAC = ∠BDF and reflecting it about BC, this is also = ∠BDP
dont really know how to continue
obtuse pebbleBOT
Let ABC be a triangle and let D be some point on the line segment AB which is ne...
shut bison
Could you provide the diagram which you drew
meager trench
Could you provide the diagram which you drew
okay hold up ill try to draw a nicer one cuz i freestyled it 😭
deep kraken
What is angle chasing?
restive gorge
Math slang
quick nova
What is angle chasing?
basically finding or equating angles using properties or relationships
meager trench
wait my drawing is not much better than it was before
i dont have my compass which is why LOL
deep kraken
I am not good enough for English
quick nova
I think you can uh use Menelaus or Ceva's Theorem for this
meager trench
quick nova
also ABDE and ABCF is a cyclic qudrilateral no?
meager trench
I think you can uh use Menelaus or Ceva's Theorem for this
menelaus is for collinearity and i dont see ceva here
wide zinc
What is angle chasing?
-# kiểu đi tìm góc bằng cách dùng các tính chất bằng nhau của các góc, không dùng tỉ lệ hay j khác
deep kraken
Oge
quick nova
menelaus is for collinearity and i dont see ceva here
I was thinking of like the sine version of it
meager trench
Use something round
i tried but its hard to trace it out such that abde and acdf are concyclic*
deep kraken
You can use Ceva here using Sine tho
quick nova
I was thinking of like the sine version of it
In any triangle $\triangle ABC$, three lines $AD$, $BP$ and $CQ$, are concurrent if and only if $$\frac{\sin(\angle BAD)}{\sin(\angle CAD)} \cdot \frac{\sin(\angle ACQ)}{\sin(\angle BCQ)} \cdot \frac{\sin(\angle CBP)}{\sin(\angle ABP)} = 1$$
warm shaleBOT
MxRgD
deep kraken
Also note that ABDE is cyclic
meager trench
yes ABDE and ACDF are cyclic quadrilaterals, ∠CDE = ∠BAC = ∠BDF and reflecting it about BC, this is also = ∠BDP
deep kraken
Can you do reflection A' here
meager trench
wdym
quick nova
like the reflection of A across BC
meager trench
mhm
meager trench
oh wait
meager trench
yes ABDE and ACDF are cyclic quadrilaterals, ∠CDE = ∠BAC = ∠BDF and reflecting i...
BDF and CDE are equal so DE and DF are images of each other about σ
i think i know how to do this now this is desargues
sorry!
.close
obtuse pebbleBOT
deep kraken
No need to sorry btw, good luck!
obtuse pebbleBOT
Available help channel!
hardy widget
<@&268886789983436800>
full pelican
!listpings
obtuse pebbleBOT
!listpings
trail musk
What
restive gorge
,help
warm shaleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
inner sierra
Get your DMs
full pelican
Yo I got to much trouble in learning those algebraic identities pls help
trail musk
Ok
inner sierra
$(a + b)^2 = a^2 + 2ab + b^2$
warm shaleBOT
1 divided by 0 equals Infinity
inner sierra
Like this one yeah?
trail musk
Yea man
full pelican
Yes😭
trail musk
What about it
inner sierra
**1 divided by 0 equals Infinity**
You know why this works?
full pelican
I can't learn it
warm shaleBOT
1 divided by 0 equals Infinity
inner sierra
Now try to expand this
trail musk
So it might help to use it with numbers instead of letters first. Like uh (5+2)(5+2) = 7 × 7 = 49. But also theres 5(5+2) + 2(5+2) = 5×5 + 5×2 + 2×5 + 2×2 = 5² + 2(2×5) + 2²
Hopefully that helps
thin halo
need help finding t value
obtuse pebbleBOT
need help finding t value
hardy widget
need help finding t value
humor me and try 1.693
I'm thinking that they used 2.4 as the mean instead of 2.38
even though you really shouldn't
viscid bronze
yeah igot 1.693 too
viscid bronze
I'm thinking that they used 2.4 as the mean instead of 2.38
thin halo
oh actually, that would make sense lol
hardy widget
yeah sometimes people aren't the brightest with rounding
thin halo
I can't check anymore but I'll just go with it
hardy widget
rip
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
steel night
I need help
obtuse pebbleBOT
I need help
proud geyser
as always, please state what you have tried and what you do not get.
steel night
!status
obtuse pebbleBOT
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
pallid willow
in fact, state what you do not get from the start next time, please. so that helpers can directly read your questions from the get go.
deep kraken
State MVT
steel night
deep kraken
Is this original question, no crop?
last pilot
this is unreadable for dark mode
steel night
yes no crop
deep kraken
I can read this
viscid bronze
i swear I've seen this q like weeks ago 😭
deep kraken
Let's construct a function
steel night
i swear I've seen this q like weeks ago 😭
haha
deep kraken
Since x here changes and the exponent doesn't change
What could be the function structure?
steel night
x^2/3
steel night
wheres f?
deep kraken
the function you just found
steel night
2/3x^-1/3
deep kraken
no
steel night
I MEAN
1/x^1/3
deep kraken
ye
steel night
im not sure
hidden compass
Of what?
deep kraken
finding the domain
hidden compass
...
hidden compass
the function you just found
@steel night
hidden compass
the domain of x of
This doesn't make sense
steel night
so the domain of the original function, not the derivative
hidden compass
Wait, are you writing these things down on a piece of paper or tablet? Or are you just writing messages here without taking notes? @steel night
deep kraken
Wait, are you writing these things down on a piece of paper or tablet? Or are yo...
Blud always ask many questions and seems to not understand any, even though these questions are the same 🥀
steel night
Wait, are you writing these things down on a piece of paper or tablet? Or are yo...
im writig on the board
yeah Im not sure what the domain is
deep kraken
yeah Im not sure what the domain is
Well you are given two value of x in the function f you found
👀
And by MVT there is a point?
steel night
But in the range of these 2
i see
hidden compass
This is MVT. Do you agree? @steel night
steel night
i dont understand the first line of the OP
hidden compass
This is MVT. Do you agree? <@1098469645347995748>
Do you see those a and b?
steel night
yes
hidden compass
Can you tell what their values are for the exercise you're working on?
deep kraken
i dont understand the first line of the OP
You are the OP
steel night
original post
steel night
first derivative value between a and b?
deep kraken
Ye
steel night
This is MVT. Do you agree? <@1098469645347995748>
I dont understand the 2nd case
<@&286206848099549185>
what does the MVT state?
meager trench
f(b) - f(a) = f'(c)(b-a) is a direct consequence of the above if you multiply both sides by b-a, is that what you mean?
meager trench
what does the MVT state?
there exists a point c on the open interval a,b such that (f'(c) = f(b) - f(a))/(b-a)
steel night
there exists a point c on the open interval a,b such that (f'(c) = f(b) - f(a))/...
a,b such that (f'(c) = f(b) - f(a))/(b-a)
what about in in words?
meager trench
a,b such that (f'(c) = f(b) - f(a))/(b-a)
you have an interval a to b yes
there exists a number between a and b such that it fulfils the condition (f(b) - f(a))/(b-a)
essentially, (f(b) - f(a))/(b-a) is the slope of the straight line connecting the points (a, f(a)) and (b, f(b)) (just like y2 - y1 all over x2 - x1)
we call this straight line the secant line
there is a point on the graph between a and b such that the derivative (the tangent line to that point) has the same gradient as that secant line
deep kraken
I dont understand the 2nd case
Thats the conditions
meager trench
visually, it is something like this
Lagrange's MVT merely states that there exists this point c such that these two lines are parallel
steel night
how do we know the interval, if we are not given the interval
dire moss
Lagrange's MVT merely states that there exists this point c such that these two ...
Just an extension of Rolle’s Theorem (or, Rolle’s Theorem is a special case of the Mean Value Theorem)
dire moss
how do we know the interval, if we are not given the interval
It’s an arbitrary interval (a, b)
deep kraken
how do we know the interval, if we are not given the interval
You were given
meager trench
It’s an arbitrary interval (a, b)
so long as this interval fulfils the conditions of being continuous and differentiable
deep kraken
Ngl i started studying MVT just 1 week ago😂
meager trench
Just an extension of Rolle’s Theorem (or, Rolle’s Theorem is a special case of t...
yup
dire moss
so long as this interval fulfils the conditions of being continuous and differen...
Exactly! Continuous on closed, differentiable on open
meager trench
Ngl i started studying MVT just 1 week ago😂
MVT is so fun u get to prove Taylor's theorem (which is arguably the best thing in calc)
dire moss
MVT is so fun u get to prove Taylor's theorem (which is arguably the best thing ...
YIPPIE!!
deep kraken
MVT is so fun u get to prove Taylor's theorem (which is arguably the best thing ...
I have enough trauma after EVT and IVT 💀
Still havent able to fully understand sequences 😂
dire moss
Still havent able to fully understand sequences 😂
Think of sequences as like listing the outputs of a function
Instead of x’s they are indexes, positive integers based on ‘n’
steel night
so let me say what MVT is
deep kraken
Think of sequences as like listing the outputs of a function
Maybe i will make a help channel later to ask
steel night
MVT states that there is a point c, in a closed interval [a,b], where when differentaiated, it is parallel to the chord AB
meager trench
I have enough trauma after EVT and IVT 💀
The pipeline is just
Fermat's theorem -> Rolle's Theorem -> Lagrange's MVT (Standard MVT) -> Cauchy's MVT -> Taylor's Theorem
meager trench
MVT states that there is a point c, in a closed interval [a,b], where when diffe...
yup
steel night
anything else I should add to it
meager trench
specify its continuity
deep kraken
The pipeline is just
Fermat's theorem -> Rolle's Theorem -> Lagrange's MVT (Stan...
Alright i dont understand fermat
Dont kill me 😂
meager trench
Alright i dont understand fermat
wait maybe its differences in terminology but isnt it just there exists f'(c) = 0 if there is a local min or max between the interval (a,b) (continuous, differentiable)
dire moss
The pipeline is just
Fermat's theorem -> Rolle's Theorem -> Lagrange's MVT (Stan...
L’Hopital’s is somewhere in there
lol
meager trench
L’Hopital’s is somewhere in there
L'Hopital is after Cauchy's MVT
dire moss
L'Hopital is after Cauchy's MVT
Yeah, Ik.
steel night
MVT states that there is a point c, in a closed interval [a,b], where when differentaiated, it is parallel to the chord AB at c
so there is only one point
c
steel night
nice point
deep kraken
My L'Hôpital is not touched in my course 😂
dire moss
Anyways you guy help OP i will ask later
Look at your DM’s or message requests
meager trench
I love my boy L’Hopital
L'Hopital stole it from Bernoulli
deep kraken
Look at your DM’s or message requests
Oke
dire moss
nice point
Anything else you need clarified?
meager trench
it doesnt tell u the specific value of c, it just tells you c exists
which is why Fermat, Rolle, Lagrange's MVT and Cauchy's MVT are all theorems that are called Existence theorems, they merely describe the "existence" of something
dire moss
so the formula of MVT gives the point c?
You can find the c’s algebraically
steel night
it doesnt tell u the specific value of c, it just tells you c exists
are u sure?
dire moss
You can find the c’s algebraically
But the theorem itself doesn’t tell you which ones
meager trench
are u sure?
yes, you have to solve for c, the MVT did not give you the c
it merely states you could do that
steel night
yeah but it was possible to find c because of the formula of MVT
its just only rearranging
meager trench
sure..? like once again it only tells u that there is some c not the specific value of c
its not a formula for that reason
dire moss
However
Just saying you can do smth isn’t the same thing as doing the thing
If I were to tell you it is indeed possible to calculate 2 + 2
meager trench
Just saying you can do smth isn’t the same thing as doing the thing
thats a good point
dire moss
If I were to tell you it is indeed possible to calculate 2 + 2
Could you calculate 2 + 2?
Of course you could
meager trench
MVT tells you you can do this, MVT does not tell you how you can do this
dire moss
Of course you could
But I never told you what 2 + 2 was
steel night
I see
dire moss
I see
Think about it. Did I ever tell you what 2 + 2 is? Or did I just merely state that it could be calculated?
steel night
MVT tells you you can do this, MVT does not tell you how you can do this
Is this explanation good so far
before I proceed
steel night
Think about it. Did I ever tell you what 2 + 2 is? Or did I just merely state th...
I don’t get it
meager trench
Is this explanation good so far
specify its continuity
meager trench
I don’t get it
It can be done =/= This is how it can be done
hidden compass
interval range
It's the [a, b]
dire moss
I don’t get it
Would you agree that just because I told you that something is possible, doesn’t mean I necessarily told you the outcome of doing that thing?
hidden compass
Can you tell what their values are for the exercise you're working on?
Answer this @steel night
steel night
It's the [**a**, **b**]
yes
steel night
Answer this <@1098469645347995748>
its 8 and 8.019
steel night
the graph of [a, b] is continuous
yes ik
steel night
when u said continuous, did u mean values of a, b?
deep kraken
Closed interval
steel night
where do u want me to put a to b
meager trench
uh
meager trench
This is MVT. Do you agree? <@1098469645347995748>
^
deep kraken
where do u want me to put a to b
bro.
steel night
are we given f(b) and f(a)
dire moss
are we given f(b) and f(a)
You can calculate them
f(8) & f(8.019)
Where
f(x) = x ²/³
steel night
ah
deep kraken
should i calc them or
calculate
obtuse pebbleBOT
@steel night Has your question been resolved?
steel night
calculate
how do we know whats f(a) and f(b) respectively
because the order matters since its subtraction
steel night
I dont think we are required to do graph in exams, i mean we can if it helps
just from my professor
deep kraken
I dont think we are required to do graph in exams, i mean we can if it helps
it is not required but you need something to visualise
steel night
$f(8^{\frac{2}{3}})$
warm shaleBOT
ø
steel night
is that valid?
deep kraken
so f'(c)?
steel night
ok done
deep kraken
Correct
steel night
so is there something i need to do next
deep kraken
What else
steel night
just conclude that c does not lie in a, b
the question wants the range of error right
like the bound
deep kraken
Correct
sly elm
no sorry i dont know this 🥀
steel night
oh rip
sly elm
gl , try pinging min back
steel night
I think hes busy but all good
weak needle
you calculated the exact error
you were supposed to calculate the upper bound on error
f(b)-f(a) / b-a = f'(c)
where a<c<b
Do you understand that f(b)-f(a) is the error whose upper bound we want to calculate?
@steel night
steel night
you were supposed to calculate the upper bound on error
isnt the upper bound the absolute error? which accounts for the lower bound too
weak needle
isnt the upper bound the absolute error? which accounts for the lower bound too
upper bound means max possible absolute error
steel night
ohhh
steel night
Do you understand that f(b)-f(a) is the error whose upper bound we want to calcu...
thats the upper bound?
weak needle
that's the absolute error
f(b)-f(a) is the error
we want to guess max to max how big this error can be
using MVT
weak needle
no why would we add or subtract the error to function
we would apply MVT on f(x)=x^2/3 with a=8, b=8.019
because it says to calculate upper bound using MVT
steel night
I think i did that
steel night
my working out is here
weak needle
you calculated the exact error
weak needle
you understand this?
twilit salmon
my working out is here
Don't think that you were ever mean to evaluate exponents best to keep 2/3, and manipulate to find the upper bounds, we are not interested in point c, whose gradient is the slope from the endpoints rather we find how well does 8^{2/3} approximates 8.019^{2/3}
weak needle
similarly in the equation you get with MVT, you need to make f(b)-f(a), which is the error, the subject and calculate max[f(b)-f(a)] which is same as saying max[error] to calculate upper bound on error
steel night
you understand this?
i dont understand this because its trig combined with bounds and im not good with them 😭
weak needle
upper bound on error = max[error]
since error = f(8.019)-f(8)
we need to calculate
max[f(8.019)-f(8)]
using MVT
you get it?
steel night
yes
weak needle
In the equation you get with MVT, you need to make f(b)-f(a) the subject and calculate max[f(b)-f(a)].
This is your entire task. Try to work on this.
twilit salmon
@steel night is the question on how well does 8^{2/3} approximates 8.019^{2/3}?
twilit salmon
In the equation you get with MVT, you need to make f(b)-f(a) the subject and cal...
hey, sorry even I do not understand, the maximum of a constant is the constant though?
steel night
In the equation you get with MVT, you need to make f(b)-f(a) the subject and cal...
But how does making the subject help with calculating max
twilit salmon
You are really close to finishing it, no need to find max
Start from the equation f(b) - f(a) = f'(c) (b-a)
You know that c in (8, 8.019) i.e., 8 < c < 8.019
This is already a big hint
Try taking root 2/3 and manipulating to find the reciprocal! You will get the bound for it
weak needle
hey, sorry even I do not understand, the maximum of a constant is the constant t...
8.019^2/3 - 8^2/3 = error
we are considering error is unknown and with that we are calculating max(error) that's why it's not max(constant)
twilit salmon
8.019^2/3 - 8^2/3 = error
we are considering error is unknown and with that we a...
No, the error is known, here we are assuming that one does not have access to a calculator hence the need to use algebraic tricks and MVT instead of computing the difference of 8^{2/3} and 8.019^{2/3} using your calculator
This is to illstrutate how people before that do not have access to calculator are able to approximate them
weak needle
I need help
this is the question
twilit salmon
Try taking root 2/3 and manipulating to find the reciprocal! You will get the bo...
Yes the bound is your answer to the question
steel night
Start from the equation f(b) - f(a) = f'(c) (b-a)
(b-a)?
twilit salmon
f' means derivative
steel night
Ik
twilit salmon
Oh I read wrong, how does your course define "error"?
Did they provide a definition for you?
steel night
Don’t worry about it
twilit salmon
Anyways, error is most commonly defined to be absolute difference, i.e., |f(b) - f(a)|, in your case, 8.019^{2/3} > 8^{2/3} therefore we do not need to use absolute value here, so f(b) - f(a), I arrange it this way instead of saying frac{ f(b) - f(a) }{ b-a } is so that the LHS is talking about the error, and not the slope.
obtuse pebbleBOT
@steel night Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
icy wren
When applying the change of variables theorem for integrals, how can I apply it someting like $\int_a^b f(u(x)) dx$? and get some sort of intgeral in terms of $w = u(x)$?
obtuse pebbleBOT
When applying the change of variables theorem for integrals, how can I apply it ...
warm shaleBOT
LXDL
icy wren
For example, to take a simple example, $\int_a^b f(c - 2x) dx = \int_{c - 2a}^{c - 2b} -1 \cdot f(u) du$
where $u(x) = c - 2x$
icy wren
However when I do $\int_a^b f(c - x^2) dx = \int_{c - a^2}^{c - b^2} \frac{-1}{2x} \cdot f(u) du$
I'm not entirely sure if this is correct
warm shaleBOT
LXDL
icy wren
the normal change of variables always has $\int_a^b f(u(x)) u'(x) dx = \int_{u(a)}^{u(b)} f(u) du$
warm shaleBOT
LXDL
icy wren
For example, to take a simple example, $\int_a^b f(c - 2x) dx = \int_{c - 2a}^{c...
but more oftne i see smthing like this instead
and I'm not relaly sure what the justification/proof behidn this is (assuming nomral hcange of variables theorem)
Would this proof look okay?
Assuming that $\forall x \in [a, b] u'(x) \neq 0$, then:
$\int_a^b f(u(x)) \frac{u'(x)}{u'(x)} dx = \int_{u(a)}^{u(b)} f(u) \cdot \frac{1}{u'(x)} du$
warm shaleBOT
LXDL
shut lagoon
Yes that's the idea.
icy wren
**LXDL**
okay yes, becasue for this step I was pretty unsure if that is the machinery they are using
shut lagoon
In a way if you make the substitution $w = u(x)$, you get $\dd{w} = u'(x) \dd{x}$ and in this case it works like a fraction if you will. You get $\dd{x} = \frac{\dd{w}}{u'(x)}$, which you can plug in your integral
warm shaleBOT
Azyrashacorki
icy wren
hm, is there a reason we can jsut "plug in"?
i guess i was tryign to go for a more formal reasoning
icy wren
**LXDL**
for this example, this seems to be more like $\int_a^b f(c-2x) dx = -\int_a^b - f(c-2x)dx = - \int_{c-2a}^{c-2b} f(u) du$, is htis understanding correct? Since i dont think they need this heavy machinery, i.e. a special case where we are basiclaly multiplying a non zero constant and its recirpocal
warm shaleBOT
LXDL
shut lagoon
Yes indeed.
Sometimes you may be able to get something strictly in terms of u in the end.
But this depends on whether you can solve for u in terms of x.
icy wren
But this depends on whether you can solve for u in terms of x.
Ah I see that makes alot more sense. Yes I think we can treat/I was sloppy with my notation, but what is happenign is that we define a function $h(w) := \frac{f(w)}{u'(u^{-1}(w))}$. Then we have $\int_a^b f(u(x)) \frac{u'(x)}{u'(x)} dx = \int_a^b h(u(x)) u'(x) = \int_{u(a)}^{u(b)} h(w) dw$.
warm shaleBOT
LXDL
shut lagoon
Yep that's it
icy wren
But this depends on whether you can solve for u in terms of x.
I see thank you, and usually for like the "constant" pull out trick one, its by lineartiy of the integral? i.e. don't need to very u'(x) =0 since in this case u'(x) = c for some $c \neq 0$ baically
warm shaleBOT
LXDL
obtuse pebbleBOT
@icy wren Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lost lake
find the domain of this function
obtuse pebbleBOT
find the domain of this function
lost lake
here's what i did:
i cut out the function from the sqrt and compared it to 0
x^3+x^2 = 0
x^2(x+1) = 0
x = -1
but how do I know which one is correct?
west stratus
find the domain of this function
just try a number more than -1 and less than -1
x^3 should never be negative and more than x^2
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
deep abyss
Can somebody help me to solve this using pumping lemma? I couldn’t figure out which string should I apply the lemma to.
obtuse pebbleBOT
Can somebody help me to solve this using pumping lemma? I couldn’t figure out wh...
obtuse pebbleBOT
@deep abyss Has your question been resolved?
livid dagger
maybe something like a^n b a^n a?
ye ig
but a^n b a^(n! + n) b
and contradiction at i = 1 + (n! / y)
deep abyss
maybe something like a^n b a^n a?
We need to find a contradiction somewhere
livid dagger
|y| <= n
deep abyss
and contradiction at i = 1 + (n! / y)
Yea that works I guess
But how did you find that
livid dagger
But how did you find that
just trying cuz n! is divisible by any number <= n
i thinking bout that
digital charm
Hey what factoring method did I just use? And is there a simpler way of going about it.
obtuse pebbleBOT
Hey what factoring method did I just use? And is there a simpler way of going ab...
short crescent
that's not a factoring method, you just solved for x
digital charm
Okay
quick nova
you can get that form by completing the square of a quadratic btw
short crescent
yes, if there was something else before this then that would be the case
digital charm
Yeah but there’s many ways to solve
short crescent
but if this was given then you can just directly solve for x
digital charm
And my teacher wants me to use a variety
uneven schooner
Yeah but there’s many ways to solve
one of the easiest methods would be completing the square.
or, using the quadratic formula
or factorizing it
uneven schooner
its just solving for x.
azure heath
Is there a name for the method I just used
that’s not a factoring method
obtuse pebbleBOT
warm shaleBOT
Nyxzore
digital charm
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
azure heath
are you looking for help factoring it?
uneven schooner
$|x-2| = \sqrt{4/3}$ so $x-2 = \pm \sqrt{4/3}$
fossil crag
x-2 is not sqrt(4/3), it's already +/- sqrt(4/3)
warm shaleBOT
Annie Maqionde
uneven schooner
its the absolute value
warm shaleBOT
Nyxzore
deep kraken
Abosulte
serene elk
the fact that u took the square root of a square
short crescent
the +/- should have been written at this bottom step here
when you take the square root you automatically put the +/- there
obtuse pebbleBOT
azure heath
idk why this thread ragebaited me so hard
short crescent
$\sqrt{4} = 2$, however if we say $x^2 = 4$ then $x = \pm 2$
warm shaleBOT
Krish
sly elm
idk why this thread ragebaited me so hard
wut
sly elm
alr
obtuse pebbleBOT
Available help channel!
humble hawk
how do yall do algebraic expressions and factoring polynomials??
obtuse pebbleBOT
how do yall do algebraic expressions and factoring polynomials??
dense gazelle
how do yall do algebraic expressions and factoring polynomials??
any specific problem ?
so that there is a reference point
humble hawk
hardy widget
dense gazelle
where’d you get this? the answer should be n>12
that question is either cutting off an answer choice or really poorly put together.
humble hawk
where’d you get this? the answer should be n>12
i got this from modules / curriculum online in the philippines
dense gazelle
i got this from modules / curriculum online in the philippines
did you crop this image? if so can you show the full page
dense gazelle
i cn show the gull page
go ahead
dense gazelle
a couple of these are very oddly worded, which ones have you done so far?
humble hawk
none i js started
dense gazelle
none i js started
okay, in all honesty the wording of 1 and 4 are really throwing me off so I won’t be of much use there.
humble hawk
im still struggle with the first one💔
dense gazelle
im still struggle with the first one💔
move on to 2 for now
humble hawk
kk
i also need help for measurement too can u also help me with that?
if u dont its fine , but if u do thx
lets move on to two
dense gazelle
i also need help for measurement too can u also help me with that?
right now i have to go, if in 15 minutes nobody responds you can ping helpers
obtuse pebbleBOT
Available help channel!
deft heart
Need some help gang, i am trying to find an equation which was algebraic and its graph made a wave like structure … i remember seeing one it had no irrationals or anything complex just a simple function of x and numbers
obtuse pebbleBOT
Need some help gang, i am trying to find an equation which was algebraic and its...
deft heart
Nah a single wave
short crescent
could you draw it out?
deft heart
A single upward bump
short crescent
shut lagoon
$\frac{1}{1+x^2}$?
warm shaleBOT
Azyrashacorki
shut lagoon
That has a bump
short crescent
would be something along the lines of that
simple laurel
this is $y=\frac{1}{1+(x-2)^2}$
warm shaleBOT
Johannes Kepler
short crescent
you can do $\frac{1}{1+(x-h)^2}$
warm shaleBOT
Krish
short crescent
and h will move it left or right
short crescent
!done
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
short crescent
if you don't have any other questions
deft heart
.close
obtuse pebbleBOT
deft heart
Thanks krish and everyone
mild sandal
you're welcome
thick oracle
cat
neon vector
They did say thanks everyone
short crescent
thick oracle
lmao
obtuse pebbleBOT
Available help channel!
desert pulsar
When they say on a bearing of 310* is this what they mean visually?
obtuse pebbleBOT
When they say on a bearing of 310* is this what they mean visually?
desert pulsar
Ik how to solve the question, im just trying to understand it
honest aurora
face north
turn 310 degrees clockwise
you are at a bearing of 310 degrees
it was useful when sailing long distances, using the mercator projection
"straight line takes me to where I want to go"
desert pulsar
face north
turn 310 degrees clockwise
you are at a bearing of 310 degrees
Isn't that what I drew?
Thanks for the clarification, I appreciate your help
.close
obtuse pebbleBOT
desert pulsar
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
desert pulsar
uhh i need help with another question, disregard the original please.
Why is the resultant force drawn in the middle between the vertical and horizontal components?
Here is how i solved the 1st question
split mauve
Why is the resultant force drawn in the middle between the vertical and horizont...
You're resolving a vector. Think of it as a result of those two vectors combined.
desert pulsar
You're resolving a vector. Think of it as a result of those two vectors combined...
so when im dealing with questions like these where two forces meet at a right angle the resulting vector will always come out the middle as shown in the diagram?
split mauve
so when im dealing with questions like these where two forces meet at a right an...
Yep, when they're perpendicular (at right angle).
desert pulsar
Yep, when they're perpendicular (at right angle).
you said right angles as in plural, but there is only one right angle here?
split mauve
you said right angles as in plural, but there is only one right angle here?
Sorry, I think that's a minor error on my side.
desert pulsar
Sorry, I think that's a minor error on my side.
like this right?
and the two angles on either side add upto 90?
split mauve
and the two angles on either side add upto 90?
Yep.
obtuse pebbleBOT
desert pulsar
.reopen
obtuse pebbleBOT
✅ Original question: #help-10 message
desert pulsar
Hi back again with another question, disregard the original
How does Tx go from the top to the bottom? and something weird I've noticed is cos(60)*25 also gets the correct answer for the horizontal can someone explain why that is to me please?
<@&286206848099549185>
bright sedge
How does Tx go from the top to the bottom? and something weird I've noticed is c...
newton laws of motion
lmao
desert pulsar
newton laws of motion
lmao
?
bright sedge
How does Tx go from the top to the bottom? and something weird I've noticed is c...
wdym top from bottom
its still in top
the force is acting horizontally
but to have better undrstanding and finding the Tx we horziontally move the vector below
to form a triangle
so that we can use trigo and find the required side = force
desert pulsar
but to have better undrstanding and finding the Tx we horziontally move the vect...
ahh so the bottom is just something we draw to make calculation and understanding easier?
bright sedge
ahh so the bottom is just something we draw to make calculation and understandin...
yea
desert pulsar
Ok but why does cos(6)*25 also get the right answer?
bright sedge
Also the second part of your question is simple
cuz cos(90 - theta) = sintheta
try to learn trigonometry i would say , it will help u better understand all these concept
bright sedge
Also the second part of your question is simple
cuz cos(90 - theta) = sintheta
so cos (90 - 30) = sin 30
desert pulsar
so cos (90 - 30) = sin 30
ohh i didn't know that
i just checked in the calculator and you're right
bright sedge
yeah learn trigonometry it will be helpful,
cuz in these question u would need the help of it
desert pulsar
well thats all the questions I have, thank you for your help @bright sedge
desert pulsar
yeah learn trigonometry it will be helpful,
cuz in these question u would need ...
I know basic trig and trig graphs but I haven't gone too indepth
bright sedge
just go through basic trigonometric equations and formulae
desert pulsar
didn't cover unit circle inverse trig functions yet
desert pulsar
just go through basic trigonometric equations and formulae
Yeah I'll be sure to revise, ty for ur help.
close
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
desert pulsar
Why are we allowed to move the vectors around like this? Is it like algebra where we can manipulate equations as long as the RHS and LHS are equal?
obtuse pebbleBOT
Why are we allowed to move the vectors around like this? Is it like algebra wher...
indigo niche
i think its mean N is opposite to that component , also F
so N its opposite to the vertical mg component , and F to the orizzontal mg component
tired monolith
Why are we allowed to move the vectors around like this? Is it like algebra wher...
Yeah! Vectors are not constrained to any point in space. They consist of just 2 properties, a magnitude and direction. No matter where the vector is positioned, it is the same vector. Moving the vectors tip to tail is actually the geometric way to sum vectors.
desert pulsar
Yeah! Vectors are not constrained to any point in space. They consist of just 2 ...
" No matter where the vector is positioned, it is the same vector " could you elaborate a little bit more on this?
tired monolith
hm
Well, in this context, the vectors are all forces
wait no that's a bad example
hm
desert pulsar
Take your time explaining lol
tired monolith
You can imagine a vector like an arrow
if you use displacement as an example, if you are dispaced 2m north from like (0, 0) vs 2m north from (30, 0), it's still a displacement of 2 north
So if you are going 2m north and then 3m east
waits for desmos to load
desert pulsar
You can imagine a vector like an arrow
well isn't that the literal definition of a vector? I was taught a vector is anything that can be drawn as an arrow because an arrow has magnitude and direction.
desert pulsar
if you use displacement as an example, if you are dispaced 2m north from like (0...
Yeah you got me a little bit lost here
desert pulsar
I imagine trying to teach someone else a topic is much more diffucult than trying to learn it yourself.
Which is why I have big respect for all the helpers here, they're incredily helpful lol.
tired monolith
whether it's 2m north from the equator, or 2m north from my house, or 2m north from buckingham palace, it's still 2m north
indigo niche
do you know newton third law?
tired monolith
no matter where the arrow is, it's the same arrow
tired monolith
Which is why I have big respect for all the helpers here, they're incredily help...
yeah lol
desert pulsar
do you know newton third law?
yeah force has an opposite or equal reaction
also known as the reaction force i think when drawing free body force diagrams
indigo niche
so N its opposite to vertical mg?
desert pulsar
whether it's 2m north from the equator, or 2m north from my house, or 2m north f...
ahh i see looking at it that way makes much more sense
tired monolith
yeah
desert pulsar
so N its opposite to vertical mg?
but N is not directly opposite its drawn at an angle in the diagram
tired monolith
vectors being arrows aren't tied to a specific point in space. you can always move around
indigo niche
I mean the vertical component with respect to the reference system
desert pulsar
im gonna take a break from studying for now, i'll look back at this after dinner. Thanks for your help guys!
tired monolith
np!
obtuse pebbleBOT
@desert pulsar Has your question been resolved?
obtuse pebbleBOT
Available help channel!
cursive fox
A small republic, consisting of six states, has 250 seats in the Congress. Find the apportionment of the republic using Jefferson's method.
How many seats are approportioned for State A B C D E F
obtuse pebbleBOT
A small republic, consisting of six states, has 250 seats in the Congress. Find ...
cursive fox
I sent it and it says I have 2 wrongs among the 6 states idk which
pulsar hedge
ok
high lily
show your work
and the question
the first image seems to be for a different question (only has 4 states)
from the one you're asking about
high lily
you seem to be doing normal rounding rules instead of
what they wanted: Jefferson's method
cursive fox
oh, may I know how should I actually solve it hehe
high lily
did you get notes on jefferson's method?
cursive fox
I havent
high lily
you could look it up online but,
you should round your results down,
here adding those up will give 246
which is less than the desired 250
so in that case, you can reduce the divisor, 50k by a bit
and repeat until you sum to 250
cursive fox
ah so the overall should add up to 250
obtuse pebbleBOT
@cursive fox Has your question been resolved?
keen stream
i’ve confused myself on something to do with sketching gradient function 😭
keen stream
ii
when i differentiate the function i get something different to mark scheme i don’t even know how i can mess that up
quartz idol
when i differentiate the function i get something different to mark scheme i don...
what you got?
keen stream
1/2x 😭
deep kraken
No...