.close
#help-10
sage dagger
daring topaz
Always struggled with matrices, but this one has my brain going wacky.
Can I get an explanation to how to complete this?
obtuse pebbleBOT
Always struggled with matrices, but this one has my brain going wacky.
Can I get...
alpine raven
can you give full context ?
viral blade
Without a calculator the solution I know involves eigenvalues
Presumably find $T^{10}S_0$
warm shaleBOT
monikanicity
viral blade
find the eigenvalues and eigenvectors of T and write S_0 in terms of the eigenvectors
woeful wraith
I need help
obtuse pebbleBOT
I need help
obtuse pebbleBOT
@woeful wraith Has your question been resolved?
obtuse pebbleBOT
Available help channel!
stiff tusk
Domain of x
obtuse pebbleBOT
Domain of x
stiff tusk
Ping me
proven zephyr
,,\frac{(x - 1)(x + 2)^2}{-1 - x} = 0
warm shaleBOT
help
proven zephyr
find the possible values first, (gtg eat, brb in prob 30 min or 40 min)
stiff tusk
x ∈ (-∞,-2) ∪ (-2,-1) ∪ (1,∞)
Explain please
Domain of x ?
<@&286206848099549185>
obtuse pebbleBOT
@stiff tusk Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
shell hull
Is my solution correct?
obtuse pebbleBOT
Is my solution correct?
royal basin
not quite since you want A to be an infinite union of intervals while yours looks like it stops at n
where n is not known
obtuse pebbleBOT
@shell hull Has your question been resolved?
timid silo
i think the first interval isnt quite correct
shell hull
not quite since you want A to be an _infinite_ union of intervals while yours lo...
Why?
N contains all natural numbers and it's unlimited isn't it?
timid silo
doesnt it have to be from 1 to 1/2? (and then switch order for all of them, smaller number first)
timid silo
next interval should be (1/3, 1/2) shouldnt it?
obtuse pebbleBOT
timid silo
.reopen
shell hull
.Reopen
obtuse pebbleBOT
✅
timid silo
well the problem with the n is, you dont really specity what it is
timid silo
$(\frac12, 1) \cup (\frac13, \frac12) \cup (\frac14, \frac13) \cup ...$
warm shaleBOT
rbit ✨
timid silo
you dont need the n, just make it dotted and it will be clear its infinite
flint tartan
try using that big union notation instead ?
shell hull
your sum _stops_
But why?
I mean n ∈ ℕ
royal basin
if you had put ${}\cup \dots$ after it, you would have written down an infinite sum
warm shaleBOT
Ann
shell hull
infinite union
I'm not violating this, I'm just asking why mine is wrong
royal basin
because you are writing down a finite union and not an infinite one...
shell hull
because you are writing down a finite union and not an infinite one...
Is ℕ finitely defined?
royal basin
......
i'm not getting through to you, am i
no, the set of natural numbers is not finite.
but there is a difference between "union of n things, where n is some natural number" and "union of infinitely many things"
opal sequoia
obtuse pebbleBOT
opal sequoia
i need help
obtuse pebbleBOT
@opal sequoia Has your question been resolved?
opal sequoia
<@&286206848099549185>
molten compass
Does the logic of directional derivatives reconcile with ordinary single-variable calculus?
Like in multivariable we can find the maximum rate of change and its direction using the gradient vector.
In single variable, consider like y = f(x) = 2x^2+7x. At x = -3, dy/dx = -5. But the gradient vector for f is 4x+7. So at x = -3, we have -5. But what's the 'direction' here?
obtuse pebbleBOT
Does the logic of directional derivatives reconcile with ordinary single-variabl...
molten compass
or I might just be talking rubbish tbh, as no direction is possible I guess
yeah nvm ignore me 😅
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fallow tusk
obtuse pebbleBOT
https://imgur.com/QQV4vVL
rotund rune
a geometric series has a common ratio
see which one you can modify to get a common ratio
rotund rune
a, ar, ar^2, ar^3
high lily
a_(n+1)/a_n should be a constant if you have a geometric sequence/series
rotund rune
ye
fallow tusk
okay so i'm guessing the first one wouldn't work because that's (4/29)^n and you cant separate that into a and r
rotund rune
the first one is a geometric series
high lily
a_(n+1)/a_n
go through this process if needed
in fact i'd recommend that you actually do that for all 4
rotund rune
okay so i'm guessing the first one wouldn't work because that's (4/29)^n and you...
try inserting n = 0, 1, 2, ...
rotund rune
is the ratio constant then?
warm shaleBOT
nichoals
rotund rune
so basically, looking from this, you can see that r = 4/29, meaning it's a geometric series
fallow tusk
hmm but what would a be? just 1?
rotund rune
you can try n = 0, 1, 2, 3 for the other 3 options or you can try to modify the series to immediately notice whether it has a constant ratio or not
rotund rune
hmm but what would a be? just 1?
yes
fallow tusk
oh right because constant
rotund rune
the second option is pretty obv tbh
the third one as well (hint: you can't divide by 0)
fallow tusk
yeah about the 3rd one
if an element of the series/sequence is undefined does that mean it's not a series/sequence?
rotund rune
imagine this: you have undefined as the first term in option three. assuming it's a geometric series, how would you find the sum then?
rotund rune
then it is defined
fallow tusk
what about n greater than or equal to 0?
rotund rune
whatd happen if n=0?
fallow tusk
oh wait 0 isnt a natural number
fallow tusk
well the first term would be undefined
but everything else would work
can't type today geez
rotund rune
it won't be counted as a sequence
if you're still confused, i'd suggest this link https://math.stackexchange.com/questions/143780/are-undefined-terms-allowed-in-a-sequence to help you understand about undefined terms in a sequence
quick kayak
Hey all
quick kayak
I'm trying to find an example for a solution to a question like "Define T : R3 -> R2, T=Ax, find the vector under T whose image is b". Basically, I'm wondering how to find the answers to "find the image under T" for matrices which don't map to the same dimensionality
Since I can't use an augmented matrix
royal basin
eh?
you're given a map T : R^3 -> R^2 defined by T(x) = Ax, and you're given some b ∈ R^2, and you are asked to find all x ∈ R^3 s.t. T(x) = b?
@quick kayak do i understand your problem correctly
obtuse pebbleBOT
@quick kayak Has your question been resolved?
peak cape
Can someone explain what am I doing wrong here. Thanks in advance
obtuse pebbleBOT
Can someone explain what am I doing wrong here. Thanks in advance
lyric ember
ye
wet drift
4/100 * 255 2 * 15 /10 30/10 = 3
obtuse pebbleBOT
@peak cape Has your question been resolved?
peak cape
Can someone explain what am I doing wrong here. Thanks in advance
@earnest elk I think you are referring to someone else's query
peak cape
Np
obtuse pebbleBOT
@peak cape Has your question been resolved?
obtuse pebbleBOT
@peak cape Has your question been resolved?
past tartan
From https://en.wikipedia.org/wiki/Projectile_motion#Angle_θ_required_to_hit_coordinate_(x,_y) I can find the angle needed to hit a coordinate with a projectile.
${\displaystyle \theta =\arctan {\left({\frac {v^{2}\pm {\sqrt {v^{4}-g(gx^{2}+2yv^{2})}}}{gx}}\right)}}$
How do I change the equation to include Stokes drag with a moving target? With stokes drag the position is calculated with ${\displaystyle t={\frac {1}{\mu }}\left(1+{\frac {\mu }{g}}v_{y0}+W\left(-\left(1+{\frac {\mu }{g}}v_{y0}\right)e^{-\left(1+{\frac {\mu }{g}}v_{y0}\right)}\right)\right)}$, so I tried to solve this for theta. But I don't know where to go from there
obtuse pebbleBOT
From <https://en.wikipedia.org/wiki/Projectile_motion#Angle_%CE%B8_required_to_h...
warm shaleBOT
InCrIpTiOn
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
past tartan
I messed up
it works ig
p + Vt is the equation for the moving target, btw. cos(theta)*v is the vertical component only
obtuse pebbleBOT
@past tartan Has your question been resolved?
storm harness
I need help in general learning the, metodo de sustitucion, metodo de igualacion, metodo de reduccion, Im not sure what its called in english but i understand both languages
obtuse pebbleBOT
I need help in general learning the, metodo de sustitucion, metodo de igualacion...
robust sleet
deep ravine
Am i doing this correctly?
obtuse pebbleBOT
Am i doing this correctly?
mental plaza
aye aye
wassup
eh
this is chemistry
alr
hm
they gave
percentage mass
use that a
And
find the no of mol
and for simplest ratio
divide by the smallest
njmber if mola
mole
deep ravine
at the beginning
i thought they were percentages
deep ravine
use the percentages
like this?
deep ravine
it’s mass/Ar
What does Ar mean again?
obtuse pebbleBOT
@deep ravine Has your question been resolved?
meager trail
obtuse pebbleBOT
bold bane
They are including the coterminal angles.
obtuse pebbleBOT
@meager trail Has your question been resolved?
real cobalt
can someone exploin how to solve this, 8x−2=−9+7x
obtuse pebbleBOT
can someone exploin how to solve this, 8x−2=−9+7x
ocean nexus
can someone exploin how to solve this, 8x−2=−9+7x
to find x?
real cobalt
yes
yell its a multi step eqaution problem according to the paper the question is on so it might nit be
ocean nexus
does it say solve for x?
(8x - 7x) - 2 + 2 = + 2 - 9 + 7x - 7x
x - 2 + 2 = + 2 - 9 + (7x - 7x)
x (- 2 + 2) = + 2 -9 + 0
x + 0 = (+2 -9) + 0
x + 0 = -7 + 0
x = -7
I bracket the numbers I am subtracting in the next step to make it more understable
real cobalt
it just says solve the equation sorry i forgot i asked for help
real cobalt
ig
ocean nexus
ok well its x = -7 then
real cobalt
but the way u solved is kind of ocmplicated
ocean nexus
do you want me to shorten it?
ocean nexus
ya i just did more beginner steps
ocean nexus
i was wondering why they flipped it over
they subtract
and add
to the other side
subtract on one side and add to the other side of the equal sign
real cobalt
i get it but when they did x -2 = -9 why did they move 2 to the other side so it could be - 9 + 2
ocean nexus
bc you want x to be alone
pale gazelle
obtuse pebbleBOT
pale gazelle
could someone help with this differential eq? i know its not exact and ive tried to figure out the integrating factor
but the difference in signs keeps bugging me out
if i can figure out how to type in latex here maybe i can show you guys where im stuck haha
rigid pine
Try a integrating factor of the form x^ay^b.
pale gazelle
oh hmm ive been trying one that only involves x
and thought i got close
ill try it that way
rigid pine
pale gazelle
woah
ive been trying to get to that integrating factor naturally haha
what text is that? @rigid pine
rigid pine
Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard.
final elm
hey
obtuse pebbleBOT
@final elm Has your question been resolved?
obtuse pebbleBOT
@final elm Has your question been resolved?
daring compass
it says "sequences" because they are sequences
so, in your words, what does it mean for a sequence to converge?
obtuse pebbleBOT
@final elm Has your question been resolved?
final elm
it says "sequences" because they are sequences
but they arent tho
its confusing
it goes from n=1 to infinity
which is a summation
so i think sequence is a typo
but im not positive
daring compass
no, I don't think they're summations
if they are, then some weird notations are being used
daring compass
it goes from n=1 to infinity
this is telling you the values of n that are being used, i.e. the domain
if they were series, I would expect summation notation, not the curly brackets
final elm
this is telling you the values of n that are being used, i.e. the domain
if they are sequences, i got no clue how to find the answer. i used alternating series test for the first one and p series for the second one
daring compass
what does it mean for a sequence to converge?
(by the way, can I ask- are the answer choices selected supposed to be your answer choices or the correct answer choices?)
final elm
a sequence converges when you plug in infinity and u get a constant i think
daring compass
yeah more or less. as you bring in later and later terms, they approach a specific (finite) number
same idea as a limit
so which of the given choices approaches a particular value?
let's start with I
as n increases, what happens to the values of that sequence?
final elm
bigger and bigger
daring compass
good. So if the top stays between -1 and 1, and the bottom gets bigger without bound, what happens to the overall quotient
?
final elm
i understand II can u help me with III
i used geometric series test
but its a sequence
daring compass
yeah
i like to use a trick in these kinds of things where in any sum, if one term grows much faster than the others, you can throw the rest out
what i mean is, 2^n + 3^n, for very large n, might as well just be 3^n
do you see what i mean?
pale gazelle
obtuse pebbleBOT
pale gazelle
can anyone help with how to go about finding an integrating factor for this?
i keep getting stuck :(
rigid pine
Write in the form P(x, y) dx + Q(x, y) dy = 0.
y dx + (x - x^2 y) dy = 0
The check for exactness is P_y = Q_x. But P_y = 1 and Q_x = 1 - 2xy.
Notice that P_y - Q_x = 2xy. I would now consult my integrating factors sheet.
I find that (10.73) yields a function of xy.
I find that (xy)^(-2) is a integrating factor.
obtuse pebbleBOT
Available help channel!
peak dust
Total Class 30
I have attended (X) classes
If I attend 60% Classes I will get 6 marks
If I attend 90% classes I will get 10 marks.
this is the challenge . But I can't figure out how can I get the number for (X) ?
please help me
obtuse pebbleBOT
Total Class 30
I have attended (X) classes
If I attend 60% Classes I will get 6 ...
@peak dust Has your question been resolved?
earnest elk
There isn’t sufficient info
lofty zealot
obtuse pebbleBOT
lofty zealot
I understand part a), but im confused how to start part b)
quaint glen
Well, use the hint. What does happen to the equation c_0f_0+c_1f_1+c_2f_2=0 when x=0, 1, and 2?
It should be pretty easy to see what the equation will look like for these equations if you've already done a, its just plugging shit in
haughty coyote
The most common method to show a family of functions is linearly independent is to just evaluate it for specific values
lofty zealot
ah i see, if i plug in 0, 1, 2 then c0, c1, c2 must be equivalent to zero respectively; idk why but i thought that values > 2 would somehow change my result
is c just f(x) = c_x ??
obtuse pebbleBOT
@lofty zealot Has your question been resolved?
lofty zealot
any pointers for 5d ; - ;
obtuse pebbleBOT
quaint dust
obtuse pebbleBOT
quaint dust
hello can anyone help me with this one
placid nova
quaint dust
my answer is different from wolfram and i cant seem to find the difference
oops sorry for interrupting
this is from wolfram
and mine is this
obtuse pebbleBOT
@quaint dust Has your question been resolved?
floral void
obtuse pebbleBOT
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obtuse pebbleBOT
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sacred cove
obtuse pebbleBOT
sacred cove
for a question like this can anyone explain to me why what i have done wouldnt work?
I've put it into many calculators and havnt been able to get a reasonable answer
warm shaleBOT
wild swallow
for a question like this can anyone explain to me why what i have done wouldnt w...
what have you done that doesnt work?
apart from the fact that this is a terribly inefficient way of calculating the eigenvalues
have you actually tried calculating what they are?
sacred cove
have you actually tried calculating what they are?
ive put it that equation into many calculators and it does not give the correct answer
wild swallow
,w {{2, -1-i, -1+i}, {1, -1+i, -1-i}, {2, 2, 2}}^-1 {{-1/40, 0, 1/40},{1/40, -1/20, 0}, {0, 1/20, -1/40}} {{2, -1-i, -1+i}, {1, -1+i, -1-i}, {2, 2, 2}}
warm shaleBOT
wild swallow
?
sacred cove
?
oh wow fair enough
i tried putting into wolfram alpha and it didnt work for me
thanks!
wild swallow
well
still
this is not how you'd calculate the eigenvalues
this method is horribly inefficient
wild swallow
?
wild swallow
D = P^-1 AP
wild swallow
except
you arent reading what im saying
this is not the way you'd calculate the eigenvalues
sacred cove
this is not the way you'd calculate the eigenvalues
what would i do then?
sacred cove
nah i guess that wouldnt be efficient
wild swallow
your method would just be suffering
you know the vectors are eigenvectors
literally multiply A by the eigenvectors
calculate even just a single entry
and see what multiple it is
,w -1/40 * 2 + 0 * 1 + 1/40 * 2
warm shaleBOT
wild swallow
its 0 so the eigenvalue of the first vector is 0
sacred cove
its 0 so the eigenvalue of the first vector is 0
oh wow
nvm
ill try it for the other ones see if i get the same answer
wild swallow
,w 0 * (-1-i) + 1/20 * (-1+i) + -1/40 * 2
sacred cove
ig that makes a lot more sense
warm shaleBOT
wild swallow
divide by 2 and you get the eigenvalue
fast atlas
,w 5x²=3
warm shaleBOT
sacred cove
divide by 2 and you get the eigenvalue
divide what by 2?
sacred cove
why do we need to do that?
sacred cove
i calculated the last entry of A * (-1-i, -1+i, 2)
im sry i dont really understand how this gives 2λ
sacred cove
so that 2 on the end makes it 2λ?
wild swallow
well if you distribute the λ inside
you get A(-1-i, -1+i, 2) = ((-1-i)λ, (-1+i)λ, 2λ)
clearly you dont want to figure out what dividing by a complex number should be
so you calculate the last entry of A(-1-i, -1+i, 2) to get 2λ
sacred cove
ohh right i think i understand it ill try to do that since that seems a lot better
thanks a lot for your help
sacred cove
so you calculate the last entry of A(-1-i, -1+i, 2) to get 2λ
really quick i was told these might be the answers
do you know if they are wrong or i am wrong?
sacred cove
hmm right
yeah my friend got that as the answer and he solved the same equation too
sacred cove
none of those equations are true
ig he mustve done it wrong
wild swallow
<@&268886789983436800>
sacred cove
yeah lol
wild swallow
you couldve just started by moving P and P^-1 to the other side
and gotten D = P^-1 AP
that gives you D directly
sacred cove
yeah true lol
wild swallow
but anyway directly calculating Av is much faster
sacred cove
yeah alright thanks again
obtuse pebbleBOT
@sacred cove Has your question been resolved?
obtuse pebbleBOT
final thunder
What’s this
final thunder
final thunder
that doesn't sound like good advertising
Is this even allowed?
final thunder
Do I like ping the mods
zenith raft
maybeee
final thunder
<@&268886789983436800>
obtuse pebbleBOT
@jagged skiff Has your question been resolved?
plucky patio
What are the transformations that make S into C?
obtuse pebbleBOT
What are the transformations that make S into C?
plucky patio
There's some sort of stretch of a factor of -2
but there seems to be another transformation
<@&286206848099549185>
obtuse pebbleBOT
@plucky patio Has your question been resolved?
obtuse pebbleBOT
@plucky patio Has your question been resolved?
obtuse pebbleBOT
@plucky patio Has your question been resolved?
obtuse pebbleBOT
@plucky patio Has your question been resolved?
obtuse pebbleBOT
@plucky patio Has your question been resolved?
timid silo
for concavity, do u get ur critical numbers from the 2nd derivative
sleek mural
buoyant hawk
for finding the diriv of this can i foil bfore i take the diriv of do i have to use product
obtuse pebbleBOT
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ornate ivy
A motel owner observed that when a room at $60 per day, all 80 rooms of the motel are occupied. For each $4 increase in price, one more room is vacant. Each occupied room costs an additional $20 per day to maintain.
a) Find the demand function,p, the price charges each room per day, as a function of x, the number of rooms occupied.
b) Find the profit function
c) find the price he charges a room per day so he can maximize profit.😭
obtuse pebbleBOT
A motel owner observed that when a room at $60 per day, all 80 rooms of the mote...
@ornate ivy Has your question been resolved?
vagrant obsidian
obtuse pebbleBOT
vagrant obsidian
Hey
vagrant obsidian
think about d^2 * `what?` = 2d^5
???
high lily
?
high lily
what don't you understand about what i wrote
you already wrote that d^2 out front
implying that you somehow know that d^2 is a factor of all these terms
think about the expression when multiplied to d^2 gives the first term 2d^5
vagrant obsidian
implying that you somehow know that d^2 is a factor of all these terms
The video said to factor out the smallest exponent so I just did that
vagrant obsidian
Ok
high lily
i'd use the bot, but its down
vagrant obsidian
as represented by
d^2 * `what` = 2d^5
d^2 was supposed to be 32d^2 I think, and 2^5= 32 so 32x1=2d^5
high lily
not what i asked for
vagrant obsidian
I really don’t know
high lily
have you ever solved any equations before?
vagrant obsidian
have you ever solved any equations before?
Yes
high lily
apply the same principle here
I'm assuming you'd be able to solve something like
5x = 7
this is no different
vagrant obsidian
I'm assuming you'd be able to solve something like
5x = 7
this is no different
It’s that easy????
D^2x2= 2d^5
???
high lily
no
vagrant obsidian
??????????????
high lily
how would you solve for x in
5x = 7
high lily
yes
high lily
yes.
high lily
yes
apply that exact same principle
on the left side, you have
d^2 multiplied to k,
what would you divide both sides by to isolate/solve for k?
high lily
yes
high lily
no
high lily
why are you dividing d^2 by 2d^5
vagrant obsidian
Divide on both sides
high lily
did you divide 5 by 7 for 5x = 7?
vagrant obsidian
Yes
vagrant obsidian
Yes
high lily
you're not accurately representing what you're doing
high lily
my instructions were excessively broken down intended to be extremely simple
you shouldn't need to think to hard about them
after dividing both sides by d^2,
can you simplify that fraction
vagrant obsidian
O
vagrant obsidian
what's with
> O
are you implying that you didn't have that?
No I was extremely confused, I was overthinking this entire equation
So what do I do for my original question?
high lily
can you simplify that fraction
using exponent laws
vagrant obsidian
2d^3
high lily
yes
d^2 when multiplied to 2d^3 gives 2d^5
factoring d^2 out from 2d^5 leaves you with 2d^3
and same idea for the other terms
d^2 * what = 16d^4
etc
high lily
yes, 16d^4/d^2 = 16d^2
high lily
depends on the sign that's there
(and personal preference assuming you're referring to the -4d^3)
you can consider
d^2 * what = -4d^3 directly
or write a = sign and then consider
d^2 * what = 4d^3
high lily
because the original term is (+)16d^4
consider the basics of the distributive property
would you be able to factorise
ab + ac?
vagrant obsidian
Oh
Wait imma do the entire thing and you tell me if it’s right or wrong
Nvm
I’m back
@high lily what do I do next
Factoring?
high lily
identify more common factors if they exist
if you identified the gcd/hcf at the start, that would've been more efficient
vagrant obsidian
identify more common factors if they exist
Oh
obtuse pebbleBOT
@vagrant obsidian Has your question been resolved?
cobalt hatch
can anyone help
obtuse pebbleBOT
can anyone help
cobalt hatch
multiplication of polynomials
abstract flame
just try expanding it
cobalt hatch
get the product
nocturne minnow
what are you even supposed to do lmao
multiplication of polynomials
reef grotto
obtuse pebbleBOT
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timid silo
hello. i am a bit confused about how newton discovered calculus (or leibeniz). So as i understand newton discovered calculus but i mean finding the integral of a function or its derviviative seems pretty easy. was newton the first person to use an integral and everyone freaked out. It seems like someone just randomly performing a dervitive could of discovered that it would give you the instantenous rate of change.
obtuse pebbleBOT
hello. i am a bit confused about how newton discovered calculus (or leibeniz). S...
timid silo
was newton instrumentla in proving that the integral or deriviative acctually gave you iroc or area under the graph?
or was he seriously the first person to guy "ah yes, if I bring down the 2 here (x^2) and make it 2x, the new function gives me the iroc, brillant, I am so intelligent"
if so that is fucking insane lmao.
no way on earth he was the first one to use a derviviative like that.
royal basin
finding the integral or the derivative of a function seems pretty easy.
calculus wasn't built in a day.
you're standing on the shoulders of giants
so of course looking down at the basics such things seem easy
calculus itself required a conceptual leap, perhaps more than one, to become what it is today.
timid silo
definitely but i feel like anyone would be interested in bringing down a 2 in my example and seeing what it produces.
im just having trouble accepting that no one for milenia thought to do that
royal basin
people did not really think about functions the same way back then as we do
timid silo
what do you mean by that.
accutally ill search it up
wait but before i do that. was he actually the first person to do that.
true granite
the power rule and derivatives weren’t found by coincidence
timid silo
sure but that doesnt neccesarily they couldnt be found by coincidence.
just be observing the two functions, someone might discover that type of relationship
true granite
you could even argue they were created
timid silo
just be observing the two functions, someone might discover that type of relatio...
actually this is my main question. but it doesnt make sense following ann. maybe functions didnt exisit in its modern form.
true granite
back then, instantaneous rate of change made no sense
timid silo
what do you mean by that. so for like x^2, people found it bizzare to question what the iroc was at different points.
is there a book on this
like the history of calculus
no actual math beyond like hs math
jsut explaining simple development in math
timid silo
sick thank you
sorry for seeming condencsing btw. no intention of that. just hard to accept fucking issac netwon, smartest dude alive, discovered simple rules and everyone priases him. m
true granite
not really simple at the time
designing the first car must have been hard, but look how many different cars we have now
what seems so simple today might not have been simple in the past
specially when you’re a pioneer in what you’re doing
timid silo
i definitely get that, but something so trivial like the power rule being discovered so late in humanities course seems so strange
royal basin
well i mean you could say the same thing for quadratic equations or something
it also kind of matters what language you have at your disposal to express various ideas
compare:
"Half of the sum of one and the unknown minus one-sixth of the difference of the same unknown and nine equals eleven."
vs
(x+1)/2 - (x-9)/6 = 11
contrived example but one is much easier to work with than the other
timid silo
well i mean you could say the same thing for quadratic equations or something
i feel like it would be much more difficult to find the quadratic equation. applying the power rule to a simple function seems extremely simple. comparing the original and derived function also seems very simple. compared to the quadratic equation, which is much more difficult to randomly stumble upon, the power rule seems like something that someone a bit curious would eventually test. But like you said, if the notion of functions isn't the same as it is today, than it would be much more difficult to observe in my example.
the quadratic equation is the super big thing, with a lot of variables, who would randomly mix and match numbers to produce that.
bringing down a 2 in x^2, i think babies would be curious to see what that would produce.
boyers history of calculus
so yeah it seems like there were people before newton. newton just seemed to have a rigrous proof for it.
thank you everyone
and yeah it seems like anyone before this descartes guy probably could never have randomly discovered power rule.
obtuse pebbleBOT
@timid silo Has your question been resolved?
bleak sable
obtuse pebbleBOT
bleak sable
I don't get why y is in absolute value
ancient marlin
if y were negative in original equation, would y^6 be negative
ancient marlin
don't have to do it for x^4 because it's still squared even after it came out of root
so it would be redundant that's all
generally, sqrt(x^2) = |x|
bleak sable
Thank you so much!
ancient marlin
np
obtuse pebbleBOT
@bleak sable Has your question been resolved?
dark mango
.close
twin helm
obtuse pebbleBOT
left mesa
help..
left mesa
its c right? im kinda doubting it since its m^2 not x^2 in the given
<@&286206848099549185>
obtuse pebbleBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
left mesa
oh because its asking for the value of x? instead of the value of m?
left mesa
Please only use the <@&286206848099549185> ping **once** if your question has no...
mb i needed help asap
mental plaza
wtf
final thunder
More likely to be a typo imo
mental plaza
yeye
left mesa
ok then the answer is c?
mental plaza
I mean
final thunder
Yeah it would be that
mental plaza
if the cher is evil and is testing ur attention to details in the qn
it would be
D
but most prob C
left mesa
meh its ok if im wrong i still have + points bec of our last quiz lol
final thunder
This question is too ambiguous for you to be penalised for that
left mesa
fr ok ty ❤️
left mesa
we did had the quarter test first before the long test and i do remember subtly that the answer is not none of the above lol or maybe im just remembering that wrongly 🥲
.close
fast heath
a bit confused about part (b)
obtuse pebbleBOT
a bit confused about part (b)
fast heath
i did (1.5-0) × 1/10
because i assumed since it's |x| it'd be up til 0?
which is wrong according to the marking scheme, and i don't really understand why. i need the answer for doing (c) so i wanna be sure how (b) is calculated first!
obtuse pebbleBOT
@fast heath Has your question been resolved?
fast heath
<@&286206848099549185>
would really appreciate the help asap bc i've a test today 😅 i'd like to clear this doubt
fast heath
.close
bleak sable
How do I proceed? Idk what's the use of the given 44 weeks
obtuse pebbleBOT
How do I proceed? Idk what's the use of the given 44 weeks
obtuse pebbleBOT
@bleak sable Has your question been resolved?
bleak sable
<@&286206848099549185>
obtuse pebbleBOT
@bleak sable Has your question been resolved?
obtuse pebbleBOT
@uncut fulcrum Has your question been resolved?
wooden sand
What were your attempts?
How did you try these questions?
Perhaps we can find out where you lack understanding
Hmm... I'm assuming you don't have the epsilon delta definition, so
Intuitively, 1 divided by a very large number gives a very small number
As this denominator goes to infinity
1/denominator goes to 0
Oh you do? Nice!
real prawn
says there that lim_{x-> -4^+} (floor(H(x)) = -1
wooden sand
Use the epsilon delta for a limit to infinity
real prawn
doesn't make much sense
wooden sand
You know that the function goes to infinity on the right of 6
So for all M in the positive reals
There exists an f(x) that's bigger than it
real prawn
hmm, i'm wrong but i think it's something involving sine
wooden sand
For any x in the open interval from 6 to 6+delta
So flip the f(x)<M, and try to get a epsilon delta that bounds 1/f(x) within positive epsilon
And you done
Right hand limit to zero from aboce
I don't know the functional form for that, so I can't think of an epsilon delta
For 4
Do the top and bottom limits
If they exist, use the quotient rule
real prawn
factor out the x^6 and pull it out of the square root, split the fraction into two fractions, the 2nd fraction will go to zero because the denimonator dominates the numerator.
the first fraction will go to -2/3
after you pull x^6 out of the square root the denominator will look like this:
$$ x^3 \cdot \sqrt{9 + \frac{1}{x^6} } $$
warm shaleBOT
agilepotato
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
real prawn
if you want to practice latex, you can use https://mathb.in/ (there are other latex online compilers too)
real prawn
factor out the x^6 and pull it out of the square root, split the fraction into t...
read this ^^
@uncut fulcrum the limit of a product is the product of the limits
on b) they just pull out a 1/x^2 and then they identify it as an indeterminate form: infinity times zero https://en.wikipedia.org/wiki/Limit_of_a_function#Properties
drifting swan
GOOD MORNING, COULD YOU PLEASE HELP ME WITH THE FOLLOWING EXERCISE?
a bucket with water rotates in the form of a conical pendulum, suspended from the ceiling by a rope of 2 meters whose angle with the vertical is 30 degrees. If the bucket is dripping, find the radius of the circle described by the drops on the floor 4 meters below the ceiling.
Sorry
drifting swan
I got the wrong channel
obtuse pebbleBOT
@uncut fulcrum Has your question been resolved?
real prawn
here's 6 more solutions to point 3)
obtuse pebbleBOT
@uncut fulcrum Has your question been resolved?
ivory cargo
i have to find the limit of the function, which i have done like this: And is the function continious for all x? i answered no hence x=0 is in the domain. Furthermore, can we choose a value c=h(0,0) so that the function becomes continious for R^2
obtuse pebbleBOT
i have to find the limit of the function, which i have done like this: And is th...
ivory cargo
obtuse pebbleBOT
@ivory cargo Has your question been resolved?
ivory cargo
<@&286206848099549185>
ivory cargo
ay yo boys, can i have som <@&286206848099549185>
@jaunty stream
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
almost two hours
nice we are really going strong
<@&286206848099549185>
coral epoch
ivory cargo
sadge
obtuse pebbleBOT
@ivory cargo Has your question been resolved?
dreamy summit
can someone help apply finite difference formula for edge detection?
obtuse pebbleBOT
can someone help apply finite difference formula for edge detection?
obtuse pebbleBOT
@dreamy summit Has your question been resolved?
dreamy summit
.close
inner marlin
Hi
inner marlin
I am having an issue trying to find the angle as i keep finding different answers
and i am not sure which is correct
i found many solutions online which says that the angle <ACD is also <DMB
which results into two different answers
using the cosine rule
obtuse pebbleBOT
@inner marlin Has your question been resolved?
inner marlin
i end up with 51 degrees with <ACD and <ABD and 62 with <DMB
and technically <ACD is also <DAC as triangle CDA is isosceles
.close
elder cosmos
Hi there, still trying to figure out the following
obtuse pebbleBOT
Hi there, still trying to figure out the following
sage geode
BDC angle?
elder cosmos
yes
sullen terrace
1,2,3,4,5
Basically all of them
obtuse pebbleBOT
1,2,3,4,5
Basically all of them
stable rain
bit small
sullen terrace
The 2nd one
Discrete mathematics is pain
But the only way to be a data scientist
rigid lintel
obtuse pebbleBOT
@sullen terrace Has your question been resolved?
sullen terrace
No
sullen terrace
<@795959348806418463> Has your question been resolved?
No
I am talking to a bot 😭
obtuse pebbleBOT
@sullen terrace Has your question been resolved?
sullen terrace
<@795959348806418463> Has your question been resolved?
Nah
obtuse pebbleBOT
@sullen terrace Has your question been resolved?
dire imp
1,2,3,4,5
Basically all of them
For the first problem plug all possible Boolean values of p and q into the equation and see if they are all true. If all the outcomes true then the expression is a tautology
Since you have two Boolean variables per expression (p and q) then you’re going to evaluate the 4 cases
dire imp
1,2,3,4,5
Basically all of them
For the second one use demomorgan’s law to distribute a negative into each one of the statements. Take each expression such as “go to graduate school” as a variable and then solve from there. Treat all instances of “or” and “and” as logical operators
timber zinc
hi, i need help with complex limit
obtuse pebbleBOT
hi, i need help with complex limit
timber zinc
when i try to factor it it doesn't give cancelable values
and i can't use l'hopitals rule
knotty crow
factor of both denominator and numerator is 1 + i
obtuse pebbleBOT
@timber zinc Has your question been resolved?
obtuse pebbleBOT
https://gyazo.com/9fcc1e8bbaf67aeab569849e421d3042
final thunder
It’s just power rule
nova stump
and linearity of derivatives
nova stump
you can distribute the -1/3 to both terms in the parenthesis
and compute the derivatives separately
silent imp
you can distribute the -1/3 to both terms in the parenthesis
wouldnt this make more compicated
nova stump
no
$f(x) = 1/3x^{-3} +1/3x^6$
sorry forgot a negative sign
$f(x) = -1/3x^{-3} +1/3x^6$
warm shaleBOT
colin davis
nova stump
now you can do power rule on the terms separately
$f'(x) = (-1/3x^{-3})' + (1/3x^6)'$
warm shaleBOT
colin davis
silent imp
**colin davis**
this wrong
final thunder
$\frac{d}{dx} \left( -\frac{1}{3}(x^{-3} - x^6) \right) = -\frac{1}{3} \left( \frac{d}{dx} (x^{-3}) + \frac{d}{dx} (x^6) \right)$
silent imp
x^-3 on top
warm shaleBOT
Pure
nova stump
it is on top
final thunder
You can also do this
nova stump
just that i typed it ambiguously
nova stump
derivative is a linear transformation
in this case you can use that to say the derivative of a sum is equal to the sum of the individual derivative
and that a derivative of a function times a constant is equal to a constant times the derivative of the function
silent imp
in this case you can use that to say the derivative of a sum is equal to the sum...
hmmm i think ima use power rule
multiply
i mean
nova stump
if you think carefully, using the product rule with a constant is the same thing, but it makes your life harder
silent imp
if you think carefully, using the product rule with a constant is the same thing...
ok thinking carefully....23%
.....34%
....56%
....78%
...100%
i look on youtube
nova stump
Thnk about it this way
product rule says
$d/dx (f(x)*g(x)) = f'(x)g(x) + f(x)g'(x)$
warm shaleBOT
colin davis
nova stump
if f is a constant, then f' is zero, so the first term is 0
then we get f(x)g'(x)
which is the constant times the derivative of the other function
obtuse pebbleBOT
@silent imp Has your question been resolved?
frosty shale
How do I do #28 and #29?
obtuse pebbleBOT
How do I do #28 and #29?
gloomy valve
well whats the property of an odd function?
frosty shale
well whats the property of an odd function?
No clue