imo atleast
#help-39
swift narwhal
opaque wave
warm tiger
4.4k
swift narwhal
🗣️
warm tiger
Ohh all the best
swift narwhal
thanks
averaging like 200+ in mocks have to hope for the best 😭
not really able to cross that
warm tiger
Thats good
swift narwhal
yo damn
warm tiger
Tough paper
warm tiger
Depends on lot of factors, like quality of students but that's not in our hands
swift narwhal
yep
sharp smelt
pearl pondBOT
pearl pondBOT
pearl pondBOT
Available help channel!
young plover
might be an easy question but what would the answer for this be
young plover
im getting 1/2(ln2) but answer key says ln2
twin portal
The sum is equal to:
(2-1)/(2 * 1) + (4 - 3)/(4 * 3) + ........ = 1/1 - 1/2 + 1/3 - 1/4 + ....... = ln(2)
young plover
oh wait i found my mistake i messed up in the partial fractions, srry for wasting ur time guys
i got it
tyy
toxic lichen
The sum is equal to:
(2-1)/(2 * 1) + (4 - 3)/(4 * 3) + ........ = 1/1 - 1/2 + 1/...
!nosols
pearl pondBOT
The sum is equal to:
(2-1)/(2 * 1) + (4 - 3)/(4 * 3) + ........ = 1/1 - 1/2 + 1/...
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
twin portal
No problem.
young plover
.close
pearl pondBOT
twin portal
As a helper, please do not give out answers that could be copied as a homework s...
okay
pearl pondBOT
Available help channel!
novel dirge
f is continuous
i) solve f(x) = 0 (I've done that)
ii) if f(1/2) < 0 and f(2) > 0 then find f(x)'s equation (idk if equation is the right word that's what translate said)
novel dirge
in other problems it said f(x) <> 0 and f continuous so I had to find for example f(2) > 0 and then say that f maintains its sign and "..."
but here it's completely different
void lintel
f^2 (x) is just another way of writing (f(x))^2, so its saying that the square of the function f is (ln(x))^2. Hint: what possible functions f could be such that the square of f(x) is ln^2 (x)?
flint fulcrum
f^2 (x) is just another way of writing (f(x))^2, so its saying that the square o...
It doesn't say continuous tho
You could flip sign whenever you want
novel dirge
f^2 (x) is just another way of writing (f(x))^2, so its saying that the square o...
in the first part I found x = 1
f(x) = 0 <=> (f(x))^2 = 0 <=> (lnx)^2 = 0 <=> lnx = 0 <=> x=1 it's the second question that I'm stuck at
novel dirge
συνεχής means continuous?
yes
void lintel
the question is asking f(x) = ?
if f is continuous and f(x)^2 = g(x)^2 (where g is any continuous function), then there's these options:
- f(x) = g(x)
- f(x) = -g(x)
- f(x) = g(x) for some interval, then changing to f(x) = -g(x) after some value of x such that g(x) = 0 (and having the option to change between positive/negative whenever g(x) = 0)
flint fulcrum
the question is asking f(x) = ?
if f is continuous and f(x)^2 = g(x)^2 (where g...
Not really
There's more than two option
void lintel
but in this case it has the given constraints
yeah
so since the first part gives you that ln (x) = 0 only when x = 1, then you only need to check for values of x < 1 and x > 1
does this help? https://www.desmos.com/calculator/y9p1ox0mbc
novel dirge
it's okay ill solve it tomorrow in class I kinda got it but just can't get it right on paper
I have to go though so it's fine close this
glossy wave
Would this be a lattice?
pearl pondBOT
Would this be a lattice?
glossy wave
every point here is supposed to be distinct, but when I analyse this algebraically I get:
Suppose $(a\frown b)\smile (a\frown c)=a$.
Then $$a\smile (b \smile c) = (a\frown b)\smile (a\frown c)\smile (b \smile c)=(a\frown b)\smile b \smile (a\frown c) \smile c =$$
$=b\smile c$
jolly parrotBOT
Lambda
glossy wave
Would this be a lattice?
The vertices here denote elements of the supposed lattice, and arrows the relationship that defines order "$\prec$"
jolly parrotBOT
Lambda
glossy wave
<@&286206848099549185>
errant snow
@glossy wave are you looking for $\vee, \wedge$?
jolly parrotBOT
Haine
glossy wave
yup, thanks
I'll redo it
every point here is supposed to be distinct, but when I analyse this algebraically I get: Suppose $(a\vee b)\wedge (a\vee c)=a$.
Then $$a\wedge (b \wedge c) = (a\vee b)\wedge (a\vee c)\wedge (b \wedge c)$$
Now according to associative and commutative laws this is equal to:
$$((a\vee b)\wedge b) \wedge ((a\vee c) \wedge c)$$
And according to absorption laws this is equal to
$$b\wedge c$$
Sorry, done
jolly parrotBOT
Lambda
errant snow
I have not studied lattice theory, but I am interested in it, so please let me know if you get an answer
glossy wave
Sure, thanks for the latex symbols, i haven't written in it in a while
pearl pondBOT
@glossy wave Has your question been resolved?
pearl pondBOT
@glossy wave Has your question been resolved?
pearl pondBOT
@glossy wave Has your question been resolved?
pearl pondBOT
@glossy wave Has your question been resolved?
nocturne grail
Assuming I'm pinging the appropriate channel, #advanced-algebra has a higher chance of offering help
lattice theory is boolean algebra i assume.
the help channels are usually for highschool-level questions
this doesn't look very high-schooly 😔 good luck!
pearl pondBOT
@glossy wave Has your question been resolved?
pearl pondBOT
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boreal gull
" In Exercises3–8 ,differentiate the expression with respect to x,assuming that y=f(x)."
I did product rule for #3, and got it wrong (according to mathway) because apparently when u derive with respect to x, and theres a y in the problem, it is a constant. But when I applied that same logic to #7, it says I do have to do quotient rule, even though there are no x's in the problem, so wouldnt it just be constant / constant +1 , which is just 0?
light helm
no
its stated that y is a function of x
so you shouldn't be treating y as a constant
here you'd need to apply chain rule
for both questions
boreal gull
isnt it product rule and quotient
light helm
you'd need to apply chain rule as well as those
boreal gull
ah ok
light helm
sometimes you need to apply multiple rules
boreal gull
so I am differentiating the y because they are functions of f(x) \
but if they said y = constant then i wouldnt need to
got it
light helm
if you have a constant you could apply constant multiple rule
boreal gull
didnt do that yet
verbal whale
Impossibile
light helm
that'd would've come up earlier than this
verbal whale
Maybe you haven't called it with a name
verbal whale
didnt do that yet
The derivative of k•f(x) is:
k times the derivative of f(x)
light helm
(given k is a constant)
verbal whale
What's the derivative of 5x³?
boreal gull
15x^2
verbal whale
That's it
boreal gull
power rule?
light helm
combination of both
boreal gull
thats power rule is it not
verbal whale
You did 5 • (3x²)
boreal gull
oh
so basically if ur deriving a function with a constant coefficient you can factor it out and just derive the variable part and then simplify
verbal whale
thats power rule is it not
Power rule is only the derivative of x³ being 3x²
verbal whale
so basically if ur deriving a function with a constant coefficient you can facto...
Exactly
boreal gull
ok that makes sense
idk I wasnt taught that
my teacher just went from def of a derivative to power rule
ok thanks
.close
pearl pondBOT
pearl pondBOT
✅ Original question: #help-39 message
boreal gull
whoops
light helm
you didn't apply power rule correctly for differentiating
y^3
and didn't consider chain rule either
daring valley
idk also i don't see any chain rule
boreal gull
i dont see any composite functions
eager jewel
idk also i don't see any chain rule
its 3y^2 dy/dx not just 3y^2
eager jewel
dont doubt my boy pauomogranate
light helm
no
you're differentiating, then subbing, then differentiating again
with no applications of chain rule
vernal bear
do you know chain rule?
light helm
there is no chain rule tehre
boreal gull
i just dont see why ur chain ruling
light helm
consider the simplest example
$$\dv{x} y$$ is $\dv{y}{x}$ and not 1
jolly parrotBOT
ραμOmeganato5
light helm
$\dv{x} f(x)$ is $f'(x)$ (and not 1)
jolly parrotBOT
ραμOmeganato5
light helm
do you work better with lagrange or liebnitz notation
boreal gull
liebnitz
light helm
ok so consider
$$p = y^3$$
$$\dv{p}{x} = \dv{p}{y}\dv{y}{x}$$
jolly parrotBOT
ραμOmeganato5
boreal gull
okay
light helm
i just dont see why ur chain ruling
chain rule is relevant because you're differentiating one variable with respect to another
he's more comfortable with liebnitz so lets stick with that for now
vernal bear
k
light helm
yes
boreal gull
ok now
because its y^3, and y=f(x), the setup for chain rule is (x^2y^3)^3
is that it
verbal whale
No
light helm
i'd write the first term as
$$(y^3 ) \dv{x} x^2$$
to reduce ambiguity
jolly parrotBOT
ραμOmeganato5
boreal gull
okay
verbal whale
because its y^3, and y=f(x), the setup for chain rule is (x^2y^3)^3
Why do you put a power of 3 to the x² as well?
boreal gull
because its y^3
light helm
chain rule is only required for the last part: $\dv{x} y^3$
jolly parrotBOT
ραμOmeganato5
verbal whale
because its y^3
Ohhh I see the misunderstanding
boreal gull
ah ok
verbal whale
Forget the fact that f(x) is usually called y
verbal whale
Nope
boreal gull
oh
verbal whale
Forget the "names" f(x) and y = f(x)
boreal gull
okay
verbal whale
what is y
y is just y 😅
But it's not a constant, rather it's a function of the variable x
light helm
no
boreal gull
man
light helm
refer to what i wrote out earlier
ok so consider
$$p = y^3$$
$$\dv{p}{x} = \dv{p}{y}\dv{y}{x}$$
jolly parrotBOT
ραμOmeganato5
light helm
do you accept that bottom line as a representation of chain rule
boreal gull
no
boreal gull
okay
light helm
what's your reasoning for not accepting it
light helm
missing [] ' on the left side
verbal whale
You said you knew Leibniz notation
boreal gull
You said you knew Leibniz notation
I prefer it but my teacher goes back and forth with notations
and Ig I didnt take the time to learn the liebniz notation of chain rule
verbal whale
I prefer it but my teacher goes back and forth with notations
Well, choose one you're perfectly comfortable with, then
light helm
leibniz notation is relative simple to apply
due to notation abuse and how differentials behave similarly to fractions
light helm
normally you'd be presented with
$$\dv{y}{x} = \dv{y}{u}\dv{u}{x}$$
i changed some variables around to better suit your question
jolly parrotBOT
ραμOmeganato5
light helm
similarly
consider the example
y = (2x+1)^2
would you be able to differentiate this without expanding the binomial?
(using either approach, liebniz/lagrange)
pearl pondBOT
@boreal gull Has your question been resolved?
pearl pondBOT
@boreal gull Has your question been resolved?
flint swallow
Need some help with a mock exam question for a medical entrance exam. this is highschool level mathematics.
it is in dutch but ill translate. With what X value does the following function become zero.
I want hints not full on solutions, I want to learn while making it mostly myself. keep in mind that the use of a calculator is not allowed. only for the most basic arithmetic. Thank you 🙏
compact ridge
okay, so with $\theta = \arctan(x), \tan \theta = x$ right?
jolly parrotBOT
south
compact ridge
and then you want to find $\cos(\arctan x) = \cos(\theta)$
jolly parrotBOT
south
compact ridge
so, draw a right triangle whose tangent ratio is x/1
find the hypotenuse of this triangle, then you can figure out what cos(theta) is
flint swallow
okay Ill give it a shot
I did an attempt and got as far as x^2 = sin(arctan(x))
but I struggle a bit with understanding the triangle part
compact ridge
https://www.youtube.com/watch?v=XZne57aKl58
try watching this video
flint swallow
alright, thanks
pearl pondBOT
@flint swallow Has your question been resolved?
flint swallow
I attempted it with the method on the video making tan(theta) = x and then I determined that X is the opposite side, 1 the adjacent and the hypotenuse sqrt(1+x^2). I think I must have done something wrong because when I reinsert it in the original there cannot be a x value to make it zero. I dont think I mind seeing what you have done.
oh i followed it too closely, I assumed the adjacent side was 1 from the start
im a bit lost
flint swallow
@compact ridge I appreciate the help a lot, but it seems this exercise was a bit much for me. I looked at the solution already and it was a bit tough ngl.
how can I resolve the question?
compact ridge
how can I resolve the question?
I understand this is a new technique for you, the right triangle method
flint swallow
yeah, the solution that was with the exercise didnt seem to even use it so im like split between 2 visions lol
compact ridge
basically if you can get to $\frac{1}{\sqrt{1 + x^2}} - x = 0$, if you can solve that using the quadratic formula (and realise that you need the positive root)
jolly parrotBOT
south
compact ridge
I find the right triangle method to be the easiest though
basically try to concentrate on how to resolve the algebraic equation instead
flint swallow
yea I think i messed it up because in the vid he did it with sin and I did it wrong
compact ridge
they might throw all sorts of word problems at you / questions where the equation is not obvious
there's really no solution other than to practice more, to see more of maths and its techniques
flint swallow
**south**
yeah true, oh wait I did get this
oh man I forgot about the -x at the back
it did have a 0 value omg
but thanks a bunch south means a lot
Ill keep practicing
pearl pondBOT
@flint swallow Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
inland ivy
pearl pondBOT
inland ivy
How do I use this statement to prove the following:
If $\alpha\in\mathbb R\setminus\mathbb Q$ then the set [ \big{{n\alpha}\mid n\in\mathbb Z\big} ] is dense in $[0,1]$, where ${\cdot}$ represents the fractional part?
jolly parrotBOT
kheer257
inland ivy
Essentially for every x in [0, 1] I need to find an element of the set which is arbitrarily close to x
@versed mica I thought of this question and further stuff based on the discussion we were having earlier
sullen cedar
it is sufficient to prove that for all n, there is k such that |{k\alph} - x| \leq 1/n
sullen cedar
you have m such that 0 < {m\alph} \leq 1/n. then what does { {km\alph} | k\in N} look like ?
sullen cedar
thus we are done
inland ivy
hmm
sullen cedar
as x must fall into some partition
sullen cedar
this is mimicking the pigeonhole principle used in proving the existence of m
sullen cedar
it follows from 0 < {m\alph} \leq 1/n
this might also be helpful: as long as k{m\alph} < 1, we have {km\alph} = k{m\alph}.
inland ivy
yeah just figured this out
sullen cedar
this identity will follow naturally if you think about km\alph as m\alph+m\alph+..+m\alph (k times) and m\alph as [m\alph] + {m\alph} where [.] is floor function
inland ivy
I think I've figured it out, thanks for your help!
Is there some natural way I can extend this theorem
sullen cedar
if that was addressed to me, i am not too well versed in approximation theory, so i cant say to be honest. maybe someone else can
inland ivy
Hmm
What if I consider any polynomial with at least one non-constant irrational coefficient
sullen cedar
well in my mind it looks like a similar argument should follow for density of {{n^2\alph} | n\in N} for example
this looks like a promising generalisation
inland ivy
~~well in my mind it looks like a similar argument should follow for density of ...
but is the dirichlet approximation good enough for this
pearl pondBOT
@inland ivy Has your question been resolved?
sullen cedar
i dont think so, since now the sucessive differences are linear
pearl pondBOT
pearl pondBOT
Available help channel!
grave parcel
pearl pondBOT
wooden merlin
Is this a question you're facing, or is this something that you came up with?
grave parcel
Is this a question you're facing, or is this something that you came up with?
it’s a question I’m facing,
I don’t have the actual question on me
But basically “there’s these 2 campsites with these 2 towers in between them” and they give you this network
And ask you to put it in a matrix
wooden merlin
Right, I don't think I got the answer for you. Maybe someone else could solve it?
pearl pondBOT
pearl pondBOT
Available help channel!
fair comet
I don't understand proving uniqueness as a process
I get the proving existence step, but the uniquness I don't get at all
fair comet
could we try this question?
prime bramble
when we want to prove uniqueness of some object, we typically assume the existence of two such objects, and then show that they’re actually the same object
fair comet
right see objectively written out I know that
but somehow when I try to actually do that I'm not sure what exactly my end goal is and what the rules surrounding that is
prime bramble
for your example, assume that there are two numbers m and k with the desired property
wraith stag
right see objectively written out I know that
alright for the uniqueness half of this, we let n^2 = 8a+1 and n^2 = 8b + 1 where a and b are the two integers satisfying the property
prime bramble
same as I said, but with a and b instead of m and k 
your goal is to prove that a = b
so we have uniqueness
fair comet
yes
ok i think ik what you're getting at
one sec
So would a solution like this be valid?
ignoring the fact that I switched up the quantifiers in the problem
sorry about switching problems all of a sudden wasn't sure if I did it right there which is kind of why Idk if I get it or not
wraith stag
is v supposed to be -1?
fair comet
v=(x-3)/(3-x)
wraith stag
that's -1
fair comet
oh right
wraith stag
something weird with your existence proof
wraith stag
for v?
fair comet
the step above 3v
altho maybe I gotta figure out this whole existence & uniqueness thing idk wats going onnn ....
wraith stag
lets do existence first
yeah let's just redo the whole thing
the substitutions don't work and fixing them is gonna take longer than just redoing
fair comet
ah srry i gtg rn didn't realise i have stuff to do
imma close the channel for now might come back later
at least I know I really don't know whats going on rn :)
thanks !
.close
pearl pondBOT
wraith stag
just ping me ill prob be around
pearl pondBOT
Available help channel!
robust oar
helo i need to check something here bc i forgor
pearl pondBOT
helo i need to check something here bc i forgor
robust oar
$\left[ \ln(x) \cdot \frac{(x - 4)^2}{x^2 - 1} \right]^{\frac{2}{3}}, x > 4$
jolly parrotBOT
Akιρɑ
robust oar
i applied the power rule of this but not sure what to do with x>4 here 
plush bramble
what's the question
robust oar
seperate each product and quotient into multiple logarithms, convert each power with an exponent into a coefficient. use the properties of logarithms to accomplish this
$(\ln x)^{\frac{2}{3}} \cdot \left( \frac{(x-4)^2}{x^2-1} \right)^{\frac{2}{3}}$
jolly parrotBOT
Akιρɑ
rough forge
feels like xy and gtg sleep
plush bramble
feels like xy and gtg sleep
!xy
pearl pondBOT
feels like xy and gtg sleep
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
robust oar
seperate each product and quotient into multiple logarithms, convert each power ...
this is the question
robust oar
wait
$\ln\left[\frac{(x - 4)^2}{x^2 - 1} \right]^{\frac{2}{3}}, x > 4$
i hate latex
rough forge
the given domain implies a function so an equation
robust oar
i forgor
rough forge
and then you could just do ln on both sides
jolly parrotBOT
Akιρɑ
robust oar
the given domain implies a function so an equation
the question is asking to convert each power with an exponent into a coefficient
rough forge
just send a picture 🥀 cant latex anyway
robust oar
5th
shouldn't it be $\frac{2}{3} \ln \left[ \frac{(x - 4)^2}{x^2 - 1} \right] = \frac{2}{3} \left[ \ln((x-4)^2) - \ln(x^2-1) \right]$?
jolly parrotBOT
Akιρɑ
robust oar
right?
wraith stag
yeah but not done
wraith stag
log rules
robust oar
yeah my mistake
wraith stag
nvm i see now
robust oar
yeah but not done
and wdym by this
wraith stag
because ln0 is undefined
rough forge
yeah my mistake
you little fart
wet swallow
wet swallow
where is ln0 coming from here
ln(x-4)²
robust oar
You can still split ln(x-4)² and ln(x²-1)
$\frac{4}{3} \ln(x-4) - \frac{2}{3} \ln(x^2-1)$
jolly parrotBOT
Akιρɑ
robust oar
this is what i got
wet swallow
Yes but you can express x²-1 as a product of 2 factors
robust oar
oh factor it?
wet swallow
Yes
wet swallow
im worried about complex numbers
Why
rough forge
complex numbers are cool
wraith stag
im worried about complex numbers
thats a whole seperate thing
you're not having these mixed with logarithms
plush bramble
complex numbers are cool
No u
robust oar
complex numbers are cool
help with this
u know what
ill keep it later
and yap in ur dms
.close
pearl pondBOT
wet swallow
rough forge
j
wet swallow
What are the exponent laws
robust oar
What are the exponent laws
,tex .exp rules
jolly parrotBOT
Akιρɑ
robust oar
i got it tho
pearl pondBOT
Available help channel!
young sun
pearl pondBOT
young sun
have to analyze that
first for domain, then for discontinuities (and possibly asymptotes), symetry, odd or even, critical points, turning point and graph
soo whats the domain
i know its (0,infinite) but i assume since theres a square it doesnt matter if its negative
so id guess its x+1 cant be 0
so domain would be all real numbers but -1
thats ok?
rotund ferry
so domain would be all real numbers but -1
It's (-1, inf)
Because the ^2 is outside the ln
So reals less than -1 don't work out
young sun
Because the ^2 is outside the ln
i assume it affects the (x+1)
so any negative in there would turn positive
rotund ferry
Oh wait
young sun
im not sure if it affects de whole Ln(x+1) or just the argument of ln
rotund ferry
I'm not sure whether this is ln((x+1) ^2) or (ln(x+1)) ^2
young sun
I'm not sure whether this is ln((x+1) ^2) or (ln(x+1)) ^2
im not sure either
rotund ferry
im not sure either
We can't solve this problem without knowing that vital information sadly
young sun
ill check the graph to see which is simpler
and ill go with it
doesnt let me
put the exponent inside
young sun
It should be possible
ill just write ln (x+1) x ln (x+1)
rotund ferry
ill just write ln (x+1) x ln (x+1)
But that is the same as what you already wrote down in the photo
young sun
But that is the same as what you already wrote down in the photo
yea i meant for both things, ill just write square expanded
rotund ferry
G is supposed to be ln(x^2+2x+1)
Oh
Wait lemme check
I have a feeling those two functions should NOT be the same
I'll use my desmos
young sun
I have a feeling those two functions should NOT be the same
wait
no they are not
i talked with a friend
and he said that if it affected ln as well
the square should be above Ln
not on the argument
rotund ferry
rotund ferry
the square should be above Ln
I see
young sun
cant it be negatives behind as well?
i dont understand this
i have to check for discontuinities
never operated with Ln and a squared argument
rotund ferry
never operated with Ln and a squared argument
Didn't you say the square should affect the Ln and not the argument?
young sun
Didn't you say the square should affect the Ln and not the argument?
ill stick to the blue graph
how is that function written
rotund ferry
ill stick to the blue graph
It's the one where the square affects the Ln and not the argument
young sun
It's the one where the square affects the Ln and not the argument
ill stick to that one then
or which one do you think would be easier to do
from what i spoke with my friend, then its the red graph
blue one is different
but im not sure which is which so id rather pick the easier one to analyze
rotund ferry
Both of them are relatively easy, as in not that hard to do
young sun
Both of them are relatively easy, as in not that hard to do
then ill stick to blue
how do i check for discontinuity
or do i just write that since its continue in its domain
i know theres a horizontal asymptot
on y=0
but how do i check for vertical
which value do i take to analyze limit by left and right
<@&286206848099549185>
.close
pearl pondBOT
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sharp galleon
pearl pondBOT
dense jasper
the root is between 0.8 and 1, so it's not unreasonable to start at 0.8
you could've picked 0.85 or 0.9 or whatever though
it would still eventually converge to the root
hello?
alright cya
sharp galleon
the root is between 0.8 and 1, so it's not unreasonable to start at 0.8
wdym 0.8
arent i supposed to sub in smth
sub
Sub*
<@&286206848099549185>
nvm j get it
.close
pearl pondBOT
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void grail
mobiusstrip can be spanned by circle
pearl pondBOT
mobiusstrip can be spanned by circle
pearl pondBOT
@void grail Has your question been resolved?
void grail
I think this is good because it's like cutting the strip makes for a circle
so the hole of mobius strip become the inside / two sides of the circle
so maybe the point is that one side of the circle becomes one side of the mobius strip, while the other becomes a hole, so mobius strip has one side, circle two?
void grail
where is orientability implemented? in Top?
topological-orientation ≈ linear-algebra determinant? 
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@void grail Has your question been resolved?
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boreal raptor
kinda random, but say i have an equation like
y = 2x + 3 + 5
= 2x + 8
in this case, i put an equals sign and manipulate the rhs
but like what if i want to keep the rhs and want to manipulate the lhs only?
is there a way to denote this
boreal raptor
idk if my yap makes sense but like
2x + 3 + 5 = y
2x + 8 = y
is there a way to not rewrite the rhs
tropic saddle
just switch lhs and rhs around?
its not like there is anything fundamental about one side being on the left or right
pearl pondBOT
@boreal raptor Has your question been resolved?
boreal raptor
But I don't know honestly, I've never thought of this
yeah ig it's hella random 😭
boreal raptor
manipulate what is simplifiable
yea but like
nvm that's not what i was asking
alberto and dena got the gist tho
boreal raptor
its not like there is anything fundamental about one side being on the left or r...
hypothetically, if i couldn't swap the sides for some reason, would there be another way of expressing it
tropic saddle
big if
start a new equation where you have switched the sides
on paper you can always just write a vertical = sign under the lhs and then do a new chain of equalities in the next line
boreal raptor
on paper you can always just write a vertical = sign under the lhs and then do a...
oh interesting
.close
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void grail
void grail
eg monic(⊤) ⟹ monic(m) in
A --m--> X
!| |χₘ
v v
1 --⊤--> Ω
brittle pike
id try to help but i dont understand a single bit of this
void grail
id try to help but i dont understand a single bit of this
monic arrow is like injective function
this much I know 
brittle pike
this much I know <:cat_uwu:606547033691521057>
all i know is square
void grail
all i know is square
I'm sure that's meaningful also, because this is maybe like geometry of logic
brittle pike
i dont understand what vectors are doing in it nor how u are suppose to go find out if it's an injective function
void grail
i dont understand what vectors are doing in it nor how u are suppose to go find ...
injective is given
brittle pike
I'm sure that's meaningful also, because this is maybe like geometry of logic
oh wait
void grail
the arrows are the functions
brittle pike
if you prove that the function lets call it t(x) where u go from a to c is equal to the function b to d
- K
where k is any real number
then u can prove g is an injective function since you will have a square and so g(x) || f(x) && g(x)=f(x)+K
void grail
Nice
brittle pike
im not 100% of my work as i have no idea what this is but it makes most ammount of sense to me
void grail
im not 100% of my work as i have no idea what this is but it makes most ammount ...
thx @brittle pike
brittle pike
np
void grail
the pullback structure is important also, which I am trying to figure out
sweet bone
take any object P with maps p,q into A, such that the formed square commutes
(I'm drawing the diagram, hold on)
I think this should be the initial setup
so suppose we have p,q such that gp=gq
then, precomposing with the morphism B->D (call it h), we have hgp=hgq
(let A->C be called j) so the commutativity of the pullback square gives fjp=fjq
and since f is monic, jp=jq
so this forms a commutative square, and the universal property of the pullback gives the result (there is a unique map into A such that the square commutes and factors through the pullback, so p=q)
void grail
P⟶B
|
v
C
important?
sweet bone
yes
these two maps are given by the composition of p/q and the two pullback projections g and what I'm calling j
void grail
P--->B
| ^
v |
C<---A
A--->B
| |
v v
C--->D
not sure what the first diagram is there
void grail
these two maps are given by the composition of p/q and the two pullback projecti...
like gq and jp
sweet bone
as in what's the point of showing stability under pullback?
void grail
general pattern? I know these patterns apply to all sorts of things in life also
void grail
as in what's the point of showing stability under pullback?
yes, and having pullback square
sweet bone
well, I use pullbacks a lot in topos theory
one of the main definition of the area is phrased in terms of pullbacks
but you'll have to be more specific about what areas you're interested in if you want some specific relevant examples
void grail
area in geometry?
sweet bone
logic
but certain types of topoi also appear in algebraic geometry, yes (grothendieck topoi)
void grail
a logic area? wow
sweet bone
and morphisms between those topoi are defined to preserve a kind of pullback
sweet bone
nw
pearl pondBOT
@void grail Has your question been resolved?
pearl pondBOT
warm dagger
What u need help with?
split void
What is the original question?
warm dagger
Square root the 36 and separate into cases
crimson haven
crimson haven
(x-1) ^2 = 0
Then what about this
vernal bear
What about the power
0^ any power = 0
crimson haven
Oki thanks
vernal bear
np
pearl pondBOT
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crimson haven
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fading nexus
How is this correct because 95•2 is not 380
pearl pondBOT
How is this correct because 95•2 is not 380
strong relic
380 is 4 x 95
ivory basin
You took the 2 out of the square root
strong relic
try and connect the dots from there
ivory basin
You took the 2 out of the square root
Think of it as two steps combined as one
$\sqrt{380} = \sqrt{4*95}$
jolly parrotBOT
Xavier 🌺
warped violet
$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$
jolly parrotBOT
USS-Enterprise
ivory basin
,tex .exp rules
jolly parrotBOT
Xavier 🌺
fading nexus
Sorry I should of mentioned this. This is the answer key. I thought it would be four b ut it says 2
fading nexus
I’m still confused because wdym we took the 2 out of the square root m? Cus it’s still there
fading nexus
sorry I’m confused where was the four
Oh wait
Is it the square root of four times the square root of 95
Also for number 2 on th is one do we have to find a specific slope?
Because I would think the slope would just be 1
proper nova
wdym specific slope?
fading nexus
wdym specific slope?
I am not sure if she wanted us to find the slope or just draw the line without a slope
proper nova
for 2.
you simplified
you found the domain restriction
you graphed
write limit statements uh what?
fading nexus
I just don’t understand why the slope is not 1 , so rise one over 1 . Since our equation is 1x^3+0 so shouldent our slope be 1
Maybe it could be 3 over 1 because of the ^3 but that doesn’t work either
verbal whale
Slope? It's not a line
pearl pondBOT
@fading nexus Has your question been resolved?
vernal bear
Ig she means tangent at specific point
worthy canopy
help
worthy canopy
can someone help me do this plss 9th grade maths btw
compact ridge
can someone help me do this plss 9th grade maths btw
do you know that $\sqrt[6] {x} = x^{1/6}$?
jolly parrotBOT
south
worthy canopy
yes but idk where to go from there
compact ridge
im not sure
you need the rule for $(x^a)^b$
jolly parrotBOT
south
worthy canopy
is it 1/216
compact ridge
is it 1/216
no
compact ridge
thats x to the power of a x b right
yep!
worthy canopy
the one u sent
compact ridge
yes
compact ridge
cool
so what we did was actually to raise both sides of $\sqrt[3]{ y^2} = \sqrt[6] x$ to the power of $3$
worthy canopy
yes so now its just y swuare
jolly parrotBOT
south
worthy canopy
on that side
worthy canopy
so now we root it?
compact ridge
yep!
worthy canopy
is y=x?
jolly parrotBOT
south
worthy canopy
OHHH
that one sounds kinda similar to the one above
and so the answer is
holdup
n=4?
thank you so much btww hope u have a great day
.close
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foggy hound
i need help. i dont understand integrals. and i need proof? bcz i know how the riemann sum becomes an integral but i do not know how this concept of using the difference between max image of the primitive minus min image of the primitive gives that area, how is that possible. i tried asking chatgpt it didnt get my point at all and kept repeating the same thing over and over without giving the proof i want
foggy hound
like i used desmos to create graphs and all but it seems so weird to me, like i am using a formula without knowing what that formula even is in reality
the main question is: how does the primitive simplify the work? what is the link between it and between the area under the function's curve?
shrewd mist
I think the best way to understand the antiderivative is to go by the limit definition, just like you did with the derivative
foggy hound
I think the best way to understand the antiderivative is to go by the limit defi...
well the definition itself doesnt do much to me...
foggy hound
i know that one yes
but the thing is that why we use integrals, like how does the primitive link to the area under the given function
it s as if i take f(x) and f'(x) if i want the area under f'(x) between two points i ll just find the difference between those 2 points from the primitive
but why
how
plush bramble
,tex .FTC1
jolly parrotBOT
riemann
plush bramble
That's just the fundamental theorem of calculus
foggy hound
how does this become this
plush bramble
what is "this"
foggy hound
the left side and right side of the equal sign lol
how does the integral become a difference between the image of the 2 points of the primitive
consider me a toddler atp
foggy hound
yesssss
thank youuuuuu
its the mean value theorem part that was missing thanks again!
.close
pearl pondBOT
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copper patio
how do i differtiate e^7x-3, like what do i do, im confused i can differntiate e^3x which is 3e^3x
weary ledge
how do i differtiate e^7x-3, like what do i do, im confused i can differntiate e...
is it e^(7x - 3) or e^(7x) - 3
toxic lichen
do you know chain rule
cause this is just chain rule
if you find that chain rule is barriered, then write $e^{7x-3}$ as $e^{7x} \times e^{-3}$ and apply your knowledge of how to differentiate $e^{kx}$
jolly parrotBOT
Ann
copper patio
yh mate you gotta do them seperatly, but the thing is i know you gotta differentiate whats in the bracket seperatly, but how do i differentiate e^(7x-3)
toxic lichen
the inside function is 7x-3
copper patio
would it be (7x-3)(e^7x-3))
toxic lichen
no
it would be (derivative of 7x-3) * e^(7x-3).
do you know how to differentiate 7x-3
copper patio
so 7(e^(7x-3)
toxic lichen
stray opening bracket but yes
copper patio
so what happens if you get something weird like this e^(9x+3x^2)
like u see this is where the confusion comes from
shit gets my brain messed if you add in another x with another exponent
toxic lichen
chain rule strikes again
$\dv{x} [e^{9x+3x^2}] = e^{9x+3x^2} \cdot \dv{x} [9x+3x^2]$
jolly parrotBOT
Ann
copper patio
so the e part will just stay the same
toxic lichen
thats the whole deal with the exponential function e^x
blissful cloak
from the chain rule, one has (\dv{x}[e^{f(x)}]=\dv{x}[f(x)]\cdot e^{f(x)})
jolly parrotBOT
ΠαϳαμαΜαμαΛλαμα
copper patio
then why is it when its e^(9x+3) you would use the rule Ke^kx, but when you introduce some other thing into it which isnt a constant like 3 you just let it be e^(whatever)
toxic lichen
then why is it when its e^(9x+3) you would use the rule Ke^kx, but when you intr...
the "ke^kx" rule is actually just a special case of the chain rule
pearl pondBOT
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Available help channel!
blissful brook
pearl pondBOT
blissful brook
not sure how to do this
vast atlas
observe that some lines are the same length
do you know how to get the entire logo area?
pearl pondBOT
@blissful brook Has your question been resolved?
pearl pondBOT
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Available help channel!
pearl pondBOT
somber adder
how to graph these
graph what?
weary ledge
yeah be a bit specific pls
nocturne plover
@prime hill Hi You are giving away your entire name by showing the first paper
prisma kernel
In the first one here too
quick star
😭
prisma kernel
Well have you been given the points?
prisma kernel
Can you send me the points separately please
pearl pondBOT
@prime hill Has your question been resolved?
prime hill
A=(1, 2)
B=(4, -1)
C=(6, y)
vertices of isoscles triangle
How to illustrate this in cartesian plane
Send help flz
pearl pondBOT
@prime hill Has your question been resolved?
prime hill
<@&286206848099549185>
polar totem
<@&286206848099549185>
What's your question? Could you please send again?
polar totem
Don't you just plot the points onto the graph?
And draw dashed lines to represent the distance?
pearl pondBOT
@prime hill Has your question been resolved?
turbid lark
please explain what im doing wrong here
pearl pondBOT
please explain what im doing wrong here
pearl pondBOT
please explain what im doing wrong here
Show your work, and if possible, explain where you are stuck.
versed mica
please explain what im doing wrong here
did you use the ratio test?
turbid lark
did you use the ratio test?
versed mica
😭
turbid lark
never happening
versed mica
lol
versed mica
wait did they actually pull the plug now?
turbid lark
OH MY GOD.
versed mica
you need |x + 8| < R
versed mica
so multiply by 8
turbid lark
gotta cover power series, power seires as functions, taylor and maclaurin series
versed mica
i used to be dry scooping my pre workout all night
versed mica
i think i would average like 5 scoops per all nighter
turbid lark
dry scooping?
versed mica
the car ride home the next day was terrible
versed mica
dry scooping?
just pouring the powder in your mouth without mixing it
bad for your teeth tbh
i stopped doing it
slender marsh
whats with all the names of these channels
versed mica
850 mg
😭
man last semester i fucked up my sleep so bad because of the caffeine
id wake up and my eyes wouldnt open
turbid lark
850 mg
ok bro
i need ur help again
cuz i have no idea how to find the interval for this roblem
versed mica
does your brain feel empty yet from sleep deprivation
versed mica
mhm
turbid lark
how do i prove 1/(ln(n)) is conv or div
versed mica
brain wants to sleep
turbid lark
NO TIME
turbid lark
9:41
turbid lark
n > ln(n)
ok
the I i got is (-16,0)
however that is. wrong
apparnetly
but i got divergent for botrh
turbid lark
sighhhh.... i didnt sleep much the other night bc i banged a girl i dont like and have been avoiding her so the energy is being taken up in regret
#collegelife
versed mica
sighhhh.... i didnt sleep much the other night bc i banged a girl i dont like an...
that you didn't like?
😭
turbid lark
that you didn't like?
i thought i failed my ochem exam
she offered me alcohol
i crashed out said whatever yes
we fuck
versed mica
💀