now what does this mean for the derivative
#help-17
solemn spear
chrome kite
if a function is decreasing in an interval then f`(x)<0 considering that the function can be derivated in all points
the opposite being true as the function increases f`(x)>0
chrome kite
if thats your only option i guess so
solemn spear
chrome kite
its deffinetly not less than
chrome kite
is that an increasing or decreasing function?
chrome kite
yah
chrome kite
the opposite being true as the function increases f`(x)>0
u use the same thing
solemn spear
so maybe the other 2 will be less than or equal to 0 ?
tidal marlin
Yes
chrome kite
exactly
solemn spear
so in words that would be...
the derivative of the function is less than or equal to 0 when x is less than 0, and f(x) is greater than 0
its less than zero because its a negative slope?
chrome kite
the derivative of the function is less than or equal to 0 when x is less than 0,...
not necessary
solemn spear
only for this function?
chrome kite
the derivative of the function is less than or equal to 0 when if u consider x1>x2 it results that f(x1) is <f(x2) which means the function decreasees as x gets bigger
tidal marlin
only for this function?
Derivative is basically the slope of the tangent line of the point
chrome kite
only for this function?
its not true for this function either since in the third quadrant f`(x) is < 0 but f(x) is negative
vast shale
lets say i want to move a remote control car that weighs 30kg
vocal sleetBOT
lets say i want to move a remote control car that weighs 30kg
vast shale
how do i calculate the force needed for this. would we account gravity into this or no
dim quail
we have a lot to account for
some are: air friction, rolling friction, heat loss, gravity etc
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
light panther
Help
regal slate
the code?
regal slate
i dont see the need for a code but the steps dictate:
the hour hand seems to move +1
the minute hand seems to move +2
the seconds hand seems to move +3
idk tho
vocal sleetBOT
@light panther Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
hello, just a quick question because i somehow always forget
vocal sleetBOT
hello, just a quick question because i somehow always forget
rose raft
🥴
vast shale
what is the difference between [
\subsetne \textss{and} \subsete
]s
rose raft
uh
vast shale
uhh
pale perch
hmm
rose raft
still hm
torpid talon
vast shale
why am i forgetting the command now
rose raft
hard atlas
One is explicitly a proper subset, the other can be a proper subset or the whole thing
vast shale
its the one with the dash underneath
hard atlas
\subsetneq ?
twin meteorBOT
vast shale
oh yep okay
vast shale
One is explicitly a proper subset, the other can be a proper subset or the whole...
oh okay thank you
.close
vocal sleetBOT
hard atlas
It's like < vs <= just that with sets also some use < to mean the other so there is a more explicit notation
blissful saffron
lix caught
vast shale
oh sorry
blissful saffron
using \subset to mean \subseteq is such cursed notation
vast shale
i meant like
cobalt crypt
vast shale
.reopen
vocal sleetBOT
✅
cobalt crypt
$\lneq$
twin meteorBOT
blissful saffron
vast shale
difference between [
\subsetneq \text{and} \subset
]
twin meteorBOT
vast shale
aren't they technically the same
blissful saffron
sure
hard atlas
Yes but only psychos use the second
torpid talon
only psychos use the first
vast shale
\subset is when you want to be ambiguous af
hard atlas
Cause it's ambiguous
blissful saffron
maybe in some cursed way it could also mean its not a subset at all
how is it ambiguous
\subset clearly means proper subset
hard atlas
No, a lot of people also use it to mean both proper subset or equal
blissful saffron
vast shale
so whats the consensus boys, first one or second one
blissful saffron
please just use \subset to denote proper subset
vast shale
oh but i heard something from my teacher that went like
one of them includes the empty set the other doesn't
but i am preetty sure i misheard that
$\smash{{}^{\not\subset}_{-}}$
blissful saffron
wot
twin meteorBOT
Toby
torpid talon
cobalt crypt
one of them includes the empty set the other doesn't
this is also cursed
because the notation doesnt suggest it at all
if you want it to not be the empty set its best to just write it explicitly like $A \ne \emptyset$
twin meteorBOT
hard atlas
Or just say "let A subseteq X be nonempty"
blissful saffron
just don't use notation that will make your readers come to your house at 2am and shove a hachet into your eyeballs
define your notation at the start if you're using anything ambiguous
\section{Notation}
blissful saffron
textbook authors be like
cobalt crypt
https://tenor.com/view/reading-sign-cant-stop-me-no-one-can-stop-me-gif-13921932
thats exactly what everyone does
nobody will read your notation section 
so just use more intuitive notation
blissful saffron
In this textbook, \bN means {2,3,4...}
vast shale
oh yeah guys another question
let epsilon be a big number
because like
i forgot this too
blissful saffron
then there exists M > 0 such that when
vast shale
whats the difference between [
A \longrightarrow B \textss{and} a \mapsto b
]
twin meteorBOT
plain minnow
I usually just let the interpretation of notation be an exercise for the reader
vast shale
one is maps into, the other is maps to
cobalt crypt
let epsilon be a big number
let $\epsilon < 0$
twin meteorBOT
vast shale
one is maps into, the other is maps to
oh hmmgee
vast shale
,tex $1i\rotatebox[origin=c]{180}{w}{o\leftarrow f}x(\text{f})=\rotatebox[origin=c]{180}{7}$ $\Leftarrow\hspace{-15pt}\raisebox{1pt}{$\implies$}$ \rotatebox[origin=c]{180}{A}$\in\gneq O$, {\Huge\rotatebox[origin=c]{180}{$\in$}}6$\not\leq$O, such\tHat f,\rotatebox[origin=c]{-90}{$w$},\rlap{b}\rotatebox[origin=c]{-180}{$d$}$\phantom{.}\delta$($\emptyset$) $\rlap{=}>$ $|\mid \times(f)-\rotatebox[origin=c]{180}{7}||<\epsilon$
twin meteorBOT
Toby
blissful saffron
ive seen the mapsto be used when they dont want to define an explicit function
for example
$x \mapsto xN$ to denote the canonical projection from a group to the quotient group
twin meteorBOT
cobalt crypt
i use mapsto when im too lazy to write function notation
$f : A \to B, a \mapsto b$
twin meteorBOT
plain minnow
cobalt crypt
why do you use \longrightarrow 
plain minnow
Because it's l o n g
twin meteorBOT
cobalt crypt
vast shale
\to is beta \longrightarrow
plain minnow
vast shale
wait this is wrong
cobalt crypt
well technically it is
plain minnow
Yes
vast shale
it should it be
cobalt crypt
but like
plain minnow
Domain and codomain needs to be switcherooni
vast shale
[
f: \R\setminus\set{0} \longrightarrow \R\quad x \mapsto \f 1x
]
cobalt crypt
too lazy to correct you rn 
vast shale
LMAO
twin meteorBOT
vast shale
there
i mean u can bullshit the codomain to be anything
as long as it is bigger or equal to the defined range
right
cobalt crypt
well maybe
but then you might care about properties of the codomain
like
vector space structure
group structure
topological structure
etc etc
cobalt crypt
plain minnow
[
f :
\begin{array}{c}
\R\setminus\set{0} \to \R \
x \mapsto \frac{1}{x}
\end{array}
]
vast shale
begin array
plain minnow
I don't know how to LaTeX
cobalt crypt
i got this
twin meteorBOT
Mikkel
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cobalt crypt
<tikz-cd>\begin{tikzcd}[column sep=0pt]
f & {{}:{}} & \R\setminus\set0 & \R \
&& x & \f1x
\arrow[from=1-3, to=1-4]
\arrow[maps to, from=2-3, to=2-4]
\end{tikzcd}
oh thats shocking
twin meteorBOT
cobalt crypt
\[ \begin{array}{@{}c@{}c@{}c@{}c@{}c@{}} f & {}:{} & \R \setminus \set 0 & {}\longrightarrow{} & \R \\ && x & {}\longmapsto{} & \f1x \end{array} \]
Almost there 
vast shale
should there be a colon between the R and the x?
twin meteorBOT
vast shale
so boys like
\begin{tabular}{cc}
$f: \R \setminus \set{\pm \s 2} \longrightarrow \R$ &\quad $f: \R \longrightarrow \R$ \
$x \mapsto \f{x}{x^2-2}$&$x \mapsto \f{x}{x^2-2}$\
is a function &is not a function
\end{tabular}
twin meteorBOT
vast shale
basically
plain minnow
I should probably continue my analysis revising instead of this...
cobalt crypt
wdym, this is excellent use of your time
\[ \def\arraystretch{1.2} \begin{array}{@{}c@{}c@{}c@{}c@{}c@{}} f & {}:{} & \R \setminus \set [\big] {\s2, -\s2} & {}\longrightarrow{} & \R \\ && x & {}\longmapsto{} & \f x {x^2 - 2} \end{array} \]
vast shale
```latex
\[ \def\arraystretch{1.2} \begin{array}{@{}c@{}c@{}c@{}c@{}c@{}} f & {}...
I will array stretch ur m-
cobalt crypt
I will array stretch ur m-
cobalt crypt
vast shale
plain minnow
I'm stuck at this one question. The book wants me to find a very specific upper bound for |Δf| of a function f
cobalt crypt
post it here we'll help
plain minnow
It's a logistic function f(x) = exp(x)/(1 + exp(x))
vast shale
plain minnow
It wants be to find an upper bound of |Δf| <= 3exp(a)|Δx| for |Δx| where a is just a fixed point, that is Δf = f(a + Δx) - f(a)
plain minnow
I like to break the rules
cobalt crypt
plain minnow
I'm different like that 
cobalt crypt
twin meteorBOT
cobalt crypt
plain minnow
Sorry
sage dust
Hello, so i'm searching on the internet for an equation to calculate quartile 1,2 and 3 but when i found it, i was left asking why is the equation for counting quartile in an odd single data different ? since for the others it's simple enough you just add 1 or just repeat it in the nearly same equation
vocal sleetBOT
Hello, so i'm searching on the internet for an equation to calculate quartile 1,...
@sage dust Has your question been resolved?
vocal sleetBOT
Available help channel!
verbal turtle
Can anyone help me with understanding with 2-norm of x comes from?
verbal turtle
any context?
Not really, x1 and x2 can be any real numbers.
twin meteorBOT
Toby
verbal turtle
then what is |x|
2-norm of x
vast shale
what is x
vast shale
ah ok, that makes a lot more sense
so you want to show that |x_1| ≤ |x|
write out the definition of the 2 norm
and write |x_1| as sqrt(x_1^2)
verbal turtle
and write |x_1| as sqrt(x_1^2)
Ah, ok, so sin(x_2) gets its own absolute value first.
vast shale
triangle inequality
vast shale
np
vast shale
how do find eulers method for delta t
vocal sleetBOT
how do find eulers method for delta t
lime gorge
Show an example problem
vast shale
can i show you my data
so i am modeling newtons law of cooling
with a cup of coffee
and so this is what I came up with
after doing that
i measured the room temp
which was 22.65
and got a diff eq
of
42.81e^(-.0171)x +22.65
but I want to use eulers method to come up with an approximation
but im confused on how
you calculate the change in x
does that make sense
oh and
I wanna know the time for which the coffee is 57.8 C
and i figured out the time for that now im just stuck on how i would implement eulers method
or how i could
use it
rugged bolt
Okay so you have the differential equation y(t) = 42.81 e^(-0.181t) + 22.65 and now you want to come up with approximations of y(5), y(10), etc?
vast shale
yeah
rugged bolt
Your "x" is just "t" for time, right?
rugged bolt
Uh wait, mb, did you already solve the differential equation and got the solution y(t) = 42.81 e^(-0.181t) + 22.65 or is this the differential equation and should be y'(t) = 42.81e^(0.181t) + 22.65?
rugged bolt
What are the constants and all?
vast shale
-k being constant of proportionality
to the difference of the temperature of the coffee and the room temp
its the diff eq for Newtons law of cooling
rugged bolt
Did you find out the constants?
rugged bolt
Just the differential equation with the constants plugged in
vast shale
K=-.0171
rugged bolt
Okay so dT/dt = -0.171(T - 22.65)
vast shale
yes
rugged bolt
Okay so by Euler's method, we have T_(n+1) = T_n + h * f(t_n, y_n), where f(t,y) = 0.171 * (T - 22.65)
vast shale
yeah
rugged bolt
And we know the initial temperature right?
vast shale
but what does h mean
rugged bolt
So we already know T_0, it is 65.466667
vast shale
yeah
rugged bolt
And then you just continue on from here
vast shale
okay im going to try it
i was just confused on what h
meant
thank you so much
you have no idea 😭
rugged bolt
np
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
wait si
so
uhh
for t_o
i got 62.26
is that right
or am i doing it correctly
can i ping sup? because he was helping me or is that not allowed
vocal sleetBOT
vast shale
.reopen
vocal sleetBOT
✅
vast shale
or
rugged bolt
you can I don't mnid
vast shale
OH REaLLY
rugged bolt
You only got to t_0?
vast shale
thank you g
rugged bolt
T_0 is already given...
rugged bolt
You need to find T_1 or the temperature at t = 5
Or basically T(5)
Then T_2, which is T(10)
Then T_3, which is T(15)
and so on
vast shale
into the diff eq is olved for right
vast shale
how much error is fine
vast shale
off by .305
vocal sleetBOT
@vast shale Has your question been resolved?
rugged bolt
Works I guess
vast shale
nvm i messed up on calculations is much lower
is there an app where i can have one data set be plotted while the other is a line
google sheets doesnt seem to let me do that
rugged bolt
you can try desmos
but you'll have to plug in the equation of the line and the points in the data set
uncut oar
im guessing we convert the limits into polar coordinates where x^2 + y^2 = r^2 therefore the inner limits are defined as 1<=r^2<=4 but how do i get the outer limits
vocal sleetBOT
im guessing we convert the limits into polar coordinates where x^2 + y^2 = r^2 t...
uncut oar
or do we even hjave to convert to polar coordinates?
flat whale
or do we even hjave to convert to polar coordinates?
try it
flat whale
draw the region
river minnow
The region is a ring
flat whale
it would be a circle right?
Nope. Draw the region
vocal sleetBOT
@uncut oar Has your question been resolved?
rugged vortex
You're gonna have to change to polar paper yeah
mellow rampart
What is the problem here?
vocal sleetBOT
What is the problem here?
mellow rampart
Why is two eigenvectors corresponding to the same eigenvalue a problem?
flat whale
Why is two eigenvectors corresponding to the same eigenvalue a problem?
"unique solution"
vast shale
whats the latex cmnd so i can display a proof
vocal sleetBOT
whats the latex cmnd so i can display a proof
regal slate
vast shale
uh i want to ask a question
For all $a, b, c \in Z^+$, gcd(a, bc) $|$ gcd(a, b) times gcd(a, c)\
Let x = gcd(a, bc), let y = gcd(a, b), and let z = gcd(a, c)\
Breaking x = gcd(a, bc) down, we have that $x | a$ and $x | bc$, which implies that $a = xm_1$ and $bc = xm_2$ for $m_1, m_2 \in \mathbb{Z}$.\\
Next we will look at y = gcd(a, b) and z = gcd(a, c). First we have that y = gcd(a, b) which implies that $y = ak_1 + bk_2$ for $k_1, k_2 \in \mathbb{Z}$. We also have that z = gcd(a, c) which implies that $z = al_1 + cl_2$ for $l_1, l_2 \in \mathbb{Z}$\\
Now lets look at gcd(a, b) gcd(a, c). This is equivalent to:\
$(ak_1 + bk_2)(al_1 + cl_2)$\
$(a^2k_1l_1 + al_1bk_2 + ak_1cl_2 +bk_2cl_2)$\
$a(ak_1l_1 + l_1bk_2 + k_1cl_2) + bc(k_2l_2)$\
As defined earlier, we have $a = xm_1$ and $bc = xm_2$:\
$xm_1(ak_1l_1 + l_1bk_2 + k_1cl_2) + xm_2(k_2l_2)$\
$x(m_1(ak_1l_1 + l_1bk_2 + k_1cl_2)) + m_2(k_2l_2)$\
gcd(a, bc) $|$ gcd(a, b) gcd(a, c), as desired \qed \
rip
twin meteorBOT
forgetmenot
vast shale
oh wait it worked
i wanted to ask if there was a better way to do my proof
because this is gross
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
Available help channel!
real stone
vocal sleetBOT
real stone
Does this look right for finding the values of x for which the series converges?
twin meteorBOT
vocal sleetBOT
@real stone Has your question been resolved?
real stone
Not sure what to do here. Is n=2 as the lower bound a significant detail? Because I’ve only encountered n=0 so far
I know I’m supposed to set this <1, but how do I find the limit?
Am I doing something wrong?
vast shale
Am I doing something wrong?
you simplified wrong
recheck your x
redo the entire thing in fact
real stone
oh the x^(n+1) should be an x, my bad
real stone
how? I don’t understand
vast shale
[
\map \ln{\f x y} = \map \ln x - \map \ln y {\c r {}\ne{}} \map \ln{x-y}
]
twin meteorBOT
vast shale
also it is better u don't do that either, you will see why after you fix up your original expression
real stone
oh god I’m out of it 🥲
real stone
also it is better u don't do that either, you will see why after you fix up your...
I’m not sure what convergence test I should use
vast shale
okay so you were on the right path with what u were doing with the ratio test
so just redo your simplification and tell me what the new expression you have is
real stone
but how do I deal with the absolute value?
ln(n)/ln(n+1) would still be infinity/infinity
but how do I differentiate |ln(n)| and |ln(n+1)|
vast shale
see
i want you to look back at your series
what is the first index of your series?
as in, where does it start from?
real stone
OH that’s why the 2 is significant
vast shale
yep
so the absolute value is unnecessary
because those ln's are always positive anyhow
so u can drop it completely except for the x
hearty storm
Am I being stupid or what? How is it convergent? What am I doing wrong?
hearty storm
Or are we saying integral of g(x) is the same range as f(x) so 0 and 1/2 rather than the usual 1 and infinity?
So in our case g(x) is actually convergent
vocal sleetBOT
@hearty storm Has your question been resolved?
vocal sleetBOT
@hearty storm Has your question been resolved?
vocal sleetBOT
@hearty storm Has your question been resolved?
vast shale
Am I being stupid or what? How is it convergent? What am I doing wrong?
Whats the integral ?
$\frac{1}{x^{something} - x^{something}}$
twin meteorBOT
hibyehibye
ripe wedge
vocal sleetBOT
outer warren
the index starts at -1
outer warren
don't chain equations,
your work is unclear
ripe wedge
my bad
outer warren
also 16 + 9 isn't 24
vocal sleetBOT
vocal sleetBOT
Available help channel!
round widget
Can I have a clue on where to begin with this question
vocal sleetBOT
Can I have a clue on where to begin with this question
round widget
I drew the graph
I think x will be 2pi bc that’s the only way u can get the area to be 0
But I’m not sure how to solve for t
half imp
solve for t?
round widget
no, you can't solve for t
I’m not sure what the question is asking me to do then
round widget
X=2pi is that the only solution?
half imp
seems to be
vocal sleetBOT
vocal sleetBOT
Available help channel!
mystic hare
vocal sleetBOT
mystic hare
,rotate
twin meteorBOT
mystic hare
hello uh- i just want to see out whether my way is right- for d- i think its 64 too as they have the same arch
:]
astral pilot
8.d)?
astral pilot
ya u r right
mystic hare
ya u r right
ty btw
astral pilot
pls send it again
mystic hare
ah sure sure
astral pilot
im missing something
twin meteorBOT
astral pilot
how did you find<ACB
astral pilot
<OBC isnt 64 for sure now
mystic hare
thingy-
astral pilot
can u tell how did u find it?
astral pilot
who are related
mystic hare
same arch
mystic hare
owh-
mystic hare
that is is only when co was a diameter
it aint?
astral pilot
to find <OBC first find <OCB
mystic hare
i uh-\
astral pilot
can u find <OCB
astral pilot
you know m<oca
astral pilot
find <OCA
astral pilot
R.I.P.
mystic hare
:]
astral pilot
⚰️
astral pilot
AOC is isoceles
mystic hare
13 plus 64 is 77-
astral pilot
now can u find <OBC?
astral pilot
obc is also isoceles
astral pilot
why is obc isocels>
vocal sleetBOT
vocal sleetBOT
Available help channel!
summer spade
What is the greatest integer k such that 80! is divisible by 45^k?
vocal sleetBOT
What is the greatest integer k such that 80! is divisible by 45^k?
@summer spade Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
unreal sparrow
Did i answer this question correctly?
vocal sleetBOT
Did i answer this question correctly?
vocal sleetBOT
@unreal sparrow Has your question been resolved?
unreal sparrow
<@&286206848099549185>
unreal sparrow
<@&286206848099549185>
boreal vector
Did i answer this question correctly?
☝️
unreal sparrow
What can I help you with?
vocal sleetBOT
@unreal sparrow Has your question been resolved?
unreal sparrow
<@&286206848099549185>
vocal sleetBOT
@unreal sparrow Has your question been resolved?
unreal sparrow
<@&286206848099549185>
final rover
lone niche
probably don't ping multiple times
final rover
yea
lone niche
is the 3.1 mph relative to the river or the bank
assuming it's relative to the river
because if it's relative to the bank than the 75° angle thing is not really possible
yeah I get 0.83 mph
narrow hamlet
B) do I need to use two line notation to do this or just use the cycle notation?
vocal sleetBOT
B) do I need to use two line notation to do this or just use the cycle notation?
@narrow hamlet Has your question been resolved?
narrow hamlet
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
dusky osprey
i'm on my last attempt
vocal sleetBOT
i'm on my last attempt
mental falcon
well plug in x = 1 and y = 0 and solve for C
F(1) = 0 just tells you when x is 1, y (aka the value f(x) is 0 )
dusky osprey
what's arctan 1
mental falcon
pi/4
dusky osprey
it's been a while since i took math sorry
mental falcon
i believe
mental falcon
remember tan = sin \ cos which is basically slope of rise \ run
dusky osprey
-(5-3pi/4)
mental falcon
so slope from 0, 0 to a point on the unit circle is 1 when the angle is at 45 degrees or pi / 4
or 3pi/ 4 but range of arctan is -pi/2 to pi/2
dusky osprey
but that doesn't matter bc it's multiplied by a constant after
so is C = -(5-3pi/4)
i would like someone to double check
<@&286206848099549185>
vocal sleetBOT
@dusky osprey Has your question been resolved?
alpine trout
hey
vocal sleetBOT
@alpine trout Has your question been resolved?
flat whale
rather than x^'/r
#old-network for physics server
vocal sleetBOT
@alpine trout Has your question been resolved?
last umbra
Hi
last umbra
Okay so my Qn is expand the following equation
log9(3x^3/y)
I am confused with the 3x part
<@&286206848099549185>
balmy yacht
last umbra
wsg
vocal sleetBOT
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.
last umbra
my bad
vocal sleetBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
cursive turret
what exactly is the question?
last umbra
it is to expand this
log9(3x^3/y)
the brackets is the product of the log
the argument
and the 9 is the base
cursive turret
cursive turret
productrule as you have 3 times something and then powerrule for x^3.
last umbra
so does it mean it is 3log9(3x)?
karmic imp
Is that 0 suppose to be there?
last umbra
Because in 3x^3 the ^3 is for x and not for the 3 as well
Oh wait
is it log9(3)+3log9(x)-log9(y)?
last umbra
are you sure? is it (3x)^3 or 3x^3?
the latter
cursive turret
productrule as you have 3 times something and then powerrule for x^3.
log9(3x^3)= (productrue) log9(3)+log9(x^3)=(powerrule) log9(3)+3log9(x)
karmic imp
is it log9(3)+3log9(x)-log9(y)?
Not quite this
last umbra
hmm
karmic imp
log9(3x^3) does equal 3log9(3x)
cursive turret
log9(3x^3) does equal 3log9(3x)
set x = 1 and you would get log9(3) =3 log9(3) which cant be right.
last umbra
so is my answer right?
cursive turret
is it log9(3)+3log9(x)-log9(y)?
this is right.
karmic imp
how to close the channel?
.close
last umbra
.close
karmic imp
the ^3 is for only the x variable not the entire 3x
.My bad, I was thinking you could do power rule first then product but it was the other way around
last umbra
.My bad, I was thinking you could do power rule first then product but it was th...
its finee
molten rain
vocal sleetBOT
lone niche
well you know the slope
can you find the equation of the tangent line (y = f(x))
lone niche
I cant really understand the question
tangent line is the line that just barely touches the curve
(this is not the actual line)
meanwhile, the normal line is the line perpendicular to the curve at the same point
molten rain
meanwhile, the normal line is the line perpendicular to the curve at the same po...
what
perpendicular
it mean
its a verticle line?
regal slate
tangent line is the line that just barely touches the curve
(this is not the act...
better way to phrase it would be to say that the tangent touches the graph at only one point
lone niche
well that's not always true..
molten rain
o
lone niche
well
there are infinite infinities of functions
so not really a way to say "most functions are..."
unless there are only a finite number of cases where it's not true
regal slate
well most functions that are taught at this level
regal slate
i guess
lone niche
are you sure that equation is the normal
lone niche
the normal is the one perpendicular to the tangent
molten rain
wha
lone niche
it makes sense that the tangent has only one intersection here
lone niche
lol
lone niche
bot summon is your question resolved
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real gale
vocal sleetBOT
real gale
I considered the numbers to be a_1<a_2<a_3<...a_50(=100)
So, (a_26+a_27+...a_50)/25=((a_1+a_2+...a_25)/25)+50
I'm stuck
urban edge
start by considering the largest possible arithmetic mean of 25 distinct integers each less than or greater than 100
urban edge
i meant equal to whoops
real gale
Hmm
paper depot
might as well multiply through by 25
real gale
I did that
real gale
Yeah
twin meteorBOT
Ann
real gale
,calc ((100101)/2)-((7576)/2)
twin meteorBOT
Result:
2200
Is this the maximum possible sum of 25 distinct integers each being less than 100
paper depot
so it would appear.
urban edge
,w sum integers 76 to 100
twin meteorBOT
urban edge
sounds good
real gale
So, the maximum possible sum of a_i for i in {1,2,3,..25} will be 2200-1250
real gale
and hence a_1+a_2+a_3+...a_50=2*2200-1250
twin meteorBOT
Result:
38
ok, we can
real gale
,calc 4400-1250
twin meteorBOT
Result:
3150
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Available help channel!
frigid raven
quickest way to find x intercepts?
vocal sleetBOT
quickest way to find x intercepts?
stiff sandal
there is no quick way, you gotta solve it
prime spear
indeed
stiff sandal
cubic in this case
prime spear
since its with a ^3 term
prime spear
you use the rational root theorem to find the first factor of the function
frigid raven
2/1?
frigid raven
are these the possiblities?
-1/-1 =1
1/-1 = -1
2/-1 = -2
2/1 = 2
for a i got -1,1
for c i got -2,-1,1,2 ?
then you do c/a and find out best fit?
frigid raven
long division of what
prime spear
divide the factor
by
the equation
you can do any type of diviosn
synthetic, long, short
you just divide it
prime spear
are these the possiblities?
-1/-1 =1
1/-1 = -1
2/-1 = -2
2/1 = 2
uh wait no what
ok so
what are factors of 2
theres
2
-2
1
and -1
you plug those values into the equation
and see which = 0
frigid raven
ok
ty
is this
the best way
?
what if i used
different quotient
what would that help find
prime spear
wdym diff quotient
frigid raven
what does using dif quotient
achieve
if i were to use it
in here, for example
i plug in h-> 0
then set = 0 ?
and i should get +- sqrt 1?
prime spear
oh ok
rain nacelle
can someone help me simplify this: https://gyazo.com/8f5ab3564ef50c3a5db747d740278dd3
vocal sleetBOT
can someone help me simplify this: https://gyazo.com/8f5ab3564ef50c3a5db747d7402...
silk comet
gray yarrow
alternatively you can write the vectors like u=(u1,u2,u3) etc and then just simplify that
vocal sleetBOT
https://cdn.discordapp.com/attachments/533157728613433344/1094584387766603806/im...
astral pilot
!15m
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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.
vale palm
hello???
vocal sleetBOT
@vale palm Has your question been resolved?
vale palm
.....
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@vale palm Has your question been resolved?
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@vale palm Has your question been resolved?
safe cedar
vocal sleetBOT
safe cedar
so they were explaining how the opposite of differentiation is integration
chrome hornet
Yuo
safe cedar
and till x^n+1 makes sense to balance the equation
chrome hornet
Yup
gray yarrow
and it is so much more ❤️
safe cedar
but why are they doing n+1
safe cedar
and it is so much more ❤️
:")
chrome hornet
Derivative it if you get x^n then your integration is right
gray yarrow
:")
in physics we use integration alot as an infinitely "narrow" summation
works wonders
chrome hornet
Derivation of answer is the question
safe cedar
i just started calculus, dont know anything
safe cedar
Derivative it if you get x^n then your integration is right
find the derivative of x^ndx?
chrome hornet
Hmm you want a brief or a summary?
chrome hornet
find the derivative of x^ndx?
No x^(n+1)/n+1
rose raft
No x^(n+1)/n+1
what
safe cedar
i dont feel so good ive been struggling with calculus forever
rose raft
it is nx^n-1
chrome hornet
it is nx^n-1
That's derivative
rose raft
ya
safe cedar
.close
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safe cedar
ty everyone
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Available help channel!
silk canopy
is -12/-7 basically 12/7
vocal sleetBOT
is -12/-7 basically 12/7