not even equal right there
#help-33
scarlet hinge
$\lim_{n \to \infty} U_n = \exp \lim_{n \to \infty} \left( \sin(2\pi \sqrt[2]{1+n^2}) \frac{1}{2} n\frac{1}{n} \sum_{k=0}^n \ln \left( 1 + \frac{k}{n} \right) \right)$\
$ = \exp \left( \left( \lim_{n \to \infty} \sin(2\pi \sqrt[2]{1+n^2}) \frac{1}{2} n \right) \left( \lim_{n \to \infty} \frac{1}{n} \sum_{k=0}^n \ln \left( 1 + \frac{k}{n} \right) \right) \right)$
elfin berryBOT
M8732
scarlet hinge
This is how you should write it.
You use product of limit
Limit of product = Product of limit of each factor IF (big IF) both factors exist as limits on their own
scarlet hinge
**M8732**
^ here the second limit in the last line is something
due to your riemann argument (only real limits, no "equivalence")
gray shale
1/2 -1 = -1/2
gray shale
ye
scarlet hinge
Does this make sense?\
$\lim_{n \to \infty} U_n$\
$ = \exp \lim_{n \to \infty} \left( \sin(2\pi \sqrt[2]{1+n^2}) \frac{1}{2} n\frac{1}{n} \sum_{k=0}^n \ln \left( 1 + \frac{k}{n} \right) \right)$
$ = \exp \left( \left( \lim_{n \to \infty} \sin(2\pi \sqrt[2]{1+n^2}) \frac{1}{2} n \right) \left( \lim_{n \to \infty} \frac{1}{n} \sum_{k=0}^n \ln \left( 1 + \frac{k}{n} \right) \right) \right)$\
$ = \exp \left( \left( \lim_{n \to \infty} \sin(2\pi \sqrt[2]{1+n^2}) \frac{1}{2} n \right) \ln(2) \right)$
elfin berryBOT
M8732
scarlet hinge
This is how you argue watertight.
scarlet hinge
for the sin i have no idea though
L'Hôpital?
gray shale
?
scarlet hinge
nevermind, not that easily
young owl
Taylor expansion and such works fine after you note that sqrt(1+n²) = nsqrt(1+1/n²)
young owl
Indeed
gray shale
the limit is n then
gray shale
Taylor expansion and such works fine after you note that sqrt(1+n²) = nsqrt(1+1/...
good idea
scarlet hinge
sin(2pi sqrt(1+n²))=sin(2pi n (sqrt(1+1/n²)-1))
gray shale
then n(1+n/2 + o(n))
young owl
be more careful about the 1/n²
gray shale
because of the sign?
young owl
no because of your expansion
gray shale
oh ye
scarlet hinge
just write it as divide by 1/n²
scarlet hinge
sin(2pi sqrt(1+n²))=sin(2pi n (sqrt(1+1/n²)-1))
^ and this
gray shale
n(1+1/2n^2 + o(1/n^2))
scarlet hinge
n(1+1/2n^2 + o(1/n^2))
no
you expand
sin(x)=x - o(x^2)
you probably do not need higher terms (you also wrote it incorrectly)
(if you wanted more terms it would be x - 1/6 x^3 + ...)
gray shale
sin(x)=x - o(x^2)
then x have to be expand it
scarlet hinge
then you need to set x=sqrt(1+n²)-n
gray shale
$\sin(2\pi \sqrt[2]{1+n^2}) = 2\pi \sqrt[2]{1+n^2} + o(2\pi \sqrt[2]{1+n^2})$
scarlet hinge
this will not work
scarlet hinge
I think the point is that sqrt(1+n²) is almost n
^ you need to do this as I said.
tayler expansion only works if argument converges to 0
sqrt(1+n²) explodes
gray shale
ye
scarlet hinge
so o(...) will explode too
gray shale
then n(1+n/2 + o(n))
then we have to do that first
scarlet hinge
subtract n first
gray shale
wrong one
scarlet hinge
you can use
gray shale
n(1+1/2n^2 + o(1/n^2))
^
scarlet hinge
sin(2pi sqrt(1+n²)) = sin(2pi (sqrt(1+n²) - n))
scarlet hinge
you put n in factor
put where
gray shale
with x=1/n^2
scarlet hinge
(if you wanted more terms it would be x - 1/6 x^3 + ...)
^
gray shale
sqrt(1+n^2) = nsqrt(1 + 1/n^2)
scarlet hinge
sqrt(1+n^2) = nsqrt(1 + 1/n^2)
correct
but what will you do with the n in front
you can't just omit
gray shale
nothing first
scarlet hinge
you need to subtract n first and use that sine is periodic.
scarlet hinge
sin(2pi sqrt(1+n²)) = sin(2pi (sqrt(1+n²) - n))
^ otherwise you will fail.
gray shale
you expand what inside and then you multiply by n
scarlet hinge
you expand what inside and then you multiply by n
it is true but still the entire argument (which includes n factor) goes to infinity
so no taylor
scarlet hinge
It's taylor series.
gray shale
,w serie expansion of n*sqrt(1 + 1/n^2)
elfin berryBOT
gray shale
,w serie expansion of n*sqrt(1 + 1/n^2) at +infini
elfin berryBOT
scarlet hinge
oh you are taylor expanding this?
gray shale
you can say that
scarlet hinge
Okay I guess that might work.
Then subtract n.
I was always thinking only about sin.
I would have only taylor expanded sin.
or actually I would have used L'Hôptial instead.
gray shale
idk what it is
scarlet hinge
You have not heard of it?
scarlet hinge
Very very useful, thought okay, let's put it aside for now.
I didn't know you didn't know. Your limits look advanced, so I assumed you would know this relatively basic rule.
gray shale
ok i'll check that
sry i must go somewhere right now
i think i have enough clue to finish, thx a lot for your help
still temple
.close
marsh citrusBOT
Available help channel!
spare current
marsh citrusBOT
marsh peak
!status
marsh citrusBOT
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
marsh peak
Can you evaluate f(6) and g(7)?
spare current
marsh peak
Are you sure about $g(7) = 2(7)^2 - 4$ given that $g(x) = 2x - 4$?
elfin berryBOT
A Lonely Bean
marsh peak
Why don't you now evaluate 6 * 46 - 10^2 + 8 though
spare current
184
okay i found my error
Yes 184 is correct
i basically did 184^2
thank q tho
.close
still temple
If R is equipped with the Discrete metric, the set (0,1) is closed. Yes or no? Justify.
On Google it says
For any subset A of a Discrete metric space, every point x in A has an open ball of radius 1/2(x) centered at x that is entirely contained within A.
This is because the open ball contains only point x and no other points from A.
{{{{{****** is it because we are taking radius of 1/2 only and it is a Discrete metric so next point will be one unit away*******}}}}?
Would appreciate if anyone could confirm this
Since, every point in A has an open ball entirely contained within a, A is open.
And then I understood how A complement would be open using the same logic. Thus, set will be closed.
marsh citrusBOT
If R is equipped with the Discrete metric, the set (0,1) is closed. Yes or no? J...
mint sonnet
,close
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
lyric bay
Not sure how to start
gentle ledge
what is the inverse of the logarithm ?
lyric bay
what is the inverse of the logarithm ?
I dunno
gentle ledge
did you study logarithms in school ?
gentle ledge
yep
gentle ledge
how can you use e^y in the expression y = ln (bla bla) ?
lyric bay
how can you use e^y in the expression y = ln (bla bla) ?
e^(y^4-5) = x?
gentle ledge
e^(y^4-5) = x?
nope
main idol
e^(y^4-5) = x?
don't skip steps
main idol
how can you use e^y in the expression y = ln (bla bla) ?
write this down
that should be your first step
gentle ledge
y = e^(ln(x^4 - 5)?
so y = ln(x^4-5) but also y = e^(ln(x^4-5)) ????
lyric bay
so y = ln(x^4-5) but also y = e^(ln(x^4-5)) ????
Can you give me a more straightforward hint?
gentle ledge
you plugged in the exponential function in the RHS right ?
lyric bay
Yes
gentle ledge
and what about the LHS ?
gentle ledge
e^y = e^(ln(x^4-5))
yes
lyric bay
what is $ e^{\ln(x)} $ ?
x
gentle ledge
e^y = e^(ln(x^4-5))
correct. use this fact here
gloomy salmon
Two events with nonzero probabilities:
a. cannot be both mutually exclusive and independent and are always mutually exclusive
b. cannot both be both mutually exclusive and independent
marsh citrusBOT
Two events with nonzero probabilities:
a. cannot be both mutually exclusive and...
gloomy salmon
ik b is right but idk if a is
static quarry
"and are always mutually exclusive"
that need not be true in general
in fact if their probabilities add up to more than 1 then they can't be mutually exclusive
marsh citrusBOT
@gloomy salmon Has your question been resolved?
rich mica
could anyone help me with solving this integral. im able to get down to the 2nd image i sent but after that im kind of lost
marsh citrusBOT
could anyone help me with solving this integral. im able to get down to the 2nd ...
stark trail
for the first integrand of your second page integral, I recommend letting u=tan(4x)
rich mica
so it would be integral u du?
stark trail
for the second integrand of your second page integral, I recommend applying the power reduction formula you used previously again
marsh citrusBOT
stark trail
can somebody help me with a basic algebra issue?
!help
marsh citrusBOT
can somebody help me with a basic algebra issue?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
stark trail
this channel is going to close
blazing oxide
can somebody help me with a basic algebra issue?
one or two
stark trail
he can learn to open a new one
pseudo ore
ill help
so I just started learning systems in school and while solving this system with x, y and z I stumbled upon this system:
x-7z=-3
-3+6z=39
can you help me solve it using elimination?
blazing oxide
so I just started learning systems in school and while solving this system with ...
sure
stark trail
so I just started learning systems in school and while solving this system with ...
!help
marsh citrusBOT
so I just started learning systems in school and while solving this system with ...
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
pseudo ore
should I open another channel?
stark trail
yes
pseudo ore
alright
blazing oxide
no
stark trail
an available one
gloomy salmon
take over dingle's channel
gloomy salmon
tyranny
marsh citrusBOT
Available help channel!
simple gull
how do i start this i have no clue
marsh citrusBOT
how do i start this i have no clue
main idol
try to use trig identities
marsh citrusBOT
@simple gull Has your question been resolved?
simple gull
try to use trig identities
which ones
main idol
which ones
the simplest ones with csc
marsh citrusBOT
marsh citrusBOT
Available help channel!
slate blaze
how would I graph
y = 5x+2
y = 3x + 0
marsh citrusBOT
how would I graph
y = 5x+2
y = 3x + 0
slate blaze
how would I graph
y = 5x+2
y = 3x + 0
or like any example works, but how would I graph it
marsh citrusBOT
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
slate blaze
obviously
vale cypress
Ok do u know what a standard degree 1 graph looks like?
slate blaze
a graph with like one line?
gray shoal
vale cypress
A linear graph
Wow my messages are laggy
Is ur question how to graph both of them with 1 equation or two diff equations?
slate blaze
2 equations
vale cypress
Ok then it’s easy
slate blaze
ok what do I do
vale cypress
2 equations
Can u show me what a linear graph looks like
slate blaze
vale cypress
now do u know what y = x+2 looks like
slate blaze
oh sorryy
slate blaze
now do u know what y = x+2 looks like
In a graph?
slate blaze
vale cypress
YEs!
oh now we know that
To graph it
- Identify the slope and y-intercept:
- The coefficient of x, 5, represents the slope of the line.
- The constant term, 2, represents the y-intercept.
@slate blaze do u understand what I mean by slope?
slate blaze
yes slope = multipler
vale cypress
yes slope = multipler
yep
vale cypress
yes slope = multipler
AI-generated answer
To graph the equation y = 5x + 2, you can follow these steps:
- Identify the slope and y-intercept:
- The coefficient of x, 5, represents the slope of the line.
- The constant term, 2, represents the y-intercept.
- Plot the y-intercept:
- Start by plotting the point (0, 2) on the graph. This is where the line intersects the y-axis.
Now plot the y- intercept
U know what the y- intercept is right?
slate blaze
U know what the y- intercept is right?
it's the number in the end I believe
so for this equation, its 2?
vale cypress
it's the number in the end I believe
its the point at where the line crosses the y axis
so it is 2 over here
vale cypress
just like u showed here
slate blaze
alr
vale cypress
Ok did u plot it?
slate blaze
slate blaze
oh
bright jay
how would I graph
y = 5x+2
y = 3x + 0
I'm not sure where you are getting confused on, you've been explained this concept multiple times. It's not any different from the other problems you've been doing, all that's different is you have a different slope and y intercept
#help-0 message
vale cypress
I just asked u to plot 0,2
slate blaze
I'm not sure where you are getting confused on, you've been explained this conce...
this is different it is 2 equations
the last ones were only 1 equation
bright jay
It's still the same process
You just have multiple to plot
There's nothing different
You just plot more than 1 equation in the same coordinate plane
vale cypress
yeah
Just plot them separately
1 by 1
its nothing but a double point = more marks question
:p
slate blaze
how would I graph
y = 5x+2
y = 3x + 0
would the run be 1
bright jay
this is different it is 2 equations
A line is in the form of y = mx + b, just different variations, like Ax + By = C is one. But the process in plotting a line is the same, plot the y intercept then use the slope. Or you can create a table of values
bright jay
If it's a whole number, like 4, that's just 4/1
.
slate blaze
ok
vale cypress
A line is in the form of y = mx + b, just different variations, like Ax + By = C...
can u do this ive got a chem question of my own tysm #help-37 imma go try to do that tysm again
bright jay
You need to label your x axis too
bright jay
Yeah but I suggest using a ruler to make the lines neater and straighter
vale cypress
Yeah but I suggest using a ruler to make the lines neater and straighter
hey sorry but can u help me in #bots
slate blaze
Yeah but I suggest using a ruler to make the lines neater and straighter
so that's what a 2 equation graph is?
that wasn't that hard honestly
it's same like what we did before
vale cypress
yes
slate blaze
thank you so much
bright jay
that wasn't that hard honestly
That's what I've been telling you
slate blaze
That's what I've been telling you
sorry mb
btw do I have to make the lines longer
or is it okay if just connect the dots
bright jay
It doesn't matter as long at your teacher understands it
vale cypress
make them arrows in the ends
marsh citrusBOT
marsh citrusBOT
Available help channel!
summer bane
marsh citrusBOT
summer bane
This is the math that i did
I just don't know how to simplify and get both sides to equal each other
elfin berryBOT
quaint elm
use the fact that $n! = n\cdot (n-1)!$
elfin berryBOT
hayley!
quaint elm
in multiple places :)
jolly sigil
marsh citrusBOT
jolly sigil
dang okay this one is a little tricky
(I'll post my work bellow )
so I'm left with the indefinite integral sinh(mt)cosh(mt) dt
This identity came to mind but it's not for hyperbolic trig functions!
marsh citrusBOT
@jolly sigil Has your question been resolved?
jolly sigil
.close
sudden hazel
marsh citrusBOT
sudden hazel
oh
rancid junco
we wrote at the same time, calm down.
hollow sparrow
relax it happens lol
sudden hazel
idk how to find ex
hollow sparrow
for the perimeter question?
hollow sparrow
nah
sudden hazel
hm
hollow sparrow
lol you havne't answered my question
hollow sparrow
well let's start there. It helps to knowthe defintion
hollow sparrow
not the area around, rather it's the outer limits of an area.
In other words, its the furthest most border of an object
ok so if we have a rectangle with length l and width w, then the permeter would be l + l + w + w. Make sense so far?
so a square is a polygon with equal lengths, so it'll be l + l + l + l = 4l.
hollow sparrow
42=4x+3
So this is very close, but not quite correct. It'd be x + 3 + x + 3 + x + 3 + x + 3 = 4(x + 3) = 4x + 12. So then it'd be 42 = 4x + 12. now just simply solve for x
halcyon wharf
so im lost
marsh citrusBOT
so im lost
halcyon wharf
I used the quotient rule to get the first part
and now
idk where to go from here
native frigate
its asking the tangent line at f(x) where x = 1
native frigate
I used the quotient rule to get the first part
do you know what a tangent line is?
native frigate
what
native frigate
formula for a line is y = mx+b
native frigate
well we know the slope is 1, and we know it goes through the point (1, f(1))
thats enough to find the y intercept
halcyon wharf
oh. so my y is just f(1)
say less
i plug it in the point slop form and done
@native frigate thansk
native frigate
no problem
lucid pond
Could anyone help me
lucid pond
Hello
queen seal
what the guy said
lucid pond
What guy
still temple
Dont occupy multiple channels @lucid pond
queen seal
lucid pond
Ohh soz I forgot to close it
still temple
Go to the previously one
lucid pond
I closed it!
still temple
Ohh soz I forgot to close it
There one more 11
tacit fjord
.close
marsh citrusBOT
tacit fjord
stop thanks.
lucid pond
.reopen
marsh citrusBOT
✅
lucid pond
It was an accident soz I’m new
tacit fjord
u have your old channels open what the hell
marsh citrusBOT
bright jay
You already posted your question in #help-11, just stay there
tacit fjord
its ok, just stick to one channel, very confusing.
still temple
I pressed off
#help-11 << click on blue
marsh citrusBOT
Available help channel!
frail raptor
simple question, is a function differentiable a point if there is a horizontal tangent?
marsh citrusBOT
simple question, is a function differentiable a point if there is a horizontal t...
main idol
its not differentiable?
That's not what you said
stoic saddle
@main idol you may have misread?
main idol
Possibly
stoic saddle
"if there is a horizontal tangent at some point, is the function differentiable there?"
stoic saddle
"if there is a horizontal tangent at some point, is the function differentiable ...
@frail raptor is this what you were asking?
main idol
Ann will help since she understands you
stoic saddle
not only is it differentiable you can even tell the value of the derivative
frail raptor
not only is it differentiable you can even tell the value of the derivative
ok thanks
one more
why cant i send image
can I dm you image?
frail raptor
i got it working
stoic saddle
ok and what's your question?
stoic saddle
it's the only answer that makes any sense yes
frail raptor
.close
sonic elm
marsh citrusBOT
sonic elm
can someone tell me how I can approach and look at this?
young laurel
Well this seems to be dealing with the derivative, so finding f'(x) and then testing each option sounds good
sonic elm
Well this seems to be dealing with the derivative, so finding f'(x) and then tes...
may I ask how I would find f'(x)?
sonic elm
no worries :) but in that case, what would I do?
cunning basin
you need to find f(0) and f'(0)
using properties of tangent line
do you know how a tangent line looks like?
sonic elm
I do know that a tangent line is a line that barely touches one point on a graph if that makes sense and cannot cross
cunning basin
more rigorously, the tangent line of f at x is a line that intersect f at x and its slope equals the slope of f at x
sonic elm
and keeping that in mind, how would I find f'(0)? as well as f(0) itself
cunning basin
the graph is tangent line at x = 0
thus it should intersect f at x = 0 and its slope equals slope of f at 0
hmm
it's easier with equations
sonic elm
i'm just not sure on how to look at this graph and find the values
cunning basin
more rigorously, the tangent line of f at x is a line that intersect f at x and ...
it means if T(x) is the tangent line of f(x) at point a, then f(a) = T(a) and f'(a) = T'(a)
to find f(0) and f'(0), calculate T(0) and T'(0)
young laurel
i'm just not sure on how to look at this graph and find the values
The tangent touches f(X) at any particular point, in this case it tells you, at x = 0
meaning the tangent shares that point with f(x) at x = 0 if that makes sense
and then f'(x) is merely just the gradient at any point, and the tangent at that point has the same gradient
marsh citrusBOT
@sonic elm Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
next folio
need to just evaluate this, but idk the order of stuff im meant to do
stark trail
please show the original question
undone bane
test or homework?
next folio
hw
stark trail
okay so you are given epsilon=1
you must now find a range of values centered around c=1
such that for all values in this range, the difference in absolute value between their output value and 4 is within 1
next folio
i plugged in the known values i just dont know how to proceed
do i do the absolute value first, the radical, or what
stark trail
you want to find the value of $\delta=...$ such that when $$0<|x-1|<\delta \implies |f(x)-4|<1$$
elfin berryBOT
Austin
next folio
f(x) being sqrt17-x
yes
but idk how to evaluate the equation further
for example this is another question thats similar just with different values
stark trail
**Austin**
so this you understand right @next folio ?
next folio
next folio
so this you understand right <@326121803971952643> ?
yes
stark trail
$$0<|x-1|<\delta \implies |f(x)-4|<1$$
$$0<|x-1|<\delta \implies |\sqrt{17-x}-4|<1$$
Consider now: for $|\sqrt{17-x}-4|$ to be less than 1, it must be the case that $-1<\sqrt{17-x}-4<1$. Do you understand that?
elfin berryBOT
Austin
stark trail
@next folio
elfin berryBOT
Austin
elfin berryBOT
Austin
stark trail
now this is something you can solve
so you tell me @next folio what is the range of x-values that satisfy this inequality?
next folio
(3,5)
stark trail
no
next folio
😭
stark trail
if needed, recall that sqrt(25)=5 and sqrt(9)=3
so your upper bound is 17-x=25
and your lower bound is 17-x=9
stark trail
you don't need my help solving those equations
likely you didn't need my help for this entire inequality
so let me know once you've decided the range of x-values
and then we can continue
next folio
-8 < x < 8
stark trail
great
now
recall that we are centering our interval around x=1
and as you have just demonstrated
our x-values must fall in -8<x<8
so what is the largest size interval centered at x=1 that stays within -8<x<8
stark trail
yes
next folio
i was just confused about the order of operations i was meant to do it ig
but yea thank you man
marsh citrusBOT
@next folio Has your question been resolved?
cyan raft
How do I convert Euler angles to Degrees?
marsh citrusBOT
How do I convert Euler angles to Degrees?
cyan raft
So Let's say I have an Euler angle orientation of (60, -180, -180)
How do I find the actual rotation in degrees? like (x value) rotated 220°
marsh citrusBOT
@cyan raft Has your question been resolved?
marsh citrusBOT
@cyan raft Has your question been resolved?
marsh citrusBOT
@cyan raft Has your question been resolved?
open relic
So Let's say I have an Euler angle orientation of (60, -180, -180)
Hello. What kind of Euler angles are these? ZYZ?
Also, do you want the rotations with respect to the original axes?
marsh citrusBOT
@cyan raft Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
tender mantle
marsh citrusBOT
What are they asking?
stoic saddle
let f be a function twice-differentiable on an interval [a,b], and suppose f has 3 roots in (a,b). what's the minimum number of roots that f'' is guaranteed to have?
marsh citrusBOT
@tender mantle Has your question been resolved?
marsh citrusBOT
@tender mantle Has your question been resolved?
tender mantle
let f be a function twice-differentiable on an interval [a,b], and suppose f has...
3?
stoic saddle
you do not calculate f'' itself
stark trail
think about how if f(x) has three zeros this means the graph has to cross the x-axis 3 times
it has to go up and then down and then back up ( in some order )
in order to do that
stark trail
(x-1)(x-2)(x-3)
tender mantle
2
stark trail
so then f''(x)
tender mantle
F" is in x terms only
stoic saddle
he might mean that in the specific case that f(x) = (x-1)(x-2)(x-3), f'' will be a linear function
and those only have one root
tender mantle
tender mantle
Option C?
stark trail
no need for computation here though arjunn
tender mantle
Why did they write in a weird way?
stark trail
it would be much quicker to imagine the graph
stark trail
Why did they write in a weird way?
idk what 2/2, 3/3, and 4/4 mean. like aren't they all just 1?
stark trail
bruh
stoic saddle
they would have written २, ३ and ४ no?
stark trail
as the Hindi expert here, no those are incorrect Ann
stark trail
I copied my response off of my brain
stark trail
Why did they write in a weird way?
Let us ask our supreme leader @static quarry
static quarry
wha
stark trail
Guide us
tender mantle
Ann knows hindi
@stark trail so f(x) has 2 place where sign vhanges
F'x will have 1 place where sign changes
F"x no sign changes
So roots will be 1 because it will cut only once
static quarry
no one said that f'' exists
oh wait
it's so blurry i miscounted the primes
nvm
static quarry
imagine losing the battle after winning the war
stoic saddle
no one said that f'' exists
f'' DOES exist
anyway
you need to use rolle's theorem multiple times here
static quarry
stark trail
you need to use rolle's theorem multiple times here
this is not rolles theorem
tender mantle
Should I upload my next question?
stoic saddle
are you done w/ this one
tender mantle
Answer is 1 but options are incorrect right?
stark trail
yes it is?
stoic saddle
Answer is 1 but options are incorrect right?
the options include a "none of these"
so they're not automatically incorrect
stark trail
sus
stoic saddle
maybe there is a disagreement about what "options are incorrect" means
when i see, read or say "options are incorrect", it means that it is impossible to pick one option to answer the question truthfully
but that is NOT the case here, since the last option reads "none of the above".
tender mantle
I do not consider the 4th option as a answer
And no doubt i choose it
4
So next doubt guys
Three vectors are given we need to find for which value of x, volume will be minimum of this rectangle quadrilateral
stoic saddle
i'm out
static quarry
what rectangle quadrilateral
tender mantle
.close
drifting trout
If I have a sum $$ A = \sum_{i=1}^n \sum_{j=1}^n A_{ij}a_ia_j$$ where $A$ is real and positive, does it follow that $$ A_{ij} = A_{ji}?$$ I can't think of a counterexample, but I also don't know how to prove it.
marsh citrusBOT
If I have a sum $$ A = \sum_{i=1}^n \sum_{j=1}^n A_{ij}a_ia_j$$ where $A$ is rea...
elfin berryBOT
thedude365
drifting trout
I know we can rewrite $A$ as $$ A = \sum_{j=1}^n \sum_{i=1}^n A_{ij}a_ja_i$$, and because the indices are arbitrary, we can also write $A$ as $$ A = \sum_{j=1}^n \sum_{i=1}^n A_{ji}a_ja_i$$
elfin berryBOT
thedude365
drifting trout
but that doesn't seem like enough to show that $A_{ij} = A_{ij}$
elfin berryBOT
thedude365
mystic minnow
so.... you need to fill in a lot of missing info here.
what is A? what is A_ij? what is a_j and a_i?
drifting trout
My question is adapted from a physics problem in which A is kinetic energy, A_ij is a generalized mass term, and a_i, a_j are the magnitudes of generalized velocities. The physics lingo only tells me that all terms are real and positive
It's completely possible that there is no way to prove this with the available information
marsh citrusBOT
@drifting trout Has your question been resolved?
sleek nimbus
Why am I wrong?
marsh citrusBOT
Why am I wrong?
unreal oyster
u' = 0
next raft
a is not dependent on x, so its a constant and its derivative is 0.
loud apex
π x a ÷ π squared
marsh citrusBOT
π x a ÷ π squared
desert dirge
$\frac{\pi a}{\pi^2}$?
elfin berryBOT
AℤØ
loud apex
Yes.
A = 68.
desert dirge
whats the issue
marsh citrusBOT
@loud apex Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
solemn rover
hello, im new to proofs and there are a few things that i do not understand about this proof:
- how does this proof prove the division with remainder theorem?
- why is b+ka used instead of aq+r?
- why must b+ka≥0?
marsh citrusBOT
hello, im new to proofs and there are a few things that i do not understand abou...
@solemn rover Has your question been resolved?
marsh citrusBOT
@solemn rover Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
rough fulcrum
idk where to begin
marsh citrusBOT
idk where to begin
silk tangle
idk where to begin
i think is something like this
rough fulcrum
oh ok ty
wet holly
Gauss is overkill for this 
rough fulcrum
whats the answer?
oh i didnt do it yet
im working on another one rn but as soon as im done ill do it
silk tangle
oh i didnt do it yet
ok do it patiently
rough fulcrum
yea
silk tangle
i know whats wrong
open kayak
Gauss is overkill for this <:bleakkekw:913344117981999125>
Absolutely, lol
open kayak
Subtract 5 times the second equation from the first, leaving you with 3y = 42 and so y = 14. Thus, x = 30.
silk tangle
making matrix is the only way i remember 😦
silk tangle
yep
rough fulcrum
could u help w one more
silk tangle
lets see
rough fulcrum
what abt the speed of the current
rough fulcrum
like the speed of the water
rough fulcrum
im confused
silk tangle
silk tangle
distance = 10
time that it took to complete those 10 km= 2
speed = v
speed = d/t
speed = 10/2 km/h
dont forget say km/h
manic peak
subtle swan
Given an arithmetic sequence a_n that has 36 elements such that:
a_3 + a_7 + a_18 +a_30 = 248
Calculate the sum first 23 numbers in the series
marsh citrusBOT
Given an arithmetic sequence a_n that has 36 elements such that:
a_3 + a_7 + a_1...
subtle swan
How can I solve this?
i used a_n=a_1 + (n-1)d and got 2a_1 +27d = 124
how can I move on
marsh citrusBOT
@subtle swan Has your question been resolved?
marsh citrusBOT
@subtle swan Has your question been resolved?
marsh citrusBOT
@subtle swan Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
earnest hound
can someone help with this pls?
marsh citrusBOT
can someone help with this pls?
whole hazel
So what’s A B and C
marsh citrusBOT
i rationalized the denominator and got (-129-44√2)/113
Show your work, and if possible, explain where you are stuck.
bright jay
but idk what to do after
$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$
elfin berryBOT
dldh06
earnest hound
So what’s A B and C
A = -129
B = -44√2
C = 113
im not sure..
marsh citrusBOT
@earnest hound Has your question been resolved?
earnest hound
To separate the fraction
so is it
A = -129/113
B = -44/113
C = √2
marsh citrusBOT
so is it
A = -129/113
B = -44/113
C = √2
bright jay
so is it
A = -129/113
B = -44/113
C = √2
You need to separate the fraction like I showed
Then simplify if needed
earnest hound
You need to separate the fraction like I showed
so i need to seperate this into fractions?
bright jay
**dldh06**
.
bright jay
Looks like it
earnest hound
thank you
marsh citrusBOT
@earnest hound Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
brave spire
marsh citrusBOT
brave spire
Source: Terence Tao's Solving Mathematical Problems
The solution provided is good, but I wanna know if what I am doing is possible to continue
I will type my solution out
Let $\phi(x)$ be the sum of the digits of x, and $\sigma(x)$ be the number of digits in x \
Now when I rearrange digits, the number of digits (i.e. $\sigma(x)$) and the digits themselves (and thus their sums i.e. $\phi(x)$) will remain same. \
$\Rightarrow$ I need to find two powers of 2 (say $2^n$ and $2^m$) such that $\phi(2^n) = \phi(2^m)$ and $\sigma(2^n) = \sigma(2^m)$ \
Now, we can rewrite $2^n$ as $10^{n \log_{10} 2}$. Since $10^x$ has x+1 digits, therefore $2^n$ has $\lfloor n \log_{10} 2 + 1 \rfloor$ digits. \
$\Rightarrow \sigma(2^n) = \lfloor n \log_{10} 2 + 1 \rfloor$ \
Now when we write the domain and range of $\sigma(2^n)$ as $n$ increases by 1, we notice a pattern. If 10 divides n, then the next three consecutive powers of 2 have the same number of digits. If 10 doesnt divide n, then the next two consecutive powers of 2 have the same number of digits.
stoic saddle
hold on what
brave spire
<:thonk:406575732563902485> hold on what
?
elfin berryBOT
ItzKraken
stoic saddle
so you're saying that if n = 10k, then 2^n, 2^(n+1), 2^(n+2) and 2^(n+3) always have the same digit count?
brave spire
so you're saying that if n = 10k, then 2^n, 2^(n+1), 2^(n+2) and 2^(n+3) always ...
no, if n=10k
stoic saddle
er yes sorry
brave spire
lemme write the proof for it
stoic saddle
,w number of digits in 2^100
elfin berryBOT
stoic saddle
,w number of digits in 2^103
elfin berryBOT
stoic saddle
you are just wrong
brave spire
Nani!
elfin berryBOT
Ann
brave spire
**Ann**
if I were to take a finer approximation
could I find a version of this conjecture which is true for all n?
crystal sand
could I find a version of this conjecture which is true for all n?
No. No matter what small part you leave out of consideration, that multiplied with a big enough n will contribute to greatest integer function.
I probably didn't put that well.
I meant like if you leave 10^(-100) then, that'll also be 1 when multiplied with numbers bigger than 10^100.
brave spire
I think i got it..What you are trying to say is that there is always a n big enough such that the conjecture will be false
brave spire
I meant like if you leave 10^(-100) then, that'll also be 1 when multiplied with...
yes thats exactly what I was thinking
brave spire
No. No matter what small part you leave out of consideration, that multiplied wi...
floor is known greatest integer function?
crystal sand
Yes.
brave spire
i see
crystal sand
Somehow, i'm used to saying greatest integer function.
brave spire
I find that term confusing
well tysm..Since everything after this is based on my conjecture being true, I suppose its also wrong
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
cold sundial
I can't understand how cos(3π/2 + θ) becomes sinθ...
My understanding is at this level.
According to which, I conclude it should be -cosθ.
ancient slate
Well, do you agree that the cos θ sort of corresponds to the "x-coordinate" in the unit circle?
Actually, you can even see it in the top left drawing
cold sundial
But from that logic, cos(90°+θ) should be -sinθ
Is that correct?
ancient slate
That's right
ancient slate
I'm guessing you guys haven't talked about sines and cosines of the sum of angles
cold sundial
ty for help.
I just miss read the sin 90+θ in google.
cold sundial
I'm guessing you guys haven't talked about sines and cosines of the sum of angle...
Yah. Sir just assumed we know.
ty for help.
ancient slate
Sure
cold sundial
.close
stark field
marsh citrusBOT
stark field
Guys last time on test i had to get lerner indeks (square below) from the thing above
but i fail
anyone understand how?
marsh citrusBOT
@stark field Has your question been resolved?
near lava
marsh citrusBOT
marsh citrusBOT
@near lava Has your question been resolved?
true iris
Hi !
stoic saddle
ok just one moment
these fucking black bars are each 13.5 times taller than the original image.
seriously?
vale cypress
Fr 😭
true iris
Yeah sorry
stoic saddle
the problem itself goes:
Solve the inequality $\sqrt{ax+1} \geq x$
elfin berryBOT
Ann
true iris
Yes
stoic saddle
do you have any info about the letter a?
true iris
No
stoic saddle
i have trouble believing you weren't told anything else.
but like ok you probably want to at least break into cases based on the sign of a
true iris
It's Say based on the values off the parametre a
stoic saddle
do you have a pic of the assignment you got this problem in
or the textbook whatever
torn quiver
?
true iris
I don't know how toi solve it
vocal leaf
I don't know how toi solve it
What
vocal leaf
Ok