how do I close this
#help-26
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hardy urchin
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fierce zealot
what's an example of a series that converges conditionally
topaz sinewBOT
what's an example of a series that converges conditionally
fierce zealot
that is not an alternating series
solemn wigeon
@noble laurel does such a series exist? Can you clear my doubt my sir?
noble laurel
Perchance we can consider sin(n)/n
fierce zealot
hmm how do we show this
fierce zealot
but f(x) = sinx/x is not decreasing
wary tulip
stupid nonexample is a series that’s eventually alternating but not alternating initially
fierce zealot
I think we need the terms to be decreasing, positive, and the corresponding function to be continuous?
solemn wigeon
I think we need the terms to be decreasing, positive, and the corresponding func...
You are trying to use alternating series test on a series that is not alternating
This is the whole point of your question sir
The alternating series test cannot work
wary tulip
i still am not sure integral test is going to work there
fierce zealot
yes, I am not trying to apply alternating series test though
noble laurel
also requires decreasing
solemn wigeon
Erm
fierce zealot
wary tulip
Perchance we can consider sin(n)/n
i would use dirichlet’s test for this
wary tulip
my real analysis sir taught me this a few years ago
solemn wigeon
I think this works or showing that the sum doesnt converge absolutely
wary tulip
no it was 3 years ago
solemn wigeon
i would use dirichlet’s test for this
How ma'am?
Really how do you show that $\qty|\sum_{i=1}^N sin(i)| < M$
thorny flameBOT
Ultimate Chad
wary tulip
euler’s formula
solemn wigeon
Like e^{in}??? GEOMETRIC SERIES:??/
Holy shits thats beautiful
Thank you slayla you have cleared me doubt
@noble laurel thats actually really cool
noble laurel
He came here to clear a doubt and instead had his doubt cleared
wary tulip
thank my real analysis sir
noble laurel
@wary tulip Are you feeling better now that you've cleared some doubts?
wary tulip
no
noble laurel
I doubt that
wary tulip
yea
solemn wigeon
is this the test youre talking abt?
Yes
fierce zealot
so we need to choose a sequence
wary tulip
it’s kinda a generalization of the alternating series test
solemn wigeon
so we need to choose a sequence
there are only two choices and only one of them is monotonic
fierce zealot
1/n
solemn wigeon
Yessir
solemn wigeon
**Ultimate Chad**
Try showing this by using eulers formula
fierce zealot
Try showing this by using eulers formula
hmm where does that show up in the statement of the test?
oh
solemn wigeon
fierce zealot
i see
Ill try that. But just to confirm, Dirichlet's test is used to show the series $$|a_n| = sinn/n$$ doesnt converge?
thorny flameBOT
WhoTao
solemn wigeon
No its to prove that series does converge
Wait what ???
why are there absolute values
wary tulip
very confusing question
fierce zealot
So to get conditional convergence, we need to apply tests on sin(n)/n and |sin(n)/n|, right?
If both converges, we get absolute convergence. If |sin(n)/n| fails to converge, its conditional
wary tulip
use dirichlet’s test to prove sum sin(n)/n converges
for proving sum |sin(n)/n| diverges there are some approaches here https://math.stackexchange.com/questions/264980/how-to-prove-that-sum-n-in-mathbbn-frac-sin-nn-diverges
fierce zealot
i see. thanks.
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tight rivet
topaz sinewBOT
tight rivet
??
tranquil verge
y = sin(u)
tight rivet
For dy/du?
mortal path
I think it's the opposite
dy/du is - cos (u)
And du/dx = 8x
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languid rivet
angle of corner a
mortal path
angle of corner a
What's the sum of all angles in a triangle
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tight rivet
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tight rivet
Why is number 3 incorrect
coarse tusk
Will the domain be closed or open at the value -5/4?
graceful smelt
can someone help me with this? i'm not stuck at a particular point, i just don't know what this question is asking me to do
topaz sinewBOT
can someone help me with this? i'm not stuck at a particular point, i just don't...
glacial adder
it’s asking which of the follow y’s satisfies the above equation
so you have to substitute in y
and differentiate y to get y’
and then plug it into the differential equation
i’d say just do one by one
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paper junco
I am trying to define f(x):
topaz sinewBOT
I am trying to define f(x):
paper junco
we start from a sine function (in blue)
when we get to certain values of x that would yield a sin(x) above y=a or below y=b,
this new function would have to 'skip' these x values to values of sin(x) that are inside the green lines
for practical purposes f(x) could be a triangle function with a different period than the sin(x)
ocean prairie
Let $D := {x \in \mathbb{R} : b < \sin(x) < a}$, then just take $f: D \to \mathbb{R}$ with $x \mapsto \sin(x)$
thorny flameBOT
DeadTomato
ocean prairie
if you mean that
paper junco
I don't have the knowledge for the notation from f : -> R and on, could please you explain?
ocean prairie
is means that f only takes x values such that the sin value is in your region
paper junco
i'm not trying to find a function that results in the black line in the upper graph, rather in the lower.
ocean prairie
ah
paper junco
right but in that case we would have the gaps, like the upper graph right?
ocean prairie
yeah
paper junco
the weird part about this function I'm trying to find is that there would be no gaps
it would look like the lower graph, which gets rid of the gaps
ocean prairie
i dont know if you can explicitly give such a function
my idea would be to give a function that maps the Reals to our set D
paper junco
it seems it would fall into a trap of dependencies
conditions that depend on things that depend on this condition 😛
but... I can think of this function, so... can't I define it?
ocean prairie
im thinking of a way to map the reals to the set D in a way that it just removes the gaps
paper junco
An idea:
because this new function will be based on a periodic function
we can add the period amount later
so its definition will look a bit ugly at first I imagine
with a few conditions
ocean prairie
well youd have to add g twice if you are at the second thing
i think the best way is to show there is an order preserving bijection phi : R -> D
paper junco
Have to go now, thank you!
ocean prairie
alright
paper junco
sorry one more thing, first time ever here for me
when roughly will this channel disappear ?
ocean prairie
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dense condor
Hello somebody! I need someone to confirm this for me please, I’ve been stuck on two answers. Thank you and have a great day!
topaz sinewBOT
Hello somebody! I need someone to confirm this for me please, I’ve been stuck on...
shut obsidian
Hello somebody! I need someone to confirm this for me please, I’ve been stuck on...
What would the other option have been?
This seems correct, f(f^(-1)(x)) should give x and it does.
,w inverse 7sqrt(x - 8)
Yeah
dense condor
My bad
I inputted a different number
Let me resend
This would’ve been my second option @shut obsidian
shut obsidian
That's the same..
shut obsidian
np
dense condor
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fathom zinc
Does anyone have any tips or have a link to somewhere i can find tips on how to find isomorphisms between groups
topaz sinewBOT
Does anyone have any tips or have a link to somewhere i can find tips on how to ...
hybrid lake
any groups in particular?
fathom zinc
Just looking for general tips it always takes ages for me to do it on tests
hybrid lake
Well a trick can be considering where to send generators
fathom zinc
What if the group isnt cyclic
hybrid lake
Right, consider D8, then you just send the rotation generator somewhere of order 4 and you send the flip generator somewhere of order 2
and then you hope that it satisfies xyxy^-1=e or something
kind tendon
I have a question about part b of this problem. Have I set up the improper integral correctly, and have I done something wrong for it to come out to negative infinity instead of positive infinity?
topaz sinewBOT
I have a question about part b of this problem. Have I set up the improper integ...
kind tendon
is it not negative infinity?
torpid sparrow
If a is getting smaller than 1 and bigger than 0 it will be negative
But u have a negative outside
kind tendon
I didn't know off the top of my head. I (incorrectly) intuited lna to aproach infinity, but that is wrong
I see what I did wrong now, thank you
So the improper integral is set up correctly?
This is my full solution. Makes sense to me
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north canyon
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
this is so crazy, where do I even begin 
topaz sinewBOT
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north canyon
what theorems have you learned?
AM-GM-HM and some simple real number ineqaulity facts like x^2 is always greater than or equal to 0
hybrid lake
okay, thats what I figured I think this has to do with AM GM
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radiant marlin
yea first step is
north canyon
yea first step is
Could you please help me figure out what a,b,c should be in this case?
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keen hinge
@north canyon rewrite given inequality as $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\le 1$, what can you get from it?
thorny flameBOT
Caroline
north canyon
**Caroline**
Ohh nice that solves (b) if we apply AM-HM on x,y,z
keen hinge
Right
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Normed
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dusk raft
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dusk raft
whats the procedure of solving questions like this
stone verge
the letter is just a placeholder
so you can let 2-u = 3x to find f(2-u)
/ f(3x) = 2x + 1
/ 2-u = 3x
/ x = (2-u)/3
/ f(2-u) = 2(2-u)/3 + 1
check the second method
topaz sinewBOT
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stark crater
hi
blissful sentinel
hello
stark crater
please can anyone gimme explanation for the result of this series whether it is convergent or divergent ?
blissful sentinel
do you know divergence tests
stone verge
the numerator is a geometric series so theres an explicit formula for it
then test convergence or divergence when you have all in terms of n
stark crater
Am sorry but I did not kinda get it can you explain the steps more for me
I mean if n= inifinity then (1/3)^k won't belong to real numbers
stark crater
the numerator is a geometric series so theres an explicit formula for it
then it is not entirely geomtric series.... I think ?
blissful sentinel
if n=infinity then the numerator sum = 1/2
stone verge
$\sum\limits_{k=1}^n 1\cdot \left(\frac{1}{3}\right)^k$
thorny flameBOT
svc
stone verge
that looks like a geometric series
stark crater
yep got it now next step now is?
stone verge
you know how to express the sum in a nice formula right
stark crater
do you mean to use the formula ?
stark crater
the series of the numerator starts from k=1
stark crater
yes
okay I used the sum of gemotric series formula here
and then used it on the substitued the value in the main series
so now I got
stone verge
do you mean to use the formula ?
i meant to say that this formula works starting at n=0
this one starts at k=1
stone verge
wdym
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feral olive
Can someone help me approach this math problem?
So, I have $u_{n+1} = \frac{1}{n+1} + \sqrt{u_n}$ a sequence and I know that $u_0 = a$ where $a \in \mathbb{R}^+$
I need to find
$\lim_{n \to \infty} (\frac{u_n - 1 - \frac{2}{n}}{\frac{1}{n}})$
How would you guys try to solve this problem?
We know that $\lim{n \to \infty} (u_n) = 1$
And that $t_n$ which is a special case of $u_n$ where $t_0 = 4$, has for limit when $n \to \infty$ the limit: $\lim{n \to \infty} (t_n) = 1$ and $\lim_{n \to \infty} (\frac{t_n - 1 - \frac{2}{n}}{\frac{1}{n}}) =0$
topaz sinewBOT
Can someone help me approach this math problem?
So, I have $u_{n+1} = \frac{1}{n...
thorny flameBOT
Smile!
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lethal yoke
could someone check if i found the right Interval of convergence
lethal yoke
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@lethal yoke Has your question been resolved?
oak quiver
A cube is divided into two cuboids. The body diagonal of the larger cuboid is 16% larger than that of the smaller cuboid. What is the ratio of the volumes of the two cuboids (small : large)?
topaz sinewBOT
A cube is divided into two cuboids. The body diagonal of the larger cuboid is 16...
stark panther
A cube is divided into two cuboids. The body diagonal of the larger cuboid is 16...
have you got a strategy so far
oak quiver
I tried it with a system of equations, but it didn't work at all
stark panther
by body diagonal im assuming that means from one corner of a cuboid to the opposite corner
vivid coral
I tried it with a system of equations, but it didn't work at all
What did you get for the dimensions of the cuboids?
oak quiver
What did you get for the dimensions of the cuboids?
none, i only know that one diagonal is 16% larger
vivid coral
none, i only know that one diagonal is 16% larger
If we set the dimensions of the original cube as x and the height of one cuboid as y, we get the height of the other cuboid as x-y
Then we can get the body diagonals of the two cuboids and compare them
rare thunder
none, i only know that one diagonal is 16% larger
It’s correct
vivid coral
Actually you don't even need that
body diagonal is cube root of (x^2 + y^2 + z^2) right
vivid coral
because two sides will be the same as cube
stark panther
yeah but we know h and b will be the same and I will be a percent of the orgianl length of the cube
oak quiver
how do I get to the ratio of the volumes of the two cuboids?
stark panther
my thought would be to first find the ratio of the two new sides and then use that to calulcate volume of each one
vivid coral
yeah but we know h and b will be the same and I will be a percent of th...
As a general equation
So we get 1.16^2 times 2x^2 times y^2 = 2x^2 times (x-y)^2
vivid coral
Length I think
vivid coral
Oh wait yeah it's additive
stark panther
not the length
stark panther
how do I get to the ratio of the volumes of the two cuboids?
do you know what the answer should be and if it needs to be exact
oak quiver
no unfortunately I don't know the answer, it doesn't have to be exact
stark panther
because i have an answer but its quite long decimals so im not sure if its correct
topaz sinewBOT
@oak quiver Has your question been resolved?
gleaming drum
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smoky sparrow
Answer sheet says t20=3,495,265
What is the root of the characteristic equation?
In other words, which function does the solution grow like?
smoky sparrow
I got 9 but 10 is waffle to me
Have a look at this
You're probably missing out on some key information
Specifically, the characteristic root technique
(It is possible to do it by iteration which is what the previous examples there show)
gleaming drum
ah hold on
I got it
I tried doing it by hand
I got it on the calc
Just baffled on the difference lol
Also
Another question to add on
smoky sparrow
ok
gleaming drum
What is the primary difference of Recursive rule and explicit?
smoky sparrow
For a recursive relation, the next term depends on the current term and the previous terms
For an explicit one, it just depends on n
gleaming drum
n is any term yes?
smoky sparrow
So for an explicit relation, you can find the value of the nth term simply by subbing in n
smoky sparrow
n is any term yes?
Yep
For a recursive relation you can't do that
So an explicit form is much more useful
gleaming drum
So for an explicit relation, you can find the value of the nth term simply by su...
so t26, n=26?
gleaming drum
right, do you know any places to further study sequences in depth?
smoky sparrow
https://discrete.openmathbooks.org/dmoi3/sec_recurrence.html
This link is nice
topaz sinewBOT
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jade knot
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jade knot
is there a formula for stuff like this
How would I go to solve this? Is it doable without a calculator and without writing out each individual iteration of 1.5^r
jade thunder
You can split them into the negative and positive parts
restive inlet
geometric series formula
jade knot
You can split them into the negative and positive parts
there are no negative parts tho
jade thunder
I mean the iteration over r
jade knot
geometric series formula
oh, is the common ratio just 1.5
smoky sparrow
oh, is the common ratio just 1.5
Yes
jade thunder
Oh I guess the formula just works as well
jade knot
sorry I don't rlly understand what you mean Frosst
smoky sparrow
Yeah it does, just keep in mind what the first term is and how many terms there are
jade knot
but yeah the geometric series formula makes sense
jade thunder
Don’t mind what I said
smoky sparrow
(The number of terms is not 5)
jade thunder
It’s a long way that reduces to the same one that they said
jade knot
(The number of terms is *not* 5)
6?
smoky sparrow
Yep
jade thunder
“Why 6?” Would be a good question to be able to answer
smoky sparrow
Yeah it's the off-by-one error
There are 10 numbers between 1 and 10
That's 10 - 1 + 1, so you need the +1
jade knot
oh I just thought it was coz of the 0
smoky sparrow
So it's not 4 - (-1)
jade knot
because -1, 0, 1, 2, 3, 4 is 6 terms 😅
smoky sparrow
Yeah same thing then
jade knot
That's 10 - 1 + 1, so you need the +1
what is the 10-1+1?
smoky sparrow
what is the 10-1+1?
Just another way of explaining the same concept
Like finding the number of numbers between a and b
That's b - a + 1
topaz sinewBOT
smoky sparrow
Npnp
jade knot
Yeah it does, just keep in mind what the first term is and how many terms there ...
wait sorry quick question why do you need to know the amount of terms?
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unique latch
What's this kind of function?
topaz sinewBOT
What's this kind of function?
jade thunder
Looks like a parabola but it could be a lot of things
unique latch
A parabola
jade thunder
Is there more context?
unique latch
Well it's data actually
How fast powder is burning
It starts off at one point, picking up speed, peaks at the top point, then slows down
jade thunder
I don’t know enough physics or chemistry to really help you here soz
split cloak
Negative parabola, i mean similar
unique latch
Similar parabola, is that what you're saying?
jade thunder
It could be a lot of things as I said
unique latch
Alright
But so far I can tell start at the same origin and move away from each other (They're a reflection)
void crow
What's this kind of function?
It looks like a parabola
At the same time it looks like it has some limits as well
Like, the domain seems to only exist within 0 and 3.5
sour estuary
theres usually 4 quadrants, but if thats all you have than its for sure a parabola
unique latch
But then that begs the question, what's the difference between a hyperbola and parabola?
sour estuary
@unique latch
unique latch
Ah thanks
sour estuary
np
unique latch
Wait, what does the text say
sour estuary
unique latch
Alright thanks
copper siren
topaz sinewBOT
ruby acorn
No, that's a valid step, that tells you what the length from the center to C is.
so what's X there?
copper siren
it was the square root symbol I/--26 - 26
i cant imput it but it looked like that
hold on
ruby acorn
X^2+6^2=10
so this should be x^2+6^2=10^2
ruby acorn
8 isn't the length from the center point to D, it's the length from the center point to C
there's another step
copper siren
solve as if it was right triangle?
ruby acorn
what do you mean?
copper siren
if we have length of center to c as 8 and 17 as a length can we solve for the missing length?
ruby acorn
yes
ruby acorn
yep
copper siren
thank you
ruby acorn
np
copper siren
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stoic shuttle
The square brackets represent greatest integer function
topaz sinewBOT
The square brackets represent greatest integer function
ivory sorrel
split it into multiple integrals
cursive patrol
The square brackets represent greatest integer function
consider what you know about the function floor(x/pi) + 1/2 (like when x > 0 and when x < 0)
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tame thistle
does anyone know how to find this?
topaz sinewBOT
does anyone know how to find this?
tame thistle
i've been struggling enough with this question
i have the answer but i just dont know how to do it
this is basically a translation of this situation:
smoky fractal
does anyone know how to find this?
It will help you a lot to simplify both f(x) and g(x) into the form ax+b, where a and b are some number. Then set f(x) = g(x), and solve for x
tame thistle
oh, is there a technique to put it into the ax+b form
i dont think ive learned that
i think i have found f(x) = -5x+2
glad otter
guys does anyone know vectors pls 😭
strange jewel
yeah i know
glad otter
pls help
smoky fractal
oh, is there a technique to put it into the ax+b form
Just multiply everything through:
-5[-1/15(x-30)]+2 = -5[-1/15x+2]+2 = 1/3x-10+2 = 1/3x -8
I’m pretty sure that’s it but doing this on a phone is kinda tricky so double check my work
glad otter
ABCD parallelogram, M middle of BC and N middle of CD. find m knowing that AM+AN=mAC. all are vectors
i think its supposed to be easy but i have no clue how to do it
strange jewel
its simple just apply loop law
smoky fractal
Guys this channel is still being used by someone else
tame thistle
Just multiply everything through:
-5[-1/15(x-30)]+2 = -5[-1/15x+2]+2 = 1/3x-10+2...
isnt it -5 x [x] +2
cus like [-1/15x+2] gives me 1 so
glad otter
its simple just apply loop law
i dont know what that is.. TT
smoky fractal
cus like [-1/15x+2] gives me 1 so
You aren’t given a value of x yet, all we know is that x>15, but we don’t know it’s actual value yet.
strange jewel
i dont know what that is.. TT
summation of all vector in a loop = 0
tame thistle
You aren’t given a value of x yet, all we know is that x>15, but we don’t know i...
oh true
tame thistle
You aren’t given a value of x yet, all we know is that x>15, but we don’t know i...
it doesnt work
glad otter
summation of all vector in a loop = 0
thank you, i managed
smoky fractal
it doesnt work
I’m just finishing up my lunch, then I’ll do the work on my laptop to check
tame thistle
I’m just finishing up my lunch, then I’ll do the work on my laptop to check
pkay thank u so much
tame thistle
this is basically a translation of this situation:
the answer is in red but idk how to get that
smoky fractal
the answer is in red but idk how to get that
Sorry I don’t speak French, can you send a screenshot of the translation?
tame thistle
for a purchase of ]40,45]$, the client gets 7 points in both stores
40 is excluded
so its an interval
glad otter
that problem is so weird, are u in high school? i would do f(x)=g(x) and find x but its not the same answer as yours so its wrong
smoky fractal
that problem is so weird, are u in high school? i would do f(x)=g(x) and find x ...
That’s what it should be, but the fact that the answer is a range is a bit weird
glad otter
right, from the way its formulated i understand the same amount of money are being spent and the same amount of points are being obtained
topaz sinewBOT
@tame thistle Has your question been resolved?
tame thistle
that problem is so weird, are u in high school? i would do f(x)=g(x) and find x ...
in high school yeah
smoky fractal
for a purchase of ]40,45]$, the client gets 7 points in both stores
Yeah im not sure about this question, I got an answer but its not within the range (40,45] like you said it should be. Also with the number I got, the person would only get 3 points
I also checked it with this
tame thistle
its so weird
smoky fractal
Also at x=45 the values are not even close
tame thistle
Yeah im not sure about this question, I got an answer but its not within the ran...
i dont think we can do it algerbricly
i think drawing it its better
topaz sinewBOT
@tame thistle Has your question been resolved?
topaz sinewBOT
@tame thistle Has your question been resolved?
topaz sinewBOT
@tame thistle Has your question been resolved?
topaz sinewBOT
@tame thistle Has your question been resolved?
topaz sinewBOT
https://math.stackexchange.com/questions/2671078/how-to-prove-two-matrices-are-s...
spiral yoke
ok
neon iron
Can anyone please tell me how they find p matrix?
Don't we construct p using eigenvectors associated with the matrix
loud oasis
P has its columns consisting of eigenvectors, yes
neon iron
P has its columns consisting of eigenvectors, yes
So if I have matrix A and I'm checking if it is similar to B
Do I use eigenvectors of A in matrix P?
In this quora answer the guy however didn't use the eigenvectors of A or B to construct P
Idk how he got it
<@&286206848099549185>
topaz sinewBOT
@neon iron Has your question been resolved?
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@neon iron Has your question been resolved?
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dusk raft
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dusk raft
what would be the process?
I subbed in ax for y
and then I made them both have a common denominator
brave brook
for the answers I think x = ab/(a²+b)
y = a²b/(a²+b)
acoustic tangle
!nosols
topaz sinewBOT
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.
steady void
!nosols
topaz sinewBOT
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.
steady void
oh jinx
brave brook
this isnt integration
yes but you can treat them as constants
brave brook
As a helper, please do not give out answers that could be copied as a homework s...
ok
steady void
yes but you can treat them as constants
you cannot treat them as constants
brave brook
but can I put it in a spoiler?
steady void
no
brave brook
you cannot treat them as constants
why not?
steady void
give working out to guide
brave brook
ok
brave brook
yes I know but you treat them as constant here, as in for all the possible a's and b's you just find the x and y as a general solution?
steady void
keyword: for all the possible as and bs
x=y is for all possible x and ys, yet x and y are not constants
all of these pronumerals are variables, not constants
constants are things that are CONSTANT
meaning they do not change
steady void
yo why nobody ping me
i was explaining to someone who was attempting to help you
dusk raft
😭
steady void
they gave you the answer tho
dusk raft
uhhhh
I MAY have cropped out a bit at the to
p
saying a and b are constants ☠️
my bad
topaz sinewBOT
brave brook
that doesnt affect anything
what I meant by saying treat it like a constant means that it can just be any number
steady void
what I meant by saying treat it like a constant means that it can just be any nu...
that means treat it as a variable
brave brook
constants are things that are CONSTANT
I meant that a and b can still change as constants so they can be any number but if a = x², then it would be a variable
steady void
not the definition of a constant
brave brook
that means treat it as a variable
kinda like ax² + bx + c where a, b and c are constants but not like a = x
steady void
kinda like ax² + bx + c where a, b and c are constants but not like a = x
because they dont change in the setting of the question
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tawdry marten
How to do this?
topaz sinewBOT
How to do this?
tawdry marten
I do know basic derivative and basic l hospital but idk how to do when there is minus like that
L hopital*
delicate drift
the - means you have to calculate the left hand limit
delicate drift
basically, when we calculate limits, we are tending the value of the variable to some value right?
tawdry marten
Yes
delicate drift
like here, the value of x is tending to be pi/2
tawdry marten
Yes
delicate drift
now, the value can tend to pi/2 from both ways
pi/2 - 0.00000001
or pi/2 + 0.000001
tawdry marten
Ohh okay
delicate drift
pi/2 - 0.00000001
this is tending to be pi/2 from the left
tawdry marten
Yes
delicate drift
so you consider that value of left hand limit
basically, the question wants to say that you have to consider sign convention of first quadrant while solving the limit
delicate drift
pi/2 - 0.00000001
because the value of x will be less than pi/2, therefore in the first quadrant
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spice adder
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spice adder
Can anyone help me with this?
ember lodge
Is this question telling you to find m?
ember lodge
2m + 2 - 4 = m
spice adder
DAMN these parenthesis
spice adder
and luckily, m = 2 if I didn't make a mistake on calculation]
HOW
It gives me 0
I open the parenthesis and i get -4+2
Which is -2
Wait
restive inlet
show your work
spice adder
restive inlet
where's m=-1 coming from / why are you using htat
restive inlet
spice adder
I've prove that m is -1 because 2 times -1 equals -2
restive inlet
2 * -1 is indeed -2
but that says NOTHING about m being -1
why do you think that justifies m being -1
spice adder
Because the problem says to replace x with m+1
So we can get m
And I've did
I've opened the parenthesis
And it gave me after that m is -1
restive inlet
you don't have clear work showing how m is -1
restive inlet
i still have no idea how you ended up getting m=-1
spice adder
i still have no idea how you ended up getting m=-1
I literally just replaced
The x
Like how it ask me to do it
restive inlet
yes, and then jumped to m=-1
spice adder
And I calculated
restive inlet
well there are multiple issues
restive inlet
you started with
$$2(m+1) - 4 = m$$
expanded to get
$$2m + 2 - 4 = m$$
THEN, the right side / presence of an equation disappeared (which was invalid btw) leaving you with
$$2m +2 - 4$$
which upon simplification gave
$$2m - 2$$
then BOOM out of nowhere
$$m = -1$$
thorny flameBOT
ℝαμΩℕωⅤ
spice adder
I'm cooked
restive inlet
go back to this equation
2m + 2 - 4 = m
restive inlet
you recognised that the left side simplifies to $2m - 2$ which leads to getting
$$2m - 2\ \red{ = m}$$
then solve that
thorny flameBOT
ℝαμΩℕωⅤ
restive inlet
is what right
spice adder
Now what the fuck do I do
restive inlet
then solve that
spice adder
HOW
restive inlet
,tex .algebra lesson
thorny flameBOT
ℝαμΩℕωⅤ
restive inlet
tldr, same operations to both sides of the equation to work towards isolating what you want
spice adder
tldr, same operations to both sides of the equation to work towards isolating wh...
I still don't understand
So o move 2 over equal?
While changing the sing in front of him?
Coming as 2m=m+2?
restive inlet
yes, continue
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elfin escarp
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elfin escarp
help needed
mint crescent
Didn’t someone already answer this
elfin escarp
no
mint crescent
topaz sinewBOT
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ionic oar
If you have the equations of 3 lines is there an effective way to get the coordinates of the centroid of the triangle formed
topaz sinewBOT
If you have the equations of 3 lines is there an effective way to get the coordi...
topaz sinewBOT
ionic oar
.reopen
topaz sinewBOT
✅
ionic oar
monseiur garrrlic
icy sky
best i can give you is find the intersections then average
topaz sinewBOT
ionic oar
:)
icy sky
its not really brute force
ivory sorrel
If you have the equations of 3 lines is there an effective way to get the coordi...
if the lines are co-planar yes
the shoelace formula might work
ivory sorrel
yes
ionic oar
coplanar yes
icy sky
not quite the right theorem to use
ionic oar
.reopen
topaz sinewBOT
✅
ionic oar
the hell is shoelace
ivory sorrel
icy sky
theres a mathologer video
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rugged plank
could someone help me determine whether this series converges or diverges?
$$\sum_{n=1}^\infty (-1)^n \frac{\ln n}{\sqrt n}$$
my book solved it by determining it is decreasing by the following:
$$f(x) = \frac{\ln x}{\sqrt x}$$
$$f'(x) = \frac{2 - \ln x}{2x^\frac{3}{2}} < 0 \text{ when } x > e^2$$
and then doing l'hopitals to get the limit of the series
$$\lim_{n \to \infty} \frac{\ln n}{\sqrt n} = \lim_{n \to \infty} \frac{\frac{1}{n}}{\frac{1}{2\sqrt n}} = \lim_{n \to \infty} \frac{2}{\sqrt n} = 0$$
and then stating it is convergent by the alternating series test
this makes total sense but i don't know how they found the bounds on which it is decreasing ($x \gt e^2$) and i would not be able to do this method on a test.
i tried comparing it to a p-test with the absolute value of the series, but it came out divergent and i had some flaws in my reasoning.
thanks!
topaz sinewBOT
could someone help me determine whether this series converges or diverges?
$$\su...
thorny flameBOT
declspecl
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rugged plank
like i can understand that $2 - \ln e^2 = 0$ but i honestly doubt i would be able to remember that quickly for a test, so im wondering if there are other methods
thorny flameBOT
declspecl
glacial adder
they just solved for when f’ equals 0
rugged plank
oh wait actually i guess you can do the numerator trick
and just ask when $2 - \ln x = 0$
thorny flameBOT
declspecl
rugged plank
hmm alright ill just have to keep that trick in my mind
glacial adder
taking the absolute value sometimes help
but if the absolute value version diverges, it doesn’t mean the original series diverges
only if the abs version converges then the original converges
rugged plank
right, like the alternative harmonic i gotcha
makes sense ty 🙏 i get it conceptually ill just have to practice it
.close
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glacial adder
yeah practice makes perfect
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gloomy jacinth
Prove that for any numbers a, b, c, d belonging to the interval ⟨0, 1⟩ the inequality is true
topaz sinewBOT
Prove that for any numbers a, b, c, d belonging to the interval ⟨0, 1⟩ the inequ...
topaz sinewBOT
@gloomy jacinth Has your question been resolved?
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@gloomy jacinth Has your question been resolved?
gloomy jacinth
<@&286206848099549185>
elder shoal
this is an olympiad problem, and is probably not best asked here, but try expanding lhs and recall x^n>x^m for n<m, x in (0,1)
topaz sinewBOT
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bright panther
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@gloomy jacinth Has your question been resolved?
fierce zealot
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fierce zealot
I dont understand the first example
So we have $$a(x) = x^3+x+1, b(x) = x+1 \in \mathbb{Z}_3 (x)$$ and $$f(x) = x^2 \in \mathbb{Z}_3 (x)$$. But $$a(x) - b(x) = x^3 \equiv 0 \pmod{x^2}$$? WHy is that true
thorny flameBOT
WhoTao
fierce zealot
But x^2 | x^3, so x^2 |x^3
I dont think thats true?
Oh, I guess x^2|x^3 means there exists another polynomial q(x) such that x^2 * q(x) = x^3
where q(x) = x
Like that?
topaz sinewBOT
@fierce zealot Has your question been resolved?
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@fierce zealot Has your question been resolved?
wise osprey
How do I find the vertices of a hyperbola with the form xy=c? The exact problem is 9xy=16?
topaz sinewBOT
How do I find the vertices of a hyperbola with the form xy=c? The exact problem ...
terse nest
i think the intersection between the line y=x and a hyperbola in the form of xy = c will be its vertices
so you are just solving the system of equations of
9xy = 16
x = y
sub the values in and you will find the vertices
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knotty tapir
topaz sinewBOT
knotty tapir
my question is on the second page
but u need the graphs from the first page
why is 5 b,c and d different
i thought if u wanted to go back u would take inverse
why do you ahve to change order of f and g for one not the order if ur going back in both
topaz sinewBOT
@knotty tapir Has your question been resolved?
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dull ravine
topaz sinewBOT
ruby mural
,calc 41*41
thorny flameBOT
Result:
1681
what
ruby mural
Nvm that
dull ravine
i c
low nymph
they were clever enough to make answers match =w=
sour estuary
do you know what every value is?
low nymph
?
dull ravine
oh it was a trick one
dull ravine
ya opposite of right angle is hypo
low nymph
AB = 41 is clearly the hypotenuse 🤔
sour estuary
no tell me the values
low nymph
correct 👍
dull ravine
and adjacent of B is 9 and A is 40
low nymph
to be fair, we already have a perfect answer 🤔
dull ravine
sinA= 9/41, sinB= 40/41
OHHH
ye ty i think i understand why E isnt a correct answer
sour estuary
and whys that
dull ravine
because only sinB can have 40/41
im wrong bout this
sour estuary
itd be good to write those down because if you mess those up everything is then messed
topaz sinewBOT
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granite lintel
Hey i have problem how to find out range of function like this
topaz sinewBOT
Hey i have problem how to find out range of function like this
granite lintel
it's inverse proportion
jovial wren
Range is all the possible outputs. Is there any value on the number line that y could never have?
topaz sinewBOT
@granite lintel Has your question been resolved?
granite lintel
Range is all the possible outputs. Is there any value on the number line that y...
like range is H (f) or am i wrong ?
because in the answers i have a R - (some number)
jovial wren
I don't understand what you mean by H(f).
Try throwing this equation up on desmos and looking at it. Is there any value that can never be reached on the y axis?
granite lintel
sorry i thought it's the same in the english
so when you have a function you domain which is or x and there is the other one for y
granite lintel
Try throwing this equation up on desmos and looking at it. Is there any value t...
wait
granite lintel
not x ?
jovial wren
Domain is all the possible x values you could stick in
Range is all the possible y values you could get out
granite lintel
yes
jovial wren
So... look at the equation on desmos and see... are there any y values you can't get out?
granite lintel
i don't think so
granite lintel
?
jovial wren
0
granite lintel
why ?
jovial wren
You can't divide 2 by anything and get 0
granite lintel
yes
jovial wren
The horizontal line is a y value that you can never have. The vertical line is an x value that you can never input.
I mean the dotted lines on desmos
topaz sinewBOT
granite lintel
and if i would have this
jovial wren
That will shift the lines around.
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jovial wren
Start by viewing a whole bunch on desmos and look for the patterns
jovial wren
You probably can't use desmos on the test
jovial wren
Correct. You are shifting the horizontal asymptote down
granite lintel
yes but how can i find asymptote for y in the prescription ?
jovial wren
asymptote for y is the horizontal asymptote
granite lintel
like some method
jovial wren
Well, the method is to see that if you subtract 2 from the fraction, then the asymptote moves down by 2. So before the rnage was all reals except for 0, now the range is all reals except for -2.
granite lintel
ok
jovial wren
good luck!
granite lintel
thanks
topaz sinewBOT
@jovial wren Has your question been resolved?
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ancient crag
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ancient crag
Anyone that can explain this better than photomath?
Im supposed to use the formulas sin(2v)=2sin(v)cos(v), and cos(2v)=cos^2(v)-sin^2(v) to help solve it, but im a bit confused as to how
kind forge
does someone help me with this geometry question?
or knows an ai that solves geometry ?
topaz sinewBOT
does someone help me with this geometry question?
or knows an ai that solves geo...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@ancient crag Has your question been resolved?
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