kind fellow
#help-0
karmic vortex
languid bolt
np
karmic vortex
have a nice day
languid bolt
you too
karmic vortex
or night
languid bolt
@karmic vortex .close after you finish btw
karmic vortex
.close
lone heartBOT
lone heartBOT
Available help channel!
gilded quarry
lone heartBOT
gilded quarry
hello again guys
So how am i meant to find out what these family of vectors are?
I didnt understand what a generating/spanning family is
and what the method of finding it for something is
Im also confused about the formating of the question
take 3 for example
usually i get vectors like this
Not a family
lone heartBOT
@gilded quarry Has your question been resolved?
novel night
Can you explain the notation $\bR_2[X]$? Meaning, can you give a description of what vector space this is?
ocean sealBOT
daveamayombo
gilded quarry
Can you explain the notation $\bR_2[X]$? Meaning, can you give a description of...
and a vector space is a set defined over a field that satisfies certain axioms
i cant really understand what that actually means though
novel night
See, to my eyes, it looks like it must be some weird notation for the set of all polynomials of degree two or less. I.e. polynomials of the form aX^2+bX+c, where a,b,c are real numbers. That set is a 3-dimensional vector space over the real numbers.
novel night
Hmm. Then I'm not sure what the question is asking either, sorry!
gilded quarry
alright thanks for the help :)
vale crag
hi again
vale crag
these are the correct answers someone sent me btw
if that's the case, your friend is pranking you then
vale crag
well yeah R_2[X] represents the polynomials of degree two or less
do you understand why it is a vector space ? like what are some operations you can define on polynomials ?
vale crag
uh, check this out #โhow-to-get-help @magic plank
magic plank
uh, check this out <#488120190538743810> <@696296724133707798>
Omg ok Do I have to go to another channel ?
I mean
I'm too lazy to do so
vale crag
Yeah it's one channel one person here
gilded quarry
I'm too lazy to do so
? dont get help then lmao
magic plank
Omg ur too cute saying that idk why
U guys are cuties, continue with ur question please ๐
gilded quarry
i was just confused about the notation in the question
because im used to the format
like 3 vectors
u v w
and here it was a family of vectors
instead of 3 direct vectors
so i made up 3 vectors that could be in the family
vale crag
and here it was a family of vectors
I mean, it just means here's this three vectors
gilded quarry
and then i just followed the process to check if its dependant / independent
gilded quarry
I mean, it just means here's this three vectors
usually the questions are like this
vale crag
There's no real difference
vale crag
Yeah okok
Also good idea of using R^3 from the start if you're confused by polynomials
Secretly all finite dimensional vector spaces are like some R^n anyway so that's all good
vale crag
And yeah they're independent indeed
vale crag
so you said you weren't that familiar for what it means for some vectors to be "spanning" right ?
@gilded quarry
gilded quarry
so you said you weren't that familiar for what it means for some vectors to be "...
yup
i know the definition
it means that a family of vectors in a vector space
whos linear combinarions can generate all other vectors
in that vector space
so here the family is (1, X+1, X^2)
and its asking us if that family can generate all vectors
in R2
by linear combination
vale crag
whos linear combinarions can generate all other vectors
yeah that's the general idea
gilded quarry
this is a little thing i made here
vale crag
ok
well now what's remaining to show is that any vector can be written in the form (gamma, beta, alpha+beta)
gilded quarry
so thats where my next question is
what do they mean by any vector
any vector in R2?
vale crag
any vector in R2?
if I tell you some vector x=(a,b,c), can you give me some alpha, beta, gamma, such that alpha*u+beta*v+gamma*w=x ?
that's what's meant by any vector
vale crag
or in a more formulaic manner $$\forall x \in\mathbb{R}_2[X], \exists \alpha, \beta, \gamma \in \mathbb R, x=\alpha u+\beta v+\gamma w$$
ocean sealBOT
aPlatypus
vale crag
maybe not because of the middle one
what do you mean by that ?
btw I'm restarting my pc it's freaking slow
brb
gilded quarry
yeah np
vale crag
I mean actually checking if a family of vectors is free or spanning uses almost the same process
For checking if it's free, you set the linear combination to 0 and you want to see whether the coefficients are 0
vale crag
Let me finish
gilded quarry
alright
vale crag
For checking if it's generating, you take some vector (a,b,c), you set the linear combination equal to (a,b,c) (that gives you a system of equations just like before) and you want to check if this system has a solution
I.e. are you able to find alpha beta and gamma as a function of a,b,c
vale crag
if I tell you some vector x=(a,b,c), can you give me some *alpha*, *beta*, *gamm...
Do you get how you can derive this method from the definition of spanning I wrote earlier ?
gilded quarry
yes
vale crag
then it is a spannign
I mean actually this is true (cause we know R2[X] has dimension 3) but I'm trying to make you think through the definitions a little bit
gilded quarry
im sure that
alphau+betav+gamma*w=x
this is correct
as in
its possible
so it is spannin
yeah sure
well I just thought of it like
the first position in vector is gamma*1
so gamma = x
same for second position its just beta = x
and for third its alpha = x - beta
vale crag
uh x is a vector as we wrote it right ?
Gamma = x makes no sense to write
They're not even the same type of object
Like if I told you 2 = ABC (ABC being a triangle), you'd probably ask me what drugs I'm on rn
vale crag
Here it's a bit more subtle but it's the same idea
vale crag
but you get what i mean?
Yeah x1 x2 x3 that's a better start
You could probably think about it on paper
(Or like paint if you want)
vale crag
So alpha = x3-x2 then
gilded quarry
yup
vale crag
So yeah how can you interpret this solution ?
If I give you a vector x=(x1,x2,x3), can you now give me a linear combination of u,v,w which equals x ?
vale crag
I mean we just solved for the coefficients in the linear combination
That's what's the alpha beta and gamma are
gilded quarry
oh okay
vale crag
I mean we could just check our solution works if you want
gilded quarry
vale crag
So we just showed we can write any vector as a combination of u,v,w
That means we won
Or at least we can answer the question now
@gilded quarry
gilded quarry
the answer is A
vale crag
wait is that not correct?
It is it is
Yeah it's spanning indeed
Btw I want to show you something nice before we end that convo
It's going to link what we did yesterday to what we did just now
vale crag
So yeah I'm going to define a linear transformation for you
It's a transformation f, from R^3 to R_2[X]
As input it takes a vector (a,b,c) from R^3
And it outputs you au+bv+cw
So it takes some scalars, and outputs you a linear combination of u v and w
vale crag
what is it?
You ok with that ?
vale crag
what IS R_2[X] though?
It just means polynomials of degree 2 or less
It's a vector space with dimension 3 though, so it looks like R^3 in some sense
vale crag
So it takes some scalars, and outputs you a linear combination of u v and w
Anyway, the idea now is, can you link the fact that u,v,w is free/spanning to facts on the linear transformation I got you there ?
gilded quarry
oh alright
so the power is the dimension
of the space
and the small number is the degree
gilded quarry
what does it represent?
vale crag
It's means I consider the polynomials with variable X
gilded quarry
ah alright
vale crag
Anyway, the idea now is, can you link the fact that u,v,w is free/spanning to fa...
That question still stands
gilded quarry
oh yeah
well i think its spanning because
you can create any vector x
in the subapce
by linear combination
with scalars
vale crag
well i think its spanning because
Yeah, does this say something about f ?
The transformation
vale crag
I mean f is a function not a family of vectors
I'll spell the connection more clearly
If u,v,w are spanning that means that for any p in R2[X], I can find a,b,c such that au+bv+cw = p
vale crag
yeah I'm just restating it
vale crag
If I rewrite that using the transformation f
"If u,v,w are spanning, that means that for any p in R2[X], I can find a,b,c such that f(a,b,c) = p"
vale crag
yeah
but that clearly tells you something about the transformation we just defined
"for any output, I can get an input such that f(input) = output"
does that ring any bells?
@gilded quarry
lone heartBOT
@gilded quarry Has your question been resolved?
gilded quarry
does that ring any bells?
oh alright and yes it does
it sounds just like the definition
for a spannign function
vale crag
for a spannign function
I guess you mean surjective
but yeah it's the idea
so that's for spanning family <-> f surjective
what about if the family is free ?
does that tell something about f ?
lone heartBOT
vale crag
.reopen
lone heartBOT
โ
vale crag
.close
solid imp
lone heartBOT
wary stream
Factor out cos(2x) in the numerator
wary stream
Gets multiplied to the -8xsin(2x)
alpine sable
Please could someone help me with this question?
lone heartBOT
Please could someone help me with this question?
median oar
what did you try?
alpine sable
divide by 4
median oar
Divide?
alpine sable
Divide all the terms in this expression by four
languid bolt
that would change the expression
i think he meant dividing the denominator and numerator by 4
median oar
i know, he needs to figure out the terminology though
alpine sable
@median oar any hint?
verbal cargo
@median oar Hey I'm bored
median oar
<@244390699431100416> Hey I'm bored
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
How can we identify which number we can factorise?
ocean sealBOT
Frosst
alpine sable
yeah
alpine sable
that would change the expression
no it won't tbh
he is dividing the numerator and denominator by 4
alpine sable
he is dividing the numerator and denominator by 4
he edited the comment
fiery adder
can someone help me provide some motivation for axiom of choice please? it's a lil silly but still - from what i understand it just states that given a collection of sets, we can make another set by picking an elt from each one
fiery adder
but why does it matter to formalize that why cant we just do that? or when we "just do that" are we invoking axiom of choice without saying so
lone heartBOT
@fiery adder Has your question been resolved?
fiery adder
seems awfully similar to cartesian products
tacit arch
Try #foundations
prime badge
but why does it matter to formalize that why cant we just do that? or when we "j...
well yeah
fiery adder
will i lose anything from just blackboxing it
fiery adder
like might i be hurt later on if i just know what it is without really reading much about it
tacit arch
Hurt you how? Are you being tested on it
tight thunder
lone heartBOT
tight thunder
guys
half of 2 is 1
2+1 is 3
half of 5 is 2.5 + 5 = 7.5
therefore X=7.5 am i right
tepid drum
do u have a given that the side of length 3 is parallel to the line which has a segment of length x ?
placid zinc
I wouldn't try to shortcut the process. Write the equation, solve.
tepid drum
if yes then u can use thales theorem
placid zinc
Actually nvm you are right.
slender gull
therefore X=7.5 am i right
This isn't those problems you get to see on some group chat which has some weird logic you have to follow by discarding maths.
I'm referring to the method.
Your answer is correct.
tepid drum
do u have a given that the side of length 3 is parallel to the line which has a ...
wait if these two are parallel then the answer is wrong
because if they are parallel then by thales' theorem u get that 2/7 =3/x which gives x = 10.5
tepid drum
u know that they are similar if the 2 sides i talked abt are parallel
right ?
bc youll have alternating angles and thus u will have A.A.A but if these 2 sides are parallel then using thales' theorem will give another answer
slender gull
u know that they are similar if the 2 sides i talked abt are parallel
Yes, only then.
tepid drum
yes but in this case you will get 2 different answers
while the length of the side has only 1 value
lone heartBOT
@tight thunder Has your question been resolved?
next flax
lone heartBOT
gray isle
to the power of 1/12 is NOT the same as multiply by 1/12
tacit arch
,calc (2/3) * (1/12)
ocean sealBOT
Result:
0.055555555555556
,calc (2/3)^(1/12)
ocean sealBOT
Result:
0.96677570572707
if you're plugging into a calc be sure to put parentheses around the ( 1/12)
next flax
yeah lol
I'm stupid
i'm doing this question
and i'm thinking (15/16)^(60)
but that gives me a very small number
much smaller than if i was to just do (15/16)^(1)
next flax
if you're plugging into a calc be sure to put parentheses around the ( 1/12)
if it's decreasing rapidly, why would it decrease with a much less factor with more time? surely in a minute something would have a much larger factor than the factor of a second?
,calc (15/16) ^ (1)
ocean sealBOT
Result:
0.9375
,calc (15/16) ^ (60)
ocean sealBOT
Result:
0.020810215807527
First calculation is a second. Second calculation is a minute. Why is the second larger?
<@&286206848099549185>
fallen verge
the amount of bacteria is dying off so the number is decreasing as time goes on
median oar
First calculation is a second. Second calculation is a minute. Why is the second...
a number less than 1 when u take it to greater and greater powers
will go smaller and smaller
next flax
a number less than 1 when u take it to greater and greater powers
i mean yeah
but i feel like this answer is wrong
0.02
Every minute the number of bacteria decays by a factor of 0.02.
Every second the number of bacteria decays by a factor of 0.94.
median oar
so there's less bacteria as time goes on
next flax
Ahh!
next flax
so there's less bacteria as time goes on
1.04521125295
This rounded to 2 decimal points, would be 1.05 ?
median oar
what number does this represent
ocean sealBOT
Result:
1.0452112529529
would 1.0452 rounded to two decimal places be 1.05 or 1.04?
median oar
to 2 decimal places will be 1.05 yes
next flax
okay
median oar
0.045 is closer to 0.05 than 0.04
lone heartBOT
@next flax Has your question been resolved?
next flax
lone heartBOT
next flax
.close
alpine sable
Sin (x) + sin(-x) = 0
lone heartBOT
Sin (x) + sin(-x) = 0
alpine sable
Help pls
alpine sable
Need to find x
naive valley
sine is an odd function, it's true for all x
tame hound
|2-x| = 1
tame hound
How do I solve this?
tame hound
so when (2-x)<0, then |2-x| = -1?
tacit arch
no
tacit arch
|y| = y if y >= 0 and |y| = -y if y < 0
plug y=2-x
tame hound
so when (2-x)<0, then |2-x| = -(2-x) => -2+x?
tacit arch
yes
tame hound
and when (2-x)โฅ0, then |2-x| = 2-x
tacit arch
also yes
tame hound
$\left| 2-x\right| =\begin{cases}-2+x&\left( 2-x\right) <0\ 2-x&\left( 2-x\right) \geq 0\end{cases}$
2-x = 0
=> -x = -2
=> x = 2
ocean sealBOT
AuHasard
tame hound
so |2-x| = 1 is basically the distance between 2 and x is 1
alpine sable
yes, basically
tame hound
$\cdots 0\cdots 1\cdots 2\cdots 3\cdots 4\cdots$
ocean sealBOT
AuHasard
tame hound
so x could be 1 and 3 here?
tacit arch
yup
lone heartBOT
@tame hound Has your question been resolved?
molten pivot
|2-x| = 1
As long as you're working over the reals a much easier way to think about it is to say that the inverse of absolute value is +-
lone heartBOT
molten pivot
Of course you will have to verify that your solutions actually work when plugged back in
lone heartBOT
Available help channel!
lyric linden
In an electrical circuit, a resistor is switched such that the relationship between the current I through this resistor and the time t is given by I=I0(1-e-t/ฯ). Here I0 and ฯ are positive constants determined by the other components present in the circuit. Which of the following figures shows the graph of this relationship?
lone heartBOT
In an electrical circuit, a resistor is switched such that the relationship betw...
@lyric linden Has your question been resolved?
lyric linden
<@&286206848099549185>
crisp pine
As t becomes very large, what happens to $e^{-t}$
ocean sealBOT
Jammy
lyric linden
Get's bigger as well I suppose
lyric linden
mb
crisp pine
$e^{-x} = \frac{1}{e^x}$
ocean sealBOT
Jammy
lyric linden
I just don't understand the reasoning behind this solution quite yet
crisp pine
I unfortuneately dont undertand the language the solution is written in so I cant help clear up specific bits
Unless you have specific questions about it? Sorry for not being helpful haha
lyric linden
Maybe this will help ๐
crisp pine
Ok so does the first line of reasoning follow?
No worries at all
If you plug in t = 0
$e^{-t} = e^0 = 1$
ocean sealBOT
Jammy
lyric linden
hmm
crisp pine
No worries if you arent happy with that bit
But basically $x^0 = 1$, thats just sort of a fact
ocean sealBOT
Jammy
lyric linden
yeah obv
ocean sealBOT
Jammy
ocean sealBOT
Jammy
crisp pine
$I_0(1-1) = I_0(0) = 0$
ocean sealBOT
Jammy
lyric linden
Oh yeah so that eliminates graph B & D
crisp pine
Yes ๐
And then to eliminate C, they make a point about a second derivative
Are you happy with how to differentiate the formula we have for I
karmic rapids
But basically $x^0 = 1$, thats just sort of a fact
$x^0 = x^{n-n} = \frac{x^n}{x^n} = 1 \implies x^0 = 1$
ocean sealBOT
illuminator3
lyric linden
I just don't know why you would differentiate the function to come to the conclusion that c isn't right
crisp pine
$x^0 = x^{n-n} = \frac{x^n}{x^n} = 1 \implies x^0 = 1$
Oh cool thats pretty
crisp pine
I just don't know why you would differentiate the function to come to the conclu...
Ok so, looking at the formula for the second derivative
lyric linden
Differentiating pretty much anything isn't that hard but -why- is another question ๐ฅฒ
crisp pine
Can you see why it will always be negative
crisp pine
Differentiating pretty much anything isn't that hard but -why- is another quest...
Hahaha yeah I agree
lyric linden
Can you see why it will always be negative
not at first glance
ocean sealBOT
Jammy
ocean sealBOT
Jammy
crisp pine
$e^x > 0$
ocean sealBOT
Jammy
crisp pine
We can prove that $I_0 > 0$, but are you happy that that is intuitive?
ocean sealBOT
Jammy
lyric linden
The thing I'm probably most confused about is '-t'
crisp pine
In the power of e?
lyric linden
yeh
crisp pine
Ok so are you happy with $e^{-x} = \frac{1}{e^x}$?
ocean sealBOT
Jammy
crisp pine
Oh no worries
So basically all of the terms are positive, but there is a minus sign
so
$-\frac{I_0}{\tau^2}e^-{\frac{t}{\tau}}$
is negative
ocean sealBOT
Jammy
crisp pine
Does that make a little more sense, no worries if not
lyric linden
not really atm my brain is a clusterf rn
lyric linden
it approaches 0 but why is it negative
crisp pine
The whole thing?
lyric linden
yeah
ocean sealBOT
Jammy
crisp pine
are you happy with that?
lyric linden
hmmm
lyric linden
So it's just because of the derivative?
ocean sealBOT
Jammy
crisp pine
$\frac{I_0}{\tau^2}$ is therefore positive, right?
ocean sealBOT
Jammy
lyric linden
yep
crisp pine
And are you happy with the fact that $e^x > 0$
ocean sealBOT
Jammy
lyric linden
Yeah
ocean sealBOT
Jammy
lyric linden
ofc
ocean sealBOT
Jammy
crisp pine
is negative right?
lyric linden
Okay
crisp pine
So
The second derivative
Is the rate of change of the gradient
So a negative one means that the gradient of our graphs is always decreasing
lyric linden
I feel stupid for asking your help
crisp pine
No please dont its fine
lyric linden
lmao thanks for helping xd
crisp pine
Sometimes problems just dont click
lyric linden
Yeah I noticed
crisp pine
Its fine you are welcome, it all makes sense now yeah?
lyric linden
.close
lone heartBOT
lone heartBOT
Available help channel!
burnt galleon
lone heartBOT
burnt galleon
wary stream
Isn't this a site that checks your answer?
burnt galleon
Isn't this a site that checks your answer?
No my teacher disabled that feature
Can you please check my work
wary stream
I'm gonna be honest with you. That's a bunch of words and lots of checking that not many people would like to do
burnt galleon
Oh sorry
wary stream
So the chances of you getting someone to check it, will be slim
burnt galleon
Ok ๐ฅบ
wary stream
Ask to compare answers with your friends
burnt galleon
Ok
lone heartBOT
@burnt galleon Has your question been resolved?
wintry pier
lone heartBOT
wintry pier
theres two parts to this problem, i dont really understand it, parts a and b thank you!
finite flax
theres two parts to this problem, i dont really understand it, parts a and b tha...
Where are you stuck
What have you tried
What is your current thinking
Give us a reason to help you with this many problems
Also, @wintry pier, the first question is very easy. The way to do that one comes right after the definition of what
$\lim_{x\rightarrow a^-} f(x)$
ocean sealBOT
Disorganized
finite flax
means.
You need to read your notes
You need to read your textbook
And if you don't want to do those things, you need to look online and get as far as you can on your own BEFORE you ask us for help
You need to read your definitions for the content you are being introduced to
alpine sable
Can someone explain the effect of how cubing the square root makes the domain change like that?
karmic rapids
โ(-1) is not a real number
Yea, sqrt(-1) is fake news!
lime bobcat
but there are not real square roots of -1
alpine sable
ah
lime bobcat
The same way there are no real even-index roots of negative numbers!
alpine sable
so it creates a negative which we cant have so thats why its negative infinity infinity and nothing in between
lime bobcat
But there are odd-index real cubic roots of negative numbers
last ether
Yea, sqrt(-1) is fake news!
Liberals
lime bobcat
Everything in between!!
last ether
Conservatives
livid raven
lone heartBOT
livid raven
The first step to solving this u substitution would be getting rid of hโ(x)
Right?
And that would be by dividing everything by 2 and getting rid of the x so that we have sqrt(1-x^2)/2 * 2x and then we can remove 2x as itโs hโ(x)
Right?
Im not sure about that step
weary wyvern
wth is h(x)
livid raven
Sorry Iโm not sure whatโs considered universal math language
Itโs all u substitution
Which Iโm trying to learn but itโs a journey ๐
lone heartBOT
@livid raven Has your question been resolved?
ocean crater
Can anyone give me a a lead on how to approach this problem?
lone heartBOT
Can anyone give me a a lead on how to approach this problem?
@ocean crater Has your question been resolved?
lone heartBOT
@ocean crater Has your question been resolved?
tacit arch
Can anyone give me a a lead on how to approach this problem?
Just plug in the recurrence
p0 = 0. p1 = 1-p0. p2=p1. And so on
ocean crater
p0 = 0. p1 = 1-p0. p2=p1. And so on
Ok gotcha thank you!
lone heartBOT
lone heartBOT
Available help channel!
plucky lantern
need help with slope and equation for it
lone heartBOT
need help with slope and equation for it
plucky lantern
i dont understand it and need a quick explanation
median leaf
what is "it"
median leaf
oh like equation for the slope?
plucky lantern
yeah
median leaf
are you talking about $y=mx+b$
plucky lantern
yuh
ocean sealBOT
meek
plucky lantern
i have my final exam and i've missed like 2 months of this semester so i'm rlly behind and i'm just stuck on this
median leaf
okay so first, what part do you not get about it
plucky lantern
i literally don't knoiw anything abt slope
so i don't know how to make the equation
median leaf
okay so well the slope of an equation, is just the rate of change between two points
if you want to find the slope of a linear line, you can use the equation $\frac{y_2 - y_1}{x_2 - x_1}$
ocean sealBOT
meek
plucky lantern
and how would I use that
median leaf
so like let's say you have a point (1,2) and the point (4,8) okay?
can you imagine where they would be on the graph
plucky lantern
no
median leaf
it'd look something like this, alright?
plucky lantern
oh, alright
median leaf
so the slope BETWEEN the lines is when you do this:
you take the y value of one point
let's do 8
and then you take the y value of the other, 2
you get 6
and then you divide that number by the difference of the x values
which is 4 and 1
so you get
$$\frac{8-2}{4-1} = \frac{6}{3} = 2$$
ocean sealBOT
meek
median leaf
and remember, this value after doing the division is m in the equation $y=mx+b$
ocean sealBOT
meek
median leaf
so, it's $y=2x+b$
ocean sealBOT
meek
median leaf
because, everytime you get a value 'x', you multiply it by the slope, 2, and get the proper value 'y'
like going back to the points i gave you
(1,2) and (4,8)
if you take 1 = x, then multiply it by the slope of 2, you get 2 which is the y value
plucky lantern
and remember, this value after doing the division is **m** in the equation $y=mx...
bro i got lost here
median leaf
same thing goes for the 2nd point
$$\frac{y_2 - y_1}{x_2 - x_1} = \frac{8-2}{4-1} = \frac{6}{3} = 2 = m$$
ocean sealBOT
meek
lone heartBOT
@plucky lantern Has your question been resolved?
lone heartBOT
@plucky lantern Has your question been resolved?
ember snow
lone heartBOT
ember snow
Limit using sterlings formula
I know answer is infinity since n! grows faster
But i dont know if my last step is justified
Because anything times infinity is infinity
But we "dont know" if y is defined or not, or non-zero
The steps seem kind of circular to me
Can someone help?
edgy flare
I'm not sure but Instead of just saying y is infinity you could divide by y and get 1= infinity, which is incorrect. So maybe we need to look at your work but it's hard to see from my screen.
weary wyvern
there's no reason to use stirling
ember snow
there's no reason to use stirling
Its required for my hw
weary wyvern
$\lim_{n\to\infty}\frac{n!}{0.00001n}$
ocean sealBOT
giannis_money
weary wyvern
is it this?
ember snow
Yes
ember snow
I'm not sure but Instead of just saying y is infinity you could divide by y and ...
Yeah that is true. I used LH rule
And it says that the limits are equivalent
So I tried setting them equal
edgy flare
Could you post the actual problem you are being asked to answer?
weary wyvern
literally just cancel n from numerator and denominator
ember snow
I'm not sure but Instead of just saying y is infinity you could divide by y and ...
I think this doesnt work because y = inf
weary wyvern
n! grows WAY quicker than n
ember snow
We cannot divided by inf i think
edgy flare
No look:
n! = n * (n-1) * (n-2)
you can cancel the first n and the bottom one to get
(n-1)!/0.00001
which is infinity
ember snow
Yes I know that but we are required to use sterlings formula
weary wyvern
that's a bit dumb
ember snow
Yeah... i could argue that y >= 0 since both numerator and denominator are positive when n -> inf
To argue that y is not equal to zero, we need to use the fact that n(n-1)(n-2)..../n would not tend to zero
But yeah that would be using factorial properties and seems kind of circular
edgy flare
Your series is literally (n-1)! / 0.00001
The denominator stays the same while the numerator grows to infinity.
This limit is 100% infinity
lone heartBOT
@ember snow Has your question been resolved?
tight locust
This limit is 100% infinity
Can you prove it
lone heartBOT
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stable juniper
how do i solve thisproblem
lone heartBOT
how do i solve thisproblem
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Available help channel!
odd umbra
so the power of x-1 is to cancel out x in subsitution?
lone heartBOT
so the power of x-1 is to cancel out x in subsitution?
native granite
Yes
When you evaluate p (and in fact p', p'' and p'''), many terms cancel out thanks to the x-1 writing
Notice that you can still rearrange the terms by powers of x by expanding each (x-1)^k term. Not recommended here of course, but I hope this gives a bit of intuition as to "why we have the right to do that". (The intuition being, "it's basically the same")
odd umbra
Notice that you can still rearrange the terms by powers of x by expanding each (...
thank u
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@odd umbra Has your question been resolved?
raven rover
Small square root question:
Supposed we say the following:
x = โ9
Whatโs wrong with the argument that x = +-3: x = -3 because -3 is a square root of 9?
raven rover
Is there a small difference between saying that x is a square root of b and that x = โb?
languid bolt
if you write โx , the result will be postitive (unless x < 0)
โ = positive square root / principle square root (if im not wrong)
alpine sable
square root function always returns a positive value it should be +x=3 and -x=3
languid bolt
Basically, when we calculate โx, we try to find sides of a square whose area is x , hence it can not be negative.
alpine sable
For a nonnegative real number a, sqrt(a) is definitionally the unique nonnegative real number y for which y^2 = a
This was not the best choice of variable names, gonna edit that
alpine sable
Can anyone help me prove this?
lone heartBOT
Can anyone help me prove this?
tawny schooner
Stop trolling
Expecting a proof of fermat's last theorem here is maybe being a lil too optimistic
tacit arch
.close
alpine sable
lone heartBOT
alpine sable
Can anyone help me in this
<@&286206848099549185>
Please anyone
I have a final in 15 minutes
<@&286206848099549185>
paper ridge
Looks correct to me, did you have some side work to elaborate how you got that val
lone heartBOT
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alpine sable
lone heartBOT
alpine sable
Anyone can help me with c part
vale wigeon
what did you get for part a?
alpine sable
Hmmm nope
alpine sable
right
I get confuse bcz they said that use a b for to express the general term4,0,4,0...
@vale wigeon ๐
alpine sable
why not multiply the sequence in (a) by 2
So what will be the answer of third part??
vale wigeon
well one of them will be 2(1+(-1)^n) as i suggested...
alpine sable
And for part b??
vale wigeon
what do you mean? you already said the answer for part b.
alpine sable
No no they have asked for to express it in 2 different way
vale wigeon
well *one* of them will be 2(1+(-1)^n) as i suggested...
for the other i suggest you do some more thinking to see how the sequence cos(n*pi) (which begins 1, -1, 1, -1, ...) can be transformed into 4, 0, 4, 0, ...
vale wigeon
write out the sequence 1+cos(npi).
alpine sable
write out the sequence 1+cos(npi).
Then multiply it with 2??
I mean second one will be 2(1+cos(npi))??
vale wigeon
yes congratulations
vale wigeon
question is malformed
there exist many such correspondences
again, question is malformed
there are many such one to one correspondences
you should not be expected to magically come up with the same bijection as what the authors had in mind
vale crag
you should not be expected to magically come up with the same bijection as what ...
that's probably why they have 99 tries for the question
so that they can merge their minds with the authors'
vale wigeon
so you need to 100% this homework assignment under threat of death?
lament root
lone heartBOT
alpine sable
Then do it. Writing tan as sin/cos and cot as cos/sin is helpful too
split dust
what is the normal curve area to the right of ๐ฅ = 17?
lone heartBOT
what is the normal curve area to the right of ๐ฅ = 17?
pulsar aspen
what is the normal curve area to the right of ๐ฅ = 17?
Can you repost the context?
split dust
Given a normal distribution with ๐ = 30 and ๐ = 6, find:
ocean sealBOT
alpine sable
Given a normal distribution with ๐ = 30 and ๐ = 6, find:
ah, then you need to normalise your normal distribution
split dust
what is the normal curve area to the right of ๐ฅ = 17?
is this the correct answer 0.9850? 
alpine sable
you need to first find the z value
my answer before was assuming mean and sd was 1, as you didn't mention any parameters
the z value is given by $\frac{x-\mu}{\sigma}$
ocean sealBOT
Toby
alpine sable
then we can look this number up on a table
brittle summit
hello, can you help me to get the formula for how to calculate odds? for example, I have the odds winner 2.51 for a draw 3.11 and for the second team winner 2.86 how do calculate 1- st half odds 1 X 2 if someone helps it will be great thank you in advance
brittle summit
What does 1- st half odds 1 X 2 mean?
I have main odds like I said above and how calculated first-period odds if you know betting you can understand what i mean
noble sinew
first-period odds?
brittle summit
can you post the original problem
original problem is I am seeking mathematical formula for calculate odds
noble sinew
They are made by the betting companies - there is no formula
brittle summit
first-period odds?
first half
brittle summit
They are made by the betting companies - there is no formula
but they use some mathematical formula and i am seeking it
noble sinew
No they donโt
Well they probably have some set in stone thing but it changes all the time and is obv not public
brittle summit
I truly believe that there is some formula because I find some methods how to calculate the odds it depends on many factors and when i have these factors after some mathematical formula can calculate the odds
lone heartBOT
@brittle summit Has your question been resolved?
lone heartBOT
@brittle summit Has your question been resolved?
lone heartBOT
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Available help channel!
strange fractal
hi this is kind of maths i guess
lone heartBOT
hi this is kind of maths i guess
true pulsar
Can you find the average number per quadrat
strange fractal
5.2
true pulsar
And how many quadrats is in 50 sq meters
true pulsar
What
true pulsar
Nope
lone heartBOT
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lofty oasis
I need help with sum of them roots
lone heartBOT
I need help with sum of them roots
lofty oasis
I've done all i know as to simplify them, however i can't really tell how to deal with the big root on the left
Any tips?
vale wigeon
$5-2\sqrt{2}\sqrt{3} = 2 + 3 - 2\sqrt{2}\sqrt{3}$
ocean sealBOT
Ann
lofty oasis
$5-2\sqrt{2}\sqrt{3} = 2 + 3 - 2\sqrt{2}\sqrt{3}$
I have to train my eye as to spot these chances but i see it now. Thanks!
.close
lone heartBOT
lone heartBOT
Available help channel!
halcyon escarp
need help with no. 4
split heath
Hey, I was just wondering if I did these questions right and properly with correct solutions.
split heath
Iโll appreciate it so much!
lone heartBOT
@split heath Has your question been resolved?
split heath
<@&286206848099549185>
split heath
Hello ๐ญ
lone heartBOT
@split heath Has your question been resolved?
royal wren
in general how could i simplify this
lone heartBOT
in general how could i simplify this
royal wren
just that n greater than 1
we cant bring that n inside the floor function and work with it in there?
alpine sable
no, unless n is an integer
stiff tree
Can you guys tell if this is correct
lone heartBOT
Can you guys tell if this is correct
alpine sable
,rotate
ocean sealBOT
alpine sable
looks fine to me
stiff tree
Alright
alpine sable
just making sure that there's no power on the bottom, n right?
stiff tree
Nope
alpine sable
ok, its correct then
stiff tree
Someone said to me that if the power is lesser, it means it goes down of the fraction, is it true?
alpine sable
yeah, if it's negative it goes on the bottom and becomes positive
alpine sable
yes
stiff tree
How do I do this?
alpine sable
yeah, if it's negative it goes on the bottom and becomes positive
the division makes the square root go to the bottom. Then the square root becomes a power of half according to the fractional exponent rule
stiff tree
What?
alpine sable
$\sqrt{xy^2}=(xy^2)^{\frac{1}{2}}$
ocean sealBOT
Toby
stiff tree
Woah, I see
What do I do next?
While I was waiting, I did other questions, I did this one and I checked the answer and it
aโต
-โ
bโน
Why negative?
What did I do wrong
stiff tree
A and B are still negative form?
stiff tree
But why it still stayed negative
proud basin
its supposed to stay negative