parallelogram right? Think about what angle JCE could be
#help-23
mellow cypress
frail cobalt
Sorry i just dont get it, do i have to look for that to ACJ as well?
frail cobalt
cje is then x+10
frail cobalt
why do I have x?
mellow cypress
why do I have x?
you have written in the answer space that x = 70
safe radishBOT
safe radishBOT
Available help channel!
granite badge
Help 😭
cosmic grove
Help 😭
factor by x² in the sqrt
and factor by x both on the numerator and denominator
granite badge
Like this?
pure agate
,rotate ccw
flat frigateBOT
granite badge
I think I did something wrong
flat frigateBOT
Herels
granite badge
Wait so am I pulling out a x^2? Or dividing within the root?
Sorry I don’t understand what to do 😭
cosmic grove
Wait so am I pulling out a x^2? Or dividing within the root?
lemme write
$\frac{x - \sqrt{x²} \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})} = \frac{x - \lvert x \rvert \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})} $
$\frac{x - \sqrt{x²} \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})} = \frac{x - \lvert x \rvert \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})}$
flat frigateBOT
Herels
cosmic grove
and since x approaches - infinity, it's mean that x is negative, so |x| = -x
$$\frac{x - \sqrt{x²} \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})} = \frac{x - \lvert x \rvert \sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})} = \frac{x + x\sqrt{1 - \frac{1}{x} + \frac{7}{x²}}}{x(3 + \frac{7}{x})}$$
flat frigateBOT
Herels
cosmic grove
Thank you!
granite badge
.close
safe radishBOT
safe radishBOT
Available help channel!
worldly wedge
hey, i have a question. This was on my last test. if figure nr 1 had 6 dots, figure nr 2 had 12 dots, figure nr 3 had 20 dots and figure nr 4 had 30 dotd, whats the form for figure nr n?
safe radishBOT
hey, i have a question. This was on my last test. if figure nr 1 had 6 dots, fig...
solid shell
What were your thoughts on the problem when you saw it on the test?
worldly wedge
well i did calculated a form
but the teacher gave me wrong
but it did match up with the folloeing numbers
and i just realised that this should be in #math-discussion right?
solid shell
It's fine here
worldly wedge
my final thoughts was to do st like this: (n+1)^2 + (n+1)
since the dots were in a rectangle
junior raven
that seems right
junior raven
its the same
worldly wedge
yea its what i thought
thx for confirming, im gonna try to argue with her tomorrow
.close
safe radishBOT
safe radishBOT
Available help channel!
versed dawn
I was doing AM-GM inequality questions and got to this one. I thought you could just use the 3 terms it gives you and say their sum divided by 3 is equal to the cube root of their products because the x's in the radicand would cancel and you'd be left with 512. This led to the sum of the 3 being 3 times the cuberoot of 512 which is 24. The solution breaks everything up though and I have no clue why they did that or what purpose it serves.
safe radishBOT
I was doing AM-GM inequality questions and got to this one. I thought you could ...
frank horizon
I was doing AM-GM inequality questions and got to this one. I thought you could ...
the issue is that for equality to be reached, you need the terms to be equal
and x^2=8x=64/x^3 doesn't have solutions
versed dawn
So to use the AM-GM inequality, with the equality part, the terms have to share a solution/all be equal at an x value?
versed dawn
okay that makes sense actually
thank you
So solving those type of problems kind of starts with looking for a way to have terms that share a solution?
like "how can I make x^2, 8x, and 64/x^2 equal at some x value"?
frank horizon
yeah, that's a necessary condition
rustic fern
safe radishBOT
rustic fern
domain refers to x values
so if I swapped those out it would be right?
is this correct?
bronze gust
You're using the wrong inequality sign btw
rustic fern
You're using the wrong inequality sign btw
there's no option to use the other one
bronze gust
Then just switch the numbers
rustic fern
Then just switch the numbers
switch what numbers
bronze gust
2 and -1
And 3 and -3
Because -1>y>2 suggests that y is greater than 2 and less than -1
Which obviously is not what you intended
bronze gust
Should be
bronze gust
Well the arrow I think suggests the function continues
rustic fern
Well the arrow I think suggests the function continues
so what should I type instead
neat kiln
Why is domain y
bronze gust
Yeps
neat kiln
.close
bronze gust
.
rustic fern
actually wait wait
what's the difference between open dot
and closed dot
what do I type instead
bronze gust
Uh usually this means the point is also included in the function
Open dot means it's not
But didn't u say you only had one inequality sign
rustic fern
But didn't u say you only had one inequality sign
I have < and >
but not the one with the line under
bronze gust
Ya sure
rustic fern
wdym "sure"
bronze gust
Try typing < then =
bronze gust
Well that's for you to work out
rustic fern
Well that's for you to work out
what
theres a reason im in the math server
idk wtf im doing
neat kiln
Do you go to school 💀
rustic fern
Do you go to school 💀
ya obviously
neat kiln
Like physically or is it online
rustic fern
Like physically or is it online
physically
bronze gust
Might wanna reconsider the answer for this since we've discovered that you can type less than or equal and more than or equal
rustic fern
Might wanna reconsider the answer for this since we've discovered that you can t...
well im gonna circle back to what I asked, do I put the underline "<" for closed dot questions?
bronze gust
well im gonna circle back to what I asked, do I put the underline "<" for closed...
Uh yes but do you know why
rustic fern
Uh yes but do you know why
no
but thats good to know for this shitty ass final tmrw so thanks denzio
lemme work this out
hold up
bronze gust
Because the closed dot means that endpoint is also included in the function
So by putting the "less than sign with an underline" we show the point is also part of the domain
rustic fern
rustic fern
Because the closed dot means that endpoint is also included in the function
oh oookkkkkkk
rustic fern
is this right
bronze gust
Looks alright
I think you got this in the bag
You can do the rest of the questions yourself I figure
rustic fern
probably not but ill see
lemme check this one
k correct good
I think im done for now
thanks
.close
safe radishBOT
safe radishBOT
Available help channel!
drifting arch
What could I have done wrong here
safe radishBOT
What could I have done wrong here
drifting arch
if it’s -1 how could I get to 4
drifting arch
the - in the parentheses?
last wren
this is what you should have done
also, you're not taking sin(pi/4) in the denominator, it's just π/4
drifting arch
And distribute the - so it’s going to become -3pi/4 + pi/2 -1
?
Ohh
I got it thank you
Wait but I’m getting this
how do I get rid of the denominator
last wren
this was the closest you got
when you distribute the 4, it doesn't go inside the square root
drifting arch
Ahhh
drifting arch
when you distribute the 4, it doesn't go inside the square root
What about here
safe radishBOT
@drifting arch Has your question been resolved?
rustic fern
safe radishBOT
rustic fern
i've been on this for 20 minutes
mellow cypress
What have you tried
rustic fern
What have you tried
Nothing, because I literally don't know how to do this
I tried looking at the numbers
they dont make sense
ml/c l
like what
mellow cypress
where else have you seen the phrase 'rate of change'
rustic fern
like in a bunch of other math questions
I know what that means
but I cant figure this one out
in particular
it's basically like what number does something change at
mellow cypress
and what do you usually do to get that number
rustic fern
and what do you usually do to get that number
look at the slope and see how fast it goes
mellow cypress
and how fast would that be in this case
rustic fern
and how fast would that be in this case
no idea
safe radishBOT
safe radishBOT
Available help channel!
thin stream
how do i factor f(x)=8x^3+27
safe radishBOT
how do i factor f(x)=8x^3+27
thin stream
ive been trying to figure it out for like an hour now and i cant even get the first step
viscid gyro
a^3 + b^3 = (a+b)(a^2-ab+b^2)
thin stream
what
solid shell
It's the sum of cubes formula
f(x) is a sum of two cubes, i.e. each term is something cubed
That's the formula for it, though the intuition is that you want to find two factors where the x^2 and x terms will cancel to leave you with just the x^3 and constant
solid shell
That's certainly a way to do it, though if your instructor had a different method they might want you to practice that
Depends on what you've been learning
thin stream
im not even gonna lie i was playing kirby plant robobot on my 3ds for that entire unit
no idea what he taught
whoops
solid shell
Lol
thin stream
yeah
solid shell
That's the reward for playing kirby plant robobot
solid shell
https://www.youtube.com/watch?v=hixEq9KKcFE
https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-advanced-polynomial-factorization-methods/v/factoring-sum-of-cubes
Here's some vids
next dirge
In matrices while converting the matrix to row echelon form if we get correct rank . Can we get marks for atleast finding rank?
safe radishBOT
In matrices while converting the matrix to row echelon form if we get correct ra...
@next dirge Has your question been resolved?
upper arrow
In matrices while converting the matrix to row echelon form if we get correct ra...
no obviously not
next dirge
no obviously not
Atleast 1 ?. I did two correct steps for conversion. Question was for 4 marks
tiny tusk
safe radishBOT
https://cdn.discordapp.com/attachments/1240836816752607263/1319174173515448320/i...
tiny tusk
we are doing mirror stuff in math so
idk if i should put it here
cuz it physicsy (but which is the correct place for the arrow to go to
idk which imaginary lines u are suppost to draw
median vigil
you draw the virtual rays from the reflected rays
tiny tusk
you draw the virtual rays from the reflected rays
so the bottom cirlce would be where the img would be
median vigil
yes
median vigil
it's a virtual image, yes, and virtual images are upright (same orientation)
tiny tusk
it's a virtual image, yes, and virtual images are upright (same orientation)
ok thanks
safe radishBOT
@tiny tusk Has your question been resolved?
buoyant plume
hello, stuck on this problem (all parts really), pls do help if possible
i tried a few cases with small primes and n, but am not able to figure out any pattern for b_n
buoyant plume
eh
wind abyss
of c chat gpt is wrong again
buoyant plume
it might be, but 3 seems more likely to me idk
wind abyss
i hate sigfigs
buoyant plume
fr
buoyant plume
hello, stuck on this problem (all parts really), pls do help if possible
i trie...
<@&286206848099549185>
covert yoke
@buoyant plume for the first problem, this is actually just a combinatorics problem in disguise. A polynomial of n degrees has n roots. What is the probability that if you choose n values at random from a list of p numbers that you select at least one of them twice?
Well, actually this is not true, because the polynomial could be irreducible.
safe radishBOT
@buoyant plume Has your question been resolved?
buoyant plume
<@938381509088403507> for the first problem, this is actually just a combinatori...
Yeah I did realize it was a combi problem, but had issues because the other roots could also not belong to the field, the polymomials can be irreducible as you said etc
And also even with the selection as you said, the coefficients of the full polynomial could still just not belong to the field given
covert yoke
And also even with the selection as you said, the coefficients of the full polyn...
We are adjoining x to the field, the field is where the coefficients are coming from. So this part you don't need to worry about.
So maybe there is some sort of way to determine how many irreducible polynomials are of a given degree n in a given finite field Fp
buoyant plume
No, i don't think so right? Because say p=2, then (x-1)^2 = x^2 + 2x + 1 would have 2 as a coefficient which doesn't exist in the field right?
covert yoke
In F2, (x+1)^2 = x^2 + 1
(because 2x = 0x)
So we have two ways of writing a polynomial of degree n
[
\sum_{i=0}^n a_i x^i = a_n \prod_{i=1}^n (x - r_i)
]
Where a_n ≠ 0
flat frigateBOT
OmnipotentEntity
covert yoke
And because we have a field and $a_n \ne 0$, we can rewrite as
[
x^n + \sum_{i=0}^{n-1} a^{*}i x^i = \prod{i=1}^n (x - r_i)
]
flat frigateBOT
OmnipotentEntity
covert yoke
So we have p^(n-1) choices on the left (order matters) and the right order doesn't matter
So the left will give us all of the possibilities for polynomials, and the right only the reducible ones.
Oh god, this gets harder, because polynomials can be only partially irreducible, and can still contain a double root.
You'll probably need to try to make a recursive relationship between the number of multiple root polynomials of degree n and degree n+1 or something.
@buoyant plume I hope the sketches above help a little bit in developing a solution.
Seems non-trivial. Maybe there's a better way
It's slightly after 2AM here though, so I ought to sleep
covert yoke
[
x^n + \sum_{i=0}^{n-1} a^{*}i x^i = \prod{\lambda \vdash n} (x^{\lambda_i} + \sum_{j=0}^{\lambda_i - 1} b_{\lambda_i,j} x^j)
]
flat frigateBOT
OmnipotentEntity
covert yoke
Where $\lambda \vdash n$ indicates that $\lambda$ is an integer partition of $n$.
flat frigateBOT
OmnipotentEntity
covert yoke
So we need an integer partition that contains at least two 1s, which we can get from the integer partition of n-2.
And then we need the number of irreducible polynomials of degree at most n-2 to ensure we do not double count.
This is a fascinatingly gross problem. I must admit to being somewhat hooked.
Oh god
There is an easy solution
Of course there is an easy solution.
@buoyant plume gcd(Q, Q')
safe radishBOT
@buoyant plume Has your question been resolved?
buoyant plume
<@938381509088403507> gcd(Q, Q')
Sorry I was a bit busy
Will just go through this
desert pasture
safe radishBOT
desert pasture
I started with $\del{f(x,y)} =(2x-2,2y-4)$
flat frigateBOT
ƒ( wai ina teacup)= I don't know
vagrant ice
great, now you must have $2x - 2 = 2y - 4$
flat frigateBOT
south
desert pasture
yes, I;m trying to figure out why that is true
vagrant ice
reasoning being you want the gradient to be a scalar multiple of i + j
vagrant ice
so if you had i + 2j you would need 2(2x - 2) = 2y - 4
and so on
hey didn't know you moved onto MVC
but you should take a rest
don't spend all your holidays just on maths
desert pasture
I have, I'm working less than I did before
desert pasture
don't spend all your holidays just on maths
Yeah, I know, whenever I'm stressed, maths distracts me, hence I do maths
vagrant ice
lol
desert pasture
even now, i have some triggers
vagrant ice
good fit for maths major?
safe radishBOT
safe radishBOT
Available help channel!
lunar forge
$lim_{x \to \infty} \sqrt{4x^2+4x+1} - \sqrt{4x^2-x} = lim_{x \to \infty} \frac{4x^2+4x+1-(4x^2-x)}{\sqrt{4x^2+4x+1} + \sqrt{4x^2-x}}=lim_{x \to \infty} \frac{5x+1}{\sqrt{4x^2+4x+1}+\sqrt{4x^2-x}}$
safe radishBOT
$lim_{x \to \infty} \sqrt{4x^2+4x+1} - \sqrt{4x^2-x} = lim_{x \to \infty} \frac{...
flat frigateBOT
prograce
lunar forge
Now what ?
vagrant ice
all good so far, so now you have $\sqrt{4x^2 + 4x + 1} \approx \sqrt{4x^2 - x} \approx 2x$
flat frigateBOT
south
vagrant ice
(both would be $-2x$ if $x \to -\infty$ btw)
flat frigateBOT
south
lunar forge
Final answer is 5/4 ?
lunar forge
(both would be $-2x$ if $x \to -\infty$ btw)
It's positive infjnity
vagrant ice
It's positive infjnity
yes just making sure
vagrant ice
Final answer is 5/4 ?
yes
worth noting, you can approximate the square roots to first-order (ax + b), because the numerator is also first-order
you just need the top and bottom to 'match'
lunar forge
Okay yes
lean otter
all good so far, so now you have $\sqrt{4x^2 + 4x + 1} \approx \sqrt{4x^2 - x} \...
Its a square of sum (2x+1)^2
lunar forge
This is kind of repetitive but I'm stuck again $\lim_{x \to 0} \frac{\sqrt{4+x}-\sqrt{4-x}}{x}= \lim_{x \to 0} \frac{2x}{x(\sqrt{4+x} + \sqrt{4-x})} = \frac{0}{0}$ ?
flat frigateBOT
prograce
vagrant ice
no, cacnel out the x on top and bottom first
flat frigateBOT
prograce
flat frigateBOT
Result:
0.50000000004102
.....
safe radishBOT
safe radishBOT
Available help channel!
tardy violet
for part c, the answer says it only has 1 x-int. Why is it not 3?
queen ingot
were you able to factor it?
lean otter
for part c, the answer says it only has 1 x-int. Why is it not 3?
you need to find the zeroes of the polynomial
a polynomial has x intecepts at its zeroes
queen ingot
a cubic doesn't necessarily have 3 zeros
it is guaranteed to have at least 1 though
lean otter
it should be
tardy violet
huh i cant find a factor
tardy violet
hm maybe i typed it into the calculator wrong
queen ingot
i don't think it's a rational zero
tardy violet
Wait am i doing this wrong? Do I plug the values into the equation straightaway or do I have to factorise it into 1/3 (x^3 -9x^2...) first
queen ingot
check the derivative and you'll see that y is an increasing function
tardy violet
but he said answer is three
huh i said answer is 1
queen ingot
check the derivative and you'll see that y is an increasing function
if you do this, you don't have to factor it
tardy violet
so is the root possible to find
tardy violet
if you do this, you don't have to factor it
oh
wait why does that mean it only has one 0
queen ingot
it's increasing, so once it crosses the x-axis, it can't go back down
tardy violet
it's increasing, so once it crosses the x-axis, it can't go back down
ohhhh ok i see
lean otter
oh wait
safe radishBOT
tardy violet
.reopen
safe radishBOT
✅
tardy violet
wait i just realised smth how do you know y' is increasing? Is it cus x^2 - 6x + 11 is positive?
nvm i get it
.close
safe radishBOT
safe radishBOT
Available help channel!
dense sphinx
Here's the situation.
safe radishBOT
Here's the situation.
dense sphinx
Because I didn't go to classes, I'm forced to take the hard mode version of calculus test.
I have failed it already, and teacher thinks I should not try again; that should I go to classes next year and pass it.
now, I do want to do the hard mode version and pass it; if I don't pass it that would be I'm dumb enough to not be able to do something like that.
What are your tips for the upcoming test?
dense sphinx
what does the test look like
I actually remember some of the question of the test.
1
e^3x/(x-1)
Find the max, mins, concavity etc
narrow ridge
do u know what to do here
dense sphinx
2 find the value of x
Comb (x 5) = 3 (x-1 3)
3 given the vector
(1, √3) (K,-√3)
Find K so: they're perpendicular; parallel; area of parallelograms is equal to (don't remember name)
4 find the area below the function: x*cos(2x) or something like that.
between Y=0 and X=1 and x=2
narrow ridge
let's start with the first one
dense sphinx
Alright, alright.
narrow ridge
ok what do you get
dense sphinx
Well, I get 3e^3x*(x-1)-e^3x/(x-1)
narrow ridge
First derivative
$\frac{e^{3x}(3x-4)}{(x-1)^2}$
flat frigateBOT
wasu
dense sphinx
Exactly!
dense sphinx
Now, the second derivative is hard.
dense sphinx
now what info does first derivative give
We gotta find the values where such derivative becomes 0
and where the derivative doesn't exist.
narrow ridge
obv derivative = 0 at 4/3
dense sphinx
Yeah, I did that part nicely.
narrow ridge
okay
dense sphinx
My problem was: the second derivative.
narrow ridge
it's not difficult? just messy
narrow ridge
$\frac{e^{3x}(9x^2 - 24x + 17)}{(x-1)^3}$
flat frigateBOT
wasu
dense sphinx
Yeah, that's what I got after a few minutes.
narrow ridge
nice
dense sphinx
Now, I gotta find the values where x=0
the thing is
that's a cuadratic equation
and they don't allow us to use calculator
narrow ridge
yes
narrow ridge
how many problems are there
narrow ridge
So, how am I supposed to find the answer?
so we have to solve a quadratic
we can test to see if it even has real roots
,calc (2424)-49*17
flat frigateBOT
Result:
-36
wdym?
narrow ridge
To get determinant
or
Oops
Discriminant
The quadratic has no real roots
so what does that say about our function
you have first and second derivative, apply the tests
narrow ridge
between Y=0 and X=1 and x=2
this is just an integral
dense sphinx
you have first and second derivative, apply the tests
We gotta evaluate in values lower and higher than 4/3
dense sphinx
you have first and second derivative, apply the tests
I have a question.
Do I have to evaluate below and above 1?
safe radishBOT
@dense sphinx Has your question been resolved?
safe radishBOT
@dense sphinx Has your question been resolved?
safe radishBOT
@dense sphinx Has your question been resolved?
polar cipher
@dense sphinx still need help?
next dirge
What is definition of union of sets?
dense sphinx
<@357244707367026689> still need help?
Yes.
dense sphinx
<@357244707367026689> still need help?
Do you think you can help me?
There's no inflection point.
So, how can I determine the concavity intervals?
safe radishBOT
@dense sphinx Has your question been resolved?
safe radishBOT
@dense sphinx Has your question been resolved?
thick escarp
hi
gleaming hawk
@dense sphinx can you resend the question
dense sphinx
Wdym "resend?"
gleaming hawk
What is your question
dense sphinx
<@357244707367026689> can you resend the question
In any case:
Find the inflection point, max and mins, concavity intervals of the function
e^3x/(x-1)
gleaming hawk
!status
safe radishBOT
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
I have problems with the second derivative.
It's too big and I'm unable to properly factorize.
dense sphinx
**wasu**
This is the first derivative.
second derivative is easy to get, hard to factorize.
queen parcel
You can check your derivatives on derivative calculator dot com, or use the wolfram bot
gleaming hawk
For second derivative
After factorising
You get -
$\frac{e^{3x}(9x^2-24x+17)}{(x-1)^3}$
flat frigateBOT
lex.in.a.teacup
gleaming hawk
@dense sphinx
dense sphinx
<@357244707367026689>
Yeah but how do we factorize?
And how am I supposed to find the zero values of that in an one-hour test?
gleaming hawk
Their aren't any
dense sphinx
without a calculator, yo boot.
dense sphinx
How can we know that.
gleaming hawk
e^3x is always positive is common sense?
dense sphinx
Keep cooking...
gleaming hawk
Since D<0
And a >0
It's an upward facing parabola
That doesn't ever cut the x axis
So no "real" roots
dense sphinx
What's a discriminant?
gleaming hawk
$D = b^2-4ac$
flat frigateBOT
lex.in.a.teacup
dense sphinx
the problem being
gleaming hawk
Still
gleaming hawk
The calculations aren't that rigorous
dense sphinx
Aren't they?
gleaming hawk
Everyone kinda remember 24^2
dense sphinx
I don't.
gleaming hawk
How long can multiplication really take
dense sphinx
For a low intelligence folk like me, a long time.
In any case, there's no inflection point
what about the concavity intervals, then?
gleaming hawk
Multiplication speed isn't related linked to intelligence but much rather practice
gleaming hawk
In any case, there's no inflection point
Who said that
dense sphinx
I mean, yeah?
gleaming hawk
See this is where it becomes ambiguous
dense sphinx
wdym
gleaming hawk
In some exams what ends up happening is some points despite being not part of domain need to be included as part of the answer
Function doesn't exist for x=1
So we use limiting values
For lim h tends 0 x = 1 + h
Function facing upwards
For lim h tends 0 x = 1 - h
Function facing downwards
So while writing the answer
We using limiting values
And write 1 as the inflection point
Idk what your teacher want you to do here tbh
gleaming hawk
Ur welcome
dense sphinx
@gleaming hawk do you have exercises like this?
where I gotta differentiate and factor?
gleaming hawk
You can find many on khan academy
Or just randomly
I don't have any on hand
I have some related to like Calculus but idk if they will help with ur situation
dense sphinx
If you do, I would gladly take them.
dense sphinx
You can find many on khan academy
Are they for free.
dense sphinx
Yup
Yeah, I guess?
When I did the test
I do not remember the exercise exactly
but basically, it was the integral of x*cos(2x) if I'm not mistaken
and I think it was between x=1 and x=2
and my teacher said something like "The sin function cross the X line, multiple times"
so, I do not know what they mean with that.
gleaming hawk
By parts should do the trick
dense sphinx
By parts should do the trick
The mistake was while calculating área, it seems.
gleaming hawk
Integral and area aren't exactly the same thing
In area all of the region is taken as positive
dense sphinx
Like I said, I think my teacher said something regarding the sin function crossing Y=0 multiple times
gleaming hawk
In integral it's not necessary
dense sphinx
so, what should be done in such case?
dense sphinx
Yeah.
dense sphinx
Yes.
gleaming hawk
,w sinx
flat frigateBOT
dense sphinx
Yeah?
gleaming hawk
Look at the region from 0 to pi
It's exactly the same as that from pi to 2pi
Just on the other side
dense sphinx
Yeah!
gleaming hawk
If I was asked the integral of sinx from 0 to 2pi I would say 0
dense sphinx
Keep cooking...
gleaming hawk
But for area
I gotta take that negative region as positive
So I will now integrate |sinx| to area
dense sphinx
SHIT!
gleaming hawk
So it will split into region
First I gotta integrate from 0 to pi
Then from pi to 2pi
Make both values positve
And add
To get area
dense sphinx
...
gleaming hawk
Please focus on the keywords here
dense sphinx
Alright, I guess.
gleaming hawk
That's it
dense sphinx
I have one question.
gleaming hawk
Go on
flat frigateBOT
gleaming hawk
Yup
dense sphinx
Exactly, exactly.
gleaming hawk
Do think about positive and negative regions
dense sphinx
Alright, how do I do that.
My teacher said something about changing from positive to negative
dense sphinx
Yeah?
dense sphinx
How do you know that?
gleaming hawk
Put values
dense sphinx
Put values?
dense sphinx
I mean, yeah
gleaming hawk
f(1.5) = 0
gleaming hawk
Cos (3pi/2) = 0
Anything * 0 = 0
...
Anyways
So the region from x=1 to x =1.5 is negative
And from 1.5 to 2 is positve
So calculate from 1 to 1.5
Take mod
And then from 1.5 to 2
No need to take mod as it is already positive
Add these 2 value
Get answer
Make sense @dense sphinx?
dense sphinx
Cos (3pi/2) = 0
I mean, how do you know 3 * pi/2 is zero?
flat frigateBOT
lex.in.a.teacup
gleaming hawk
Where n is any integer
dense sphinx
@gleaming hawk just one more thing, please.
Do we have to find the roots of the original function, not the integral we got, right?
dense sphinx
In this case, we gotta find the values that x*cos(πx)
gleaming hawk
Ye
gleaming hawk
Cool
dense sphinx
except for the trigonometry part
Look.
My teacher gave me a cos sin and tan table
From 0 to π/2
however, he said I should be able to get the following values using that table
that I should be able to get cos(120) knowing the values for cos and sin from 0 to 90
but, how?
dense sphinx
2pi being 360
gleaming hawk
Yup
gleaming hawk
What don't you get
gleaming hawk
It's not about intelligence
dense sphinx
It is though.
gleaming hawk
You think, me knowing all this makes me intelligent
Lol
No it doesn't
Your basics are just not clear
For whatever reason
That's why you are facing this much trouble
Find some suitable video online
Take an hour or 2
Clear all this up
It's not that hard
Trust me
Got it @dense sphinx?
dense sphinx
Anything else?
Yeah.
dense sphinx
<@357244707367026689>
Got distracted watching a beautiful lady outside my window...
Ah, yes?
Hmm, yeah.
How do we solve ∞-∞ indeterminate if we don't have fractions to use l'hopital
gleaming hawk
Got distracted watching a beautiful lady outside my window...
💀
dense sphinx
Let's say we have, I don't know
I mean, who the hell is so fucking noisy at damn 1AM
That's a joke, I actually forgot I said something here xD
dense sphinx
<@357244707367026689>
But yeah, how do we solve ∞-∞ indetermination if we don't have fractions to work with?
dense sphinx
Let's say we have lim x-> ∞ X-X
gleaming hawk
X-X =0
dense sphinx
??????
gleaming hawk
.-.
dense sphinx
Ah, fuck.
Yes, you're right.
Hmmm, let's see.
What about lim x->∞ X + Ln (0)
What about that?
gleaming hawk
Ln(0) doesn't exist
I think you mean
Lim x tends to infinty (x + ln(1/x))
Which is just infinity btw
@dense sphinx
dense sphinx
<@357244707367026689>
What???
Ln(0) doesn't exist?
Ah, yeah.
Lim x tends to infinity (Ln(x) - x)
how do we solve that @gleaming hawk
gleaming hawk
Thing is lnx < x
Always
So ln (infinity) < infinity
And the difference between them will be
Infinity too
In infinity- infinty to get finite answer
You need comparable infinities
dense sphinx
Thing is lnx < x
Okay okay
then what about this this
what if we get ∞-∞
but we don't have fractions to work with
essentially being (something)/1
gleaming hawk
@dense sphinx as I said
Varies from problem to problem
Rationalization is one of the popular method
But only tends to work with algebraic terms
gleaming hawk
@dense sphinx
@dense sphinx
Since you haven't responded in an hour
I am closing this channel
.close
safe radishBOT
safe radishBOT
Available help channel!
lean otter
Can anyone please explain me the approach to solve this Q
safe radishBOT
Can anyone please explain me the approach to solve this Q
lean otter
The answer is 0.471
desert belfry
Richardson is just a distraction, you don't care about that team at all.
So you have 2 teams, 18 people.
P(together) = 1 - P(apart)
P(apart) = the probability you select 8 people out of 17 and none of them are Jefferson.
$\frac{16}{17}\frac{15}{16}...\frac{9}{10} = \frac{9}{17}$
flat frigateBOT
LooseEthics
desert belfry
@lean otter
lean otter
I didn't understand why 8 people out of 17? I understand outof 18 , we subtract one position for jefferson so it's 17 but why 8?
safe radishBOT
@lean otter Has your question been resolved?
thin narwhal
I didn't understand why 8 people out of 17? I understand outof 18 , we subtract...
maybe because youve already set alfred in some other heat
so you can disregard him(?)
lean otter
but if we did that shouldn't it have been 8 out of 16?
@desert belfry Could you please explain this part why is it 8 out of 17
waxen bay
They are both because you fix Alfred. There's 9 per team, 8 left to choose after fixing Alfred and 17 to choose from
I'd imagine
safe radishBOT
@lean otter Has your question been resolved?
wicked widget
Hi, I have had this issue for days... I cant find a mathematical way to calculate the difference in angles between two lines in 3d space where they intersect at (0,0,0). I am a HS Junior, who knows 2d trig, not 3d.
safe radishBOT
Hi, I have had this issue for days... I cant find a mathematical way to calculat...
icy lance
angle from where to where?
angle between the two vectors? or between some axis to the vectors?
wicked widget
between the two vectors.
icy lance
do you know of the dot product?
wicked widget
nope
icy lance
if i have vector A=(a1,a2,a3,...,an) and another vector B=(b1,b2,b3,...,bn)
A.B=a1b1+a2b2+a3b3+...+anbn
A.B also = |A| * |B| cos(x)
where x is the angle between the vectors
this is it in two dimensions
but you can go to as many as you want
wicked widget
So A stands for what aspect of vector A?
wicked widget
yeah
icy lance
thats the magnitude sqrt(a1^2+a2^2+...+an^2)
safe radishBOT
safe radishBOT
Available help channel!
rotund dew
Consider a function g that is differentiable on (-1,8) s.t. g(0)=-1 and g(3)=8. Prove that the derivative of g intersects x²
safe radishBOT
Consider a function g that is differentiable on (-1,8) s.t. g(0)=-1 and g(3)=8. ...
queen ingot
x^2 - g must be continuous and we can use the intermediate value theorem
wait...
oh it says the derivative must intersect x^2, not g itself
sorry
austere magnet
Consider a function g that is differentiable on (-1,8) s.t. g(0)=-1 and g(3)=8. ...
If it does not, the line made by thr graph of the derivative at [0, 3] is either always above or always below x²
If it's always above, the difference between the values of g shall be more than the area under the graph of x² from 0 to 3 (I don't know how to write integrals), and if always below - below that
The area under the graph of x^2 in [0, 3] is 1/3 * 3^3 + C, (but C=0), so it is exactly 9
safe radishBOT
@rotund dew Has your question been resolved?
queen ingot
another way - let f(x)=g(x) - (x^3 /3)
then by the mean value theorem there's some k in (0,3) such that
f'(k) = (f(3)-f(0))/3
which simplifies to
g'(k)=k^2
digital palm
I think this could work, I mean proof that there is a point at c for g' and it would only remain to show that f can take that value
safe radishBOT
safe radishBOT
Available help channel!
proud wagon
I heard about a formula called the almighty or quadratic formula, could i get someone to help or teach me about it
safe radishBOT
I heard about a formula called the almighty or quadratic formula, could i get so...
split moss
@proud wagon
proud wagon
yes pls
split moss
i writed above
proud wagon
thank u
split moss
proud wagon
could u solve a question using the quadratic formula step-by-step
fathom adder
could u solve a question using the quadratic formula step-by-step
Do you have an exercice ?
fathom adder
Well you see that a = 1, b = 4 and c = 3
Plug in the formula
b² - 4ac = 16 -4*3 = 4
So sqrt that is 2
Then
(-b +- 2)/2*a
(-4 +- 2)/2
So x = -1 or x = -3
Heres a full step way to do it
proud wagon
erm....
safe radishBOT
Available help channel!
clever pawn
safe radishBOT
clever pawn
DI?
clever pawn
Do you know the DI method of integration by parts?
dont think so
clever pawn
am watching it rn XD
odd arch
Nice
After you've finished the video try ln(x+√(1+x^2)) to be differentiated (D) and rest in I
clever pawn
i dont think ill be able do do that untill it reaches 0
clever pawn
After you've finished the video try ln(x+√(1+x^2)) to be differentiated (D) and...
especially with this ln(x+√(1+x^2))
its like ill need to do it 10 times
clever pawn
w8
clever pawn
what did u take exactly for I and D
the i
i dont get it why is it like that
oh i see know nvm
odd arch
For D ln(x+√1+x^2) and every thing else for I x/√1+x^2
clever pawn
For D ln(x+√1+x^2) and every thing else for I x/√1+x^2
how did u fint out that its 1/srt(1+x^2)
lean otter
looks like a u sub
lean otter
:P mb
safe radishBOT
@clever pawn Has your question been resolved?
odd arch
how did u fint out that its 1/srt(1+x^2)
Because it's very difficult to integration ln(x+√1+x^2) (sorry for the late reply)
clever pawn
Because it's very difficult to integration ln(x+√1+x^2) (sorry for the late repl...
i get it but am asking how did u found the socond part of D
no worries
odd arch
When ever you see product of two functions being integrated always first try to pick out the function to be integrated (I) and it should be easy to integrate. In your problem I see that x/√x^2+1 can be integrated easily because derivative of x^2 +1 is present in the numerator and we can do a substitution
odd arch
Omg
flat frigateBOT
jesko
$\dv(\ln(x+\sqrt{1+x^2}){x}=\dfrac{1}{x+\sqrt{x^2+1}}\cdot\left(1+\dfrac{1}{2 \sqrt{1+x^2}}\cdot 2x\right)$
odd arch
it is with respect to x
odd arch
Simplifying it would lead to this..
clever pawn
how can i write like that to show u what i mean
odd arch
I hope you know derivatives right? I have just differentiated ln(x+√x^2+1)
clever pawn
yes
when we have ln
and we differentiating it
isnt the answer f ' (x)/f(x)
w8
ehtre is an x
didnt u take the x with the other part i mean in the i
odd arch
Ignore
odd arch
didnt u take the x with the other part i mean in the i
Yes
I did take the x in the part which has to be integrated
clever pawn
1 sec lemme show u
flat frigateBOT
jesko
clever pawn
clever pawn
f ' (x)/ f(x)
odd arch
**jesko**
Check this
Don't forget the chain rule. You forgot to multiply the derivative of x^2
clever pawn
what should it be then i mean the part that i made a mistake
odd arch
Replace the 1 (that I marked with an arrow) to a 2x (derivative of x^2) and it will be correct
clever pawn
at one point i must multiply srt(1+x^2) with the same doesnt the srt removes?
odd arch
I don't get it pls elaborate
clever pawn
when i have srt(x)*srt(x) doesnt the srt desapear?
i have the same here with srt(1+x^2)
on the second step
odd arch
when i have srt(x)*srt(x) doesnt the srt desapear?
Yes they do √x √x =x
clever pawn
flat frigateBOT
jesko
odd arch
Can you cancel a ?
clever pawn
no
odd arch
Let a =√(1+x^2) and b=x
You have the same situation
Oh so dumb of me
Now I get why you are tryna say
clever pawn
if u understood then u can see that it doesnt make sense with this
odd arch
If you cancel the 2, you can see that x + sqrt(1+x^2) will cancel
clever pawn
odd arch
Almost there, now factor out sqrt(1+x^2) from the denominator in the last step
clever pawn
huh?
clever pawn
yes
odd arch
Ggs
clever pawn
and how u found out the integration part?