in this case it does make sense, that is basically how "if" works
#help-33
ripe glen
Thx👍
sleek lake
ok i see the problem
it's hard to see that "If Bob is at home, it's tuesday" can be true or false
it seems like it's some kind of third type of thing
like it can be a lie
but it can't be a "truth"
idk
so actually there's no difference between "If Bob is at home, it's tuesday" and "It's wednesday or thursday"
it's still a way to say what can't happen
so you check the same way, if it's true or false
"It's wednesday or thursday"
in reality it's thursday
not a lie!
"If Bob is at home, it's tuesday"
in reality bob is at work and it's wednesday
not a lie
ripe glen
I get it now
sleek lake
great
marsh citrusBOT
marsh citrusBOT
Available help channel!
pallid agate
Would this question be a yes? because each person on each team has an equally random chance at getting picked?
marsh citrusBOT
Would this question be a yes? because each person on each team has an equally ra...
@pallid agate Has your question been resolved?
trim quest
Would this question be a yes? because each person on each team has an equally ra...
Do you know the difference between a simple random sample and a stratified random sample?
A simple random sample means you put all the people in one big pool, and select the sample at random
A stratified random sample means you divide the people into groups first, based on some criteria, and then choose some number from each group at random
pallid agate
Do you know the difference between a simple random sample and a stratified rando...
no I didn't know the difference
So that would not satisfy a simple random sample
because its divided into smaller groups?
trim quest
Right, it's a stratified random sample
A simple random sample wouldn't guarantee that you get players from every team
trim quest
no problem 👍
pallid agate
so justification would be that it is divided into smaller groups
with reason that a simple random sample wouldn't guarantee players from every team
would that ^ be a suffice answer?
trim quest
yeah that should be fine
pallid agate
ok thank you
trim quest
np 👍
pallid agate
.close
pallid agate
is part c) correct?
marsh citrusBOT
marsh citrusBOT
Available help channel!
gilded ember
marsh citrusBOT
gilded ember
where did this GPE come from
fervent rampart
anything with mass that is above the ground has gravitational potential energy
gilded ember
does KE not account for the GPE
fervent rampart
kinetic energy is separate from gravitational potential energy
fervent rampart
you add GPE whenever it is off the ground, whether that is in the initial or the final state
marsh citrusBOT
@gilded ember Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
novel juniper
Prove that $\lim_{x\to 0} f(x) = \lim_{x\to a} f(x-a)$
marsh citrusBOT
Prove that $\lim_{x\to 0} f(x) = \lim_{x\to a} f(x-a)$
elfin berryBOT
Veni, vidi, perii
novel juniper
So to start
the LHS means
$\forall \varepsilon>0 \exists \delta>0 st0< |x-0|<\delta \implies |f(x)-f(0)| \leq \varepsilon$
still temple
Something is missing
novel juniper
huh?
novel juniper
ah
elfin berryBOT
Veni, vidi, perii
novel juniper
and the RHS is
$\forall \epsilon >0 \exists \delta >0 st 0<|(x-a)-a| \implies |f(x-a)-f(0)| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
novel juniper
which feels off
marsh citrusBOT
@novel juniper Has your question been resolved?
novel juniper
<@&286206848099549185>
torpid plover
what happened?
novel juniper
**Veni, vidi, perii**
This is the problem
rugged cobalt
you can assume the limit exists and put like L instead of f(0)
novel juniper
okie
rugged cobalt
and you want to show that L works for both
novel juniper
Yes
rugged cobalt
did you try anything so far
novel juniper
Writing both defns to see if that proves they're equivalent
novel juniper
**Veni, vidi, perii**
Right so far?
torpid plover
it's no difficult, but I don't have the mathematical rigor to express it.
rugged cobalt
apart from some minor typos yea defn looks ifne
novel juniper
oops
yeah
made a few mistakes
$\forall \epsilon >0 \exists \delta >0 st 0<|(x-a)-a| \implies |f(x-a)-f(a)| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
novel juniper
$\forall \varepsilon>0 \exists \delta>0 st0< |x-0|<\delta \implies |f(x)-f(0)| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
delicate prairie
tex tip, only wrap the math in dollars so that you can write english cleanly
novel juniper
👍
delicate prairie
$a$ or $b$
elfin berryBOT
RokettoJanpu
torpid plover
use sustitucion
novel juniper
I haven't proven that substitution works yet
delicate prairie
use sustitucion
this isnt like calc class where you can just plug stuff in, he needs to go by epsilon delta
torpid plover
i see
novel juniper
so $2a-\delta <x<\delta +2a$
elfin berryBOT
Veni, vidi, perii
novel juniper
and $-\delta <x<\delta$
elfin berryBOT
Veni, vidi, perii
novel juniper
so let $\varepsilon= min(\delta, \delta+2a)$
elfin berryBOT
Veni, vidi, perii
torpid plover
is something like that and using using triangular inequality
triangular inequality that key
novel juniper
maybe
Why didn't I think of that 😭
$\forall \epsilon >0 \exists \delta >0 st 0<|(x-a)| \implies |f(x-a)-f(0)| \leq \varepsilon$
wait
this should be the second defn , righ
novel juniper
That's NOT the triangle inequality for subtraction
torpid plover
What is it like?
novel juniper
$||g(x)-|h(x)|| \geq |g(x)-h(x)|$
novel juniper
Ok
so just to restate
these are my defn
$\forall \epsilon >0 \exists \delta >0 st 0<|x-a| \implies |f(x-a)-f(0)| \leq \varepsilon$
and
oops
elfin berryBOT
Veni, vidi, perii
novel juniper
$\forall \varepsilon>0 \exists \delta>0 st0< |x-0|<\delta \implies |f(x)-f(0)| \leq \varepsilon$
rugged cobalt
consider a translation function g(x)=f(x-a)
elfin berryBOT
Veni, vidi, perii
novel juniper
I mean sure, but is substitution allowed
torpid plover
i ment
torpid plover
**Veni, vidi, perii**
i don't think so
rugged cobalt
no substituion i what you want to prove i think
that you can just write x-a and f(x-a) directly
if it works for x and f(x)
novel juniper
OK. Let's start from square one
$\forall \varepsilon>0 \exists \delta>0 st0< |x-0|<\delta \implies |f(x)-f(0)| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
novel juniper
is the LHS defn
torpid plover
but never mind, that's not the point
novel juniper
$\forall \varepsilon>0 \exists \delta>0 st0< |x-a|<\delta \implies |f(x-a)-f(0)| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
delicate prairie
Prove that $\lim_{x\to 0} f(x) = \lim_{x\to a} f(x-a)$
this statement lacks a bit of rigor, maybe its better like this
novel juniper
That's literally what's given in spivak
delicate prairie
its an equation of limits, implicitly assuming beforehand that at least one exists
if one of $\lim_{x\to0}f(x)$ or $\lim_{x\to a}f(x-a)$ exists then the other exists, in which case they are equal
elfin berryBOT
RokettoJanpu
delicate prairie
its a bit more rigorous this way, and in fact it reflects a good strategy for proving equality
novel juniper
I don't folllow
delicate prairie
take cases
novel juniper
what do I have to prove
delicate prairie
take the case where the former exists, i.e. $\lim_{x\to0}f(x)=L$ for some $L$, then prove $\lim_{x\to a}f(x-a)=L$
elfin berryBOT
RokettoJanpu
novel juniper
its an equation of limits, implicitly assuming beforehand that at least one exis...
I don't get this part
delicate prairie
the case where the latter exists is handled similarly
delicate prairie
I don't get this part
do you know limits dont always exist?
novel juniper
Yes
delicate prairie
we're writing an equation with limits on both sides. you dont know beforehand whether both limits exist, so the equation doesnt necessarily make sense
elfin berryBOT
Veni, vidi, perii
delicate prairie
pay attention to my EXACT wording
if one of $\lim_{x\to0}f(x)$ or $\lim_{x\to a}f(x-a)$ exists then the other exists, in which case they are equal
elfin berryBOT
RokettoJanpu
delicate prairie
i said this is what we're really proving
elfin berryBOT
Veni, vidi, perii
delicate prairie
take the case where the former exists, i.e. $\lim_{x\to0}f(x)=L$ for some $L$, t...
.
novel juniper
Let $\lim_{x\to 0} f(x)=L$ we now attempt to prove $\lim_{x\to a} f(x-a)=L$
elfin berryBOT
Veni, vidi, perii
novel juniper
so this being L implies
$\forall \varepsilon>0 \exists \delta>0 st0< |x-0|<\delta \implies |f(x)-L| \leq \varepsilon$
delicate prairie
f(0)?
elfin berryBOT
Veni, vidi, perii
novel juniper
Now on the right hand side we have
$\forall \varepsilon>0 \exists \delta>0 st0< |x-a|<\delta \implies |f(x-a)-L| \leq \varepsilon$
elfin berryBOT
Veni, vidi, perii
novel juniper
Not too sure how to proceed form here
delicate prairie
its a more abstract limit, so you need to think more logically than computationally
delicate prairie
**Veni, vidi, perii**
we know this
delicate prairie
**Veni, vidi, perii**
we need to prove this
delicate prairie
to guide your logic, every epsilon delta proof should go like this
let eps>0
some string of arguments to find suitable delta
let x be such that 0<|x-..|<delta
some string of arguments to show |..-..|<eps
ill do the easy bits for you
let $\ep>0$
elfin berryBOT
RokettoJanpu
delicate prairie
since $\lim_{x\to 0} f(x)=L$, there exists $\delta>0$ such that $0<|x|<\delta$ implies $|f(x)-L|<\ep$
elfin berryBOT
RokettoJanpu
elfin berryBOT
Veni, vidi, perii
novel juniper
so I have $-a-\delta <x-a<\delta-a$
elfin berryBOT
Veni, vidi, perii
novel juniper
let $\delta =a+1$
elfin berryBOT
Veni, vidi, perii
delicate prairie
i need to head out so ill leave some questions associated to epsilon delta proofs, especially abstract ones like this where we have assumed limits:
if im guaranteed a delta from an assumed limit, is that the right delta for another limit? turns out sometimes yes, sometimes no
should i apply an assumed limit directly to epsilon, or is it better to apply it to another positive function of epsilon (eps/2, eps^2 etc)? sometimes just epsilon is enough, sometimes you need a smarter choice
delicate prairie
ill answer these for this problem for you
the delta i picked from the assumed limit will work for the limit we need to prove
and its enough to apply the assumed limit to just epsilon
there are no smart choices required here. you just need to think very logically through the proof structure
delicate prairie
to guide your logic, every epsilon delta proof should go like this
let eps>0
so...
.
and the proof is much simpler than you think. no clever inequality tricks needed. just decent logic
marsh citrusBOT
@novel juniper Has your question been resolved?
pure current
marsh citrusBOT
marsh citrusBOT
pure current
Thanks Taiwan bro ! If u rmemeber me lmfao
marsh citrusBOT
Available help channel!
steady juniper
i want to use euler identity of split complex number but argument of hyperbola only defind in the blue area i wonder how can i write it in polar form
marsh citrusBOT
i want to use euler identity of split complex number but argument of hyperbola o...
steady juniper
i try this but it only defind in the blue area
i try switch x and y term but its wrong if i do the power of 2
even tho 1+3j or anything outside the blue area exist but how can i even write it in polar form
steady juniper
i try switch x and y term but its wrong if i do the power of 2
i get j^2=j so its wrong
thorny bison
i want to use euler identity of split complex number but argument of hyperbola o...
By eulers identity u mean e^itheta ?
thorny bison
mb i can't answer this then
steady juniper
wait it should be hyperbolic sine i misspelling
im fk up rn
i think about it all day
marsh citrusBOT
@steady juniper Has your question been resolved?
marsh citrusBOT
@steady juniper Has your question been resolved?
smoky widget
marsh citrusBOT
cunning oak
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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
raw hawk
Do you know sum of first n terms of an arithmetic progression
cunning oak
can you find the general term for this series?
smoky widget
Do you know sum of first n terms of an arithmetic progression
yes
raw hawk
a+(n-1)d
yes
Next
You have a simultaneous equation
6=a
12=a+(5-1)d
Solve for common difference
smoky widget
i'll get 1.5
raw hawk
Correct
smoky widget
then?
raw hawk
Next
$S_n = \frac{n}{2} [a+a+(n-1)d]$
elfin berryBOT
David
raw hawk
In this case S_n =90
raw hawk
i'll get a quadratic equation
Yes
smoky widget
ok
raw hawk
Type . close if you are done
smoky widget
.close
smoky widget
Q3
smoky widget
glass silo
,rccw
elfin berryBOT
lucid turret
so
let a be the first erm
and common difference = d
I don't want to make this slow
smoky widget
Ok
lucid turret
first term = a
second term = a+d
smoky widget
Yeah
lucid turret
atq a(first term) = 5
a+d = 9
so d = 4
smoky widget
Yea
lucid turret
now let the last term be of the form a+nd = 5+4n = 4n + 4 + 1
Now equate 4+1+4n and 500
4n = 495
n = 123.75
now since n must be an integer
we need to add 1 to 500 to make 501
So 5+4n = 501
4n = 496
n = 124
substitute this value in 5+4n to find the term (the last one)
marsh citrusBOT
lucid turret
welcome
marsh citrusBOT
Available help channel!
livid falcon
is it alright if someone could explain the process for this? im really confused
livid falcon
you can pick which ever question !!
livid falcon
yup
worthy obsidian
X^4 = 16 it is asking which number when multiplied 4 times has its ans as 16 so to solve these kind of questions you should find all prime factors of 16
lucid turret
x^4 = 16
x^4 - 16 = 0
(x^2+4)(x^2-4) = 0
either x^2 + 4 = 0 or x^2 - 4 = 0
for x^2 + 4 = 0
x^2 = -4
x = -2i or 2i
For x^2 - 4 = 0
x = -2 or +2
livid falcon
X^4 = 16 it is asking which number when multiplied 4 times has its ans as 16 so ...
oh thanks!! only prime numbers?? also wld u do the same for the rest??
livid falcon
x^4 = 16
x^4 - 16 = 0
(x^2+4)(x^2-4) = 0
either x^2 + 4 = 0 or x^2 - 4 = 0
for x...
ohhh aight
wait whys it either negative or positive
worthy obsidian
x^4 = 16
x^4 - 16 = 0
(x^2+4)(x^2-4) = 0
either x^2 + 4 = 0 or x^2 - 4 = 0
for x...
this is the more elegant solution
worthy obsidian
wait whys it either negative or positive
-2 x -2 = +4
livid falcon
it's real nice
worthy obsidian
-4 x -4 = +16
velvet root
I’m so stuck on Part D, how do I do it? I can’t find any examples like this online
marsh citrusBOT
I’m so stuck on Part D, how do I do it? I can’t find any examples like this onli...
velvet root
Are you still stuck?
YES
wooden bloom
hola, hablas español cierto?
torpid plover
replacing by dx
wooden bloom
necesito ayuda con las funciones
tengo prueba y aun no las entiendo bien
funciones cuadraticas
velvet root
wait so what did you find, that is that the integral of (1-4x^2)^2/3?
torpid plover
tengo prueba y aun no las entiendo bien
preguntame y te digo
wooden bloom
tengo que analizar funciones y describirlas ? sin realizar los calculos, saber si tiene un maximo o un minimo, si pasa por el inicio o no, o cual es su vertice
torpid plover
wait so what did you find, that is that the integral of (1-4x^2)^2/3?
nop, that just the Integral that u write
i though that that was your confusion
torpid plover
tengo que analizar funciones y describirlas ? sin realizar los calculos, saber s...
Y que no sabes?
torpid plover
i though that that was your confusion
how to proceed
wooden bloom
Y que no sabes?
como realizar esas observaciones
torpid plover
como realizar esas observaciones
viendo el grafico TODO ESO? o con solo la expresion
?
wooden bloom
viendo el grafico TODO ESO? o con solo la expresion
con la funcion que me entreguen
torpid plover
pero te la dan graficada?
wooden bloom
tambien debo saber si crece o decrece
wooden bloom
pero te la dan graficada?
no
torpid plover
No te puedo ayudar, porque no se que sabes y que no. Por lo que me decis estas medio en la nada. Yo te puedo responder una duda puntual. Pero explicarte todo no jajaaj
wooden bloom
No te puedo ayudar, porque no se que sabes y que no. Por lo que me decis estas m...
entiendo entiendo, no te preocupes
me ayudas con las formulas del vertice y eje de simetria?
velvet root
So what is the way to solve this integral? You find the integral of the denominator first?
I don’t understand the steps
torpid plover
me ayudas con las formulas del vertice y eje de simetria?
Si, el eje de simetria en justo en la mitad de la parabola, si tienes las dos raices puedes hacer (x1+x2)/2. Sino tienes una formula por ahi. O si sabes derivar... Es donde la derivada es 0. y el eje de simetria es lo mismo, siempre coincide con el vertice en las cuadraticas
porque son funciones pares
torpid plover
So what is the way to solve this integral? You find the integral of the denomina...
ok
one sec
wooden bloom
Si, el eje de simetria en justo en la mitad de la parabola, si tienes las dos ra...
perdoname, estoy empezando con la matematica y no comprendi bien lo que me dices, si no te es tedioso o una molestia me lo explicarias de otro modo?
velvet root
perdoname, estoy empezando con la matematica y no comprendi bien lo que me dices...
where u from bro
wooden bloom
where u from bro
chile
como puedo saber donde estan las intersecciones con el eje x y el eje y en una funcion cuadratica?
velvet root
como puedo saber donde estan las intersecciones con el eje x y el eje y en una f...
Put the equation = to zero.
wooden bloom
luego?
velvet root
Solve for x that will give you the intersecciones con el eje y
velvet root
u understand the steps now?
Yes that’s great, but then what do you do after just solve that and put a 1 over it? Since the og equation is a fraction
torpid plover
yes, everything in time, first it is important that you understand the steps.
is it clear to u?
velvet root
is it clear to u?
ya but why are you multiplying by both dx and d theta, when dx is in the numerator not denominator
Like dx is on top why are you multiplying it with the denom
torpid plover
ya but why are you multiplying by both dx and d theta, when dx is in the numerat...
is the same
u can put it on top like a number, and is better couse if u are lazy and don't want to write 1 and then dx, just write dx on top
it doesn't matter, but smart people do it
an example
marsh citrusBOT
@velvet root Has your question been resolved?
velvet root
note that I subtract the powers by using properties
wow bro you helped me a lot thanks
real lichen
marsh citrusBOT
proud portal
Rep
real lichen
Do I just use the points on red line with y is 2 and for blue y is 2
real lichen
Huh?
proud portal
Thank you @real lichen
real lichen
I'm confused
valid cape
valid cape
Do I just use the points on red line with y is 2 and for blue y is 2
blue is not 2
real lichen
So uh how do I start this off
valid cape
you are on the right track
torpid plover
0 is the answer
real lichen
Is it the 2nd point they have
valid cape
0 is the answer
!nosols
marsh citrusBOT
0 is the answer
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.
valid cape
Blue 2,-2
yes
generally when you add two functions, you add the y-value of each function at every x
real lichen
Ohh
valid cape
so when they are asking you (f + g)(2), it means "combine f + g into one function, then find the value of that function at x = 2"
real lichen
So it's like I draw a vertical line at 2
And every point there for each corresponding line
I would use that point
valid cape
yes
real lichen
And then I just add the x toghter and they y together
Or do I just add everything together
proud portal
So like what do u gain from helping others
valid cape
And then I just add the x toghter and they y together
no no no
proud portal
Oh shit sorry
valid cape
you do not add the x
real lichen
Ok
Just the y
Ok now 2nd question
Same thing but with 4
I do same thing as the first one?
Ok i got that one
Now it f - g(6)
valid cape
real lichen
Do I add the negative symbol to the term
Or
Nvm
Ik
Wait
So would it be -2-(-6)
real lichen
<:mikuapproves:1189282221933207572>
I have a new question
marsh citrusBOT
@real lichen Has your question been resolved?
solid solstice
D
solid solstice
multiply both sides by 30, it should be easier to do the equation after this
can i ask, why 30?
gaunt gate
can i ask, why 30?
because you have 5, 3 and 6 as denominators, so 30 is multiple of all those
so will be left no fractions
gaunt gate
you're welcome
solid solstice
@gaunt gate do i put the x's at one side b4 multiplying or after
gaunt gate
<@1001753854225961081> do i put the x's at one side b4 multiplying or after
it doesn't matter
you can multiply first
then isolate the x's
solid solstice
I’d use elimination method
explain please
meager badger
👍
idle vessel
What does it mean by (A, B; C, D)?
fervent rampart
they seem to be defining (A, B; C, D) to be the cross ratio of the points A, B, C, D
idle vessel
Is it because ; is a cdot with a comma 💀
idle vessel
they seem to be defining (A, B; C, D) to be the cross ratio of the points A, B, ...
But why (A, B; C, D)?
fervent rampart
well the ; seems to sort them in to two distinct groupings of AB and CD
there seem to be a lot of different notations for this (wolfram mathworld has completely different notation), this is just the one that wikipedia went with
fringe thistle
i need assistance with polynomial functions
marsh citrusBOT
i need assistance with polynomial functions
lucid bridge
!justask
fringe thistle
yes
lucid bridge
!da2a
marsh citrusBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
glass silo
What exactly do you need help with? Do you have a literal question?
fringe thistle
i have some yes
an example being (4x²-8x-2):(2x-1)
mainly i want to understand both the subtractions and additions of the polynomial functions
fringe thistle
is this division?
yes but i first want to understand how the addition and subtraction of the polynomial functions
main idol
fringe thistle
now could you explain the multiplication and division of the polynomial function?
still temple
Just wanted to check my answer
The curve C1 is given by the following equation
$$e^{xy} + \ln(y^2) + e^y = 1 + e$$
Determine the gradient at point (0, 1)
marsh citrusBOT
Just wanted to check my answer
The curve C1 is given by the following equation
...
elfin berryBOT
Edmund Cloudsley
still temple
For this particular question, we would have to utilise implicit differntiation
$$\frac{d}{dx} e^{xy} + \frac{d}{dx} \ln (y^2) + \frac{d}{dx}e^y = 0$$
$$ = e^{xy} (xy)^\prime + \frac{2}{y} \frac{dy}{dx} + e^{y} \frac{dy}{dx} = 0$$
$$\frac{dy}{dx} = \frac{-ye^{xy}}{\frac{2}{y} + xe^{xy} + e^y}$$
and if we substitute the mentioned value of x and y
we should get
$$\frac{dy}{dx} = -1/(2+e)$$
elfin berryBOT
Edmund Cloudsley
still temple
I am unsure if the implicit differentiation of $e^{xy}$ is correct in my case
elfin berryBOT
Edmund Cloudsley
still temple
and let's say if I have somethign like the derivative of $\tan(xy)$
would it be:
$$(xy)^\prime \sec^2{xy}$$
gilded cedar
**Edmund Cloudsley**
yes sec^2(xy)(y+x dy/dx)
still temple
yes sec^2(xy)(y+x dy/dx)
great!
sharp vessel
You need the partial derivatives for the gradient, do you not?
still temple
You need the partial derivatives for the gradient, do you not?
do I? because I am pretty sure I haven't covered them in my course yet tho
sharp vessel
Idk maybe I'm wrong
still temple
do I? because I am pretty sure I haven't covered them in my course yet tho
can this question be solved with implicit differentiation only?
still temple
its wrt x if u want (xy)' thats xdy+ydx
yup
partial derivative is the same as total derivative here as there is only one variable
still temple
partial derivative is the same as total derivative here as there is only one var...
oh okay
I will look into partial derivatives
I remember doing them 2 months ago for something else not related to maths 😓
and I don't remember a thing
thanks anyways guys
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
dusty stump
marsh citrusBOT
dusty stump
Cant figure out where I keep on going wrong
stoic slate
!show
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
meager badger
Cant figure out where I keep on going wrong
Degree on top and bottom are equal
U need long division
marsh citrusBOT
marsh citrusBOT
Available help channel!
final badger
can yall explain how to do sine/cosine rule i watched yotube videos i still dont understand
marsh citrusBOT
can yall explain how to do sine/cosine rule i watched yotube videos i still dont...
glossy flint
What does sine rule tell?
glossy flint
can yall explain how to do sine/cosine rule i watched yotube videos i still dont...
Usually you'd better label all sides and angles, unless you are savvy with the topic
limber hearth
Oh it was on two channel
marsh citrusBOT
@final badger Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
neon adder
is there a more efficient way of solving this problem?
marsh citrusBOT
is there a more efficient way of solving this problem?
paper raptor
Yes, generating functions:
$G(x)=G_X(x)*G_Y(x)=(2x+x^2+x^3+x^4+x^5)(x^2+x^3+x^4+x^5+2x^6)$
elfin berryBOT
PajamaMamaLlama
paper raptor
,w (2x+x^2+x^3+x^4+x^5)(x^2+x^3+x^4+x^5+2x^6)
elfin berryBOT
paper raptor
2x^11+3x^10 (11,10 are higher than 9), sum the coefficients to get 5
or 5/36 odds to get a combination higher than 9
vernal granite
Hi, I have to proof that the sequence {a_n}, where a_n is that summatory Σ 1/k^3 is a cauchy sequence, I did this, but I arrive at point where I don't know what to do :(
marsh citrusBOT
Hi, I have to proof that the sequence {a_n}, where a_n is that summatory Σ 1/k^3...
vernal granite
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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
2
marsh citrusBOT
@vernal granite Has your question been resolved?
vernal granite
<@&286206848099549185>
marsh citrusBOT
@vernal granite Has your question been resolved?
main idol
from here, did you learn that $\sum_{k=1}^{\y} \frac{1}{k^2} = \frac{\pi^2}{6}$?
elfin berryBOT
riemann
vernal granite
eeh nop :(
cobalt swan
does anyone know where I went wrong? The answer is -2 but I put 2 because of the boundary change ( 0 to 1 ).
marsh citrusBOT
does anyone know where I went wrong? The answer is -2 but I put 2 because of the...
cobalt swan
digital robin
cobalt swan
3 sorry for my handwriting
main idol
,w 35 * int pi/2 to pi sin^4(x) * cos^3(x) dx
elfin berryBOT
main idol
-2 was right, not sure why you changed it to 2
cobalt swan
i put it on 2 because i have the boundary from 0 to 1 because i wanted to stay on u instead of going back to sin x
and when it’s from small to big or something you swap the sign
if i remember properly 😭
main idol
and when it’s from small to big or something you swap the sign
this is not a rule
$[7 (0) - 5 (0)] - [7 (1) - 5(1)] = 0 - (2) = -2$
elfin berryBOT
riemann
cobalt swan
my life is a lie 😭
main idol
that's it, no other "small to big swap the sign" business needed
fervent rampart
we have it that [ \int_1^0 f(x) \odif x = -\int_0^1 f(x) \odif x ] but that's the same as saying [ F(0) - F(1) = -[F(1) - F(0)] ]
elfin berryBOT
cloud
marsh citrusBOT
@cobalt swan Has your question been resolved?
marsh citrusBOT
static quarry
define critical point, to start with
lilac siren
extrema? roots? ...?
iron orbit
sorry my friend replied to me and helped me but thank you guys @static quarry @lilac siren
marsh citrusBOT
marsh citrusBOT
Available help channel!
glass crest
I just started limits in AP Calc AB and I have no idea how to solve this problem: lim x-> pi/4 (2cos^2x-1)/(cosx-sinx)
marsh citrusBOT
I just started limits in AP Calc AB and I have no idea how to solve this problem...
glass crest
So I know that 2cos^2x-1 = cos2x
So I'm guessing I get lim x-> pi/4 (cos2x/(cosx-sinx) but what happens then or am I going in the wrong direction?
glass crest
I know there are 3 but in this case I would guess you use the cos^2x-sin^2x
dry prawn
that's a good guess
you want cos^2x-sin^2x, and in the denominator you have cosx-sinx... perhaps there's something there
wraith sun
I know there are 3 but in this case I would guess you use the cos^2x-sin^2x
Don't forget your basic algebra 😉
glass crest
So now I just cancel the square to get lim x -> pi/4 cosx-sinx
dry prawn
no you certainly do not
glass crest
wait you don't
dry prawn
that would be implying cos^2x-sin^2x = (cosx-sinx)^2
wraith sun
Cancel correctly 😅
glass crest
cosx+sinx
marsh citrusBOT
Available help channel!
hearty wasp
how do i find the line on this graph
marsh citrusBOT
how do i find the line on this graph
paper raptor
intercept-intercept form
$\frac{x}{a}+\frac{y}{b}=1$ where $a$ is the x intercept and $b$ is the y intercept
elfin berryBOT
PajamaMamaLlama
hearty wasp
$\frac{x}{a}+\frac{y}{b}=1$ where $a$ is the x intercept and $b$ is the y interc...
what
smaller terms please
lol
elfin berryBOT
PajamaMamaLlama
hearty wasp
i already got 2/1
paper raptor
where does the line touch the x-axis?
hearty wasp
1
paper raptor
and the y-axis?
hearty wasp
2
paper raptor
therefore b=2, and a=1
above the formula for the line given two intercepts :)
done
paper raptor
parentheses are important
so are negative signs
you need to distribute the -2 to both the x and the -1
marsh citrusBOT
marsh citrusBOT
Available help channel!
strange fable
I need help with a show that question
marsh citrusBOT
I need help with a show that question
dire mirage
How many T would you expect at equilibrium if you repeated the experiment, starting with 1000
H and 0 T and using a probability of 99.9% that a collision turns H into T? I am really confused is this like a trick question.
heads and tails
zenith lily
c
austere glacier
Hello
austere glacier
Oh I was just saying hello
zenith lily
oh hello lol
pallid tapir
hello i asked this earlier, but incorrectly
what's the question?
zenith lily
I just realized it cropped incorrectly. If an and b are real numbers. Then if a^2 + ab + b^2 >=0
pallid tapir
and we're using trig to do it?
zenith lily
Yeah just trying. I have other proofs
pallid tapir
what you have is chicken scratch so it isn't a proof, but there may be something there
zenith lily
Oh yeah it’s scratchwork lol my bad. I’m wondering if showing this relationship is correct though
pallid tapir
you want to argue that for this arbitrary a,b pair, there is an angle x for which you can do this representation
but what concerns me is that it isn't true if a=b=0 so you need a separate case
zenith lily
Yes
pallid tapir
sorry, you need to address that particular case separately
so we must assume at least one of a,b are nonzero
zenith lily
Okay, so because
This relationship idea doesn’t work to satisfy sin theta = cos theta = 0
Correct? Like there’s not a theta to satisfy this
pallid tapir
yeah like, to me you're constructing a circle of radius sqrt(a^2+b^2)
that's radius 0 if a=b=0
zenith lily
Ah okay. Are we “allowed to say”
A=b=0 then a^2+ab+b^2 >= 0
Which satisfies what we need to prove.
And say for like “in the case that an and b are both non zero” and use this proof ?
zenith lily
Okay, the reason I said nonzero is because I saw cases such as a=0 and b≠0
Or
a≠0 and b=0 as quick cases that simplify to a^2 >= 0 and b^2 >= 0 respectively
So case 3 would be
a and b are both non zero and then go onto the trigonometric proof
pallid tapir
the trig argument still works as long as at least one of a or b are nonzero
pallid tapir
well it isn't exactly valid in my opinion because you still have to assume you have a rigorous construction of trig functions
zenith lily
Oh okay
pallid tapir
we're assuming that you're asked to prove this inequality in an introductory real analysis course where you're only given that the real numbers is a field with an ordering
zenith lily
Nah. It’s just an intro to discrete math class. This is the question from the first day of class a week ago
pallid tapir
they're still introductory so ok
it's cute to invoke trig functions but not rigorous enough because you're just invoking a higher power
zenith lily
The prof really liked a proof with inflection points. I think the prof is just trying to get people’s brains turning , yk?
zenith lily
I’m not in the class , it’s my friend who is. I completed the course but we just been having fun talking about different proofs for it
pallid tapir
oh word
zenith lily
im on a gap semester currently. Im really liking math but want to be a software engineer for the money
I completed the course during the month of June. (Accelerated summer class) and I feel like I didn’t get to have the full experience because of it. And that I’m probably worse at proof writing than others who completed it at a normal pace
I’m thinking of just starting real analysis though (I kinda already did) like last week
With understanding analysis although I’d like to go through 2 books concurrently
pallid tapir
so in constructing a circle of radius $r=\sqrt{a^2+b^2}>0$, we identify that there is some angle $\theta\in[0,2\pi)$ for which $r\cos\theta=a$ and $c\sin\theta=b$, and we argue that $$a^2+b^2+ab\geq 0\ \ \ \iff\ \ \ \frac{1}{c^2}\left(\cos^2\theta+\sin^2\theta+\sin\theta\cos\theta\right)\geq 0$$
elfin berryBOT
Flip
pallid tapir
the rightmost component of the iff is equivalent to dropping the 1/c^2 because it's positive
pallid tapir
I completed the course during the month of June. (Accelerated summer class) and ...
you get better at writing proofs when you write more of them, and you write more of them in higher math classes
zenith lily
Yeah fosho. Need to get through understanding analysis
I’d like to get through the book and partially a second book before my analysis course starts next semester
pallid tapir
self-study is hard, so you'd probably benefit from making a schedule for it, and a study group or some other incentive for reading and doing exercises
make your own due dates for responses to book exercises or problems, or give your friends a lecture on what you worked on
the friends should hopefully be willing to hear you lol
choose people who encourage you
zenith lily
Noted, me and my roomate are trying to learn from different sources and have a white board to write down interesting problems .
He’s using Spivak and tao analysis
I’m using understanding analysis and to be determined
Love the idea of hard, I think of math as an intellectual navy seal training boot camp for my brain
pallid tapir
sounds fun
zenith lily
Even if they do not correlate directly. I think a degree in math will benefit “everything” cognitively
Plus I like math 😎
Haha
pallid tapir
some treatments of real analysis feature a careful and frankly long-winded construction of the real numbers (in two ways) from the peano axioms
zenith lily
I have read this (as in, I am on the screen activity waiting for messages to let you know I’m here)
pallid tapir
lots of equivalence classes to rise from one number system to another
zenith lily
I remember what equivalence classes are, but I know I’m not amazing on the topic right now
pallid tapir
other treatments assume we're already at the finish line and that we have the real numbers, which is a totally-ordered field
an equivalence class is a formal lumping-together of things that are considered equivalent to some element under some (equivalence) relation
every equivalence relation begets a partitioning of your set (the equivalence classes are what makes the partitioning), and every partitioning of your set begets an equivalence relation
they can be very pretty
pallid tapir
this is good
zenith lily
Al this is mentally noted and screenshotted , thank you
pallid tapir
sure thing
also in case you don't know latex already, you should experiment with it
I used it for every college assignment I had once I learned the basics
so you should consider using latex to write up your proofs, just to give yourself non-obvious editorial and presentation problems to solve lol
super super helpful
for example I took a graph theory course and used it as an excuse to learn tikz, a latex package for creating graphs and other wacky pictures
it's very important to learn latex especially if you want to write papers, because a lot of journals don't even accept papers written in other editors
and also because it of course makes for nice presentations
marsh citrusBOT
@zenith lily Has your question been resolved?
zenith lily
.close
still temple
I just had a question on the bi nominal
marsh citrusBOT
I just had a question on the bi nominal
still temple
I wanted to know what the difference it when it asks me to find the sum/difference and when it asks me to find the product?
Sorry if that questions a lil dumb
terse relic
the sum/difference is just adding the polynomials, the product is multiplying them
i.e. the sum/difference uses the process you have there, the product uses FOIL
without variables, 2 + 3 = 5, 2 x 3 = 6
with variables, its (2x^2 + 5) + (3x^2 + 3) = 5x^2 + 8, (2x^2 + 5)(3x^2 + 3) = 5x^4 + 21x^2 + 15
still temple
What is FOIL? Is that a math acronym?
pallid tapir
What is FOIL? Is that a math acronym?
it's a terrible acronym that says that $$(a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd$$
elfin berryBOT
Flip
pallid tapir
ac is the product of the 'first' terms, ad the product of the 'outer' terms, bc the product of the 'inner' terms, and bd the product of the 'last' terms
you never need to remember this acronym if you understand it's nothing more than distribution done twice
still temple
Thank you!
I also wanted to know if anyone could check my math
For 13, 19 and 21 if that’s okay
I have assignment regarding the solve the equation in full formula and full explanation and the title is translations
pallid tapir
For 13, 19 and 21 if that’s okay
this is all correct
pallid tapir
I have assignment regarding the solve the equation in full formula and full expl...
occupied
still temple
Thank you! I really appreciate the help from everyone!!
pallid tapir
19 in particular has a shortcut: $$(6b^2-6)(4b^2-4)=6(b^2-1)4(b^2-1)=(6\cdot 4)(b^2-1)^2$$
elfin berryBOT
Flip
still temple
Oh wow thank you!
I had no idea I could do it that way
I’ll write that down too
I appreciate the shortcut and explanation, I’ll use it for class tomorrow 😼 I hope u guys have a good night!
.close
marsh citrusBOT
still temple
. reopen
marsh citrusBOT
Available help channel!
outer ravine
Find me two numbers such that when they are added together, they make as much as the cube of the lesser added to the product of its triple with the square of the greater; and the cube of the greater added to its triple times the square of the lesser makes 64
more than the sum of these two numbers.
marsh citrusBOT
Find me two numbers such that when they are added together, they make as much as...
marsh citrusBOT
@outer ravine Has your question been resolved?
honest topaz
marsh citrusBOT
honest topaz
I'm trying to show that this is a tautology without using truth tables
But I get stuck
when using logical equivalencies
devout mauve
use the distributive property
honest topaz
use the distributive property
the distributive property works with not p?
like i thought you needed 3 seperate variables
not p counts as one?
slate yarrow
not p counts as one?
yes
honest topaz
.close
honest topaz
marsh citrusBOT
honest topaz
Using logical equivalencies, how would I proceed?
elfin berryBOT
Flip
pallid tapir
to attack the $(p\land\neg q)\lor(q\land\neg r)$
elfin berryBOT
Flip
pallid tapir
maybe it brings joy, idk
honest topaz
so i would treat (p and not q) as p and distribute it to (q and not r)?
pallid tapir
it looks like there's a little more joy from that yeah
honest topaz
no joy to be found
pallid tapir
you find a -q or q, which is nice
pallid tapir
best of luck
honest topaz
honest topaz
it looks like there's a little more joy from that yeah
don't tell me
that i can distribute again
honest topaz
?
i dont see it
am i even doing this correctly
like i dont see what to do next
<@&286206848099549185>
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
lyric kelp
for gaussian
marsh citrusBOT
for gaussian
lyric kelp
.close
unique timber
hey guys wanna join a minecraft server pls dm me
marsh citrusBOT
hey guys wanna join a minecraft server pls dm me
open seal
this is not math
still temple
let's talk about the maths behind procedural generation
cobalt sedge
L fractal noises
marsh citrusBOT
@unique timber Has your question been resolved?
restive ledge
marsh citrusBOT
night mica
$ln 5x= lnx+ln4x$ can you go on?
elfin berryBOT
everg
restive ledge
I I think you made a mistake
night mica
could be
night mica
ohh right
restive ledge
I did that and got an integral with lnx in denominator
let me show
Wrong pic
I tried lnx = u but it didn't help
I also tried graphing to see if I could gain something
still temple
you sure it is not sine?
elfin berryBOT
still temple
then the question is simply wrong, because it does not exist
restive ledge
then the question is simply wrong, because it does not exist
How'd you know that?
grave dove
no matter what you do, you wouldnt be able to find the antiderivative of that function, cuz it has ln(x) in the denominator
this is called a non-elementary integral
grave dove
How'd you know that?
the function explodes around x=1
and you are integrating from 0 to π
including x=1
boom!
restive ledge
the function explodes around x=1
If I change the limits from 0 to 1?
grave dove
still
restive ledge
i tried an online integral calculator and it failed
I tried Wolfram too
still temple
it seems like someone haphazardly remove the s from sin though
grave dove
lol plot twist
restive ledge
Then it'll be easy I think
expand sin(5x) by the sum formula
thanks again
I'm gonna close this
.close
restive venture
idk how to interpret this situation and fit it into the formula
marsh citrusBOT
idk how to interpret this situation and fit it into the formula
restive venture
like is only 2 ft of water moving up?
marsh citrusBOT
@restive venture Has your question been resolved?
restive venture
<@&286206848099549185>
marsh citrusBOT
@restive venture Has your question been resolved?
vernal granite
Let {a_n} be a sequence of non-zero real numbers such that (image), Proof that a_n converge to zero. I don't know how to solve it, I tried using the definition of converge, |a_n+1/a_n - L | < e
-e < a_n+1/a_n - L < e
L - e/a_n+1 < a_n < L + e/ a_n+1, but doesn't feel that it help me with something :c
marsh citrusBOT
Let {a_n} be a sequence of non-zero real numbers such that (image), Proof that a...
vernal granite
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I 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
1
marsh citrusBOT
@vernal granite Has your question been resolved?
vernal granite
<@&286206848099549185>
glass silo
Have you happened to cover series, by any chance? 
marsh citrusBOT
@vernal granite Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
past hamlet
can anyone help me with this
marsh citrusBOT
can anyone help me with this
wraith cobalt
Have you done anything so far?
past hamlet
nah Im confused 😭
wraith cobalt
Generally if you have a fraction and something added together, and you want to express it as a single fraction
a good start is to write both things with a common denominator
since then you can add the two into one fraction
in this case, you could write 4x with the same denominator as x/(1-x) by multiplying and dividing it (which is ok because those two things cancel out) by (1-x)
marsh citrusBOT
@past hamlet Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
marsh citrusBOT
static quarry
pls at least use brackets so we can tell what is grouped with what
do you have a screenshot or a photo, you could just paste that
ok
well first thing i notice is that 7 x 3 is not 27
oh i see
it's fine, i'll read it as 21
lemme see if there are other issues
your answer is right, the key is wrong
mighty barn
I don't understand what I'm doing wrong. I multiplied the top one by 2 and the bottom one by 5 and found 4/5 for k but shouldn't h NOT be 5/4? why is it not working?
marsh citrusBOT
I don't understand what I'm doing wrong. I multiplied the top one by 2 and the b...
lucid zenith
I think you mean h should not be equal to 5/2
mighty barn
that worked but HOW
ohhhhhhhhh
wait ok i get it thank you so much
i had messed up
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
opal vector
hi, im stuck trying to fin sin(t)
marsh citrusBOT
hi, im stuck trying to fin sin(t)
dreamy pollen
hi, im stuck trying to fin sin(t)
Well if you have tan(t) , cos(t) . Then sin(t) is straightforward
opal vector
i think im messing up when squaring cos
dreamy pollen
tan(t) = sin(t) / cos(t) isn't it?
lean zodiac
marsh citrusBOT
lean zodiac
a discontinuity like this is not removable right
night lion
isolated discontinuity
wraith sun
It is removable
marsh citrusBOT
marsh citrusBOT
Available help channel!