The first ones ?
#help-17
gilded osprey
brisk idol
oh very sorry🙏
gilded osprey
In one variable
vocal sleetBOT
@brisk idol Has your question been resolved?
gilded osprey
,w
integrate piecewise[{{sin(pinx/3)(2x^2+1), 0 <= x <= 3}, {3xsin(pinx/3), 3 < x <= 6}}] dx from 0 to 6
twin meteorBOT
vocal sleetBOT
gilded osprey
.reopen
wild meteor
vocal sleetBOT
wild meteor
how am i supposed to know what will be on a intersection
before i calc it
or am i just suppost to take 0, -1
then use my slope to know i add 3 to the x
and add 4 to the y
so
3, 3
?
<@&286206848099549185>
glass grove
!status
vocal sleetBOT
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
@wild meteor
vocal sleetBOT
@wild meteor Has your question been resolved?
glass grove
im not sure if i didi it using the correct method
I think its fine, just that you chose other values
wild meteor
I think its fine, just that you chose other values
wdym
vocal sleetBOT
@wild meteor Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
outer hare
I have a maths exam tomorrow and pythagoras and some quadratics are coming up on it please could you help?
vocal sleetBOT
I have a maths exam tomorrow and pythagoras and some quadratics are coming up on...
tawny nacelle
and what do you have to do with that? 
outer hare
and what do you have to do with that? <:catthink:526983414226747393>
Factorise it
tawny nacelle
what have you tried
outer hare
A weird long working out that my math teacher taught me that I can never get right
tawny nacelle
show?
outer hare
1 second
tawny nacelle
np
outer hare
This is a simpler one as an example
tawny nacelle
right, factoring by decomposition
tawny nacelle
I would normally do this in my head but the teacher goes mad
well, it is usually good to show your work, even if you can do it in your head
there's no way for the teacher to know that you understand what's going on otherwise!
outer hare
My old math teacher wasn't like that
tawny nacelle
Do you know any other methods?
I do not, unfortunately
this is the standard way to do it
outer hare
Okay
tawny nacelle
try it, and let me know what you get
outer hare
Is it the same type of thing for these questions as well?
6r²-5rt-4t²?
tawny nacelle
yes, it should be similar
outer hare
Okay
I can not find any numbers for it
None of them multiply for 7 and add for 56
This
tawny nacelle
None of them multiply for 7 and add for 56
no, you need to find two numbers which multiply to ac, and add to b
outer hare
Oh
tawny nacelle
a = 8, b = 30, c = 7
outer hare
It is these type of questions that confuse me
outer hare
Thank you 💙
tawny nacelle
❤️
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
outer hare
.close
vocal sleetBOT
tawny nacelle
vocal sleetBOT
Available help channel!
vocal vector
vocal sleetBOT
mellow oyster
if you're asking if this is correct, it is
vocal sleetBOT
@vocal vector Has your question been resolved?
real galleon
Hello,
I need help with the following problem
If X is a Hausdorff compact and countable topological space, then {x in X: {x} is an open set} is dense in X
vocal sleetBOT
Hello,
I need help with the following problem
If X is a Hausdorff compact and co...
real galleon
I really don't know how to start
I thought maybe using something about the complement of the union of this element is closed and then compact
using some open cover of this, but wasn't productive
vast shale
If the adjacent side is sqrt3 and opposite side is 1
Why can’t those be the coordinates
Instead of sine and cosine
Of the point
gaunt sparrow
It's not a unit circle anymore though
vocal sleetBOT
vast shale
I messed up
vocal sleetBOT
Available help channel!
eager zenith
vocal sleetBOT
eager zenith
could you check if this is correct
idk if they want exact words
but i think it should be equations, points, slopes, and (unknown so far)
if anyone could help me find the last missing word
im not confused on this topic its just im trying to figure out the word
eager zenith
oh
thanks
also im not sure if its slopes
would it be better fit if i had coordinate pair instead of slopes?
vocal sleetBOT
@eager zenith Has your question been resolved?
exotic bluff
vocal sleetBOT
exotic bluff
hi! I wanted to know how does one go from the first step to the second
dull bear
Factor numerator and denom
dull bear
Literally just factor them "as normal": n^2 + 3n factors to n(n + 3), and n^2 + 3n + 2 factors to (n + 1)(n + 2)
exotic bluff
the denominator is the one i’m not getting
sorry if this is really basic lol
but like thats a cuadratic
dull bear
,w expand n(n + 3)
twin meteorBOT
exotic bluff
yeah that one I get
dull bear
the denominator is the one i’m not getting
Numerator [top] or denominator [bottom]?
glacial osprey
do you know how to solve quadratic equations by factoring
exotic bluff
yup
glacial osprey
so solve n^2 + 3n + 2 = 0
vocal sleetBOT
vocal sleetBOT
Available help channel!
nova marten
hi
nova marten
um very easy math but i dont have the notes 4 it
to expand (2x + 5)(3x + 8) do i cross multiply?
tawny nacelle
to expand (2x + 5)(3x + 8) do i cross multiply?
you would distribute
nova marten
Yeah I have absolutely no clue how to do that let me google this real quick
tawny nacelle
"cross multiply" is usually the term used when you have an equation that looks like a/b = c/d and want to get rid of both denominators
nova marten
This is like a full semester review and this is like the earliest work we did I don't remember any of it
nova marten
"cross multiply" is usually the term used when you have an equation that looks l...
Ah
Okay one moment
tawny nacelle
Yeah I have absolutely no clue how to do that let me google this real quick
no worries
mellow oyster
have you heard of FOIL?
mellow oyster
look it up again rq
it's exactly this
you'll see the formula and you'll see what to do
nova marten
Man thats so confusing let me try to write it out and see if it makes sense
mellow oyster
(a+b)(c+d) = ac + ad + bc + bd
multiply the first elements of the parentheses, then the outer elements, then the inner elements, then the last elements
nova marten
(2x + 5)(3x + 8)
Okay chat I got this
(2x + 5)(3x + 8)
2x(3x)
5(3x)
2x(8)
5(8)
Ok my bad forgot discord has text format met me fix
mellow oyster
it's close
nova marten
What'd I do wrong here the x is confusing me
mellow oyster
2x * 3x is not 6x
nova marten
Oops
mellow oyster
but 2x * 3x is multiplication, the 2 and 3 multiply to give 6
and x and x multiply for x^2
mellow oyster
can you simplify that any further?
mellow oyster
that can't be combined with anything
no no
31x and 6x^2 are different terms
you can only combine terms where the power of x matches
nova marten
Okay thought so
mellow oyster
so 6x^2 + 31x + 40 is as far as you can go
nova marten
Okay lets see if I can work this one out on my own
(x-3)(x-4)
x* x
-3* x
x* -4
-3* -4
x^2 + -3x + -4x + 12
x^2 + -7x + 12
Am I still supposed to be adding or no
i did that properly?
Hell yeah dude
I don't understand exponent law wtf
The online explanation is so confusing
Use exponent law to simplify and then evaluate
Negative law
3^-4
celest adder
$a^{-b} = \frac{1}{a^b}$
twin meteorBOT
BoiledAnchovies
twin meteorBOT
BoiledAnchovies
celest adder
$=a^0$
twin meteorBOT
BoiledAnchovies
celest adder
=1
wait i will rewrite that
$a^1 \times a^{-1} = 1$
dividing throughout by $a^1$,
$a^{-1} = \frac{1}{a}$
twin meteorBOT
BoiledAnchovies
vocal sleetBOT
vocal sleetBOT
Available help channel!
edgy sparrow
Can i know the answer for 13th question
vocal sleetBOT
vocal sleetBOT
Available help channel!
warm spindle
here is my current working out: https://docs.google.com/spreadsheets/d/1fgYVlVmd6LeCGpA6zHHu59NMP5WjCyT6GEJ9bzFNPAc/edit#gid=0
its a project me and some top students have been working on for a few months, and its super difficult to get a lead
help would be much appreciated
vocal sleetBOT
here is my current working out: https://docs.google.com/spreadsheets/d/1fgYVlVmd...
warm spindle
anomalies keep popping up, such as how n=1.03 has no solutions even though it isnt a perfect square
its so weird and idk what to do
heres the python code for finding solutions if it helps
``import math
n = 2
for a in range(1, 10000000001):
if (math.sqrt((4a**2+4a)/n+1)-1)/2== math.floor((math.sqrt((4a**2+4a)/n+1)-1)/2):
print(a, (math.sqrt((4a**2+4a)/n+1)-1)/2)``
something strange is that perfect square values of n have no solution (proof in the attached sheets)
additionally, the geometric mean products of the two oscillating ratios for those which have them seem to match with the convergence ratio of other values of n, at a seemingly random pattern
warm spindle
``import math
n = 2
for a in range(1, 10000000001):
if (math.sqrt((4*a**2+4...
for this dont just highlight and copy, the notation is a bit messed up so use "copy text"
<@&286206848099549185>
vocal sleetBOT
@warm spindle Has your question been resolved?
warm spindle
sadness
vocal sleetBOT
@warm spindle Has your question been resolved?
gaunt sparrow
Hmm. I'm reading into it. For a fixed n this amounts to finding integer points on a conic curve. For n>0, this is a hyperbola. If n<0 this looks like an ellipse?
Have you looked into Pell's equation? It's possible you could find some way to rephrase the problem as an instance of that in some way?
warm spindle
Hmm. I'm reading into it. For a fixed n this amounts to finding integer points o...
i know how to find integer pairs for n values
however that isnt my concern
my problem is that 1. some n values oscillate ratios while others converge at a seemingly random times and 2. some multiplied geometric means equal the covergence of some random other ratios for an n value that seems unrelated
warm spindle
Hmm. I'm reading into it. For a fixed n this amounts to finding integer points o...
pell's equation (or so far what weve discovered of it) is just that it allows to solve the equation
sudden compass
``import math
n = 2
for a in range(1, 10000000001):
if (math.sqrt((4*a**2+4...
could u format this using ``
warm spindle
and gives no insight into the patterns within it
sudden compass
thanks
sudden compass
``import math
n = 2
for a in range(1, 10000000001):
if (math.sqrt((4*a**2+4...
i dont trust python maths, i was working on a codewars problem that involved solving quadratics, it gave random answers
warm spindle
i dont trust python maths, i was working on a codewars problem that involved sol...
oh why is that
sudden compass
here is my current working out: https://docs.google.com/spreadsheets/d/1fgYVlVmd...
could u give an eg. of the ratio thing?
sudden compass
oh why is that
god knows
warm spindle
could u give an eg. of the ratio thing?
which ratio thing
sudden compass
which ratio thing
oscilating ratios
warm spindle
oscilating ratios
some numbers have both the firsr and second ratio column filled in
im outside on phone so i cant really access anything rn though ill try
warm spindle
oscilating ratios
ive asked my friend for ratio values for n=5 (hes abt to perform something so it might take a while sorry)
sudden compass
kk
sudden compass
some numbers have both the firsr and second ratio column filled in
what is this the ratio of again?
warm spindle
what is this the ratio of again?
a:b in the integer pair solution (a,b)
sudden compass
i see
warm spindle
for now trust the python code ig
gaunt sparrow
however that isnt my concern
I see this now. I just want to make sure I understand what you're doing. You've made me quite curious about this hahaha
When you say the ratios converges for some fixed n, or talk about the limit of the ratios, you mean they converge in terms of a? As in we're taking larger and larger values of a?
I also think rak3en's concerns about numerical error is something to consider, especially if you're going to be testing for equality in floats. Maybe you can set some reasonably small error bound ? That could account for possible solutions that could get thrown out because your algorithm for finding the solutions induces some error. Perhaps it could even explain why some values of n for which you would expect infinitely many solutions (such as non perfect squares) haven't been fruitful.
warm spindle
I see this now. I just want to make sure I understand what you're doing. You've ...
perhaps my explanation was a little inconcise, should i explain it in more depth here or in private messages?
gaunt sparrow
I don't mind DM, but you could also try and make a thread? I think they do that on the server. Might prevent having to refresh the channel timer every now and then
gaunt sparrow
Ah shoot
warm spindle
Ah shoot
main points:
- "ratio refers to a:b in the solution integer pair (a,b)
- some values of n such as 2 and 3 have their ratios converging to some value
- some values of n such as 5 and 6 have a property where ratios oscillate: as in solution numbers 1,3,5,7 etc converge to a particular value, while the rest converge to a different one
the question is to fins a pattern
(among other strange anomalies)
gaunt sparrow
Okok that helps clear things up a bit I think.
I'm playing with the sheets you've made a bit. Probs will go to bed but it's interesting.
Have you found any value in the fact that the product of the ratio limits are pretty much the geometric means to the power of the number of ratio limits you found in the first place?
warm spindle
Okok that helps clear things up a bit I think.
I'm playing with the sheets you'v...
i dont recall one but everything is on the sheet i may be mistaken
viral plover
is this meant to be an exercise in coding mainly?
like what is the source of the question
warm spindle
like what is the source of the question
a student from my institution made it thinking it to be a simple exercise, but it turned out to be quite difficult
gaunt sparrow
Forget what I wrote :p
warm spindle
oh lmao okie
viral plover
has it been solved by them or is it just something to think about
viral plover
right but im saying is there anyone that does have a proof or know the right answers
or is it just an investigation to see if you can discover anything
warm spindle
right but im saying is there anyone that does have a proof or know the right ans...
no
warm spindle
or is it just an investigation to see if you can discover anything
yea
we are also writing a paper on it
viral plover
ah fair enough
gaunt sparrow
I'm going to sleep on it, but I'll keep it in mind tomorrow
viral plover
from math import sqrt
# a^2 + a = n(b^2 + b)
# finding integer solutions for fixed n and investigating limit of a/b
n = 5
maxB = 1000000
minB = 1 #-maxB solutions mirror. if (a,b) a solution then (a, -(b+1)) also a solution. in the limit will not result in different ratio
intPrecDec = 4 # number of decimal places to check to when confirming if integer e.g. when =4 1.9999... is considered an integer but 1.9998... will not be
ratioPrintPrecDec = 7 # how many decimals to print the ratio to
intPrec = 10**(-intPrecDec)
isNearInt = lambda x: int(x) > x - intPrec or int(x + intPrec) > x
for b in range(minB, maxB + 1):
if b == 0: # avoid divide by zero error
continue
# positive solution
a1 = (-1 + sqrt(1 + 4*n*(b*b + b)))/2
r1 = a1/b
# negative solution
# a2 = (-1 - sqrt(1 + 4*n*(b*b + b)))/2
# r2 = a2/b
if isNearInt(a1):
print(f"n={n}: b={b} -> a={a1:.{intPrecDec+1}f}, r={r1:.{ratioPrintPrecDec}f}") # considering only positive solutions
#print(f"n={n}: b={b} -> a1={a1:.{intPrecDec+1}f}, a2={a2:.{intPrecDec+1}f}, r1={r1:.{ratioPrintPrecDec}f}, r2={r2:.{ratioPrintPrecDec}f}")
ratio seems to tend to sqrt(n) which makes sense considering Pell's equation
but additionally we can do a transform from $(a,b)$ to $(r,b)$ by dividing the equation by $b^2$:
\begin{align*}
a^2 + a &= n\left(b^2 + b\right) \
\frac{1}{b^2}\left[a^2 + a\right] &= n\left(1 + \frac{1}{b}\right) \
\left(\frac{a}{b}\right)^2 + \frac{1}{b} \cdot \frac{a}{b} - n\left(1 + \frac{1}{b}\right) &= 0 \
r^2 + \frac{1}{b} r- n\left(1 + \frac{1}{b}\right) &= 0 \
r = \frac{-\frac{1}{b} \pm \sqrt{\frac{1}{b^2} + 4n + \frac{4n}{b}}}{2} &\sim \sqrt{n} \text{ as } b \to \infty
\end{align*}
twin meteorBOT
Acman
viral plover
i dont understand where you are getting your ratio limits from in the sheet @warm spindle perhaps i am misunderstanding?
warm spindle
i dont understand where you are getting your ratio limits from in the sheet <@92...
me neither honestly - three people from my group created it
however someone else also suggested this
i am also confused and i will clarify
viral plover
alright well lmk when you know haha
warm spindle
mk
warm spindle
alright well lmk when you know haha
ill friend u and add u to a group with the guy who made the code
viral plover
sounds good
vocal sleetBOT
@warm spindle Has your question been resolved?
dusk helm
I am to prove the Rodrigues formula for Jacobi polynomials.
I am given two helpful hints as seen in the second picture.
I have been pretty stuck since i cant see how to prove it. I tried an induction proof that ran into trouble with the alpha and beta. I tried just seeing if f = (1-x)^(n+α) and g = (1+x)^(n+β) and inserting it into the given hint would result in anything but havent been able to find a good approach there either. Any help?
vocal sleetBOT
I am to prove the Rodrigues formula for Jacobi polynomials.
I am given two helpf...
@dusk helm Has your question been resolved?
vocal sleetBOT
@dusk helm Has your question been resolved?
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@dusk helm Has your question been resolved?
tiny holly
Hi, I know that this is probably very primitive for some people but I need help. I am stuck at very basic math and I desperately need to pass lol. I am supposed to determine the field of definition and range of function values. (I hope the terms make sense as I used translator for them)
vocal sleetBOT
Hi, I know that this is probably very primitive for some people but I need help....
tiny holly
I'm not sure what to imagine under domain, english isnt my first language
scenic ravine
ok, so the domain is the range of inputs a function can take
what would the domain of (a) be?
tiny holly
wild guess but -2x?
knotty pendant
What values can you plug in for x and get a real answer with?
tiny holly
god this is like twice as hard in english while it already is like 300% hard for me… i mean -2x?
knotty pendant
What is your first language?
tiny holly
czech
knotty pendant
hmmm
You're going to get a range of numbers from ? to ?
I know it's not recommended but, want to try to see if chatgpt can handle translations?
tiny holly
actually maybe yeah
knotty pendant
ok
tiny holly
You're going to get a range of numbers from ? to ?
like real numbers? 0 to infinite?
knotty pendant
like real numbers? 0 to infinite?
Na jaká čísla můžete dosadit do x a získat reálnou odpověď? Můžete dosadit i záporná čísla?
Does this czech sentence make sense?
tiny holly
language wise yes
knotty pendant
grammar wise no?
tiny holly
that too, i just cabt figure out the real answer/numvers
knotty pendant
Can you plug negative numbers into -2x + 5?
tiny holly
id say no because you cant mix x and numbers? like + -
knotty pendant
...
tiny holly
i genuinely cant do math, im stuck at 5th grade math:,)
knotty pendant
These are equations where you plug numbers in for x and get a number out y
This is precalc?
What numbers can you plug in for x and get a number out for y?
tiny holly
is it the y = ax + b? because otherwise i can only think of real numbers as i said (R) like anything that is positive and not negative
knotty pendant
real numbers can be negative
tiny holly
oh
knotty pendant
like real numbers? 0 to infinite?
so...
tiny holly
so - infinite to infinite?
tiny holly
oh okay okay well thats something
knotty pendant
You got a), what about b)
vocal sleetBOT
@tiny holly Has your question been resolved?
tiny holly
sorry my bad ill get back to this soon something came up i have to deal with it rn
knotty pendant
You're good
vocal sleetBOT
@tiny holly Has your question been resolved?
tiny holly
wait are both these things literally just D(f) = R and H(f) = R ??
junior adder
vocal sleetBOT
junior adder
yea so appart of finding the limit. i need to find the derivative
so (log_2 n)^3/n should be 0
as n approaches infinity
but i need to find the derivative of (log_2 n)^3
and that has me mixed up
mellow oyster
yes, so you try plugging in inf, you get inf / inf, you try to do l'hopitals
the n becomes 1
and to differentiate (log_2(n))^3
junior adder
ahh ok so now i need to learn l'hopitals
elfin surge
ahh ok so now i need to learn l'hopitals
its ezz wont take much time
mellow oyster
and to differentiate (log_2(n))^3
you can think of this as a composition of two functions, with f(x) = x^3 and g(x) = log_2(x)
then what you have here is exactly f(g(x))
which you differentiate with the chain rule
junior adder
so in l'hopitals.. i need to turn some things into a prime?
so its not finding limits. its just flat out using l'hopitals to solve this
mellow oyster
l'hopitals is used to find limits
junior adder
so all i need to do is look up what l'hopitals is and learn that
mellow oyster
yes
junior adder
so when i search on youtube i should focus on l'hopitals only
mellow oyster
sure
junior adder
ahh ok
so i need to figure out how to find the derivative
of (log2 n)^3
so that first video i was watching was basically the same thing
and now im back to getting stuck on finding the derivative of this
(ln n)^3
this is what mathway says the derivative is
but then that makes it much more confusing on proving the limit
hmmmm
any ideas?
do i need to use "e"?
@mellow oyster
so after the derivative of the top it would be : (3(log_2(n))^2/ln(2)n)/n
but that does not intuitivle prove to me that it is 0
mellow oyster
no, you would have to do l'hopitals multiple times
there's a slightly simpler way i think
(log_2(n))^3 / n is the same as (log_2(n) / n^(1/3))^3
so to show the first one goes to 0, show the second one goes to 0
twin horizon
this is what mathway says the derivative is
Why is that ln 2
mellow oyster
it's quicker to show that log_2(n) / n^(1/3) goes to 0
mellow oyster
Why is that ln 2
comes from derivative of log base 2?
junior adder
yes
mellow oyster
it's quicker to show that log_2(n) / n^(1/3) goes to 0
you only have to do l'hopitals once here
junior adder
my god this is confusing
when u say show that "t log_2(n) / n^(1/3) goes to 0" that to me is confusing
without me plugging in specific numbers
one after another
junior adder
hmmmmmmm
ok so just need to really go in on lhopitals
no other way around it
and l'hopitals will require me to know how to find the derivative of that thing
vocal sleetBOT
@junior adder Has your question been resolved?
twin horizon
Maybe try log_2 n = x
vocal sleetBOT
Maybe try log_2 n = x
vocal sleetBOT
vocal sleetBOT
Available help channel!
strong grove
Dumb question but
vocal sleetBOT
Dumb question but
strong grove
let's say you have 200 trials and the probability of success is 1/20
how many successes can you expect to see?
Is expected success 10?
desert hornet
are all the trials independent?
strong grove
Yes
desert hornet
then yes
vocal sleetBOT
vocal sleetBOT
Available help channel!
dry cedar
vocal sleetBOT
sly sierra
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Available help channel!
prisma badger
vocal sleetBOT
prisma badger
could anyone that knows physics helkp me
i dont know what im doing wrong here
apparently there is no roots
but one should be negitive and one should be positive
livid drum
Are you sure you are getting no roots? At a cursory glance everything seems ok. I seem to get a positive discriminant, too
prisma badger
tried it both on my calculator and on a website that does quadratic formula for you
i think my equation wrong
prisma badger
Are you sure you are getting no roots? At a cursory glance everything seems ok. ...
i asked chatgpt and it arranged it so the 4.9 was positive
rearranging on the right side instead of left
wsit
livid drum
Ah, I see the problem
livid drum
Yes
prisma badger
just saw that
vocal sleetBOT
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Available help channel!
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merry sky
Hello does this look right?
mellow oyster
yes
merry sky
Could u also check this one for me too
dull pine
pretty sure that's not a one-to-one (in the sense of bijective mapping) function
merry sky
pretty sure that's not a one-to-one (in the sense of bijective mapping) function
Oh, how should I go about it?
dull pine
that aside, your h⁻¹ is correct
the exercise is just a little weird, but that's not your fault
merry sky
the exercise is just a little weird, but that's not your fault
Oh I get you! But everything looks good in terms of the question though?
dull pine
yes
merry sky
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final furnace
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final furnace
how do I find the area of the shaded region
The shape is a square
and since the area 3,4 triangles have the same base the ratios of their side length is 3:4
so I put 3x and 4x
vast shale
Yk the total area right?
final furnace
no
vast shale
…
final furnace
That’s why I’m trying to solve for x first
final furnace
Yes
So I did this by using formula for triangle on the area 5 triangle
Ok so I plugged it in and I got 12+4root 6
For area of the whole square
vocal sleetBOT
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dreamy cliff
I need a proper explanation on Lopital's Rule
vocal sleetBOT
I need a proper explanation on Lopital's Rule
dreamy cliff
I'm not sure I quite understand what it means
warm spindle
I need a proper explanation on Lopital's Rule
alright so l'hopitals rule
do you understand what limits are
warm spindle
so first, take an example
dreamy cliff
mhm
warm spindle
say you wanted to calculate this limit
however what happens when you plug in the value
dreamy cliff
0 on top and bottom
warm spindle
yeah and thats undefined
dreamy cliff
yep
warm spindle
so you could factorise or use lhopitals rule
desert hornet
yeah and thats undefined
Not undefined, it’s indeterminate
warm spindle
for the sake of demonstrating we use the rule
desert hornet
Which means it can take any value
warm spindle
Which means it can take any value
right
uh so when you apply the rule, take the derivative of the top and bottom of the original function
then simply reevaluate with the limit subbed in
dreamy cliff
ok, so then it'd be quotient rule or independent of each other?
warm spindle
independant
desert hornet
$$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f’(x)}{g’(x)}$$ provided $$\lim_{x\to a}f(x)\text{ and }\lim_{x\to a}g(x)\text{ are either both 0 or both }\pm\infty\text{ and the resulting limit exists }$$
dreamy cliff
what i was about to ask lol
twin meteorBOT
kheerii
desert hornet
The last condition of the resulting limit existing is very important
dreamy cliff
ok gotcha
desert hornet
If the resulting limit after differentiating doesn’t exist, it means the L’Hopital’s rule is inconclusive, not that the original limit doesn’t exist
dreamy cliff
mmm
ok
so if it was indeterminate again AFTER applying the rule, then it's inconclusive?
desert hornet
Yeah
dreamy cliff
cool beans
dreamy cliff
oh, so just keep applying it?
desert hornet
As soon as you get a limit that’s evaluatable that becomes the value of all the previous limits
desert hornet
oh, so just keep applying it?
Yeah, as long as you keep getting 0/0 or inf/inf
desert hornet
As soon as you get a limit that’s evaluatable that becomes the value of all the ...
But if you reach a limit which doesn’t exist it means you can’t conclude anything about the previous limits
dreamy cliff
gotcha
desert hornet
Take $\lim_{x\to\infty}\frac{x}{x+\sin x}$
twin meteorBOT
kheerii
desert hornet
First tell me is this an indeterminate form?
desert hornet
Why undefined?
dreamy cliff
cause of sin infinity?
desert hornet
cause of sin infinity?
Whatever that is, it’s between [-1,1]
It’s the x that takes it to infinity
dreamy cliff
so then it's 1 plus infinity on bottom
desert hornet
1+infinity is infinity only
dreamy cliff
which means infinity over infinity
dreamy cliff
uh
desert hornet
Does $\lim_{x\to\infty}\cos x$ exist according to you?
twin meteorBOT
kheerii
dreamy cliff
yes
desert hornet
Which means?
dreamy cliff
and because of that, we can't apply L'Hopital's rule again
meaning the original limit DNE
desert hornet
No.
dreamy cliff
WHAT
desert hornet
That’s exactly why I pointed this limit out to you
dreamy cliff
ok
damn!
thought I had it
so that mean's that we just can't apply the rule again?
desert hornet
What’s our conclusion based on the fact that the limit after differentiating does not exist?
dreamy cliff
it doesn't mean the original function DNE
desert hornet
so that mean's that we just can't apply the rule again?
No, since $\frac1{1+\cos x}$ is not an indeterminate form
twin meteorBOT
kheerii
dreamy cliff
**kheerii**
ok ok
desert hornet
it doesn't mean the original function DNE
Yes
Which means L’hospital’s rule doesn’t work for this question
You need to find another way
dreamy cliff
but if it was, we'd just apply it again until we got a DNE or a value
desert hornet
but if it was, we'd just apply it again until we got a DNE or a value
Yeah
If the resulting function was also an indeterminate form
desert hornet
Nw
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cedar linden
area under the curve
y = 2x - x^2 in [0, 3]
vocal sleetBOT
area under the curve
y = 2x - x^2 in [0, 3]
drifting terrace
scenic ravine
?
yes
it's area here
so you can't just compute the definite integral
wherever the area is negative, take the positve area
scenic ravine
$\int_0^2 f(x)dx +| \int_2^3 f(x)dx|$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
cedar linden
$\int_0^2 f(x)dx +| \int_2^3 f(x)dx|$
you are right because we are evaluatin in 2 differents quadratics
thanks
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toxic pasture
umm
toxic pasture
hi
vocal sleetBOT
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tawdry aspen
There are 17 points on a plane and are connected by lines colored red, blue, and yellow. Prove that there is a monochromatic triangle. (No three points are in a straight line)
vocal sleetBOT
There are 17 points on a plane and are connected by lines colored red, blue, and...
tawdry aspen
Asked this question yesterday in help 19.
Haven't been able to prove it yet because:
- I don't understand Ramsey's theorem yet.
- I have no idea how to prove something in combinatorics like this yet.
@solar barn I would like to have more help if that is possible (I'm sorry for pinging)
solar barn
Hello. What's confusing for you about the theorem?
tawdry aspen
Hey
So from yesterday i understood the six vertices example with two colors
This one
so ive watched some youtube videos
if there are two colors, the minimum amount of vertices needed to guarantee a monochromatic triangle is six
but what if there's three? and what effect does the pigeonhole principle have on three colors?
my work is due tomorrow so I guess I have to prove it today.
solar barn
yes, I don't know if you read what I wrote yesterday in my last message, but I can take that again. Imagine you have 17 vertices and you select one of them.
tawdry aspen
yes, I don't know if you read what I wrote yesterday in my last message, but I c...
I think I accidentally slept yesterday, my bad haha
solar barn
No worries. This one is to be connected to 16 other vertices.
so if there are 3 colors, pigeonhole principle says that at least 6 of the edges have the same color.
Do you understand so far?
tawdry aspen
so if there are 3 colors, pigeonhole principle says that at least 6 of the edges...
okay I understand
solar barn
now we look at the 6 vertices we connected with the original vertex we chose. These have also to be connected to each other.
but, the edges cannot be red.
tawdry aspen
the edges cannot be the same color with the edge we connected to the main vertex, right?
is that what you mean?
solar barn
yes, otherwise you form a red triangle.
tawdry aspen
Wait I have a question
So what we are actually trying to do is to not make a monochromatic triangle until we are forced to?
solar barn
yes, that's the gist of it. But you will see soon that this is not possible.
tawdry aspen
Alright thank you, cleared up some of the confusion I had yesterday.
Now what do we do from here?
solar barn
Well, we know that we cannot connect these 6 vertices with red edges, so we are forced to color the edges either blue or yellow.
You may notice that this is actually the 2 color version of Ramsey's theorem, you want to connect 6 points with each other using 2 colors without forming a monochromatic triangle.
We know that this is impossible, as proven.
so we will guaranteed end up with some monochromatic triangle no matter how we color the edges.
tawdry aspen
Okay that's amazing!!
I most definitely understand now.
Now what can I do to prove it, though.
I've never proven anything in mathematics yet.
Let alone write it on paper.
solar barn
What I wrote can be said to be a proof, it is mathematical truths that together lead to a conclusion.
solar barn
To be more formal you may need to write up definitions for the vertices chosen and so on.
The important part is to be clear, concise, but also correct, the proof must be valid and logically sound.
hexed plume
how to multiply and divide decimals without a calculator
vocal sleetBOT
how to multiply and divide decimals without a calculator
hexed plume
so 2.7x3.3?
dark kiln
or 2.7 × 0.33
hexed plume
its stil difficult even if you convert it to a whole number
ionic merlin
Just how you calculate 27 * 33
Then since 27 * 33 = 2.7 * 10 * 3.3 * 10, you get result of 27 * 33 and divide by 100
For 27 * 33 itself, you calculate 27 * 30 then add 27 * 3 to it
ionic merlin
Basically
2.7 = 27/10, right?
And 3.3 = 33/10
To multiply and divide decimals, just convert them to fractions
2.7 * 3.3 = 27/10 * 33/10 = (27 * 33)/(10 * 10)
hexed plume
yes
ionic merlin
As for 27 * 33 itself, think of it maybe like this:
27 * 33 = 27 * (30 + 3) = 27 * 30 + 27 * 3
hexed plume
any other method?
ionic merlin
27 * 33 = (30 - 3) * 33 = 30 * 33 - 3 * 33
oblique quarry
multiplication of numbers is the kind of thing that comes with experience. you can’t figure it out in less than 24 hours because every problem is different and you need experience looking for the patterns. in this problem the fastest method is not the standard method but to use the pattern (A-B)(A+B)=A^2-B^2. Plug in A=30 and B=3 and this becomes (30-3)(30+3)=30^2-3^2. And that just means (27)*(33)=900-9=891
ionic merlin
Or
27 * 33 = (30 - 3) * (30 + 3)
Which looks like:
(a - b) * (a + b) = a^2 - b^2
So
(30 - 3) * (30 + 3) = 30^2 - 9
ionic merlin
multiplication of numbers is the kind of thing that comes with experience. you c...
Yea exactly this
hexed plume
im confused does the * stand for multiplication or a fraction
and what does the upside down v mean
oblique quarry
im confused does the * stand for multiplication or a fraction
what grade are you in?
hexed plume
what grade are you in?
7
oblique quarry
Ok. * is multiplication (same as x or print parentheses next to each other like (3)(5)=(15)). ^ means a power. So 5^2 is 5 to the power of 2 which is just 5*5=25.
oblique quarry
But in grade 7 you probably don’t have much experience with powers. I would try to use the method your teacher taught you in class
hexed plume
well i did powers
but at the start of the year
i should know enough
i also dont think i needed powers for dividing simple decimals
oblique quarry
and you don’t have enough experience with them to use the pattern we suggested which comes from algebra
hexed plume
can you teach me the whole number method
oblique quarry
you don’t. they can make things easier when you know more math
here. give me second i have a link to a visual activity explanation
try that
hexed plume
this is area and model
oblique quarry
do the game it will help
hexed plume
which one
oblique quarry
there is no “magic shortcut” if that’s what you’re looking for. the only way is to practice with a lot of examples
whichever level you want to. level 1 is easiest
hexed plume
but which one do i go to there is 3 different games
oblique quarry
the third one is called game
hexed plume
ok
oblique quarry
i used to teach 7th grade. i highly recommend telling your teacher you’re confused about this topic and would like to ask for some help or tutoring. teachers will respect you for asking for help
this one does decimals
and if you’ve never seen the area model method before, this one is more basic and shows how it works. https://phet.colorado.edu/sims/html/area-model-introduction/latest/area-model-introduction_all.html
vocal sleetBOT
@hexed plume Has your question been resolved?
oblique quarry
You will not get a more satisfying answer than what you’ve seen here. There is no magic shortcut. If there was, your teacher would have told you it. The only secret to success is to spend time trying examples until you start to get it. This is the experience of learning. This is what we all had to do.
The confusion you are having is with the basics of multiplication. When you first learned multiplication in 3rd grade, you might have tried to memorize the answers without understanding what they mean. Now you’re having trouble because it doesn’t seem you know what multiplication means enough to extend to a new context (decimals). The area model helps to show what multiplication means. I think you’ll need someone to sit down next to you and show you if you need more detailed help than that.
vocal sleetBOT
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rigid lake
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rigid lake
how can i find this anti derivative
tawny hollow
One route is to maybe do a u-sub, say by u = 2^x
scenic ravine
start by writing $4^x$ as $2^{2x}$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
rigid lake
thanks, ill try u=2^x. i tried doing u=2^x+1 and it didnt work
scenic ravine
that should work too
rigid lake
**ƒ(Why am. I here)=I don't Know**
i did that and then tried u=2^x+1 but didnt work
should work with u=2^x tho
scenic ravine
,w integrate (4^x+1)/(2^x+1)
astral pilot
rigid lake
then you will need to use partial fractions
used long div
full bobcat
show your work
tawny hollow
long div is fine here
vocal sleetBOT
@rigid lake Has your question been resolved?
tawny hollow
Take the derivative to check
rigid lake
hold up
tawny hollow
Yeah you missed to actually use ln2 u dx i think
tawny hollow
<@848258301333602314> Has your question been resolved?
press the cross btw, unless ure done
its gonna timeout otherwise
rigid lake
ok
yep, all good
i just missed the uln2dx for some reason lol
all good now tho, thank you
.close
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kind horizon
How do j solve this
vocal sleetBOT
How do j solve this
scenic ravine
do you know the formula $cos(2x)=1-2sin^2(x)$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
kind horizon
Yep
scenic ravine
use it here
kind horizon
1 - psin^2(x) ????
kind horizon
use it here
.
scenic ravine
$1-cos(px)=2sin^2(\frac{px}{2})$
twin meteorBOT
ƒ(Why am. I here)=I don't Know
warm path
**ƒ(Why am. I here)=I don't Know**
But you still get 0/0
scenic ravine
now multiply and divide by x^2/2
vocal sleetBOT
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vocal sleetBOT
i need help
narrow sage
for my back sub
vocal sleetBOT
@narrow sage Has your question been resolved?
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@narrow sage Has your question been resolved?
cursive turret
Did you ask a question?
narrow sage
north frost
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@narrow sage Has your question been resolved?
cursive turret
!status
vocal sleetBOT
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
empty berry
empty berry
pls explain whats the right answer
wraith python
Do you understand the difference between a positive and negative slope?
empty berry
yeah
wraith python
So when the curve is going upwards the graph of the slope should be above the x-axis and when the curve is going downwards the graph of the slope should be **below **the x-axis. This leaves three possibilities from the possible answers.
From the given graph, you can see the slope is positive when x<0 and the slope is negative when x > 0.
empty berry
So when the curve is going upwards the graph of the slope should be **above** th...
is it the bottom right?
wraith python
No. Do you know magnitude is?
empty berry
mb i meant boittom left
but uh no lol
but from your explanation i think it can be bottom left
wraith python
No.
empty berry
dam
wraith python
The bottom left is never negative.
empty berry
oh i thought it was based of slope
wraith python
Yes, imagine a tangent line on the curve at any given point. Which direction would the right end of that line be pointing in relation to the left end. Would it be above or below?
vocal sleetBOT
@empty berry Has your question been resolved?
empty berry
Yes, imagine a tangent line on the curve at any given point. Which direction wo...
above?
vocal sleetBOT
@empty berry Has your question been resolved?
wraith python
above?
Look at the slope at any given point. Note when the line is green, the slope is positive, and when the line is red, the slope is negative.
wraith python
Notice how the slant of the tangent line changes.
The more it slants, the higher the magnitude of the slope.
The lower the slant, the lower the magnitude of the slope meaning the slope will be closer to zero, or y = 0.
empty berry
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tidal mesa
I need assistance finding the derivative. I evaluated the derivative of 5 sqrt(t) and 6/sqrt(t) individually and tried to sum them up but was incorrect
vocal sleetBOT
I need assistance finding the derivative. I evaluated the derivative of 5 sqrt(t...
flint idol
try finding the derivative of $\frac{-6}{\sqrt{t}}$ again
twin meteorBOT
y0shi
flint idol
it isnt 1/t^2
im assuming the second picture there is the form before it was simplified
or combined into one giant fraction
tidal mesa
Can we go through it step by step, I've worked it out 5+ times and been wrong each
twin meteorBOT
y0shi
flint idol
and now we just utilize the power rule here
tidal mesa
3t^-3/2
flint idol
yep
thats it
so all in all your final derivative is $\frac{5}{2\sqrt{t}}+\frac{3}{t^{\frac32}}$
twin meteorBOT
y0shi
tidal mesa
How does the t get to the denominator? $3t^{-\frac{3}{2}}$
twin meteorBOT
Axlqwotl
tidal mesa
Ohh, its that the exponent is negative
gloomy nacelle
Hi @tidal mesa
spare hull
$x^{-n} = \frac{1}{x^n}$
twin meteorBOT
Mar the Marey
tidal mesa
Hi <@307350562372845568>
Hello! Thought I had it, then got stuck
Several times
I started on this one, applied the power rule and constant rule, but don't know what I should do next
spare hull
so for e the rule is:
$\frac{\mathrm{d}}{\mathrm{d}x}\left[\textbf{e}^x\right] = \textbf{e}^x$
twin meteorBOT
Mar the Marey
spare hull
so the derivative of e^x is just e^x!
tidal mesa
I'm also having trouble matching derivatives to their graphs
I don't think B can go to I since it would go through and that disqualifies it right? Same for III?
I think A and D are right as well, but I can't tell with C
I think there's something wrong with my understanding in general as a couple other answers and lines of reasoning have all been incorrect as well.
gloomy nacelle
Hi again @tidal mesa
tidal mesa
Hi again <@307350562372845568>
Hello!
gloomy nacelle
I'm also having trouble matching derivatives to their graphs
Did you solve this?
gloomy nacelle
The curves given to you (in blue) are polynomials, can you see that?
Can you revisit a bit of derivatives?
Especially the power rule
That would help you instantly
Otherwise, ping a helper because I'm off to sleep
tidal mesa
Alright, thank you for your help!
tidal mesa
Can you revisit a bit of derivatives?
Also, even though it's what I'm doing homework on, I'm basically learning as I go, so there's not a lot to revisit. But thanks to you and the help of everyone else here I'm much better than I was 2 days ago when I understood nothing!
vocal sleetBOT
@tidal mesa Has your question been resolved?
tidal mesa
I'm also having trouble matching derivatives to their graphs
<@&286206848099549185>
elfin fiber
tidal mesa
Yes, matching the derivative to the graph