since the boundary of D is a circle
#help-28
waxen raven
but i don't really see the connection between g and f
f pulled back along the circle?
wait sorry
here is our curve (boundary is in blue)
now we've gone (x,y) = (cos t, sin t)
which draws out the circle
now f(cost, sint) will be the height of the graph
at any t
im like
i don't know how to word it
sorry wdym by "f pulled down along the curve"?
and can i use the second derivative test on g to find whether it's maxima or minima on the boundary?
<@&286206848099549185> sorry!
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cursive crow
<@547342841781944331> Has your question been resolved?
u yap too much lil brody
waxen raven
i agree
waxen raven
<@&286206848099549185> anyone!!
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robust slate
The boundary is only dependent on x and y, so any y coordinate in the boundary is precisely determined by the x coordinate
So even though you have two coordinates, picking one of them restricts everything up to sign
And ofc cos(t)=cos(2pi-t) but sin(t)=-sin(2pi-t)
I’m assuming this if your question at least
Don’t entirely follow
waxen raven
The boundary is only dependent on x and y, so any y coordinate in the boundary i...
ok I'm liking where this is going
waxen raven
So even though you have two coordinates, picking one of them restricts everythin...
I see
honestly
I love the elegance
waxen raven
The boundary is only dependent on x and y, so any y coordinate in the boundary i...
this actually cleared it up
thank you so much
waxen raven
and can i use the second derivative test on g to find whether it's maxima or min...
also sorry this
robust slate
and can i use the second derivative test on g to find whether it's maxima or min...
Second derivative test applies to critical points
So unless your entire boundary is critical points, no
robust slate
mhm
waxen raven
for example at t=pi/4, g(pi/4) = 3/2
and at t=pi/4 the second derivative is negative
making it a maximum of the boundary and a possible maximum of f
robust slate
Oh you’re talking about the second derivative test for single variable
Yeah you could
But why
sin 2t is between -1 and 1
waxen raven
haha in a more general case
robust slate
ok
waxen raven
in this case it's easy to see of course
anyhow thank you so much for answering😭
I'll close this channel now
.close
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proven lynx
hello so
proven lynx
how tf do i know the expected value isnt in the original unit
like i was calculating this shit and i realized i didnt do 500 * 3,0
how do i know if the expected value is given in the original unit
round gust
how tf do i know the expected value isnt in the original unit
wdym
ionic knoll
There's no units in this question
ionic knoll
What's the question
proven lynx
What's the question
to find out a b and c
round gust
expected value just means the average grade
round gust
where does it say that
ionic knoll
The expected value is 1/500th of the sum of the grades
proven lynx
The expected value is 1/500th of the sum of the grades
yes
so in a problem like this
its never given directly?
in the already multiplicated value
ionic knoll
You multiply it by 500 to get the sum of the grades
Expected Value:
$$a1+b2+1673+1224+b5+c6=500*3.0$$
proven lynx
You multiply it by 500 to get the sum of the grades
yes
glossy valveBOT
BBMaths
proven lynx
oh
ionic knoll
Because a people got grade 1, b got grade 2, ...
ionic knoll
There's 3 sources of information that gives equations
Counting
Expected Value
Variance
proven lynx
yes ik
i was just confused by the 3,0
they like to make it so u think
in these problems
ionic knoll
Gotta use 100% of the brain 🧠
proven lynx
like instead of saying its the expected value is 3.0 theyll maybe say the average grades are 850
or some shit like that yk
round gust
you can also think about it like:
expected value = 1* a/500 + 2* b/500 + 3* 167/500 + 4 * 122/500 + 5* b/500 + 6* c/500 = 3
when calculating expected value you always multiply the grade by it's probability to occur
ionic knoll
Expected value just means "mean" or "average"
proven lynx
Expected value just means "mean" or "average"
so the average grade was 1500or
ionic knoll
No that's the sum of everyone's grade numbers
proven lynx
huh
round gust
you can also think about it like:
expected value = 1* a/500 + 2* b/500 + 3* 167/...
do you understand this
proven lynx
do you understand this
yes
ionic knoll
Average means you divide by number of people (500 here)
ionic knoll
No that's the count of people
I mean imagine you have all 500 people's grades
And add them up
That's 3.0*500=1500
proven lynx
I mean imagine you have all 500 people's grades
ohhhh
i get it
imagine i had to interpret this in an exam holy shit
ionic knoll
you can also think about it like:
expected value = 1* a/500 + 2* b/500 + 3* 167/...
I would say "multiply the grade by the proportion of people who got it"
ionic knoll
It's like a bar chart but the bars width and area also have meanings
proven lynx
ok ill take a look at that
and then normal distribution and hypothesis tests and im done holy shit
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spring verge
I’m working on a combined circuit problem (see attached picture). I want to find the total resistance and total current, but I’m stuck on how to start simplifying the series and parallel parts correctly.
Can someone guide me on how to approach calculating total resistance and current for this type of circuit?
spring verge
Ohh, mb thank you!
wraith wolf
I’m working on a combined circuit problem (see attached picture). I want to find...
Ok so basically R2, R4, and R1(right) are the resistors in parallel, so you need to use the formula 1/R_t = 1/R_1 + 1/R_2+ 1/R_3... +1/R_n to calculate total resistance in parallel, and then R1(top) and R3 is in series you add them toegether using the formula R_T = R1+R2+R3....+R_n. Note that 1 k ohm is 1000 ohms. Then add both resistances you calculated and add together to find total resistance in the circuit.
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Ok so basically R2, R4, and R1(right) are the resistors in parallel, so you need...
@wraith wolf Has your question been resolved?
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urban jacinth
did you have a question?
if not, please close this channel and dont use it to post unnecessary things
you can go #chill
fallen ivy
if not, please close this channel and dont use it to post unnecessary things
I mean those have numbers so it’s related to math
urban jacinth
I mean those have numbers so it’s related to math
so do you have a question or not
rare dock
how much is that in usd dollars?
stiff pier
<@&268886789983436800> self-promo..? 
odd locust
uh. please dont use help channels for this
wintry smelt
Can we host math tournament on this server? with a prize pool?
wintry smelt
Well it’s about math.
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rapid beacon
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stiff musk
what's the question? you cut the top part off
stiff musk
ah seems reasonable to assume that in each case b or h is some constant for which the interval makes sense
like for 5, the interval is [1,b], so b should be some constant greater than 1
(your answer will be in terms of b)
stiff musk
yep, any number strictly greater than 1
it doesn't mean you get to pick the value ofc
rapid beacon
so 0.999 wouldn t be correcty
stiff musk
right, 0.999 wouldn't make sense unless they're defining [1, 0.999] to mean [0.999, 1], which would be weird
rapid beacon
Okay
then would i just use those 2 equations 1 and 1.001 into the slope formula?
and plug them in
stiff musk
no you can't choose 1.001
rapid beacon
wtf
stiff musk
yes b stands for some number greater than 1, but you don't get to choose which number
rapid beacon
ah i see
stiff musk
your answer will have the letter b in it, not numbers
stiff musk
ok good
so what would y2 - y1 be for #5?
well let's start with the easier part
what would x2 - x1 be?
rapid beacon
is x1= 1
stiff musk
yep
stiff musk
ok so x2 - x1 = ?
rapid beacon
b-1
rapid beacon
-3
rapid beacon
4b2-10
stiff musk
not quite right
rapid beacon
tff
stiff musk
haha nw
rapid beacon
yeah
stiff musk
so now you just need to divide to get (y2 - y1) / (x2 - x1)
stiff musk
yea you'll get some formula that has b's in it, and that will be your answer
(it might be possible to simplify, let's find out)
rapid beacon
oh so if it isnt then ill leave b as is
stiff musk
yep correct
stiff musk
they didn't give you a value for b, so you won't give them one either 🤣
yea, and that can be simplified a bit
stiff musk
yea now try factoring b^2 - 1
rapid beacon
wb 9?
stiff musk
you know how to factor quadratic polynomials?
stiff musk
yea
stiff musk
nah i prefer to just engage in the help channels
stiff musk
sure, yw
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queen flame
Do you still need help
glossy valveBOT
stiff musk
plotting on different y axis scales maybe?
the scale chosen by wolfram is a bit crazy, it's impossible to see if the function dips below zero for example (it does)
fast peak
that y scale is way too zoomed out to see anything for small x
stiff musk
if you do it on WA directly instead of via the bot, the first plot is scaled much more reasonably
rapid beacon
ok
i see
how do i estimate the extrema
and intervals and stuff
what even is an extrma
stiff musk
an extremum is a generic word for either minimum or maximum
rapid beacon
bruh
rapid beacon
got itt
so the max aint infinity?
its the point in the middle of the parabola correct?
stiff musk
the global max would be infinity (or you could say it doesn't exist)
the one in the middle is a local max
torn jolt
How do I do this btw I forgot the concept🥀
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How do I do this btw I forgot the concept🥀
turbid badge
How do I do this btw I forgot the concept🥀
for some output of the function k, i need 3 inputs which will will give me k as an output
looking at the graph, and the options, can you tell which output corresponds to three different inputs
slate violet
or more simply, f(x) = k is a horizontal line
try drawing different horizontal lines on the graph
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tulip tartan
Hello was just wondering why -7 is rejected when we are trying to find the value of k in the pgf
rapid rain
Hello was just wondering why -7 is rejected when we are trying to find the value...
The PGF must be well defined on [0,1], since for such t G_X(t) is a converging series
rare dock
if you look at the coefficients in G_X when k = -7, some will be > 1 i think
tulip tartan
The PGF must be well defined on [0,1], since for such t G_X(t) is a converging s...
Ahh alright thank you so much
rare dock
so, doesn’t make sense as a pgf
tulip tartan
if you look at the coefficients in G_X when k = -7, some will be > 1 i think
Oh ya dang
rapid rain
Yes, alternatively notice that G'_X(0) = 63/32 > 1
rare dock
,w 9/(4-7x)^2 series
glossy valveBOT
tulip tartan
Dang, is there a way for me to identify if the expansion converges in more complex equation or do I just need to expand it until I find one that's >1
rapid rain
If you don't want to compute every series terms, there are other ways
tulip tartan
If you don't want to compute every series terms, there are other ways
Ahh ok
rapid rain
The PGF must be well defined on [0,1], since for such t G_X(t) is a converging s...
Like here where we can find out that G_X(t) isn't actually well defined on [0,1]
In the case that G_X(t) does work, then G_X must be a non-decreasing function on [0,1]
So you can also look at if G_X' >= 0 or not
rapid rain
Like f(t) = t(3-2t) is not a PGF
Because f'(t) = 3 - 4t, which isn't non-negative on [0,1]
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knotty grail
i understand the answer key given but my method doesnt seem to work
sturdy valve
a is 17/2 right not 17
knotty grail
yeah
sturdy valve
nvm its a bit tough for me to follow sorry
sonic stratus
gimme a quick sec
queen flame
i understand the answer key given but my method doesnt seem to work
can you resend the diagram
img is low resolution
knotty grail
guess this works
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queen flame
hm..
you there?
if you just consider mod e^2-1 here then the 1-e^2 works idk why it rejects e^2 -1
oh right 0<e<1
and LHS can't be negative
sonic stratus
,tex We know $A = 30 = \frac{BH}2$\
$\mathrm{distance}(F_1,F_2) = 2c = 2\sqrt{a^2-b^2}$\
Notice, $B = 2c$ and $H = c\sin\theta$ where $\theta$ is the angle at which P is located
The problem now becomes: $$c^2 \sin \theta = 30$$
glossy valveBOT
sonic stratus
or: $(a^2 - b^2) \sin \theta = 30$
glossy valveBOT
sonic stratus
we already know a.
tall onyx
that's what he did
sonic stratus
yea, im doing this to follow up myself, mostly cause while writing down on paper i ended up with a neg. square root
tall onyx
if you just consider mod e^2-1 here then the 1-e^2 works idk why it rejects e^2 ...
That shouldn't be e^2-1 yeah
But the answer still remain incorrect for some reason with that fix 
queen flame
But the answer still remain incorrect for some reason with that fix <:holothink:...
wym
you got a^2 - 30 in the root
289 - 120 = 169
tall onyx
f*ck, I forgot to divide it by 2
queen flame
oh
knotty grail
if you just consider mod e^2-1 here then the 1-e^2 works idk why it rejects e^2 ...
ohh its 1-e^2 my badddd
tall onyx
I mean the major axis
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sonic stratus
thanks
tad late, but i managed to solve it through algebra on a similar method, i got the correct answer, but i didnt precisely use e
c makes it a lot easier since it appears all over the equation.
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hollow moth
in class, the prof alleged this integral was equal to lambda/2. I am supposed to check it with desmos, but im a little confused on how to do so.
minor crater
yes you haven't defined a so it doesn't know what to do with it
write a=1 on the next line and see if the integral is 0.5
minor crater
(where k = 2.7)
but also what the heck 
minor crater
in class, the prof alleged this integral was equal to lambda/2. I am supposed to...
this is false
hollow moth
oh i see. Thank you. I see that it's .57, so it's close
minor crater
ah you mean approximately
you can in fact measure how off it is by computing the ratio for every a
hollow moth
yeah but they're still not equivalent.
Oh cool
Thanks for your help, i just didn't really know how to use desmos
minor crater
and if you plot this is a function of a you'll get this
so i guess when a is really big it's close to a/2
minor crater
Thanks for your help, i just didn't really know how to use desmos
ofc :) if you don't have any more questions, feel free to type ".close"
hollow moth
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umbral dome
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quasi river
Hello I couldnt find my mistake
The answer is 39 but I got -39
But I see no mistake
ionic knoll
It should be $0-0+(-1)(3-15-(-1*6))=39$
For the 3rd part of determinant it's positive
glossy valveBOT
BBMaths
whole lily
The answer is 39 but I got -39
Yeah, you just forgot to include an extra negative
The double negative can mess people up
ionic knoll
I think there was too many negative
Just one negative (per term) inside the brackets
nova kestrel
ae you solvinf a or b
ionic knoll
a
quasi river
Hi
nova kestrel
i got 39 for a and 26/507 for b but i could be wrong
ionic knoll
!nosols
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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.
nova kestrel
As a helper, please do not give out answers that could be copied as a homework s...
ok sry
ionic knoll
Even if the answers already in the picture ig
quasi river
It should be $0-0+(-1)*(3*-15-(-1*6))=39$
Ohhhh yeee
Thank you so much
I did the inverse wrong
quasi river
Yeah, you just forgot to include an extra negative
Thank you!!
quasi river
i got 39 for a and 26/507 for b but i could be wrong
Thank you!
nova kestrel
I did the inverse wrong
yeah i was bouta say that but bot wouldnt let me messgae for 1 min lol
quasi river
Thank you so much everybody I see my mistake now have an amazing day or night
quasi river
yeah i was bouta say that but bot wouldnt let me messgae for 1 min lol
haha xdd
Cya :D.
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azure sky
$\text{prove that } (-a)(-b) = ab \text{ using field axioms}$
glossy valveBOT
joseph
stone matrix
-# Just wrap the math part in dollars and you can leave the rest outside without using \text next time
rapid rain
$\text{prove that } (-a)(-b) = ab \text{ using field axioms}$
what did you try?
azure sky
what did you try?
whenever i see a negative, i think of additive inverses, so i tried to add 0
so (-a)(-b) = (-a)(-b) + 0
tf
stiff musk
<@&268886789983436800>
azure sky
yo dont click on those pics btw
rapid rain
that's the third time in 20mins
azure sky
(-a)(-b) + 0 = (-a)(-b) + (a + (-a)) + (b + (-b))
and i dont think that really brings me anywhere
rapid rain
with a "+" in between yeah it won't matter much
rapid rain
(a+(-a))(b+(-b)) already sounds more promising, but I'm not sure we need to do it that way
you would need to show (-a)b = a(-b)
so a similar problem, but maybe it helps you see how to prove the original thing quicker
If you're still looking for a "0 cancel" I found a better one
||a(b + (-b)) + (a + (-a))(-b)||
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rapid rain
got it, thank you
btw another way to do it is to prove $-x = (-1)x = x(-1)$
glossy valveBOT
Rafilouyear2026
rapid rain
then $(-a)(-b) = a(-1)(-1)b = ab$
glossy valveBOT
Rafilouyear2026
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supple bloom
[This is a test]
HELP MODS I SPILLED MY JICE MY JICE
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umbral dome
slender onyx
[This is a test]
HELP MODS I SPILLED MY JICE MY JICE
gritty rose
Juice is just sugar water
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steady ginkgo
Can anyone check my answer plz
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Can anyone check my answer plz
steady ginkgo
(I'm not sure that i even did this right, cause my classmates all got different answer)
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icy zealot
help
dire swallow
So is the question to find x in terms of y or?
wary condor
So is the question to find x in terms of y or?
we can find every angle no?
grave elm
this is a pretty well known problem i think
but i dont remember the sol
it included drawing some random line which made some triangle equilateral
icy zealot
So is the question to find x in terms of y or?
no find in degrees
icy zealot
is AEB a triangle
yes
icy zealot
this is a pretty well known problem i think
we can solve it by angle chasing too i think so
wary condor
thats what i think too
grave elm
try drawing a better sketch lmao
30 = 130 < 50
anyway, i dont think i can chase more angles here
well, i can do one more
but then it ends
wary condor
yeah so the first person was right, its find a equation between y and x (hopefully)
icy zealot
by making angle EDB as y, we get more eqwuations
icy zealot
yeah so the first person was right, its find a equation between y and x (hopeful...
x+y=130
grave elm
yeah so the first person was right, its find a equation between y and x (hopeful...
it is solvable
it has to have a unique solution
grave elm
its just not findable by simple angle chasing
icy zealot
it has to have a unique solution
ong
icy zealot
ok bet
stiff goblet
ok hi
grave elm
possibly
grave elm
i forgot ur user, u were in sm saudi force or smth
dont go off topic here
icy zealot
yes pls
stiff goblet
btw. for sm reason all equations keep spiraling to x + cde = 130 for me
icy zealot
i spent like an hour on ts
icy zealot
btw. for sm reason all equations keep spiraling to x + cde = 130 for me
x+EDB=130 u mean
grave elm
its a problem well known to be difficulkt
stiff goblet
x+EDB=130 u mean
yeye edb
stiff goblet
hmm
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icy zealot
https://en.wikipedia.org/wiki/Langley%27s_Adventitious_Angles
is there NO way to solve this without construction?
icy zealot
https://www.youtube.com/watch?v=knc3cqiwJeQ
yeha i saw it
but cant it be solved without construction??
ts video is so complicated
congruency and shi
ashen bramble
Well, if there was an easier way, it obviously would have been in the video 😑
It really isn't that complicated of an explanation, the guy explains it really nicely.
icy zealot
ok
grave elm
but cant it be solved without construction??
if u know trig, you could probably put it all to equations and then do some stuff with that
but it cant be done with pure angle chasing (even when i chased all the angles i could, it still wasnt enough)
icy zealot
if u know trig, you could probably put it all to equations and then do some stuf...
ik trig only for rigth angle triangles
icy zealot
but it cant be done with pure angle chasing (even when i chased all the angles i...
ok then case closed ig
.close
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✅ Original question: #help-28 message
queen flame
have you found a way
grave elm
or why the reopen
queen flame
try drawing a better sketch lmao
didn't it just end here x = 180 - 50 - y
grave elm
didn't it just end here x = 180 - 50 - y
you can solve for x exactly
there is a unique solution
queen flame
oh
grave elm
it doesnt need to depend on y
grave elm
If you look at the sketch, there is nothing uncertain. You draw an isosceles triangle with angles 80° at base, then a line inclined 10° from one of the sides, mark the intersection E and then draw 20° from the other end, mark the intersection D and then just join ED
so there is only one triangle like this, and hence the angles can be exactly determined
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sturdy valve
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rapid rain
dont know how to start
Did you find T_r?
sturdy valve
Did you find T_r?
no
onyx glen
then find that first
sturdy valve
how to finf
onyx glen
maybe it will be easier to phrase if you think of finding T_n
sum of first n terms minus sum of first n-1 terms
leaden steeple
ill try something
the numerator is in ap how about break it into something and maybe telescopy?
sturdy valve
sum of first n terms minus sum of first n-1 terms
so i sub n-->n-1 in that (2n-1)(2n+1).. expression and then subtract it from the (2n-1)(2n+1) expression?
rapid rain
so i sub n-->n-1 in that (2n-1)(2n+1).. expression and then subtract it from the...
yeah
$T_n = \sum_{r=1}^nT_r - \sum_{r=1}^{n-1}T_r$
glossy valveBOT
Rafilouyear2026
sturdy valve
ok it is (2n-1)(2n+1)(2n+3)/8
rapid rain
Yeah that's the one
sturdy valve
next?
rapid rain
Well, have you ever done sums of rational fractions before?
like $\sum_{n=1}^\infty\frac{1}{n(n+1)}$
glossy valveBOT
Rafilouyear2026
onyx glen
i mean if its 2 brackets i can telescope but 3 is kinda tough
have you actually worked it out
sturdy valve
have you actually worked it out
worked what out
onyx glen
and what did you get
sturdy valve
d
rapid rain
ok it is (2n-1)(2n+1)(2n+3)/8
.
sturdy valve
A/(2n-1) + B/(2n+1) + C/(2n+3) = ?
queen flame
🔭
onyx glen
A/(2n-1) + B/(2n+1) + C/(2n+3) = ?
A/(2n-1) + B/(2n+1) + C/(2n+3) = 8/((2n-1)(2n+1)(2n+3))
queen flame
not that bad is it
-# it is better with 2 fractions
rapid rain
(after multiplying by the problematic denominator)
onyx glen
(after multiplying by the problematic denominator)
yeah im talking abt the standard procedure for pfd
there aren't really any weird places there
rapid rain
yeah im talking abt the standard procedure for pfd
Yeah so I was talking about ||multiplying by (2n-1) before inputting n = 1/2||
sturdy valve
you put n=1/2, -1/2, -3/2 to solve for each one individually
but even after we do that are we sure it will telescope?
onyx glen
but even after we do that are we sure it will telescope?
try it
onyx glen
there's no certainty before you do it
rapid rain
From an exam purpose, you can only know once you try. And if you're less confident about a question compared to others, then you'll tackle the easier questions first
leaden steeple
in denominator if you have 2-3 terms whose difference is constant (over the series) , yes that thing works
rapid rain
why restrict to 3 terms xd
sturdy valve
in denominator if you have 2-3 terms whose difference is constant (over the seri...
oh alr alr fine then
thanks every1
leaden steeple
why restrict to 3 terms xd
no restrictions , its just that it becomes hard to see after 3
sturdy valve
.close
sturdy vine
$\lim_{x \to 0} \frac{\sin(3x)-3x}{x^3}$
full forumBOT
$\lim_{x \to 0} \frac{\sin(3x)-3x}{x^3}$
onyx glen
!status
full forumBOT
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
Goofy Joe
onyx glen
"significant limitations"?
sturdy vine
Yes
onyx glen
... what language did you translate from
first off the lim thing is called a LIMIT in English. not limitation.
sturdy vine
Like sin(3x)~3x
onyx glen
Like sin(3x)~3x
ok so that is not enough precision for you, yes.
do you know Taylor series?
sturdy vine
Yes
onyx glen
ok then expand sin(3x) up to and including x^3
sturdy vine
I mean
flat cosmos
**Goofy Joe**
expansion of sinx or L'Hopital
sturdy vine
Let's say I know it conceptually,
but not the details.
queen flame
Let's say I know it conceptually,
but not the details.
what does conceptually mean
onyx glen
Let's say I know it conceptually,
but not the details.
so you don't know the taylor series of sin(x)?
sturdy vine
so you don't know the taylor series of sin(x)?
I know it exists and is used for approximations, but I don't remember the exact terms now...
So no
onyx glen
ok then i guess you have no other option but l'hôpital.
grizzled copper
But wouldn't it be easier with Taylor?
lhopital is easier
onyx glen
But wouldn't it be easier with Taylor?
it would but you are unable to do it
rapid rain
But wouldn't it be easier with Taylor?
If you don't have the tools to justify and/or even use it, just do l'hôpital
onyx glen
But wouldn't it be easier with Taylor?
you yourself said you don't know how to expand sin(x) into a Taylor series. so like, yes it would be easier, but it's out of your reach by your own admission
rapid rain
There are a lot of things that are easier once you learn and are allowed to use better tools
sturdy vine
9/2 pretty standard
sturdy vine
lhopital is easier
👍
onyx glen
There are a lot of things that are easier once you **learn** and **are allowed t...
until your permits expire
grizzled copper
lhopital is easier
wait sorry i merely took a cursory look at the question and didnt see it in full lhopital is not the sol here sorry
flat cosmos
wait sorry i merely took a cursory look at the question and didnt see it in full...
why?. differiatiating N and D 3 times each will get us -9/2
queen flame
,w Limit[ (sin(3x) -3x)/x^3 x->0)]
glossy valveBOT
queen flame
I was wrong
what is wrong
full forumBOT
@sturdy vine Has your question been resolved?
ionic knoll
,w Limit[ (sin(3x) -3x)/x^3 x->0)]
!nosols
full forumBOT
,w Limit[ (sin(3x) -3x)/x^3 x->0)]
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.
rare pine
For real numbers $a,b,c,d$, define $(a,b)(c,d) = (ac + bd, ad + bc)$. Suppose that [ (1,\frac{1}{2}) * ((1,\frac{1}{3})((1,\frac{1}{4})...((1,\frac{1}{n-1})*(1,\frac{1}{n})...) = (u,v) ] If $\frac{u}{v} = \frac{1243}{1242}$, determine $n$.
glossy valveBOT
Copter
rare pine
there has to be some way to simplify this but i have no idea ;-;
verbal crater
If (x,y) = (a,b)(c,d) look at x + y and x - y
full forumBOT
@rare pine Has your question been resolved?
rare pine
wait how does that help me..
verbal crater
x+y=(a+b)(c+d), x-y = (a-b)(c-d)
So sums multiply and differences multiply
rare pine
verbal crater
Basically instead of getting u/v we can also get (u+v) + (u-v) / (u+v) - (u-v).
We just proved that when we multiply pairs (x,y) = (a,b)(c,d),
then x+y=(a+b)(c+d), x-y = (a-b)(c-d)
That means in the long product the quantity u+v= (1+1/2)(1+1/3)...(1+1/n) and u-v = (1-1/2)(1-1/3)...(1-1/n)
Those products will telescope giving you u+v and u-v thus giving you u/v
full forumBOT
verbal crater
thanks batman
welcome
full forumBOT
Available help channel!
knotty grail
erm what the sig
full forumBOT
erm what the sig
grave elm
f is the integeral?
knotty grail
guess so
queen flame
kings
knotty grail
then what
queen flame
hm..
grave elm
maybe d/dx it
knotty grail
oooh interesting
queen flame
yh
grave elm
that should simplify it to a doable integral
hm maybe redefining it to ln(sin^2(theta) + x cos^2(theta)) would be better actually
knotty grail
maybe d/dx it
$(x^2-1)\int_0^{\frac{\pi}{2}} \frac{\theta \sin(2\theta)}{\sin ^2 \theta + x^2 \cos ^2 \theta}d\theta$
glossy valveBOT
knotty grail
after ibp
grave elm
ew
yeah, this is ugly.
$\frac{2x\cos^2\left(\theta\right)}{\sin^{2}\left(\theta\right)+x^{2}\cos\left(\theta\right)}$
glossy valveBOT
MathIsAlwaysRight
grave elm
this was before IBP?
knotty grail
uh how was this befor ibp
grave elm
oh no
verbal crater
wait yes, this is the derivative
yeah it is
grave elm
**MathIsAlwaysRight**
yeah, so x is a constant
so we could just trig sub now ig
and itll be some ugly rational thing
knotty grail
**MathIsAlwaysRight**
derivative of $ln(\sin^2(\theta) + x^2\cos^2(\theta))$?
glossy valveBOT
grave elm
derivative of $ln(\sin^2(\theta) + x^2\cos^2(\theta))$?
yeah
grave elm
yeah, and then int dx it in the end
queen flame
**MathIsAlwaysRight**
shouldn't it be sin in numerator
grave elm
shouldn't it be sin in numerator
no, cos^2 is just a const
knotty grail
i have a faint recollection of this method somewhere
so like d/dx -> integrate wrt theta -> integrate wrt x?
grave elm
yes
knotty grail
weird
grave elm
i think its called feynmans trick or sth like that
i have seen people use it here, but never used it myself
queen flame
no, cos^2 is just a const
right partial
queen flame
**MathIsAlwaysRight**
wait but you shouldn't be getting this if you used kings
knotty grail
not kings
seems a bit solvable although nasty after feynmans trick
oh hold on y = $\pi ln|x+1| + C$??
grave elm
it simplifies to rational function after substitution
glossy valveBOT
knotty grail
or let me just backtrack\\
$f'(x) = \int_0^{\infty} \frac{2x}{(t^2+1)(t^2+x^2)} dt$, where $t=\tan(\theta)$
glossy valveBOT
queen flame
yeah how to vanish C 
verbal crater
yeah how to vanish C <:thonk:406575732563902485>
evaluate at x = 1
queen flame
evaluate at x = 1
oh
queen flame
feynman shit
knotty grail
$= \frac{2x}{x^2-1}\int_0^{\infty} \frac{1}{t^2+1} - \frac{1}{t^2+x^2} dt$
glossy valveBOT
knotty grail
$= \frac{2x}{x^2-1} \left(\frac{\pi}{2} - \frac{1}{x}\frac{\pi}{2}\right)$
glossy valveBOT
glossy valveBOT
cinder thorn
swapping integrals and derivatives is totally okay
hmm it depends though
sometimes the derivative won't be integrable
grave elm
it was meant to be slightly sarcastic
its usually okay for nice enough functions
i dont know the exact conditions
is it just integrability of the derivative?
cinder thorn
from what I've learnt (so maybe these are not optimal) you mainly want the derivative to be "dominated" like in the DCT and the function to be continuous enough
full forumBOT
@knotty grail Has your question been resolved?
proven lynx
A die is rolled 1500 times. What is the probability that a number greater than 4 is rolled at least 750 times but at most 1050 times?
queen flame
,rccw
glossy valveBOT
proven lynx
i did it in 2 ways
once with calculator and once with the Fi table but
16,49 isnt in the table
proven lynx
Sorry?
onyx glen
you wrote $\Phi(30.15) - \Phi(13.66) = \Phi(16.49)$. how did this happen?
glossy valveBOT
Ann
onyx glen
but like... Phi is a function, not a number.
proven lynx
am i stupid
onyx glen
Phi, a.k.a. the CDF of the Gaussian, is not linear... Phi(a+b) ≠ Phi(a) + Phi(b). and Phi(a-b) ≠ Phi(a) - Phi(b).
proven lynx
Phi, a.k.a. the CDF of the Gaussian, is **not linear**... Phi(a+b) ≠ Phi(a) + Ph...
oh
so what can i do
onyx glen
hold on
let me re-check all of your calculations
but also can you supply the original problem statement?
a number greater than 4 is rolled at least 750 times but at most 1050 times (in 1500 rolls)
you found that the mean is 500, so the entire range [750, 1050] is pretty fucking far from the mean
Phi(anything above, like, 5) is scary close to 1
show the original problem. in german. i want to be 120% SURE that NONE of us misread ANYTHING.
proven lynx
okay
will do
but its in bad hand writng
the orignal question
i literally translated it 1:1
but okay
onyx glen
well, i want to see it anyway.
what i can tell you right now is: as you wrote it, the probability they ask for is ridiculously tiny.
onyx glen
8e-43 is not what i'm getting
proven lynx
8e-43 is not what i'm getting
its from the calculator
onyx glen
i'm getting something like 3e-28
does that say "grösser 4"?
so you are sure it means >4 and NOT ≥4 ?
proven lynx
so you are sure it means >4 and NOT ≥4 ?
yes
bigger than 4
2/6 is p
im 1000% sure
onyx glen
then yeah it'll be tiny as fuck
27 decimal places just to tell it apart from 0 kind of tiny
onyx glen
you would ordinarily just have to look up values of Phi in your table
but the thing here is, what you've got is OUT OF RANGE for most z-tables.
they only go up to 3.something stdevs.
here you are working with TENS of standard deviations.
which is normally just. yeah. way out of anyone's reach.
onyx glen
is there any possibility of getting some kind of correction or clarification from your professor, or is the probability of that as small as the answer to this question?
onyx glen
guh
proven lynx
he just wrote 0.000 and caled it a day
onyx glen
that's your friend?
onyx glen
proven lynx
wtf did he do
onyx glen
yeah idfk
proven lynx
i mean for the Fi-Fi
OH wait
i get it
im stupid
he looked at the table and then
subtracted the actual values
onyx glen
and then saw how way out of range it was
proven lynx
and then saw how **way out of range** it was
also
if i put it in my calculator
and 0 comes out
its not actually 0 right
restive geyser
"A die is cast 1500 times. How much is the probability that
a. a 5 is rolled exactly 900 times? (with calculator and formula)
b. an even number is rolled at most 1000 times?
c. an odd number is rolled at least 755 times?
d. a number greater than 4 is rolled at least 750 times but at most 1050 times? (using a calculator and formula)"
-# Falls man's noch braucht
-# Should it still be needed
proven lynx
my teacher said that once
onyx glen
its not actually 0 right
as i said before, and as i can repeat if you didn't hear me the first time,
onyx glen
this doesnt make sense
what doesn't?
proven lynx
why did you get 3e even though i got 8e usng the calculator
is the calculator wrong or is fi wrong
onyx glen
i don't know what you put into your calculator.
also you're focusing on the smaller part of the difference between our answers.
proven lynx
Oh ik why
onyx glen
like uhh
why did it not strike you as odd that our answers differed by TWELVE FUCKING ORDERS OF MAGNITUDE
proven lynx
why did it not strike you as odd that **our answers differed by TWELVE FUCKING O...
Uhhh
Wdym magnitude
restive geyser
"Grossenordnung"
onyx glen
you understand that the exponent on the ten is a much more significant indicator of difference than the mantissa?? like.
you know what this feels like?
proven lynx
749,5 and 1050,5
proven lynx
you know what this feels like?
I apologize if ive hurt u in any way
Can we calm down
onyx glen
it's as if you were comparing the numbers 7,332,312 and 1,000,000,000,000,000,000,421,002
proven lynx
it's as if you were comparing the numbers `7,332,312` and `1,000,000,000,000,000...
yeah
onyx glen
and went "oh but the second one has 002 while the first has 312"
like
thats precisely the part that matters the least
onyx glen
I apologize if ive hurt u in any way
you did not hurt me, you baffled me
restive geyser
@onyx glen I'm gonna have to agree though that you need to calm down a little bit
onyx glen
fuck it im out completely
restive geyser
Ich wiederfrags auf Deutsch - was hast du im TR eingegeben?
proven lynx
Ich wiederfrags auf Deutsch - was hast du im TR eingegeben?
Also es gibt ja upper und lower
Bei der kumulierten normal verteilung
Für upper habe ich 1050,5
Lower 749,5
Mü ist 500
und Sigma ist 18,26
restive geyser
Wovon der 18,26 nochmal?
proven lynx
Wovon der 18,26 nochmal?
Standard abweichung
restive geyser
nö ich wusste das schon
Meinte, kann ich deine Rechnung dafür mal sehen
nah warte mal, habs auch
restive geyser
okay, ich habs auch
restive geyser
ungefähr 8e-43
(it's a one-time punishment, and you're pulling out the bold letters)
(that's a first)
restive geyser
ungefähr 8e-43
@proven lynx Ich hab also the same answer wie du
restive geyser
Is this from Desmos?
proven lynx
Btw
restive geyser
Because then the question remains why this is any different
proven lynx
Wenn ich ma im taschenrechner irgendwie 1 oder 0 bekomme
dann heisst es eigentlich
0.0000000….9
oder 0.999999999…
oder?
restive geyser
vom Kontext abhängig
proven lynx
Hm okay
safe nova
Da hätte ich gerne geholfen aber habe gesehen das ist eher uni niveau und das befindet sich ausserhalb meines Bildungsstandes 🙏
restive geyser
Hier "weniger als 1050, von 1500" ist definitiv nicht Eins
proven lynx
Da hätte ich gerne geholfen aber habe gesehen das ist eher uni niveau und das be...
😭 Bro
Ich bin in der 13.
restive geyser
Da hätte ich gerne geholfen aber habe gesehen das ist eher uni niveau und das be...
Es ist 13. Statistik
Ja
Auch in England
coral torrent
ich bin Stuhl
proven lynx
Hier "weniger als 1050, von 1500" ist definitiv nicht Eins
ja
Ich muss mich noch mit Kombinatorik und hypothesentests beschäftigen dann hab ich aber eigentlich alles gelernt
safe nova
Ahh bin nd ins gymi, mach gerade berufsmaturitätsschule (quasi fachabi aber schweizer)
restive geyser
Ist aber so hoch, dass es nichts anders als 1 rendiert werden kann
proven lynx
Ist aber so hoch, dass es nichts anders als 1 _rendiert_ werden kann
ahh ich verstehe
safe nova
Yeah i don’t have statistics i cant help sry🙏
restive geyser
Schweize, dh automatisch irrelevant /s