yep
#help-41
coral wigeon
sullen knoll
Perms and combs is the death of me 😔🤚🤚
fierce edge
it makes non-uniform stuffs uniform
coral wigeon
i do like uniform
coral wigeon
fierce edge
okay so
(140-a, 140, 160, 160+a) -> (10-a, 10, 10, 10+a)
10 and 10-a has the same deviation as 10 and 10 + a
10^2 + (10 + a)^2 = 50^2 * 2
(10 + a)^2 = 4900
|10 + a| = 70
shrewd elm
and a > 0, so..
shrewd elm
wha
shrewd elm
math is hard
fierce edge
😔 it is
okay thanks
i think i realize what i was doing "wrong"
well not wrong but the time consuming thing
it was expanding (10 + a)^2
when i didn't have to
bye
.close
amber waspBOT
shrewd elm
not necessarily
modern marsh
Why?
I feel like that one is 1 and other is -1, i mean the det, but idk what happened in A+B
shrewd elm
well a simple matrix with det 1 is the identity
what's a simple matrix with det -1?
hint: what can you do to a matrix to change the sign of the determinant?
modern marsh
Inverse? I'm not sure
shrewd elm
no, that will give you one over the original determinant
how about exchanging two rows (or two columns)
modern marsh
That'll change the signs? Damn I forgot so much
shrewd elm
yep it will
so what if you have the 2x2 identity matrix
that's orthogonal with det = 1
what do you have if you swap the two columns?
modern marsh
Identity matrix with a minus sign?
shrewd elm
no, literally just move column 1 to column 2 and vice versa
what is the new matrix?
wha
you started with
1 0
0 1
exchange the columns
modern marsh
0 1
1 0
modern marsh
Yes
spark cobalt
it can be much easier than that, take any nxn matrix where n is odd and mutliply it by -1 and now you have another orthogonal matrix with negative the determinant and their sum is zero which is clearly not invertable
shrewd elm
and what is its determinant?
modern marsh
-1
shrewd elm
it can be much easier than that, take any nxn matrix where n is odd and mutliply...
yea there are various ways for sure
yep
now if you add those two matrices, what do you get?
left tundra
ah matrix
modern marsh
now if you add those two matrices, what do you get?
1 1
1 1
modern marsh
No
shrewd elm
victory
modern marsh
Tysm😂
left tundra
whats the basic rule you need for the multiplication of 2 mtrix
spark cobalt
victory
you have helped a mayonnaise, now we can eat peacefully with mayonnaise around
modern marsh
Noooooo(running away
left tundra
like the no. of rows of 1st matrix = no. of column of 2nd matrix?/
spark cobalt
😂
amber waspBOT
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split sail
solve (1+tanx)/(1-tanx) = root3
amber waspBOT
solve (1+tanx)/(1-tanx) = root3
neat wind
solve (1+tanx)/(1-tanx) = root3
tan(x + pi/4) = root3
fierce edge
(1 + tan(x))/(1 - tan(x)) simplifes to tan(x + pi/4) which u could've said from the addition formula
mqnic already has said this but u reacted with what so i thought ur still confused
amber waspBOT
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ancient sparrow
Anyway to integrate this?
amber waspBOT
Anyway to integrate this?
ancient sparrow
<@&286206848099549185>
tepid widget
,rotate
grizzled pagodaBOT
ancient sparrow
😢
amber waspBOT
@ancient sparrow Has your question been resolved?
keen pawn
grizzled pagodaBOT
A dense set(Ping when reply)
split sail
what's the first fibonnaci number?
keen pawn
1
split sail
We first prove if $n \mid 3$ then $F_n$ is even
you have wrote it opposite lol
grizzled pagodaBOT
A dense set(Ping when reply)
keen pawn
so $3\mid 3$ and $F_3=2$ which is even
\
We now suppose that if $3 \mid i$ then $F_i$ is even $\forall i \leq n$
\
$F_{n+3} =F_{n+2}+F_{n+1} = F_{n}+F_{n-1} +F_{n+1} + F_{n} = F_n+F_n +F_{n-1} + F_n+F_{n-1}$
\
By inductive hypothesis $F_n$ is even and $F_{n-1}$ is odd, but $2F_{n-1}$ is even.
\
We this have $F_{n+3}$ is even , which proves the result as desired
grizzled pagodaBOT
A dense set(Ping when reply)
cunning birch
if $3\mid n$ then $F_n$ is even
and bear in mind that so far you've only proved this result
amber waspBOT
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split sail
What's an example of a non-normal mathematical constant?
sterile nymph
@split sail any rational number
split sail
That is irrational
sterile nymph
You can construct one
split sail
that have either a symbol for them or an algebraic representation
sterile nymph
That is a bit trickier
Most irrational numbers (all but measure 0) have been proven to be normal. But the proof for any specific irrational number is incredibly difficult. It is widely believed that sqrt(2), pi, and e are normal, but it is not proven
sterile nymph
Very few numbers have been proven normal or not-normal that haven't been specifically constructed for this purpose.
sterile nymph
You could easily just take sqrt(2) in its decimal expansion and turn all of the 9s into 8s and this number would not be normal in base 10
It would probably still be normal in unrelated bases though
split sail
You could easily just take sqrt(2) in its decimal expansion and turn all of the ...
wdym
turn?
cunning birch
cunning birch
isn't it like an infinite product?
?
sterile nymph
sqrt(2) = 1.4142135623730950488...
We just find everywhere that is a 9 and turn it into an 8
sqrt(2) - α = 1.4142135623730850488...
Where α is some real number that does this
α is also abnormal in this case, consisting only of 1s and 0s in decimal
modest sand
What a mess, how does one even have the intuition behind this
split sail
that has a representaion
sterile nymph
You asked for a number, then an irrational number, now an algebraic number.
It's possible one doesn't exist.
I don't know
amber waspBOT
sterile nymph
@cunning birch thanks btw today I learned
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runic kraken
solving a problem that involves finding the vector angles, i got an angle of -79, does that go left wards or do i start from the bottom up?
runic kraken
talking about gamma
amber waspBOT
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balmy moss
hello i need help with my hw (im sending more screenshots)
amber waspBOT
hello i need help with my hw (im sending more screenshots)
balmy moss
the last 2 screenshots i would love help on it first
it was the hardest
<@&286206848099549185>
winter badge
please take a screenshot, no ones trying to read scew photos
balmy moss
Okikok
balmy moss
please take a screenshot, no ones trying to read scew photos
i cant screenshot its on a school computer
balmy moss
its these @winter badge
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harsh surge
amber waspBOT
harsh surge
Hello, I don't understand how to solve/proceed with this question
celest cove
you know y=F(2)-F(sqrt(x))
so you can use the chain rule there
where F'(t)=f(t)=t^2+1
foggy kayak
first solve the definite integral and then differentiate the function you get afterwards
harsh surge
could you show me a solution please?
I'll understand it better if I can see what's going on step by step
foggy kayak
we can't give direct solution
celest cove
you know y=F(2)-F(sqrt(x))
so you can use the chain rule there
try it
harsh surge
ah alrighty, do you have any sources I could study/practice?
so it'll be something like 0-((sqrtx)^2+1) d/dx of sqrtx right?
then proceed from there
harsh surge
idk 😭
shadow stump
it's not necessary to find the definite integral to find its derivative
amber waspBOT
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weak zinc
Evaluate dy/dx when x = 2
amber waspBOT
@woeful dirge Has your question been resolved?
amber waspBOT
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bleak mason
amber waspBOT
weak zinc
Put it in exactly, 8^{2/3}
And do you know your rules of exponents?
(if not, it would be a good time to learn them)
bleak mason
Oh that was right
It’s 4
But
It doesn’t feel right
It feels to easy
Is there a way to do this without calculator
cedar plaza
severe lantern
$$a^{b/c} = \sqrt[c]{a^b}$$
grizzled pagodaBOT
spruce leaf
severe lantern
$$a^{b/c} = \sqrt[c]{a}^b$$ is also true
grizzled pagodaBOT
spruce leaf
severe lantern
where c is positive
bleak mason
Ohhhhh
While this is open I might as well…
I feel like all I can do rn is make -3a to -2a
tepid meteor
youre right
bleak mason
But so I can’t simplify it further
tepid meteor
i mean like unless the whole thing is equal to 0 thats all you can do
bleak mason
It was wrong
tepid meteor
is the equation equal to zero?
bleak mason
It’s not an equation
It’s a
Idk what it is in wbglihs
But it’s not solvable
You’re supposed to simplify it
tepid meteor
did you put -2a -7?
bleak mason
I put this
tepid meteor
brooo its 2a^2
bleak mason
tepid meteor
you need to simplify a^2
bleak mason
I can just combine them like that?
bleak mason
Ohhhh
bleak mason
Ohhhhhhhhhhhh
I’m so dumb
I can swear someone told me I can’t do that
Thanks though🩷
.close
amber waspBOT
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hearty sleet
i get how the 5sin/cos part works but how does the revolution in 4pi seconds part work
quiet cave
Barely missed
amber waspBOT
@hearty sleet Has your question been resolved?
weak zinc
You know that for the "ordinary" trig functions sin(t) and cos(t), they repeat themselves every 2pi, but now you effectively want to repeat yourself every 4pi
hearty sleet
oh
fresh gust
I was gonna say that
fresh gust
💀
amber waspBOT
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potent sandal
Hey I am looking at some benchmarking results from running code on x number of CPU cores
potent sandal
Since the benchmark will only be slowed down by noise I am taking the minimum benchmark as my result
However I would like to estimate some standard deviation
daring jetty
cap
potent sandal
Is a jackknife method appropriate here to estimate a standard deviation for the minimum?
steady snow
i dont think so
coz like u use jackknife method to estimate the variance of a statistic by leaving out one observation at a time and recalculating the statistic right? so this would be effective for smooth and differentiable statistics (like the mean or regression coefficients), but the minimum is a non smooth statistic
if u know what specific pattern the noise makes in ur benchmarking results u could model the noise explicitly using that
OR even better u could use ALL the data points, not just the minimum, to fit a distribution model then use that model for estimating variability of minima and it can also give you both the minimum estimate and its standard deviation
amber waspBOT
@potent sandal Has your question been resolved?
potent sandal
OR even better u could use ALL the data points, not just the minimum, to fit a d...
okay thanks 🙂 I'll keep that in mind
strong granite
am i on the right track here?
amber waspBOT
am i on the right track here?
strong granite
any help would greatly be appreciated 😔
im confused about if im finding the mean
and sample error of the mean correctly
<@&286206848099549185>
amber waspBOT
@strong granite Has your question been resolved?
amber waspBOT
@strong granite Has your question been resolved?
strong granite
😭
amber waspBOT
@strong granite Has your question been resolved?
chrome grotto
i need help with my math review but i don’t really understand this :( i have a 47 in math rn so im hoping somebody could please help me! much thanks
remote egret
i need help with my math review but i don’t really understand this :( i have a 4...
I haven't done geometry in years but I'll try to help
for the last question
the letters match up
so L to X, M to Y, and N to Z
chrome grotto
really tysm im sorry to disturb u 🥹
remote egret
no don't be sorry
so that means angle m matches with y
and for ln its xz
- SAS i think
the lines on the sides CA and CB indicate they're congruent (fulfills S)
angle shared with the 90 degree (fulfills A)
and then CD nudged in the middle so its shared side too (fulfills last S)
if you don't really know the postulates i recommend you learning them first through organic chem tutor
chrome grotto
ur explaning helped me understand a bit better tysm
remote egret
no problem
clever gorge
Hi
clever gorge
I’ve tried 1b so many times but still have no idea how she got 0.25
I don’t understand the logic behind it
low adder
calculate the tension force when there is no friction
use sum of forces is equal to 0 so that it is stationary as no acceleration
then u should get that friction force is equal in magnitude opposite in direction
to tension force
divide that by the normal force
and u get your minimum coefficient of friction
clever gorge
does it matter which object you do use the sum of forces on
clever gorge
ye im still stumped i think imma just ask my teacher tmr morning
ty for tonight
.close
amber waspBOT
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split sail
What a +w
sterile nymph
Context?
amber waspBOT
@split sail Has your question been resolved?
topaz pond
<@&286206848099549185>
amber waspBOT
<@&286206848099549185>
topaz pond
I am unable to solve the first question
Can someone help me solving the first question
The problem with this question is that
This has two independent variables
But problem comes with dependency
What to do
<@&286206848099549185>
amber waspBOT
@topaz pond Has your question been resolved?
amber waspBOT
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normal dove
lemme know hints other than take log 😭
amber waspBOT
lemme know hints other than take log 😭
normal dove
lol
dull pike
Are you sure the square root doesnt cover everything?
vernal surge
what does the inner factor converge to?
dull pike
@normal dove
normal dove
what does the inner factor converge to?
not sure didnt study that
dull pike
But inside u are getting a number <1, unless i am blind
normal dove
yeah would make sense
dull pike
And if u multiply over and over u get a smaller number
vernal surge
like, whats $\lim_{r \to \infty} \left(\sqrt{2} - 2^{\frac{1}{2^r-1}}\right)$
grizzled pagodaBOT
rbit
normal dove
sqrt 2 -1 i guess
dull pike
Y
normal dove
wait nvm
vernal surge
no thats correct
which is |sqrt(2)-1| < 1, so you know that there is some q < 1 and R, such that absolute value the inner term is always less than or equal to q for r > R
normal dove
erm
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solemn escarp
Let ABC be a triangle. Points M and N are on side BC such that BM = MN = NC. Extend AM to point P such that BP is parallel to AN. Extend AN to point Q such that CQ is parallel to AM. If the area of triangle MAN is 57, find the area of quadrilateral ABPQC
solemn escarp
this is a very menelaus-y looking question
oh wait
this is sick
every triangle is congruent
fire question
ABPQC = 8MAN = 456
.close
amber waspBOT
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harsh forge
how do i put this Sturm-Liouville form? Surely it is just $(y')' + \lambda y = 0$
grizzled pagodaBOT
lewis_f04
amber waspBOT
@harsh forge Has your question been resolved?
harsh forge
@hazy bluff
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@harsh forge Has your question been resolved?
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gusty plaza
Hi this is my first time doing shell method so I’m sorry if I am doing it wrong but is this the correct way to set it up
patent raptor
Hi this is my first time doing shell method so I’m sorry if I am doing it wrong ...
liar
covert onyx
patent raptor
ngl that was a smart move what you did
but you should subtract it the other way
(2-y) - y²
amber waspBOT
gusty plaza
.reopen
amber waspBOT
✅
patent raptor
Did I set this up correct number 6
washer method?
ok you did shell method
should work yea if my head right
patent raptor
,w 2pi * Integrate[y * y^(1/3), {y,0,8}] = pi * Integrate[8^2-(x^3)^2, {x,0,2}]
grizzled pagodaBOT
gusty plaza
.reopen
amber waspBOT
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patent raptor
What’s the Antiderivayige of e^-x^2?
the antiderivayige of e^(-x^2) doesnt exist in terms of elementary functions
however you can use here a u-sub since you got that extra factor x
patent raptor
Would I u sub the -x^2
Yes
gusty plaza
I think I did something wrong cause I’m not cool or something idk
patent raptor
I think I did something wrong cause I’m not cool or something idk
change bounds?
patent raptor
but then
i see you substituted again u = -x^2
then you can keep the old bounds then
then everythings fine anyway
and you are also cool
gusty plaza
then you can keep the old bounds then
Am I tripping though
Because my answer is negative
patent raptor
it seems so
patent raptor
but it isnt
gusty plaza
Oh
patent raptor
,w -pi * e^(-1^2) - (-pi * e^(0^2))
grizzled pagodaBOT
gusty plaza
Yea that’s true
I only calculated upper bound for some reason
Which was dumb
Also is it raining there
It’s raining here
patent raptor
snowing
patent raptor
yea, just open your eyes
patent raptor
i feel so tired
amber waspBOT
pallid canopy
damn kicked you out adonis to make you sleep
gusty plaza
Yea but I’m gonna come back in like 6 min anyways
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Available help channel!
eager karma
do i subtract or add -3? aaalso, its c, not b.
amber waspBOT
do i subtract or add -3? aaalso, its c, not b.
crude kite
do i subtract or add -3? aaalso, its c, not b.
It's + -3 or you just write -3
If there is no sign, it's default adding
Like for b, that 54, is positive 54
eager karma
right. everyone keeps saying that but i constantly forget lol
crude kite
Then make a note of it so you don't forget
If multiple people have told you the same thing
amber waspBOT
eager karma
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amber waspBOT
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ancient raft
Estimate the remainder of $f(x)=e^x$
amber waspBOT
Estimate the remainder of $f(x)=e^x$
grizzled pagodaBOT
Good
ancient raft
Since $$T_n(e^x)=1+x+\frac{x^2}{2}+\dots+\frac{x^n}{n!}$$
grizzled pagodaBOT
Good
tranquil shale
what is ur question? im sorry
vernal surge
you got a picture of taylors theorem?
amber waspBOT
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old drift
Can someone help me calculate the integral of Thomae's function on 0 to 1. I forgot the proof and how to make the partition. I know that the set where we're evaluating the integral on has measure zero and all of that but I want to use first level analysis techniques.
old drift
Recall Thomae's function is
$$f(x) = \begin{cases}
0 \qquad \text{ if } x \notin \mathbb{Q}\
\frac{1}{n} \qquad \text{ if } x = \frac{m}{n} \text{in lowest terms}
\end{cases}
$$
grizzled pagodaBOT
Bean Man
cunning birch
Can someone help me calculate the integral of Thomae's function on 0 to 1. I for...
I mean you could write f as the limit of a non-decreasing sequence of simple (step) functions
old drift
I kind of wanted a proof that created partitions so that the length of each interval is arbitrarily small and we get the |U(f, P) - L(f, P)| < epsilon so we get that its integrable in the first place and then that leads to it having integral equal to 0
cunning birch
I kind of wanted a proof that created partitions so that the length of each inte...
in that case inspire yourself of the proof of why any countable set is of 0 lebesgue measure
old drift
.close
amber waspBOT
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quasi meadow
If you're given f(x,y) as your joint probability distribution function
quasi meadow
is finding E[X] for exmaple, a double integral of x and y of x * f(x,y)?
quasi meadow
ah
vast scaffold
To find that expected value
vast scaffold
Ye
quasi meadow
hmm
and to find fx(x)
we hold x constant, and integrate over all values of y
so we just integrate f(x,y) with respect to y?
quasi meadow
hm
im struggling with this integral than
$$\int _0^{\infty }\frac{1}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy$$
grizzled pagodaBOT
toast
vast scaffold
,w $$\int _0^{\infty }\frac{1}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy$$
grizzled pagodaBOT
vast scaffold
What’s bound on X
vast scaffold
,w $$\int _0^{\infty }\int _0^{\infty }\frac{1}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy xd$$
grizzled pagodaBOT
vast scaffold
,w $$\int _0^{\infty }\int _0^{\infty }\frac{1}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy dx$$
grizzled pagodaBOT
quasi meadow
hmm
vast scaffold
Checks out
quasi meadow
okay so i was supposed to do a double integral
vast scaffold
No
vast scaffold
I was checking to see if it’s 1
quasi meadow
💀
im so tempted to write
"solved with an integral calcualtor"
for this hw assignment
ughhh
quasi meadow
Maybe use a transform
jacobian?
vast scaffold
,w $$\int _0^{\infty }\int _0^{\infty }\frac{x}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy xd$$
grizzled pagodaBOT
vast scaffold
,w $$\int _0^{\infty }\int _0^{\infty }\frac{x}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dy dx$$
grizzled pagodaBOT
vast scaffold
Maybe let u =x/y
quasi meadow
hmm
thats what i started off with actually
then i got tired of doing this questino and was thinking theres no way he asks such an annoying calc problem on a probability hw assignment
vast scaffold
Integrate with respect to X first
quasi meadow
alr
vast scaffold
Then it’s an exponential dist with parameter 1/y
vast scaffold
Do you see it
quasi meadow
ill give it a shot first
amber waspBOT
@quasi meadow Has your question been resolved?
quasi meadow
,w $$\int _0^{\infty }\int _0^{\infty }\frac{y}{y}\cdot :e^{-\left(y+\frac{x}{y}\right)}dx dy$$
grizzled pagodaBOT
Requested by toast.y_
clear finch
I had to use desmos to find the answer, but I dont understand it
clear finch
the period is pi/3 i believe
marble sparrow
I might be crazy but I don’t believe that’s correct
marble sparrow
That’s a good realization
clear finch
desmos says so tho...
marble sparrow
Oops I forgot about that
One second I’m gonna work it out on a whiteboard and I’ll send a pic 😓
clear finch
kay
marble sparrow
I see now
Let me know if I didn’t write something clear enough or didn’t show a step
marble sparrow
Yes
clear finch
thanks for the help
marble sparrow
No problem
clear finch
lmao, I always forget that rule
marble sparrow
Yeah it can be annoying/hard to see
amber waspBOT
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mystic solstice
Hello! I need help with this question, I'm doing yr10 maths and it's for my end of yr exam. I don't understand what the 'least squares regression line' means and therefore the rest of the question. I have the answers but I don't know how my teacher got to that
ionic zodiac
Hello! I need help with this question, I'm doing yr10 maths and it's for my end ...
ur rosa?
mystic solstice
Sorry?
ionic zodiac
r u nsw?
mystic solstice
wdym by nsw
ionic zodiac
ok nvm then
red island
Don’t worry too much about what the “least squares regression line” is, just substitute the data into the equations given in the question.
amber waspBOT
grim isle
how do i set the domain for s and t
amber waspBOT
how do i set the domain for s and t
grim isle
the video juz states since z=3sin(s) , so set s as that domain
is there a trick or smtg
amber waspBOT
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grim isle
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@grim isle Has your question been resolved?
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@grim isle Has your question been resolved?
grim isle
.close
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tough mica
amber waspBOT
tough mica
,, \textbf{ finding interval of convergence} \ \sum_{n = 1}^{\infty} \frac{(x-3)^n}{n^2 \cdot 2^n}
grizzled pagodaBOT
Renato Chavez
tough mica
I want to try root test out but I am scared of justifying the $\sqrt[n]{n^2}$ haha
grizzled pagodaBOT
Renato Chavez
wispy ermine
if you want to find the limit of n^(n/2) you can write it as e^(something)
tough mica
lets do root test then if we know the limit of n^(n/2)
,, a_n = \frac{(x-3)^n}{n^2 \cdot 2^n} \ \textbf{ applying root test} \ \lim_{n \to \infty} |\sqrt[n]{a_n}| < 1 \ \lim_{n \to \infty} \left|\sqrt{\frac{(x-3)^n}{n^2 \cdot 2^n}}\right| < 1 \ \lim_{n \to \infty} \frac{|x-3|}{|\sqrt[n]{n^2}| \cdot 2} < 1
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Renato Chavez
tough mica
,, \sqrt[n]{n^2} = n^{2/n} \ L = n^{2/n} \ \ln(L) = \ln\left(n^{2/n}\right) \ e^{\ln(L)} = e^{2/n \cdot \ln(n)} \ L = e^{2/n \cdot \ln(n)}
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Renato Chavez
tough mica
,, \textbf{ auxiliary calculation 1: } \ \lim_{n \to \infty} \frac{2 \ln(n)}{n} \overset{\text{L'Hôpital}}{=}
\lim_{n \to \infty} \frac{2/n}{1} = \lim_{n \to \infty} \frac{2}{n} = 0
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Renato Chavez
tough mica
,, a_n = \frac{(x-3)^n}{n^2 \cdot 2^n} \ \textbf{ applying root test} \ \lim_{n \to \infty} |\sqrt[n]{a_n}| < 1 \ \lim_{n \to \infty} \left|\sqrt{\frac{(x-3)^n}{n^2 \cdot 2^n}}\right| < 1 \ \lim_{n \to \infty} \frac{|x-3|}{|\sqrt[n]{n^2}| \cdot 2} < 1 \ |x-3| < 2 \implies -2 < x - 3 < 2 \ 1 < x < 5 \implies x \in (1,5)
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Renato Chavez
wispy ermine
you can just plug in the values and check if the resulting series converges
tough mica
problem is this makes the limit be equal to one and root test says thats inconclusive
we need to try another way
wispy ermine
ah not quite what I mean
I mean you have the series
$\sum \frac{(x-3)^n}{(2^{n}n^2)}$
plug the values of x into that
tough mica
,, \sum_{n = 1}^{\infty} \frac{(-2)^n}{n^2 \cdot 2^n}
tough mica
is an alternating series
wispy ermine
it is an alternating series; even better it's a well known alternating series
(i'm assuming you've seen the series $\sum \frac{1}{n^2}$ in your course by now)
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LayneTheAndroid
tough mica
p test
its a p series
,, a_n = \frac{(-1)^n \cdot 2^n}{2^n \cdot n^2} = \frac{(-1)^n}{n^2} \ a_{n+1} = \frac{(-1) \cdot (-1)^n}{(n+1)^2}
wispy ermine
its a p series
yes
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Renato Chavez
tough mica
amber waspBOT
@tough mica Has your question been resolved?
wispy ermine
does this not answer the question? you could also do something a bit simplier and use the fact you can bound the alternating series above by the non-alternating one (which is a p series, as you say, and p>1)
tough mica
,av @wispy ermine
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wispy ermine
???
tough mica
does this not answer the question? you could also do something a bit simplier an...
yeah, it does answer my stuff
I was just confused for a sec, I need more practice with this alternating series
wispy ermine
fair enough
tough mica
ty
,, \sum_{n = 1}^{\infty} \frac{(5-3)^n}{n^2 \cdot 2^n} = \sum_{n =1}^{\infty} \frac{1}{n^2}
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Renato Chavez
tough mica
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tough mica
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humble ferry
hables ingles?
tough mica
ye
tough mica
how to find the range and the k
humble ferry
and we know that inflection points occur when f”(x)=0
humble ferry
no, that’s critical point
inflection point is when you go from concave up to concave down
tough mica
,w define inflection point
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tough mica
I see
f''(x) = 0
sry
f''(1) = 0
,, f(x) = kx^2 - \ln(x) \ f'(x) = 2kx - x^{-1} \ f''(x) = 2k + x^{-2}
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Renato Chavez
tough mica
,, f''(1) = 2k + \frac{1}{1^2} = 2k + 1
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Renato Chavez
tough mica
inflection point is when you go from concave up to concave down
0 = 2k + 1 ==> 2k = -1 ==> k = -1/2
,, f(x) = -\frac{1}{2} x^2 - \ln(x)
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Renato Chavez
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Renato Chavez
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Renato Chavez
tough mica
I am trying to find the vertical asymptote
tough mica
,w lim x to 0 of ln(x)
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tough mica
I dont get it
like the limit of f(x) when x is approaching 0 is infinity
and the limit of f(x) when x is approaching infinity is negative infinity
food for thought
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@tough mica Has your question been resolved?
hard ermine
What's the problem?
amber waspBOT
@tough mica Has your question been resolved?
tough mica
What's the problem?
like I'm trying to find the range I already found f(x) and k
,, f(x) = -\frac{1}{2}x^2 - \ln(x)
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Renato Chavez
tough mica
the range of this function
hard ermine
Do you know how a regular log function graph looks like?
hard ermine
This is correct
amber waspBOT
@tough mica Has your question been resolved?
untold shoal
Was thinking if you rewrite x as e^a, so you will have
ln(e^a) = a.
lim [e^a->0] ln(e^a)
lim [e^a -> 0] a
tbh am kinda stuck here on how to write a non empirical proof that e^a -> 0 implies a -> -inf
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bitter ibex
the range of this function
just the range?
the only "restriction" here is ln x
that means x must be > 0
because for ln x, x>0 (for negative numbers and 0 the function doesnt have value), you can see that by checking ln(x) graph in desmos or somewhere else
x^2 can be any real number so its ignored
so the range is from 0 to infinity
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@tough mica Has your question been resolved?
untold shoal
,w define range
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untold shoal
,w define domain
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untold shoal
just the range?
the only "restriction" here is ln x
that means x must be > 0
b...
domain?
fossil shell
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fossil shell
I don't rlly understand what they are tryna do here
They did d^2y/dx^2=0
And that value of x has the minimum graident? I don't understand wby
hollow wolf
I don't rlly understand what they are tryna do here
you want to minimize the gradient function, which is $z(x)=\frac{\mathrm dy}{\mathrm dx}(x)$
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derivada.schwarziana
hollow wolf
so you just do second derivative test on z(x)
fossil shell
so you just do second derivative test on z(x)
Erm I'm not sure I understand
hollow wolf
well, the second derivative test says that
- any extreme value (i.e. maximum or minimum) of a function must occur on a critical point, so we find points such that z'(x)=0
- if x is a critical point and z''(x)>0, then z has a minimum at x
fossil shell
So this 1.5 is the point of inflexion on curve right
hollow wolf
So this 1.5 is the point of inflexion on curve right
yes
what I called "critical point" above but point of inflexion is another term for that
fossil shell
well, the second derivative test says that
- any extreme value (i.e. maximum or ...
What if z''(x) was smaller than 0?
hollow wolf
then z(x) would be a maximum
fossil shell
Oh
So bascially if we didint use z=graident function and y``(x) =0 if has to either be the maximum or minimum graident
fossil shell
Oh
hollow wolf
the point is, what they're doing here is calc 1 optimization but for the derivative (= gradient) of y(x)
fossil shell
the point is, what they're doing here is calc 1 optimization but for the derivat...
Hmm so if point of inflection=0 at that x coordinate the change in graident would be the maximum or minimum depending on y```(x)
hollow wolf
yes
it's a point of inflection for z(x) since we're actually finding a minimum of z(x)
fossil shell
Oh
fossil shell
it's a point of inflection for z(x) since we're actually finding a minimum of z(...
Wait isint point of inflection for z(x) be z``(x)
hollow wolf
point of inflection means a point where the derivative is zero
so a point where z'(x)=0
then you check the sign of z''(x)
(your book does it the other way around for some reason)
fossil shell
Oh
fossil shell
then you check the sign of z''(x)
Wait I don't rlly understand what does z''(x) represent
hollow wolf
it's what you check to apply the second derivative test
so if z'(x)=0, then z has a local minimum at x if z''(x)>0 and a local maximum if z''(x)<0
hollow wolf
in a sense it represents the "concavity" of the function if it's at a point of inflection/critical point
but yeah that's all there's to it
fossil shell
Hmm okay
hollow wolf
you want the minimum gradient of y(x), so you use calculus to find a minimum of z(x)=y'(x)
fossil shell
you want the minimum gradient of y(x), so you use calculus to find a minimum of ...
Oh so your saying the x coordinate where the graident of z(x) is 0 is the x coordinate where y(x) has the minimum/maximum graident depending on z''(x)?
hollow wolf
Oh so your saying the x coordinate where the graident of z(x) is 0 is the x coor...
yes
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grim isle
why are the 2 1ohm parallel
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why are the 2 1ohm parallel
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fallen chasm
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fallen chasm
The way I answered it was by finding stuff that are true about graph f’(x). Which ik is wrong cuz it’s asking about graph f(x)
I’m not sure how to visualize the graph of f(x) from that f’(x) graph
inner prawn
yea, you answered as if the graph was the f(x)
but it's not
if f'(x) < 0 in an interval (a, b) then f(x) is decreasing
distant herald
The way I answered it was by finding stuff that are true about graph f’(x). Whic...
maybe you don't need to visualize f to be able to answer questions about its properties
distant herald
f increases when f' > 0, decreases when f' < 0. and f has an inflection point where f'' changes signs, which is where f' changes from increasing to decreasing
distant herald
and inflection points are where f''(x) = 0
btw it's not enough for f'' to be 0
inner prawn
btw it's not enough for f'' to be 0
yea there's a little more
f''(x) <0 for x< a and f''(x) > 0, for x > a, and vice-versa
for some a, f''(a) = 0
but it doesn't matter here
or do
nah
fallen chasm
f increases when f' > 0, decreases when f' < 0. and f has an inflection point wh...
So at interval (Neg inf, 0) and (2,0) in the f’(x) graph, f(x) is increasing?
For the inflection part you wrote, When you say f’ changes signs, do you mean when the y coordinates change from pos to neg and vice versa?
distant herald
sorry if that was hard to read, inflection points are where f'' changes signs
there's two primes there
so f'' changes signs when it changes from negative to positive, or from positive to negative
but since f'' is the derivative of f', this means that an inflection point only occurs where the first derivative f' changes from increasing to decreasing, or from decreasing to increasing
and you have the graph of f'
fallen chasm
So if f” changes signs, it doesn’t mean f’ changed signs too?
How do I figure out where f’ changed signs then cuz i need to find inflection of f(x) for the question
distant herald
you don't care where f' changes signs
let me clarify
you want inflection of f
this is where f'' changes signs
which is where f' changes from increasing to decreasing, or from decreasing to increasing
you don't care where f' changes signs
a function can change from increasing to decreasing and still not change signs
fallen chasm
OHH
fallen chasm
Then for this graph, the inflection would just be at x=1?
hollow cape
i don't see any points of inflection
fallen chasm
Isn’t an inflection when the graph goes from increasing to decreasing ?
Or no wait
Is it for concave up and concave down?
hollow cape
inflection is when a graph goes from concave up to concave down or vice versa
fallen chasm
okok yea got it
distant herald
inflection is when a graph goes from concave up to concave down or vice versa
this is the graph of f' though
fallen chasm
Andd is it true that at interval (Neg inf, 0) and (2,0) in the f’(x) graph, f(x) is increasing?
hollow cape
oh i didn't realize that
distant herald
Then for this graph, the inflection would just be at x=1?
you are correct
hollow cape
sorry for being misleading
distant herald
f has inflection at 1, and yes f is increasing on (-inf,0) U (2, inf)
fallen chasm
this is the graph of f' though
So for f’ inflections happen when it goes from increase to decrease?
For f’’ inflection happens when it goes from concave up to concave down?
And vice versa for both
distant herald
we're always talking about f. for f, inflection happens whenever it changes from concave up to down, or from concave down to up. this is equivalent to f' changing from increasing to decreasing or from decreasing to increasing. this is equivalent to f'' changing from positive to negative, or from negative to positive
all of these tell you the same thing about f
but these are three different ways to find inflection depending on what information you're given
fallen chasm
OHHHH
I seee
I get it now, there’s different ways to get the inflection depending if you have graph of f, f’ or f’’
fallen chasm
Going back to this question, the answer is only I ?
hollow cape
yep!
fallen chasm
Awesomee tysmm guyss !!
hollow cape
once again sorry for the little bit of misleading i thought that was a graph of f not f'
fallen chasm
nah dww abt it
it actually helped me realize finding inflections would be different depending on graph type lol
So you’re gooodd
distant herald
always make sure you're clear about what you're fidning the ifnormation for and what you're given
hollow cape
Yes learn from my mistakes
fallen chasm
Loll will doo
distant herald
if you were asked to find inflection points of f', you'd have to be looking for where f' changes concavity, where f'' changes increasing/decreasing, or where f''' changes signs
so the derivatives and info you look for are all relative to what the problem asks
fallen chasm
Oh finding inflection of f’ is a thing? Is finding inflection at f’’ a thing too?
hollow cape
You can find inflection points of any polynomial so yes
Not only polynomials but all graphs of functions if I’m thinking about it correctly
Just think of it as its own problem
fallen chasm
ooo okok, I’ll wait till I learn it in class so I won’t confuse myself. But that’s good to knoww
Ty againn
.close
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runic kraken
trying to find the nth derivative of sin(3x), i found (-1)^(n/2) *sin(x+n(pi/2)) but my book says just sin(x+n(pi/2))
runic kraken
like it does not mention the change in sign
spiral zealot
both seem wrong
edgy sky
yeah what happened to the 3 that should be in front?
patent raptor
trying to find the nth derivative of sin(3x), i found (-1)^(n/2) *sin(x+n(pi/2))...
(-1)^(n/2) if n is odd you are taking the square root of a negative number
spiral zealot
and what's with the x + n(pi/2)
proven vapor
and what's with the `x + n(pi/2)`
it's to cycle the sin and cos
runic kraken
so its never negative
spiral zealot
oh right
proven vapor
so its never negative
n being negative is not the problem, n being odd is
runic kraken
ah
proven vapor
why do you need that (-1)^(n/2) part anyway?
edgy sky
first one should be 3^n sin(3x+n pi/2) if Im not mistaken?
patent raptor
so its never negative
sin(x+3pi/2) = -sin(x+pi/2)
runic kraken
is that becasue sin is a odd function?
patent raptor
sin(x+pi/2+pi) you are basically shifting it half a period which resembles negative sine
edgy sky
sin(x+pi) = -sin x
patent raptor
so it changes sign when n is odd ?
it changes sign because you are shifting it by pi every 2nd derivative
sin(3x+pi/2) = cos(3x)
sin(3x+pi) = -sin(3x)
sin(3x+pi+pi/2) = -sin(3x+pi/2) = -cos(3x)
sin(3x+pi+pi) = sin(3x)
now you would need the right factor in front
so 3^n and done
and again (-1)^(n/2) how did you come up with that
the division by 2
for n = 1 you get (-1)^(1/2) = i
runic kraken
yeah idk
i was trying many things
like -1 ^ 2n-1
didnt' work
2n+1
none of these worked
then i asked the forbidden machine
patent raptor
I also wouldn't know how to express ++--++ that it changes sign after two derivatives
patent raptor
unless you explicitly define it but the point is to find one unique closed form
patent raptor
my number 1 advocate is drawing stuff when doing math 
runic kraken
eeh its kinda clear
wait when you add pi/2 or pi or any
you go back?
like you translate the graph to the left?
yeah you do
now it makes sense
patent raptor
like you translate the graph to the left?
yup
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earnest sinew
I need help in the statistic software R
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I need help in the statistic software R
earnest sinew
I have a tsibble table with Microsoft Closure stock prices, and i want to fit Arima models to it
but i cant , cause since i am working with stock prices i dont have data at weekends and Holidays
so R can t interpret my data
But just for the Arima Models
i can make the plots
autocorrelation functions
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@earnest sinew Has your question been resolved?
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@earnest sinew Has your question been resolved?
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@earnest sinew Has your question been resolved?
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@earnest sinew Has your question been resolved?
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@earnest sinew Has your question been resolved?
vague raptor
Need help with learning series in calculus
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Need help with learning series in calculus
vague raptor
I need to be able to show that a sequence is bounded or unbounded and to calculate the limit of said sequence. I have to recognize geometric series, show whether p series converge or diverge using integral tests, and recognize when a series is positive, alternating, or neither
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