next question?
#help-10
timid silo
pseudo swift
aight
timid silo
i had to split it into two pictures
so this is my study note but im not sure how to solve it?
pseudo swift
god their questions are crap
timid silo
IKR
pseudo swift
ok so they're asking about the roots of that polynomial
timid silo
we still have four more after this
pseudo swift
i.e. for which values of x is that polynomial = 0
timid silo
high python
hii
pseudo swift
you should be able to read that from the graph
timid silo
i.e. for which values of x is that polynomial = 0
the bottom of the line
the first part
right?
pseudo swift
right
pseudo swift
they had that channel before
timid silo
oh
ok
do you mind if i grab some water really quick? and a piece of paper to take notes?
it'll take less than 2 minutes
pseudo swift
yeah np
pseudo swift
re
pseudo swift
the bottom of the line
alright so can you tell me the values of x for which f(x) = 0?
pseudo swift
that's one of them
timid silo
bc 1 times 0 is 0
pseudo swift
?
pseudo swift
look at the graph
timid silo
ok
pseudo swift
is f(1) really 0?
pseudo swift
yeah
pseudo swift
yup
pseudo swift
nah it's fine
timid silo
that's correct
pseudo swift
well remember the fill in the blanks question from earlier
pseudo swift
it gives you the answer
timid silo
and "less than"
pseudo swift
less than ?
pseudo swift
why so ?
timid silo
ummmm
pseudo swift
that question is fucking ambiguous tbf
pseudo swift
so I could see that answer
timid silo
but my teacher kinda just throws things together
he's going through lots of stuff
he's having a new baby but has issues with his wife
soooo
:))
pseudo swift
like if you only allow real roots, then "less than" can happen
timid silo
oh
pseudo swift
but if you allow complex roots, then they're always equal
pseudo swift
is 7 even an answer here ?
timid silo
oh no
it's not
my mind went to the first question oops
😭
it's not -14
ik that much
pseudo swift
"sum of multiplicities = degree", that's what the previous question tells us
pseudo swift
it's not -14
yeah it's not -14 sure
timid silo
why'd you say sure 😭
timid silo
it's 3 then
pseudo swift
yeah the degree is 3
timid silo
:DDD
pseudo swift
so the sum of multiplicities is 3
pseudo swift
you know what standard form is?
pseudo swift
you put the highest powers at the beginning
timid silo
so the five would be first
pseudo swift
yup^^
rare citrus
whats the answer to this and how do I get it
timid silo
this one is very similar to the other one
timid silo
whats the answer to this and how do I get it
.....
pseudo swift
brb
rare citrus
wait how
rare citrus
<#488120190538743810>
ty
timid silo
3
YES
THANK U
i finished 😭
my study got 19/20
ok
thank you for the help!
thanks sm!
how do i close this now so other ppl can use it?
.close
twin stump
i need help in the word problem
obtuse pebbleBOT
i need help in the word problem
twin stump
i just need the inequality
i think i can take it from there
wait so it must be x^2 + 25x + 96 < 75?
high python
obtuse pebbleBOT
dire basin
What this qn mean by? It ask us to do what? Prove this?
high python
yes
dire basin
Oh I see
final thunder
Looks like silly induction
high python
because of the n
high python
Looks like silly induction
it's not
dire basin
It seems like to do summation of series.
final thunder
Really
dire basin
And is a swing series
final thunder
Why does induction not work?
high python
i did if n=2k and if n=2k+1
that changes the sens of the sum
(-1)^2k=1
(-1)^2k+1=-1
final thunder
No yeah it does work I just did
high python
high python
I have a question is induction the same as recurrence ?
final thunder
No?
dire basin
In my opinion, they almots have the same meaning.
To do induction, you need to do 3 steps.
First, check the initial condition is True or False, like sub k with 0 or 1 as usual.
Then, make a consumption that when k = l, the equation is right, so that we have a usable condition.
Last, to prove when k = l + 1, with the consumption at 2nd step, the equation is right.
It seems like the Dominoes.
high python
ooh okay
final thunder
I’m not sure what you mean by proof by recurrence
high python
I’m not sure what you mean by proof by recurrence
I study maths in french
dire basin
you have a right beginning, and the middle wall can break well. So then the whole queue break down.
high python
and so it is very hard to give the same meaning using english
dire basin
Oh, I see
high python
we have three steps in recurrence
dire basin
The are the same meaning. We often use induction in English.
dire basin
even in programming language we use the word iteration
I think they are almost the same.
dire basin
But these two are not equation, so we cannot use induction directly.
high python
if 3 divides k then k=3p with p in N
dire basin
then? I'm still confused。
btw. Is the whole qn. If not, can you shot a whole qn pic?
hmm. It's too late. I have to go for sleep. Mb we can discuss this qn tomorrow.@high python
oblique bridge
imo the question asks if 5^3^n + 1 divides 3^(n+1)
dire basin
Okay. When awake would be better. Mb you could explain me better what the qn ask us to do tomorrow. Good night.
high python
imo the question asks if 5^3^n + 1 divides 3^(n+1)
the opposite actually
oblique bridge
damn you are correct
high python
demonstrate it
oblique bridge
have you tried induction?
for $n=0$ it is trivial, assume $n=k$ is true, then for $n=k+1$, try to expand $5^{3^{k+1}}+1$ to see if you can factorize it to multiples of $5^{3^k}+1$ so that the whole expression is divided by $3^{k+1}$
warm shaleBOT
ミコ
obtuse pebbleBOT
@high python Has your question been resolved?
obtuse pebbleBOT
@high python Has your question been resolved?
faint echo
Heya visual learner here, hoping someone can help me with the steps- not sure what to start with or how to format it
obtuse pebbleBOT
Heya visual learner here, hoping someone can help me with the steps- not sure wh...
@faint echo Has your question been resolved?
wise fossil
What’s up
next lantern
could anyone help me figure out how to start with this question
obtuse pebbleBOT
could anyone help me figure out how to start with this question
final thunder
discriminant
trail matrix
hey yall would this be correct for a proof of a sequcnce limit?
obtuse pebbleBOT
hey yall would this be correct for a proof of a sequcnce limit?
trail matrix
Im confused ab a couple things
1.Why does my prof stop at 1/n, why dosent she continue to inequality to ge to <n?
2.what does this even prove 😭
final thunder
this proof is just wrong
warm shaleBOT
$Pure$
honest reef
this proof is just wrong
ye
obtuse pebbleBOT
@trail matrix Has your question been resolved?
final thunder
hey yall would this be correct for a proof of a sequcnce limit?
The idea for this type of proof is no matter how small your epsilon is you can always wait until some a_N and after that the distance between your an and the limit will always be less than epsilon.
honest reef
The idea for this type of proof is no matter how small your epsilon is you can a...
it's like my love for you, no matter where u choose the epsilon
i will always surpass it
final thunder
stfu
trail matrix
The idea for this type of proof is no matter how small your epsilon is you can a...
my prof also wrote this but I dont see how it has anything to do with the proof
final thunder
no idea whats written
final thunder
The idea for this type of proof is no matter how small your epsilon is you can a...
Your job in this proof is to find such N for any arbitary epsilon
trail matrix
Your job in this proof is to find such N for any arbitary epsilon
is there any n that would satisy the inequality?
since epsilon is always arbitrarily small?
final thunder
for example, since you need 1/(2n-1) < epsilon
we can just pick N such that (2N-1) * epsilon > 1
final thunder
we can just pick N such that (2N-1) * epsilon > 1
whose existence is gauranteed by the archimedean property of R
trail matrix
whose existence is gauranteed by the archimedean property of R
this outta my leauge 😭
final thunder
well im not sure how you deduce 1/(2n-1) <= 1/2n
trail matrix
since its a sequence isnt n>1
final thunder
thats just not true just try some n
trail matrix
so wouldnt the be true?
oh wait
yea that isnt correct
shouhlda been
1/2n-n
then 1/n
trail matrix
yea that makes snese
this might be a really dumb question, but why dont we make it even larger?
since n>1 I know that 1/n <1
so why cant I say 1/n <n ?
final thunder
how would do define your n? (im not saying you cant)
or N
it has to be in terms of epsilon
obtuse pebbleBOT
final thunder
.reopen
obtuse pebbleBOT
✅
trail matrix
could I just say 1<epsilon/n ?
from my understanding, what you explained earlier is on the left
and what Im askign is on the right
final thunder
epsilon is greater than 1/n
trail matrix
epsilon is greater than 1/n
isnt n just all R>1?
final thunder
all natural number >=1
final thunder
right
trail matrix
sorry this is prolly really dumb but why is it that 1/n is fine, when it also could be smaller then 0.00000000001 but n isnt?
like
dose the inequality 1/n<epsilon have to be true for ALL n, or just 1 n?
final thunder
it has to be true for some N and all the ns after it
trail matrix
ah that makes sense
final thunder
if a_N < epsilon then we must have an < epsilon for all n>=N
trail matrix
ahh alot of things are clickign now
thats why my prof says ther eexists a positive integer M st n>M
final thunder
in other words, after some point the seqeunce all become less tgan epsilon away from the limit
final thunder
thats why my prof says ther eexists a positive integer M st n>M
this is essentially what im saying for any arbitrary epsilon there must be an M such that a_n < epsilon for all n>=M
trail matrix
yep yep its all making snese
final thunder
no matter how small or big epsilon is we can wait long enough and the sequence will gets less than epsilon away from the limit
final thunder
A proof should be readable from start to finish, left to right. First of all, in stead of there exists it should be for all epsilon > 0. Then what you should do here is say pick N such that blah blah blah. Now consider |a_n - L| and do some algebra to show that this is less than epsilon.
trail matrix
A proof should be readable from start to finish, left to right. First of all, in...
other then the beginning is the rest fine?
final thunder
what you just wrote starts from |a_n - 1| < epsilon which doensn't make much sense
trail matrix
esp the last line 😭
final thunder
ill write a proof for the sequence an = 1/n and you can adapt it to your proof
to show that this sequence converges to 0
trail matrix
ok sounds good
final thunder
ive got to go sorry
trail matrix
ah np
trail matrix
ive got to go sorry
before you go is there anythign wrong with the last line of my proof
and thanks for the help, really got me understanigni this 🫡
oh wai tI wouldve had to say M= nEpsilon then n>=M
warm shaleBOT
$Pure$
trail matrix
thanks
final thunder
trail matrix
I think what was confusing me a bit is that I thought of it as a normal limit proof where it has a final line, instead the sequence proof is more like get to the epsilon, represnt it as M, then go back to epsilon using n
trail matrix
I think what was confusing me a bit is that I thought of it as a normal limit pr...
atleast towards the en d
anyways, thanks a bucnh and have a good day/night wherever you are 🫡
life saviour got a midterm tmrw on these proofs
.close
inner flower
obtuse pebbleBOT
spice citrus
I think you can make some progress by rearranging to p^2 - 9 = n - q^2, so q | p^2 - 9
yeah, pretty sure that's it
@inner flower
obtuse pebbleBOT
@inner flower Has your question been resolved?
inner flower
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fluid snow
A train company has 300 passengers each day, which gets them an income of 4500€.
They decide to reduce their ticket prices.
Reducing them by 2.5€ leads to them getting 20 more passengers.
Determine by how much they should reduce their prices so that there is a maximum amount of income.
obtuse pebbleBOT
A train company has 300 passengers each day, which gets them an income of 4500€....
fluid snow
So we have that the ticket prices currently are 15€
Let x be the price reduction and y the number of passengers
Then, y = 300 + 20x, right?
Now, the income I(x) = y * (15 - x) = (300 + 20x)(15 - x), right?
My instructor did the same, but used (300 + 20x)(15 - 2.5x)
Why -2.5x?
He let x be the price reduction in 2.5€
But still used -2.5x
Shouldn't it just be x in that case
Afterwards, he got x = 2
And then he again applied the in 2.5€
And got 5€
But isn't that applying it twice?
x is already in 2.5€ units
inner stratus
How can I show that λx+(1−λ)y∈A <=> all intervals with extremities a,b in A are entirely in A
obtuse pebbleBOT
How can I show that λx+(1−λ)y∈A <=> all intervals with extremities a,b in A are ...
inner stratus
w/ λ∈[0,1]
warm canopy
Well if x and y are the extremities of the interval then λx + (1-λ)y is going through all elements in that interval as you change λ from 0 to 1
twin peak
for h) can someone explain the hint
obtuse pebbleBOT
for h) can someone explain the hint
warm canopy
It's broken the vector up into a combination of eigenvectors
And you know what S does to eigenvectors (since you know their eigenvalues)
twin peak
oh then you can just substitute the eigenvalues
warm canopy
Essentially
twin peak
damn it[
I would not have thought of that on a test
also for c)
how would i come up with an expression equivalent to producing the identity matrix
warm canopy
Hm?
pseudo swift
have you answered a)?
pseudo swift
what have you got then ?
twin peak
A (A^T A)^-1 A^T A (A^T A)^-1 A^T
warm canopy
That is just the identity matrix no?
pseudo swift
well you have some (A^T A)^-1 (A^T A) action going on here
twin peak
yeah, im ngl how did you know that was the identity matrix
thats what im trying to get
pseudo swift
why should it be the identity, it's just a projection
warm canopy
Yeah I'm not sure why you want it to be the identity
pseudo swift
(A^T A)^-1 (A^T A), these cancel out though
warm canopy
You just use (XY)^(-1) = Y^(-1)X^(-1)
But again I'm not sure why you're looking for an identity matrix
twin peak
mostly thats what the solutions suggest
warm canopy
You should have a matrix P and you want to show P² = P
twin peak
thats why
pseudo swift
twin peak
ok its just the inverses cancelling out
bruh id kwhy they made some huge dea if the identity matricies cancelling out
i fucking hate math
.close
obtuse pebbleBOT
pseudo swift
.reopen
obtuse pebbleBOT
✅
harsh remnant
$\left(A^{T}A\right)^{-1}\ne\left(A^{T}A\right)$
warm shaleBOT
LE SSERAFIM
obtuse pebbleBOT
@twin peak Has your question been resolved?
ember vector
obtuse pebbleBOT
ember vector
I just wanted confirmation these were right
Unless Im crazy 🥲 the one Im most reluctant abt is d
obtuse pebbleBOT
@ember vector Has your question been resolved?
ember vector
<@&286206848099549185>
ember vector
.close
plain spear
obtuse pebbleBOT
warm canopy
do either of those vectors lie on the plane?
warm canopy
yeah so they cant possibly be a basis if they dont even lie in the plane
plain spear
lol aight ty
solid cargo
How r they proving that limit is 0 when x approaches negative infinity???
Is the idea that they ttake the numerattor as a -ve number so the signs cancel to show that the limit is still 0 like it was with positive infinity???
obtuse pebbleBOT
How r they proving that limit is 0 when x approaches negative infinity???
Is the...
dense imp
well you are asking how they are proving it, but there is no proof provided in what you posted, they are simply stating a theorem without showing a proof
solid cargo
well you are asking how they are proving it, but there is no proof provided in w...
can u explain what the theorem theyre using means?
dense imp
limits at infinity are defined somewhat similarly as limits as x approaching a number, but when trying to show that the difference between f(x) - L < epsilon for any given epsilon you can come up with some delta such that |x - a| < delta implies |f(x)-L| < epsilon, you show that you can come up with some N such that f(x) - L < epsilon whenever x > N (or x < N if considering a limit as x -> -inf)
so you can prove this theorem from this definition similar to how you do delta epsilon proofs
solid cargo
Thank you
warm shaleBOT
QuasiStar 超新星
narrow vault
subtended arc is obviously 120 deg (either centre to either intersection point has length r so equilateral triangles everywhere)
then the football is given by 2/3 Acirc - the diamond overlap which is a diamond of length r and angles 60deg/120deg
(then take away the circle at the end)
narrow vault
portion of the circle + portion of the circle - diamond overlap - small circle in the middle
as shown in the image after counting the portions you have a diamond shaped region counted twice
right, but the blue fan is the diamond + 2 small bits, and so is the green fan. so the diamond is overcounted
which is why 1 needs to be subtracted away
if you want to do it your way too that also works and amounts to the same thing
yeeeah that didn’t need to happen lol
all 3 sides are radius r
so equilateral :D
wise trail
obtuse pebbleBOT
wise trail
lol
latent walrus
i cant conjure the will to drag my face right up to my screen and squint
latent walrus
quality wise, yeah
latent walrus
howd it go
latent walrus
what have you tried
latent walrus
how come
latent walrus
,calc 1/9 (5+31)
warm shaleBOT
Result:
4
,calc 1/9 (-4+31)
warm shaleBOT
Result:
3
show did u get 31
latent walrus
you have your x and y mixed up
wise trail
ohhh
latent walrus
youre doing change in x/ change in y
latent walrus
i do, yeah sorry
latent walrus
point-slope form
wise trail
sooo
latent walrus
y-y1=m(x-x1)
latent walrus
sure, i suppose
latent walrus
it does
wise trail
y-y1=m(x-x1)
this i dont under stand it
latent walrus
5 and 4 work sure
wise trail
thats 20
wise trail
oh we subtract or add
latent walrus
no
latent walrus
y-y1=m(x-x1)
^
wise trail
idk what that means tho
latent walrus
if you know m and a point (x1,y1) on the line
^
just sub in a point
how were you doing the other questions?
wise trail
i would just add the starting point and it wold work
like in qustion 1
i added the 3
and it was right
latent walrus
y-y1=m(x-x1)
use this then, its the most efficient
wise trail
bc y-y1=m so thats 1/9
latent walrus
y-y1 does not =m
wise trail
and x-x1 is 5?
latent walrus
x-x1 does not = 5
wise trail
oh
wise trail
ya
latent walrus
you know a point (5,4)
wise trail
ya
latent walrus
x1=5, y1=4
wise trail
oh
wise trail
so y-4=m (x-5)
latent walrus
its okay
latent walrus
yeah
wise trail
so what do i do with the plain y and x
latent walrus
thats not even an equation anymore
wise trail
so y-4=1/9(x-5)
lets start back from here
latent walrus
sensible
wise trail
nothing you want y=mx+c
what do i move around
latent walrus
what do you think you should do
wise trail
y=9/1x+4/5
wise trail
oh ok
latent walrus
expand 2(a+b)
latent walrus
?
latent walrus
no, you dont.
latent walrus
expand 2(a+b)
do this
wise trail
9* x 9* 5]
latent walrus
expand 2(a+b)
do this
wise trail
i did?
latent walrus
no you didnt
wise trail
whats 2
wise trail
ik
latent walrus
expand 2(a+b)
wise trail
2a and 2b
latent walrus
2a+2b
wise trail
ya
latent walrus
there is no 2
wise trail
ik
wise trail
but in 2(a+b)
latent walrus
that was just an example so i could see if you can expand brackets
latent walrus
write it properly
latent walrus
dont convert to decimals
wise trail
ik
latent walrus
but again, write the whole equation properly
latent walrus
thats not an equation
latent walrus
you were literally 90% done
wise trail
i dont no what to do after thsi
wise trail
ohhhhhhhhhhhhhhhhhh
latent walrus
stop overthinking it
latent walrus
,w -5/9+4
warm shaleBOT
latent walrus
magic
wise trail
y=1/9x+31/9
ohhhhhh
ok
thx
thx
is thare any way
that if i want help next time it is only u
like any time
example tmro or next week
wise trail
.close
pure jungle
obtuse pebbleBOT
zinc grove
if X <- rgamma(500,24,12) mean(x) = 1.99 how you express mean(x<=2) = 0.008 using gamma function
obtuse pebbleBOT
if X <- rgamma(500,24,12) mean(x) = 1.99 how you express mean(x<=2) = 0.008 usin...
@zinc grove Has your question been resolved?
wise trail
y-y1=m(x-x1)
sorry just needed this formula
obtuse pebbleBOT
@zinc grove Has your question been resolved?
obtuse pebbleBOT
@zinc grove Has your question been resolved?
obtuse pebbleBOT
@zinc grove Has your question been resolved?
obtuse pebbleBOT
@zinc grove Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
desert verge
For exo 22 question 1)a C is b''(t)=-b(t)? I don't understand pk we should have a second order what information does the second derivative give us Soldiers?
obtuse pebbleBOT
For exo 22 question 1)a C is b''(t)=-b(t)? I don't understand pk we should have ...
@desert verge Has your question been resolved?
obtuse pebbleBOT
@desert verge Has your question been resolved?
obtuse pebbleBOT
@desert verge Has your question been resolved?
desert verge
<@&286206848099549185>
urban kiln
@desert verge could you send a clearer picture?
desert verge
<@397085665923432448> could you send a clearer picture?
desert verge
<@397085665923432448> could you send a clearer picture?
It's better
urban kiln
wait what exactly are we supposed to make a differential equation of in part a?
all i could infer is that change in number of blue men at time t is proportional to number of red men alive at time t
so b'(t)=-r(t)
makes sense
desert verge
all i could infer is that change in number of blue men at time t is proportional...
xd it is literally written and the 1)b? but thank you 1) it was explained to me
obtuse pebbleBOT
@desert verge Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
silent cove
obtuse pebbleBOT
silent cove
I have no idea how I should approach this question
This means that, for example, if k=1, f(0)f(2)>=0 right?
obtuse pebbleBOT
@silent cove Has your question been resolved?
obtuse pebbleBOT
@silent cove Has your question been resolved?
robust raven
first all, plz consider the general form of the cubic function, with leading coeff 1, and then derive its derivative and solve the equation f'(-1/4) = -1/4
obtuse pebbleBOT
@silent cove Has your question been resolved?
obtuse pebbleBOT
fickle harness
obtuse pebbleBOT
Available help channel!
deep sphinx
obtuse pebbleBOT
deep sphinx
i dont know how to get rid of the 2 at the start
robust raven
btw: you know properties of logarightms ?
deep sphinx
barely
deep sphinx
2log3(9) would be log3(9squared) right?
robust raven
yes
deep sphinx
ok so log3,(81) + log3,2-log3,6
robust raven
yes and ?
robust raven
wait
you shud not assume x = 3,since
it wil be result )
you should use deifnion of th eloagrithm
deep sphinx
you should use deifnion of th eloagrithm
meaning what
robust raven
can you write the definition ?
deep sphinx
can you write the definition ?
nah, im a bit slow sorry
robust raven
ok giv eme moemnt i write it here
deep sphinx
👍
robust raven
$\log _b \left( x \right) = y <=> b^{y}=x$
warm shaleBOT
Joanna Angel
warm shaleBOT
Joanna Angel
deep sphinx
log3(27) = y <=>3^y=27
robust raven
bravo!
deep sphinx
yeh'
robust raven
that is result
deep sphinx
alright thanks for bearing with me 😂
robust raven
🙂
deep sphinx
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brisk arrow
obtuse pebbleBOT
brisk arrow
Is it correct
brazen gorge
yes
brazen gorge
can't help you with that
you can see it from the definition of a sum of a geometric series
that's one way to learn
i remember it because i just do
brisk arrow
i remember it because i just do
That is pure talent
warm canopy
If you use something enough you will remember it
brazen gorge
comes with experience
brisk arrow
.close
lime mural
When is absolute value used in integration?
obtuse pebbleBOT
When is absolute value used in integration?
lime mural
I saw that the function inside ln is in absolute value. but i also saw some answers with only parentheses
unreal musk
When it comes to integrating 1/x, note that because that’s defined for all nonzero x, you’d probably want to be able to integrate it for negative choices of x as well
That’s basically why you end up seeing $\int \frac1x \dd x = \ln\abs{x}$
warm shaleBOT
@unreal musk
lime mural
is it alright to use both absolute value and parentheses?
unreal musk
But in some cases if you’re only worried about e.g. positive values of x you can ignore the absolute value as |x| = x in that case
unreal musk
is it alright to use both absolute value and parentheses?
Well anywhere you can use just 
you can also use the absolute value
For the most part it’s generally “safer” to use the absolute value unless you’ve argued that whatever you’re working with will always be positive (or if e.g. context suggests that it would be)
Otherwise you might end up running into issues where you’re trying to take lots logs of a negative number
lime mural
I see. Thank you so much!
unreal musk
No problem 
obtuse pebbleBOT
@lime mural Has your question been resolved?
static marten
.close when done
proven zephyr
What is the minimum amount of sides of a polygon to have at least 400 diagonals?
grand geyser
obtuse pebbleBOT
grand geyser
Just need help wiht q1
crude coral
Just need help wiht q1
AD = DE
BD = BC
<ADB = <CDE
according to SAS postulate this is a congruent triangle
obtuse pebbleBOT
@grand geyser Has your question been resolved?
mellow fiber
hi. i need some help with determining the critical region.
H0: p=0.3 and H1: p≠0.3
the sample size is 100 and there is a significance level of 5%
i don't really know how to handle the not equal to sign
obtuse pebbleBOT
hi. i need some help with determining the critical region.
H0: p=0.3 and H1: p≠...
brave bramble
Just means the test is two-tailed
So that first bell curve, specifically not the second
mellow fiber
Oh haha hmm i looked in my textbook and i think i can figure it out now
thank!
.close
twilit gazelle
How can I prove that if a composition gof is bijective, f doesn't need to be surjective ?
obtuse pebbleBOT
How can I prove that if a composition gof is bijective, f doesn't need to be sur...
past sand
Just find a counterexample?
candid rock
proving counterexamples is easy because you can just find one silly example
past sand
I can think of a very obvious one with inverse functions
candid rock
as g . f is just a function X -> Z then hint: what if X and Z are really simple sets
then you can describe the function g . f explicitly over all elements of X and Z, and it then follows that it's a bijection trivially
but then how can you pick Y such that you don't have a surjection
twilit gazelle
Ok, let me think abou it for a while. I am running a single core CPU in my head, it'll take a little time...
This would be an easy counterexample, I think
candid rock
exactly
as long as there's lots of stuff in Y you never care about, then it can all go to the same place
you need it for the definition of the function g , and it only has 1 possible value to be mapped to
but it's completely irrelevant in the function g.f
twilit gazelle
Ok thank you
past sand
Hold on
twilit gazelle
Yes ?
past sand
It's g.f not f.g
past sand
This would be an easy counterexample, I think
Isn't f surjective here?
candid rock
no; there exists no a in X such that f(a) = 2
function composition is backwards; g in g.f is the second function
candid rock
yes
low patrol
obtuse pebbleBOT
low patrol
i know i can rewrite it with e
turning into (e^xln8-e^xln6)/(e^xln4-e^xln2)
but i dont know where to go from there
honest reef
what
this is indeterminante form of 0/0
just take derivative
that's L'hopital
8-12x
4-4x for denominator
answer is just 2
errant lark
but i dont know where to go from there
Simple L'hopital.
obtuse pebbleBOT
@low patrol Has your question been resolved?
sturdy cradle
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rotund crest
obtuse pebbleBOT
rotund crest
What is your actual question
The graph on the picture of that function shows something similar to 1 for x->0
But to me x->0± of that function is inf
tardy epoch
The graph on the picture of that function shows something similar to 1 for x->0
Does your actual question have a limit?
rotund crest
Wdym
tardy epoch
This is just the plot of some functions
rotund crest
I have to see if the function is true for x->0
tardy epoch
Where did you get them and what problem are you working on
rotund crest
H(x) if f'(x)
I need to know if f'(x) exists for x->0
So do limx->0±
Which to me is inf
But on the graph its close to 1
obtuse pebbleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
tardy epoch
Yea just because h(x) is undefined at zero, doesn't mean the limit of h(x) is undefined
You have to use one sided limits in the function
But also you haven't showed your work that h(x) = f'(x) so it could be wrong
rotund crest
But also you haven't showed your work that h(x) = f'(x) so it could be wrong
I tested it with a calculator for it
rotund crest
Yea just because h(x) is undefined at zero, doesn't mean the limit of h(x) is un...
Yeah I know, but if I do the limit of hx it results inf to me
tardy epoch
Yeah I know, but if I do the limit of hx it results inf to me
Uh your work is wrong then
tardy epoch
You have to use one sided limits in the function
Do this and show your work
rotund crest
Doing this with my mind rn on a train but the num is ~ to ln2|x| and the den is ~ to ln2|x| so it should be 1
Its 0.83 here tho
obtuse pebbleBOT
@rotund crest Has your question been resolved?
tardy epoch
Id like to but I cant rn
Then do the problem later
rotund crest
I don't know what you're asking anymore
The graph saying 0.83 confuses me because thats not 1
rotund crest
Here
tardy epoch
Graphing utilities don't have infinite precision
You should just use pen and paper and not rely on software to do this problem
obtuse pebbleBOT
@rotund crest Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
I don't understand this step
obtuse pebbleBOT
I don't understand this step
tardy epoch
I don't understand this step
they're only factoring out x+4 from the denominator
timid silo
yeah but how do they do jt
timid silo
like do they take out both x + 4's and divide x+4 with x?
tardy epoch
like do they take out both x + 4's and divide x+4 with x?
just the first part
tardy epoch
rewrite the denominator with t = x + 4
how about if you did this t substitution
t(x+1) = ?
tardy epoch
timid silo
YEAH I KNOW but it doesn't make sense cause there is no t in the expression
tardy epoch
you can make whatever substitution you want, it's algebra
tardy epoch
t(x+1) = ?
the answer to this is xt + t
timid silo
Yes yes