Can you show your work here?
#help-0
twin nimbus
fallow bolt
how did you end up getting it?
narrow elk
the things should be in brackets right
fallow bolt
but its un factorable
narrow elk
so that means we both got the signs wrong
twin nimbus
the things should be in brackets right
Yeah
fallow bolt
but its un factorable
also the answer key gives the answer 4(x+3)(2x+1)
twin nimbus
Let me work it out, rq
narrow elk
also the answer key gives the answer 4(x+3)(2x+1)
yep
fallow bolt
e got it right
narrow elk
its the brackets
fallow bolt
possibly 8x^2 + 28x +12?
wait but why does it end up being this?
twin nimbus
(3x + 4)^2 - (x - 2)^2
(9x^2 + 24x + 16) - (x^2 - 4x + 4)
9x^2 + 24x + 16 - x^2 + 4x - 4
8x^2 + 28x + 12
lone heartBOT
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gritty violet
Hello
gritty violet
Does anyone know a little abt technical draw?
small lance
technical draw?
livid sage
🤔
lone heartBOT
@gritty violet Has your question been resolved?
gritty violet
technical drawing
gleaming ermine
like an engineering blueprint?
lone heartBOT
@gritty violet Has your question been resolved?
white stump
lone heartBOT
white stump
ik this converges but im not sure how to prove this
im supposed to do tests for it but
the sin is throwing me off
wispy plaza
We can factor out the 2 since we already know 2/(n^2) converges
Then personally, I’d try the definite integral of sin(n)/(n^2) from 0 to infinity
Wait, actually, since we’re only doing sin of integers, it may be hard to prove with an integral
Sorry, I’m very new to making proofs & stuff
Sin(n) always between -1 and 1
tepid drum
hint: ||sin(n)=< 1 for all n in N||
wispy plaza
Sin(n) always between -1 and 1
So if we replace sin(n) with 1 we know the the new series is always greater than or equal to the sin(n) one
Then we can just prove 1/(n^2) converges
I don’t know why I said 2pi
I was tripping
😭
tepid drum
Sin(n) always between -1 and 1
did you mean sin(n) is between -1 and 1 ?
wispy plaza
did you mean sin(n) is between -1 and 1 ?
Yeah, lowkey tripping rn
tepid drum
dw about it
lone heartBOT
@white stump Has your question been resolved?
white stump
wait
nvrmind figured it out
you compare to 3/n^2
because 3 is the max sin can hit
and so itll be more than that function
and we know it converges by p test
and since its bigger than the given function, the given funciton also converges
tepid drum
because 3 is the max sin can hit
so maybe you meant to say something else but phrased it in a wrong way
but this is wrong
tepid drum
-1=<sin(n)=<1 for all n in N (more generally for n in N)
tepid drum
then that is correct
white stump
bad wording
white stump
+2 right
tepid drum
why +2
i mean sin(n)=< 1 for all n in N so it is < 3 for all n in N dont you agree
so my point is , you can say 2+sin(n)=< 2+1=3
you can also say something like 2+sin(n)< 2+3=5
you have many options but these may be found wierd
tepid drum
so my point is , you can say 2+sin(n)=< 2+1=3
because this is the most obvious one
tepid drum
nothing special
white stump
.close
lone heartBOT
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static wagon
for question 2 could someone check my working if it’s valid
lone heartBOT
for question 2 could someone check my working if it’s valid
visual thistle
for question 2 could someone check my working if it’s valid
Dam what is this ?
solemn juniper
how are you concluding that it's undefined?
static wagon
Dam what is this ?
wdym
solemn juniper
that's indeterminate
static wagon
that's indeterminate
what does that mean
visual thistle
what does that mean
Dam bro I was wondering if ur good in geometry?
static wagon
why is that different to undefined?
solemn juniper
have you been introduced to the limit definition of the derivative?
solemn juniper
if you haven't seen it then it's a bad example
the jist is that 0/0 doesn't immediately mean undefined. It could also be 0 (as 0/anything = 0), or it could be any other number
consider f(x) = x^2/x. You would be wise to not immediately say the limit as x -> 0 of f(x) is undefined
static wagon
oh so with 0/0 we always say indeterminate?
static wagon
but that's not the answer; that just means you have to do some more work
but is everything else fine?
solemn juniper
sure
static wagon
.close
copper siren
which property is being used here
lone heartBOT
which property is being used here
stark crater
1st arrow is triangle inequality, 2nd arrow is just ordered field definition property
(and using stuff in 1st line)
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tulip ore
I wanna check my work, i have dudes in the last
lone heartBOT
I wanna check my work, i have dudes in the last
@tulip ore Has your question been resolved?
lone heartBOT
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Available help channel!
plain flame
Hello
keen idol
look at the edge cases (intersection points when both satisfy the equality)
plain flame
How to do without desmos calculator?
keen idol
have you studied systems of equations
tawdry urchin
do you know how to solve systems of equations?
plain flame
Yes somewhat
ocean sealBOT
Dork9399
plain flame
Yes
keen idol
i mean logically speaking, u would want to spend all 15 dollars on fruits right?
to maximize your bananas
plain flame
**Dork9399**
B is 2, A is 4
keen idol
good but that doesnt maximize your bananas does it?
plain flame
Probably no
keen idol
what if we just didnt buy apples
10 bananas are 15 dollars
so 10 B and 0 A would be the maximized banana answer
this is why you check edge cases
if you want to maximize the apples, you do 0 bananas and see how many apples u can get
plain flame
6
keen idol
wdym 6
plain flame
5
lone heartBOT
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Available help channel!
sharp gate
Do you need to use the lemma to prove the general statement?
sharp gate
This is my working out.
sharp gate
Ok. I wasn't sure if the proof of the general case was completely separate or not
But otherwise I wouldn't know how to split up the k+1 and k to then use the inductive hypothesis
true rune
Ok. I wasn't sure if the proof of the general case was completely separate or no...
hmm idk if you can do it independently
In any case, it’s easier and faster to use the lemma
sharp gate
Ok thanks.
true rune
np sir
sharp gate
.close
rapid badger
how do i get the first and second derivative of the equation f(x) = Axe^(-bx)
rapid badger
the highlighted part is what im working on rn
true rune
how do i get the first and second derivative of the equation f(x) = Axe^(-bx)
by product rule ?
true rune
what u got ?
rapid badger
like so far?
true rune
for f’ ?
rapid badger
i know that it has to = 0 for the x coordinate for the stationary point, but i dont know what part i split off to use the product rule
true rune
Oh I thought you wanted f’ and f’’ 😭
rapid badger
i think thats what its asking im not to sure myself 😭
rapid badger
so for the thingo what ive needed to do is change the values of A and B, documenting what changes they make to the graph, and now it needs me to make a conjecture for said equation and prove it
im not too sure
lone heartBOT
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lethal salmon
lone heartBOT
lethal salmon
Anyone able to have the time to give a walkthrough with this? Ap stats
Im super lost
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lone heartBOT
granite light
q 10
vale wigeon
this one?
granite light
lone heartBOT
lone heartBOT
The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.
granite light
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vapid tide
help
lone heartBOT
vapid tide
compact surge
what do you need help with?
vapid tide
i dont understand what the question is saying with the origin bit
compact surge
uhhh
O is the origin and that "connected" to point A happens to be the vector a
it's like you can almost just treat vectors like points
vapid tide
so this is basically saying that the points are just position vectors some point on the plane
compact surge
yeah cuz if i tell you (2,3)
vapid tide
it just seemed kinda weird to think of it like that idk
vapid tide
ye
compact surge
anyway same logic here
the tail is at the origin O
and the head is at A
or whatever point you're concerned with
vapid tide
but idk where o is
compact surge
u don't need to
compact surge
if u like you can think of O somewhere here
in which case you know what vector a and vector p is referring to
owing to what what is p - a?
vapid tide
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static wagon
what’s the piecewise function for |x^3|?
lone heartBOT
what’s the piecewise function for |x^3|?
echo socket
It’s not clear what you mean by that, do you want to get rid of the || by giving the function a piecewise definition?
lone heartBOT
@static wagon Has your question been resolved?
static wagon
It’s not clear what you mean by that, do you want to get rid of the || by giving...
yes
cursive ruin
what’s the piecewise function for |x^3|?
it will be -x^3 for x<0
and x^3 for x>0
lone heartBOT
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Available help channel!
acoustic meteor
hello can anyone tell me how to solve this question
swift grail
@acoustic meteor do you know when a digit is divisible by 11
acoustic meteor
the divisibility rule by 11
north rover
the divisibility rule by 11
Which is?
prisma jackal
hey can any of you help me any of you have studied factorials deeply i am making a team so we can make a formula for factorials a simple formula no approximation and no reccurence relation
lone heartBOT
@acoustic meteor Has your question been resolved?
halcyon nest
This is a pretty simple question and involves more of an explanation to me than actually just finding a solution. In the question: A set of cards consist of 8 yellow and 7 red each showing a different picture. If 10 cards are selected at random, find the number of different arangements possible.
halcyon nest
My question is, how do I know if this is asking me for permutations or combinations?
lone heartBOT
@halcyon nest Has your question been resolved?
cursive ruin
My question is, how do I know if this is asking me for permutations or combinati...
when you select you will use combinations
to find the arrangements of your selections you will use the permutation function
tranquil tartan
My question is, how do I know if this is asking me for permutations or combinati...
I guess that "set" implies that order doesnt matter
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Available help channel!
cursive ruin
how do i write a proof for the 1st part
lone heartBOT
how do i write a proof for the 1st part
silent snow
i think i can try
you can see a circle equation so the frog will try to jump at circumferences
silent snow
yea seems puzzling
cursive ruin
<@&286206848099549185>
lone heartBOT
@cursive ruin Has your question been resolved?
cursive ruin
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lone heartBOT
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Available help channel!
lilac jolt
is this correct?
lone heartBOT
is this correct?
lilac jolt
limits with greatest integer function
if this is too messy to understand i can rewrite it
swift grail
$$\lim_{x \to 2^+} \frac{x^2 - 2x}{\lfloor x \rfloor - x}$$
ocean sealBOT
casework
swift grail
This?
lilac jolt
yes
lilac jolt
$$\lim_{x \to 2^+} \frac{x^2 - 2x}{\lfloor x \rfloor - x}$$
why the hell are there differents command for each bracket of the floor notation
lethal belfry
Cool, can you re-write $\floor{x}$ near 2
ocean sealBOT
What a wonderful world !
lilac jolt
couldnt they just make it so that u can use {}
swift grail
why the hell are there differents command for each bracket of the floor notation
Well left bracket and right bracket
lilac jolt
Cool, can you re-write $\floor{x}$ near 2
what does this mean
swift grail
They did $\floor{x}$
ocean sealBOT
casework
lilac jolt
i dont speak english
swift grail
They did $\floor{x}$
I just learned this. Never tried it , i just went with it \lfloor , \rfloor as its how i learned it.
lethal belfry
what does this mean
Near $2^+$, $\floor{x} = x-2$,no?
ocean sealBOT
What a wonderful world !
lilac jolt
Near $2^+$, $\floor{x} = x-2$,no?
i still dont understand sorry. not the english but the math itself 💀
swift grail
For values a little bigger than $2$ you should be able to replace $\floor{x} = 2$
ocean sealBOT
casework
lilac jolt
For values a little bigger than $2$ you should be able to replace $\floor{x} = 2...
i think i did
my [[2 + h]] did end up being 2
2 + h i mean. sorry
swift grail
Idk what you got but you couldve just replaced floor with 2 so you would get
$$\lim_{x \to 2^+} \frac{x^2 - 2x}{2 - x}$$
ocean sealBOT
casework
cursive ruin
lhopital
or write it as -x(2-x)/(2-x) and cancel the terms
swift grail
Or just factor
cursive ruin
Or just factor
das what i said
swift grail
So basically it becomes -2. So basically only a sign
fast lichen
also change lim h->0^+ from the beginning it doesnt make sense to keep x->2^+
lilac jolt
lhopital
or write it as -x(2-x)/(2-x) and cancel the terms
OH MY GODDD YESSS NO WAY I DIDNT THINK OF TJAT
swift grail
And fyi only difference between \floor and writing it as \lfloor and \rfloor is ig you can make it bigger with \lfloor and \rfloor.
For example
$$\floor{\frac{a}{b}}$$
And
$$\left\lfloor \frac{a}{b} \right\rfloor$$
ocean sealBOT
casework
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
swift grail
Idk if there is a way to make \floor bigger
lilac jolt
also change lim h->0^+ from the beginning it doesnt make sense to keep x->2^+
x -> 2^+ is the original question. i just took the limit of 2 - h as h approaches 0^+ because we know h is a really small number close to 0
fast lichen
x -> 2^+ is the original question. i just took the limit of 2 - h as h approache...
yes i understand but after rewriting x=2+h you kept writing x->2^+ in your work until the very end
lilac jolt
yes i understand but after rewriting x=2+h you kept writing x->2^+ in your work ...
ohhh yes. good one. thank you!! ill keep that in mind
im still getting used to this writing the limit every line thing
in high school our teacher didnt require us to do it so xD
lilac jolt
thank you!! so would the final answer be -2?
alpine sable
im confused how to approach this question
lone heartBOT
im confused how to approach this question
alpine sable
ping when reply
true rune
im confused how to approach this question
when you see a series with $q^n$, always think about geometric series
ocean sealBOT
tm
true rune
Obviously, $\frac{e}{\pi} >0$. Moreover you know that $\pi > e$. you can then conclude that $| \frac{e}{\pi} | < 1$
it proves the convergence @alpine sable
ocean sealBOT
tm
alpine sable
when you see a series with $q^n$, always think about geometric series
can i ask why?
thick lynx
It's a theorem; you can prove this using the geometric sum and then taking the limit
alpine sable
It's a theorem; you can prove this using the geometric sum and then taking the l...
what would i do after tho
like is it just 1/1-e/pi?
thick lynx
Yes, but you can simplify that
true rune
like is it just 1/1-e/pi?
ye
thick lynx
1 = pi/pi, then the denominator becomes (pi - e)/pi
The reciprocal of that is pi/(pi - e)
true rune
i have another question if you guys don't mind
yeah sure
alpine sable
these sequence or series wtv they are called are killing me
they both have the same sorta format
so if i can figure out one them i should be able to know how to do the other
at least i hope
thick lynx
These are so-called telescoping series
A lot of the terms vanish
Try writing out the first 10 or so
You will notice a pattern
true rune
they both have the same sorta format
When you see a series with a term in n+1 minus a term in n, think of the telescopic series
alpine sable
so what do i do?
true rune
$\sum_{k=1}^n u_{k+1} -u_k = u_{n+1} -u_1$ if i’m not wrong
identify the sequence (u_n) in your case and just apply the formula
ocean sealBOT
tm
alpine sable
what is k
alpine sable
so it's just lnsqrt(3)-ln(1)?
thick lynx
Where did the 3 come from
true rune
so it's just lnsqrt(3)-ln(1)?
it diverges 😢
thick lynx
Yes
true rune
$\sum_{n=1}^{\infty} ln(\sqrt{n+1})-ln(\sqrt{n}) = lim_{ N \to \infty} \sum_{n=1}^N ln(\sqrt{n+1})-ln(\sqrt{n}) = \sum_{n=1}^N u_{n+1} -u_n=…$
ocean sealBOT
tm
alpine sable
using this, what u have for the partial sum?
ln(sqrt(2))-ln(1)
true rune
uh
true rune
ln(sqrt(2))-ln(1)
this thing is u_N+1 - u_1 ?
alpine sable
i thought it was
true rune
$u_n = ln(\sqrt{n})$ right ?
ocean sealBOT
tm
alpine sable
yeah
alpine sable
ln sqrt(n+1)-ln(1)
true rune
yessir
so $\sum_{n=1}^{\infty} ln(\sqrt{n+1})-ln(\sqrt{n}) = lim_{N \to \infty} ln(\sqrt{N+1})$
ocean sealBOT
tm
true rune
and this thing diverges
alpine sable
why does it diverge
true rune
what is $lim_{n \to \infty} ln(n)$
ocean sealBOT
tm
ocean sealBOT
tm
alpine sable
ah i see
true rune
they both have the same sorta format
for the other one, it’s the same thing
it’s a telescopic series
but it’s u_n - u_n+1 this time
true rune
you mean arccos(3/6)-arccos(3/n+6) ?
alpine sable
yes
true rune
hmm the first term is right, it’s $u_1$
ocean sealBOT
tm
true rune
The second is pretty much right
alpine sable
3/6 - 3/n+5
true rune
What are the remaining terms of the sum: $\sum_{n=1}^N u_n -u_{n+1}$
ocean sealBOT
tm
alpine sable
3/6 - 3/n+7
true rune
yessir
alpine sable
that's what it is?
true rune
the partial sum is equal to $arccos(3/6)-arccos(3/(n+6))$
ocean sealBOT
tm
alpine sable
undefined
true rune
really ?
alpine sable
arccos(0)
true rune
yes
alpine sable
undefined
true rune
it’s pi/2 😭
ocean sealBOT
true rune
😭😭😭😭
true rune
me too i hate trigonometric functions
true rune
isn't it 1/cosx
no it’s the reciprocal of cos
ocean sealBOT
true rune
the series converges to ?
alpine sable
why did u do 1/2 instead of pi/2
true rune
it’s for arccos(3/6)
alpine sable
oh
alpine sable
,w pi/3 - pi/2
ocean sealBOT
alpine sable
-pi/6
true rune
yeah 👍
alpine sable
it said wrong
true rune
what ?
alpine sable
you made it a lot more understandable
true rune
it’s my goal, appreciate it 🙏🏼
alpine sable
.close
lone heartBOT
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Available help channel!
long tartan
lone heartBOT
jagged cobalt
nice
round moon
thats baby shit easy ur impressing nobody chump
long tartan
What’s x
jagged cobalt
a variable
hushed locust
x is a variable representing position
long tartan
the x axis is the horizontal line
get away troll
long tartan
x is a variable representing position
ok I understand. I realized I read the question wrong. #Dyslexic
.close
lone heartBOT
smoky cape
Are you serious? What is this? Baby o’clock? I solve this in my sleep
tacit arch
Are you serious? What is this? Baby o’clock? I solve this in my sleep
<@&268886789983436800> troll
smoky cape
<@&268886789983436800> troll
NO HE’S MY FRIEND
WE’RE TRYING TO FIGURE OUT STUFF TOGETHER
sly mantle
even if hes your friend pls dont mess around in help channels
smoky cape
You’re right my bad
long tartan
i’m sorry about my friend
sly mantle
thats baby shit easy ur impressing nobody chump
you too man
wide tartan
the channel will lock soon. I suggest taking the conversation elsewhere.
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Available help channel!
heady solstice
Hello
heady solstice
I am sorry i have adhd i cant understand easily plss help me
Pls i wanna understand maths
next badger
hey
young pivot
I am sorry i have adhd i cant understand easily plss help me
what is your question?
heady solstice
what is your question?
Nthing idk where to start lol its 8 grade
young pivot
what confuses you
young pivot
what is one thing that you're stuck on
heady solstice
what is one thing that you're stuck on
I just am stuck at algebra laws
young pivot
ugh idk how to narrow this down
heady solstice
Sorry if i made u angry i dont understood maths i get scared
heady solstice
I am not angry
Ok
limpid turret
Can u help me understand sets
Sets are just a collection of things
{1, 2, 3} is a set of the numbers 1, 2, and 3
heady solstice
How do i understand de morgan law
limpid turret
How do i understand de morgan law
Understand? You could try writing a truth table, and simply see that they match
young pivot
How do i understand de morgan law
heady solstice
So how do i start to solve an equation
young pivot
well first we gotta understand notation
limpid turret
If we say that the statement "A and B are both true" is not true, then it must be that either A or B must be not true. That is, A is false, or B is false.
limpid turret
So how do i start to solve an equation
Depends on the equation
young pivot
So how do i start to solve an equation
send an example from your notes or homework or something
limpid turret
But, in algebra, there are laws and identities that say what logical conclusions you can make
heady solstice
send an example from your notes or homework or something
Ok
chilly rivet
Can anyone help me I have an exam tomorrow
limpid turret
Can anyone help me I have an exam tomorrow
!occupied
lone heartBOT
Can anyone help me I have an exam tomorrow
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
young pivot
open up a different ticket
chilly rivet
!occupied
lone heartBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
young pivot
:/
heady solstice
I dont have a
chilly rivet
!occupied
Can anyone answer it here cuz this chat is dead and I have an exam in a few hours
young pivot
no
limpid turret
Can anyone answer it here cuz this chat is dead and I have an exam in a few hour...
No. This chat is not dead. Go to #❓how-to-get-help
young pivot
I don't go to school
that's not something you need to apologize for, just so you know
heady solstice
that's not something you need to apologize for, just so you know
Ok
But i am so dumb lol hahaha
limpid turret
@heady solstice, did you want help with algebra equations, or equations in set theory?
heady solstice
<@1346184479986811101>, did you want help with **algebra** equations, or equatio...
Yes pls help me understand how to solve de morgan law problems
limpid turret
Yes pls help me understand how to solve de morgan law problems
It really depends on the problem. What got you asking about solving this? I'm assuming there was something you were looking at before you came here. And I assume that there was something you saw that didn't make sense to you, which is why you are asking for help. But we need more information to better know what you are needing help with
wide harness
The problem formulation here is very vague. I believe they have not started on any math problem?
heady solstice
It really depends on the problem. What got you asking about solving this? I'm as...
Ok i am sorry pls forget i wasted ur time
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Available help channel!
charred veldt
Hi
charred veldt
I need help applying limits and continuity. I know that we can apply limit on gradually increasing value like time and velocity of car (as the time increases the velocity increases). But can we also apply it to economics for example price changes? Since economics is unpredictable and it can go up and down.
sly mantle
the limit youre thinking of is $\lim_{t\to\infty}f(t)$
ocean sealBOT
𝓡𝓞𝓚𝓔𝓣𝓣𝓞─୨ৎ─❥ ♡ <𝟹❤
sly mantle
as long as you can model smth as a function of time f(t) then you can take that limit
charred veldt
Can i apply it to price changes?
sly mantle
see what i said
as long as you can model smth as a function of time f(t) then you can take that limit
if u can define a function to say the price at any point in time then yes
charred veldt
So it all comes down to making the function deeem
sly mantle
mhm
lone heartBOT
@charred veldt Has your question been resolved?
charred veldt
I made a function for supply and demand
D(p) = a - bP
a - demand
b - reduces demand for price increase
P - price.
Is this good function? Is it a continuity or a discontinuity?
lone heartBOT
lone heartBOT
✅
charred veldt
Dem
lone heartBOT
@charred veldt Has your question been resolved?
brittle lake
Determine whether the sequence converges or diverges.
If it converges, find the limit.
brittle lake
Would I multiply num and denom by sqrt{1/n^2}
first
would that help me
(asking because i dont see how it could help)
marsh hamlet
**Determine whether the sequence converges or diverges.
If it converges, find th...
You can use $\qty(\lim_{x\to a}f(x))^n=\lim_{x\to a}(f(x))^n$
ocean sealBOT
mathisfun
brittle lake
**mathisfun**
im nto familiar with this rule
sour verge
(asking because i dont see how it could help)
You can divide the numerator and denominator by n if what you’re trying to do is take the limit
brittle lake
could i get a example
marsh hamlet
im nto familiar with this rule
Just know it exists
marsh hamlet
could i get a example
Sure
tight pier
marsh hamlet
$\lim_{x\to 2}\frac{1}{x^n}=\frac{1}{2^n}$, $\qty(\lim_{x\to 2}\frac{1}{x})^n=\qty(\frac12)^n=\frac{1}{2^n}$
ocean sealBOT
mathisfun
marsh hamlet
**mathisfun**
So try it!
brittle lake
So try it!
would i move the squared up top of the
would it be like
(4n/n)^2
(idk how this works)
marsh hamlet
would i move the squared up top of the
The square root, yeah
marsh hamlet
Then just use this
tight pier
Yes use me
brittle lake
Would i be left with $\lim{x\to \infty}\frac{\sqrt{1}+(4n)^2}{\sqrt{1}+n^2}$
this is what im trying to visualiz
ocean sealBOT
Light
brittle lake
idk how to use latex
tight pier
No
brittle lake
ok
tight pier
(1+4n²)/(1+n²) ~ 4n²/n²
brittle lake
(1+4n²)/(1+n²) ~ 4n²/n²
icic
marsh hamlet
$\lim_{n\to\infty}\frac{\sqrt{1+4n^2}}{\sqrt{1+n^2}}$ is what you mean?
ocean sealBOT
mathisfun
marsh hamlet
Sure you can do it that way, but this is not really optimal way
brittle lake
(1+4n²)/(1+n²) ~ 4n²/n²
would this indicate that it jus[t goes to infinity
marsh hamlet
,texsp ||$\qty(\lim_{n\to\infty}\frac{1+4n^2}{1+n^2})^{\frac12}$||
ocean sealBOT
mathisfun
marsh hamlet
would this indicate that it jus[t goes to infinity
No
marsh hamlet
^
marsh hamlet
Do you know what the degree of a polynomial is?
marsh hamlet
Yes.
tight pier
4n²/n² also just cancels to 4 anyway
marsh hamlet
so my limit converges to four
No
brittle lake
ok
marsh hamlet
sqrt exists too
tight pier
vonvergecence thing
brittle lake
@tight pier do you believe @marsh hamlet
marsh hamlet
<@587715738484211754> do you believe <@1340453306207572073>
?!
marsh hamlet
then thats my convergence thing
"Convergence thing"?
tight pier
no, i dont think math is particularly fun
tight pier
so your convergence thing goes to
brittle lake
2
brittle lake
yes
tight pier
thank
brittle lake
@tight pier
what does it mean when someone says
"You clearly don't understand the gravitas of the situation."
marsh hamlet
"You clearly don't understand the gravitas of the situation."
You have no foundation.
(Which is a bit of an insult.)
brittle lake
does the word gravitas have a negative connotation to it
brittle lake
its a cool word
tight pier
gn ep
lone heartBOT
lone heartBOT
✅
brittle lake
Determine whether the sequence converges or diverges.
If it converges, find the limit.
Little confused on what my first step would be
also
is it normal if it doesnt have a a_n = f(x)
cause the other problems have it
marsh hamlet
Little confused on what my first step would be
$\ln(ab)=\ln(a)+\ln(b)$
ocean sealBOT
mathisfun
marsh hamlet
is it normal if it doesnt have a a_n = f(x)
Yes.
marsh hamlet
Huh?
vague forge
Actually it might be lna/lnb= lna - lnb
marsh hamlet
Actually it might be lna/lnb= lna - lnb
That's not even a correct formula.
vague forge
Yes go ahead
marsh hamlet
what is the point of doing that?
You can let u=ln(n) in the limit.
brittle lake
oh i see
marsh hamlet
$\lim_{n\to\infty}\frac{\ln(n)}{\ln(2)+\ln(n)}$
ocean sealBOT
mathisfun
marsh hamlet
for the ln(n)
Yep.
lone heartBOT
lone heartBOT
✅
brittle lake
Why do some have a_n= and some dont
marsh hamlet
why would notation be wrong if you did a_n = sin(n)
No I'm just saying the notation is ambiguous
ocean sealBOT
mathisfun
sly dagger
How to do b
lone heartBOT
How to do b
sly dagger
yup thank u i spent so long trying to figure it out with product rule 😞
brittle lake
np
sly dagger
.close
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Available help channel!
drifting pollen
please help someone
lone heartBOT
please help someone
marsh hamlet
please help someone
Do you know how a perpendicular line is formed?
drifting pollen
Yes just i find that this is difficult since A isnt in the middle
marsh hamlet
Yes just i find that this is difficult since A isnt in the middle
It doesn't have to be. Just try to make a line that intersects CB at a perpendicular slope.
marsh hamlet
cause it just has to be 90 degree
Yep.
marsh hamlet
👍
drifting pollen
.close
lone heartBOT
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woeful furnace
Help
lavish cave
I got c but I want to double check if its correct
why do you think it's c?
woeful furnace
why do you think it's c?
because the factor introduces a different transformation compared to the other ones
lavish cave
because the factor introduces a different transformation compared to the other o...
it's the same in disguise actually
$\frac{1}{3} 3^3 (x - 2)^3 (x + 7)$
ocean sealBOT
south
lavish cave
so it would be d
mhm!
woeful furnace
thanks
lavish cave
yeah there's a huge difference between x^2 and -x^2 (one is concave up and one is concave down)
woeful furnace
I see
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unkempt imp
hellp
unkempt imp
hello
rustic ruin
hello
serene scarab
hello
opal siren
hello
does anyone know about discrete structures?
I'm new here and i've been seeking for help
vocal shard
!occupied
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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
paper thunder
@opal siren You can find help in the math help available servers
@unkempt imp You should start by looking at how the function is being shifting compared to the origin
unkempt imp
<@398953680222814260> You can find help in the math help available servers
sorry i forgot to mention is rational function
so q(x)/n(x)
i have the bottom figured out
just the top
unkempt imp
so this is correct i checked the answer q/x^2+2x-3
i did it by first putting q/(x-1)(x+3) because we can see the vertical asymptote at x= +1 and there would be an (x+3) at the top cause it would cancel out to give me a point of discontinuity at x = -3
the hollow circle is the POD
paper thunder
The reasoning makes sense but the graph doesn't seem to match up with the graph shown in the image
For the top you still have to put in the x+3
unkempt imp
alright
also there is a negative sign at the front
cause its in the other quadrants
paper thunder
Yeah
Now you can just scale it to line up with the values in the graph
Without scaling the POD is about at 2.5, solve for -3 in your current function and simplify
Then just compare the two values to see what to multiply by
unkempt imp
sorry i dont follow
lone heartBOT
@unkempt imp Has your question been resolved?
paper thunder
So multiply the rational function by the necessary number so that when you compare the graphs the points match up
unkempt imp
So multiply the rational function by the necessary number so that when you compa...
multiply what? x+3? do i just guess and check
paper thunder
So like multiply the entire rational function by 10 so that it scales properly
unkempt imp
So like multiply the entire rational function by 10 so that it scales properly
why 10
!solved
@lone heart /solve
i got it
its just the other x intercept
then do the same proccess
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lilac jolt
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cursive ruin
for 3.1 find an x for which f(x) is positive and another x for which f(x) is negative
change in sign would show that there is a value between those two values of x where the function goes to zero
lilac jolt
for 3.1 find an x for which f(x) is positive and another x for which f(x) is neg...
how do i do that
cursive ruin
how do i do that
they didnt give you an interval to check on so i'd just use values of x that seem right
try -1 and -3
lone heartBOT
@lilac jolt Has your question been resolved?
lilac jolt
they didnt give you an interval to check on so i'd just use values of x that see...
ok i got it now
18 and -64
cursive ruin
yea
so there must be a value between that that goes to zero
lilac jolt
yea
so there must be a value between that that goes to zero
how do i find it again?
equate to 0?
cursive ruin
how do i find it again?
you dont need to find it
it just asks you to show there is at least one real root
just write a statement like this :
f(-3) = -64
f(-1) = 18
f(-3)<0<f(-1)
-3< x < -1
f(x) =0
lilac jolt
oh so thats the answer
so i just say that there is at least one root because -64 < 0 < 18?
cursive ruin
yep
lilac jolt
wait how did you choose -1 and -3 tho
does it matter or no
idk what "seem right" mean
in this theorem
cursive ruin
it doesnt matter
i chose them cause -2 is a root
lilac jolt
because i just started
cursive ruin
the theorem is just telling you that
if there is a value of x let's say x=a that for which f(a) is positive
and there is a value x= b where f(b) is negative
there is a value c where f(c)=0
only that much
3.1 asks u to show the presence of a root using this concept
lilac jolt
3.1 asks u to show the presence of a root using this concept
i get it now thank you! what about 3.2?
cursive ruin
i get it now thank you! what about 3.2?
instead of showing f(c) = 0 here, you're supposed to show f(c) = c
g(x) = f(x) - x
we know that on the interval given, f(0)> 0 and f(1)<1
g(0) = f(0)-0
this will give a POSITIVE value based on the info given to us
g(1) = f(1) - 1
this will give a NEGATIVE value
now we apply intermediate value theorem: g(1) < 0 < g(0)
there is a value x= c for which g(c) = 0
g(c) = 0
g(c) = f(c) -c
therefore
f(c)-c = 0
and f(c) = c
lone heartBOT
@lilac jolt Has your question been resolved?
bright fiber
i need hlep to solve this exercise
lone heartBOT
i need hlep to solve this exercise
patent abyss
i think youre on the right track
if i were you id first construct $F_1',F_2'$ such that $\forall A\in F_1',\forall B\in F_2', A\cap B=\emptyset$
ocean sealBOT
esca
bright fiber
ok
patent abyss
then constructing $F_1$ and $F_2$ from $F_1',F_2'$ is straightforward. can you see how?
ocean sealBOT
esca
bright fiber
no not actually, I mean like we can take the power set of even and the power set of odd as $\F_1',F_2'$ resp but i dont see how to construct $F_1,F_2$
ocean sealBOT
yoru
Compile Error! Click the reaction for more information.
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patent abyss
well why dont we make every pair of sets from F1 and F2 have the same intersection?
bright fiber
i didn't get it
patent abyss
what happens if, for every set $A$ in $F_1'$, we take $A\cup{1}$?
ocean sealBOT
esca
bright fiber
oh we will get an intersection with every set in $F_2'$ that contains one
ocean sealBOT
yoru
patent abyss
yeah now lets do the same thing for $F_2'$
ocean sealBOT
esca
patent abyss
just add 1 to every set
bright fiber
oh
patent abyss
hence $A\cap B={1}$ for all A and B
ocean sealBOT
esca
bright fiber
that make sence
patent abyss
its a little silly but i think this works
lone heartBOT
pale kestrel
Is it actually always invertible
are phi and lambda arbitrary
surely u can find some where it isnt
ok. actually u have a clue in the definition of B
u at least know that thing is invertible
which is close
maybe u can show their determinants are equal
oh ur given its invertible then
the statement writes the inverse of this
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alpine sable
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hard harness
!15m
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hard harness
@alpine sable One the 2nd line, you converted 8^x to 2^3, which is wrong
Other than that, the work looks good
lone heartBOT
hard harness
I'm failing that test
I wouldn't freak out, though. Menial mistakes are common for everyone. Just make sure you double check your work
From the looks of things, you know how to solve these problems
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noble vale
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