so I'm not sure what the question specifically asks but only b) and c) fulfill the given equation
#help-28
sacred sparrow
torpid perch
All v in V such that f(v) = f(-v1+2v2+v3) are?
sacred sparrow
yes but why would it say "Pick one" then
torpid perch
usually exam is handwritten but this exam was taking during covid
sacred sparrow
All v in V such that f(v) = f(-v1+2v2+v3) are?
ah because they are meant to exclude each other
ok well then just c)
torpid perch
only one is correct tho
sacred sparrow
yeah the question is meant to be mutually exclusive
torpid perch
problem is, answer is D, we shouldnt be focusing on the alternatives tho
just, we should develop, and then see which answer matches lmao
sacred sparrow
eh no it's c)
torpid perch
wdym?
sacred sparrow
d) does not fulfill the given equation
torpid perch
are you using the matrix?
sacred sparrow
because f(2v2 + v3) != 0
sacred sparrow
are you using the matrix?
sure
so to be clear, a) and d) do not fulfill the equation
b) and c) do
but only c) represents the full set of answers
c) represents all possible v that fulfill the equation
torpid perch
can we like not focus on the alternatives though lmao
sacred sparrow
what do you want to focus on :D
torpid perch
usually is handwritten exam though
well, maybe work with M_B'B(f) . (v)_B' = (f(v))_B
sacred sparrow
ahh I misread it from the first image you posted, it's from B' to B
torpid perch
(f(v1 + v2))_B = (1,-1,2)
(f(v1-v2-v3))_B = (1,-1,2)
(f(v1+v3))_B = (1,2,-1)
sacred sparrow
ys ys
k then we need to translate a) b) c) d) first
e.g. we could represent
as
and translate v into base B'
sacred sparrow
well, maybe work with M\_B'B(f) . (v)\_B' = (f(v))_B
I see you pointed it out here
did you translate them already
torpid perch
a: v_B' = (0,0,-1)
sacred sparrow
ys for a)
sacred sparrow
b: (2/3,-4/3,-1/3)
sacred sparrow
cant do it mentally lmao
notice X+Y+Z = 3v1
and 2X+Z = 3v1 + 2v2 + v3
but we need -v1 instead of 3v1
so subtract 4 times v1
so - 4 * (X+Y+Z)/3
together: 2X+Z - 4 * (X+Y+Z)/3
= (2, 0, 1) - 4/3 * (1, 1, 1)
= (2/3,-4/3,-1/3)
so you're kinda lucky it doesn't need to be solved linearly with gauss
ok now only c) and d) left 🦩
sacred sparrow
yeah I'd start with (1,0,0)_B' = v1+v2 instead
and subtract v1 twice
because we already know v1 = (X+Y+Z)/3
sacred sparrow
np
torpid perch
(1,0,0)_B - 2(1,1,1)_B = -v1 + v2
torpid perch
yeah, my bad, again
sacred sparrow
so v1 = (X+Y+Z)/3
torpid perch
(1,0,0)_B - 2/3(1,1,1)_B = -v1 + v2
((1,0,0) -2/3(1,1,1))_B' = -v1 + v2
(1/3,-2/3,-2/3)_B' = -v1 + v2
sacred sparrow
looks good
I'll leave the rest here for you to compare
a: (0,0,-1)
b: (2/3,-4/3,-1/3)
c: alpha * (1/3, -2/3, -2/3) + (2/3,-4/3,-1/3)
d: alpha * (1, -1, 0) + (2/3,-4/3,-1/3)
yeah
(2/3,-4/3,-1/3)_B' + (1/3,1/3,1/3)_B' = 2v2 + v3
it matches but
are you saying (1,-1,0) is in the kernel of f?
same for (1/3,-2/3,-2/3) is in the kernel of f
sacred sparrow
are you saying (1,-1,0) is in the kernel of f?
well yeah
torpid perch
what I mean is, if I evaluate those, under f should map to zero
sacred sparrow
yh
k well if we go through the options, a) can't represent all since the transform has a kernel
b) not likewise
so you only have to show for (1/3, -2/3, -2/3) and (1, -1, 0) explicitly
sacred sparrow
yop
torpid perch
,w {{1,1,1},{-1,-1,2},{2,2,-1}} * {{1/3},{-2/3},{-2/3}}
glossy valveBOT
torpid perch
,w {{1,1,1},{-1,-1,2},{2,2,-1}} * {{1},{-1},{0}}
glossy valveBOT
torpid perch
and we should check (2/3,-4/3,-1/3) is a particular solution to f(v) = f(v)
sacred sparrow
and we should check (2/3,-4/3,-1/3) is a particular solution to f(v) = f(v)
dym to make sure?
sacred sparrow
hm no since we already know that (1, -1, 0) gets mapped to 0
so f(alpha * (1, -1, 0) + 🦆) = f(🦆)
torpid perch
but we still (2/3,-4/3-1/3) to be a particular solution, even tho (1,-1,0) is in the kernel
torpid perch
so f(alpha * (1, -1, 0) + 🦆) = f(🦆)
yeah exactly
how how do we know f(2/3, -4/3, -1/3)=f(2/3,-4/3,-1/3)
torpid perch
no no, I just notice something
sacred sparrow
k
torpid perch
(2/3, -4/3, -1/3)_B' = -v1 + 2v2 + v3
and we need all f(v) = -v1 + 2v2 + v3
sacred sparrow
yes
torpid perch
so f(alpha * (1, -1, 0) + 🦆) = f(🦆)
adding a multiple of the kernel does not change the result of a particular solution, is something very elementary, yet important, I appreciate the help
sacred sparrow
I think we are done, tho, it was hard as hell
yea I see you have many problems related to constantly switching bases :D
sacred sparrow
adding a multiple of the kernel does not change the result of a particular solut...
absolutely, I mean maybe I should have added a step in between
f(alpha * (1, -1, 0) + 🦆) = alpha * f(1, -1, 0)) + f(🦆) = f(🦆)
torpid perch
oh, linearity, even better
sacred sparrow
yop
torpid perch
yes, this makes it clearer
I appreciate the help though, I liked this exercise, I think it was intended to use the alternatives, because very low amount of info was given
literally one of the hardest wrt change of basis matrix with respect a linear transformation
exercises I have done a while I think
sacred sparrow
yeah, I do get confused when base changes are stacked upon another
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civic linden
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quaint verge
How do I parameterise a vector valued function of a helix that has a height of H and makes exactly n turns and has a radius of R. Where R,h and n are all positive values?
kindred grove
have you started working on that question ? @quaint verge
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digital mountain
Can anyone please help me?
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Can anyone please help me?
gritty flax
Whats the sum of angles in triangle?
digital mountain
180 degrees
gritty flax
Find the last angle
digital mountain
So the angle opposite of x is 83?
gritty flax
,calc 180 - 33-64
glossy valveBOT
Result:
83
Yes
digital mountain
Bet now how do I use law of sine to find x
gritty flax
Whats the law of sine ?
digital mountain
SinA/a=SinB/b=SinC/c
gritty flax
Ok, here the a will be your w and A the 83 angle
And let b for the other one you know value
And B
digital mountain
ohhh
Like this or
I just labed the letters
Are they all supposed to be capital?
wait is little a across from A
Like is little a 3.5?
gritty flax
Don't write the last one
digital mountain
oh bet
gritty flax
Solve cross product
digital mountain
Like that
digital mountain
Solve cross product
Like cross multiplication?
gritty flax
Yeah but you have an equal sign between
digital mountain
ohh
gritty flax
,calc 3.5* sin(83)/sin(33)
glossy valveBOT
Result:
3.3895743705721
Only if ask for
But they should mention it imo
digital mountain
ohh bet
digital mountain
But they should mention it imo
Yea
Okay so I’m done with A but can u help me find the height and the area
They want me to draw a line down the middle and use trig
zenith tangle
I'm sorry if I misunderstood but shouldn't a) be ≈ 2.12
digital mountain
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grave elm
I'd start by getting rid of those fractions
rough jackal
wdym
grave elm
which can be done by multiplying both sides by some number
hot lily
4x * 5 / 4 * 5
5 is not the best choice
hot lily
You shuold multiply by the Least Common Multiple of 4, 5, and 20
rough jackal
least common.
hot lily
Oh wait i see what youre doing
grave elm
5 is not the best choice
i think he is instead trying to simplify the fractions
hot lily
Nvm thats fine
rough jackal
yeah
grave elm
4x * 5 / 4 * 5
but this is incorrect
rough jackal
omg
grave elm
it was x / 4
rough jackal
so many
bro im getting always confused
anyways wait
here
so i get
5X/20 + 4X +12/20
gentle salmon
no you multiply the whole equation
rough jackal
wdym.
grave elm
5X/20 + 4X +12/20
this works as welll
gentle salmon
don't make them the same denominator
rough jackal
BRO
gentle salmon
this works as welll
adding steps
rough jackal
ONE IS SAYING
hot lily
don't make them the same denominator
?
grave elm
no you multiply the whole equation
it works as well
grave elm
adding steps
not really
grave elm
PLS IM ALREADY GOING MENTALLY INSANE
Your approach is fine
gentle salmon
not really
You'd just get rid of them at the end
grave elm
You'd just get rid of them at the end
yeah, so it works just fine
rough jackal
OK so after I do that I get 9X +12/20
gentle salmon
yeah so added steps wdym "not really"😭
grave elm
OK so after I do that I get 9X +12/20
and on the right hand side you have (x+12) / 20
grave elm
okay now this is not the best thing to do
gentle salmon
Instead of cross multiplying you just... Multiply everything all at once
grave elm
you got this:
(9x + 12) / 20 = (x+12) / 20
rough jackal
mhm
grave elm
you got this:
(9x + 12) / 20 = (x+12) / 20
you can now just multiply both sides by 20
grave elm
an alternative way that arya was pointing to is multiplying the equation by 20 right at the start, which would lead to exactly the same thing
rough jackal
like this
grave elm
rough jackal
wh
grave elm
these 20's are unnecessary
rough jackal
so
spring coral
hello
grave elm
you can multiply both sides of an equation by 20
rough jackal
oh
grave elm
how did you get to 10?
rough jackal
grave elm
okay so you have 8x = 0?
rough jackal
yeah
gentle salmon
How would you single out x?
ie how would you make it such that it is x=... And not 8x=0
grave elm
just a reminder of operations you can do to an equation:
- add a number to both sides
- subtract a number from both sides
- multiply both sides of an equation by some non-zero number
- divide both sides of an equation by some non-zero number
one of these will be helpful
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gusty carbon
How do i do 33-d and 35-b,c, and d
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How do i do 33-d and 35-b,c, and d
glossy valveBOT
riemann
gritty rose
Find sin(90-theta) in terms of cos
gentle salmon
I dont know how to do that
sin(90-x)=cosx
gentle salmon
**riemann**
Try drawing a triangle and you'll see the reason why
Since 90-theta is just the angle on the other side
You have sin(90-x)=A/H
and A/H=cosx
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gusty carbon
sin(90-x)=cosx
What do i do with this information now
Oh wait i figured that one out
How do i do 35c❓
gentle salmon
cos(90-x)=sinx, same reasoning as I gave above
gentle salmon
How do i do 35c❓
write cot in terms of sine,cosine and you'll see
gusty carbon
Sin(90-a)=cos(a)❓
gentle salmon
yes
gusty carbon
Now what
gentle salmon
what do you have written down
gusty carbon
Sin(90-a)=cos(a)❓
This
gentle salmon
oh what
I thought you were asking whether it is true
you should have $\frac{cos(90-\alpha)}{sin(90-\alpha)}$
glossy valveBOT
AkitoLite
gusty carbon
**AkitoLite**
Why is this❓
gentle salmon
cot=cos/sin and I just added the angle
cot=1/tan=cos/sin
And then put the angle given
gusty carbon
Is that 90 or 5❓
gritty rose
Is that 90 or 5❓
the angle is alpha, cot(angle) = 5 is the value of cotangent at that angle
gusty carbon
Im confused
gritty rose
which part
gritty rose
cos(90-x)=sinx, same reasoning as I gave above
use this
gritty rose
Sin(90-a)=cos(a)❓
and this
gusty carbon
But how
gritty rose
how what
gusty carbon
Everythinggg
gritty rose
gotta be specific
gusty carbon
How do i use it
gritty rose
i don't know where you're lost
gusty carbon
Im at cot(90-a)=cos(90-a)/sin(90-a)
And i dont know how to use sin(90-a)=cos(a)
<@&286206848099549185>
gritty rose
And i dont know how to use sin(90-a)=cos(a)
substitute this
gritty rose
Im at cot(90-a)=cos(90-a)/sin(90-a)
in for sin(90-a) here
stoic gust
Im at cot(90-a)=cos(90-a)/sin(90-a)
sin(90-a)/cos(90-a) = tan a
gusty carbon
Inlooked in my textbook and it justs says cot(90-a)=tan(a)
gritty rose
yea i'm trying to walk you through it
gritty rose
substitute this
this is half of it
gritty rose
cos(90-x)=sinx, same reasoning as I gave above
this is the other half
again, substitute
gusty carbon
How do i do these 2❓
zenith tangle
and also tan = sin/cos
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opaque junco
Why does the plus become a minus on step 3
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Why does the plus become a minus on step 3
gritty rose
4-2=2
opaque junco
gritty rose
$a - b = -b + a$
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riemann
delicate chasm
Guys
nocturne shard
The most painful part about this is to do it without stirling 😭
torn jolt
why cant u use stirling
delicate chasm
Because they didnt teach that
nocturne shard
Wait, i know how
delicate chasm
😄
nocturne shard
Focus on the inside
delicate chasm
ueah
delicate chasm
I tried to do with the definition of e limit.
nocturne shard
<@&268886789983436800>
nocturne shard
I tried to do with the definition of e limit.
im cheesing it by using natural log
delicate chasm
charred raft
,rccw
glossy valveBOT
delicate chasm
Look the middle line
hot lily
Dude clean your stuff up 💀
delicate chasm
Dude clean your stuff up 💀
That stuff helps me to do math
charred raft
huh?
nocturne shard
shouldn't the answer be 3
torpid perch
use dalembert criterion + euler limit
torpid perch
?
delicate chasm
banned on my actual test
Im on first grade
I only can use a few limitated tools
torpid perch
which are . . .?
delicate chasm
Nothing for limits. I only can use infinitesimsç
Like te definition of e
e=lim1+1/x ^x
LIke in the picture
nocturne shard
have you learnt integrals
delicate chasm
No
nocturne shard
rip...
charred raft
try applying ln, and use ln(n!) = sum ln(k) from k=1 to n
torpid perch
Nothing for limits. I only can use infinitesimsç
infinitesims
nocturne shard
try applying ln, and use ln(n!) = sum ln(k) from k=1 to n
yeah but he cant use integrals to approximate that
torpid perch
say it in spanish, I am from Argentina
delicate chasm
sinx /x -> 1 if x->0 for example
Que bueno
Infinitésimos elementales
Y algunas técnicas como el criterio de stolz
El lema del sanwitch
y poco más, y un monntón de lemas de sucesiones que no usaría aquí
torpid perch
los lemas de sucesiones están baneados?
delicate chasm
No, lo que pasa que no recuerdo haberlos usado nunca en este ejercicio. Debería de poder hacerse solo con lo que te he dicho
charred raft
el pablo escobar,
delicate chasm
,rccw
glossy valveBOT
delicate chasm
maybe yes
nocturne shard
oh thank god
delicate chasm
But is that true???
nocturne shard
almost
charred raft
can i use n! -> n^n
he cant ig, because he didnt learn of equivalences yet
delicate chasm
What equivalences u are talking about guys
charred raft
tell us what u know about factorials @delicate chasm
like what type of non-basic formulas can we use?
delicate chasm
One result of limit on talylor lagrange error and nothing more about factorials (And statistics)
charred raft
One result of limit on talylor lagrange error and nothing more about factorials ...
send picture of this "taylor lagrange error"
delicate chasm
Is not about this dont worri
nocturne shard
i dont think that is still useable :L
delicate chasm
y*
U can aproximate the error of a taylor expansion with the lagrange or cauchy form, but this is useable on this
charred raft
send picture of this "taylor lagrange error"
!
delicate chasm
nocturne shard
welp, this is the best i can do
i tried the closest basic thing i can get which is squeeze theorem
proving the inequality might be not easy (plus, it's only true when n>=1, which is good if it's about finding limit of a sequence)
idk if induction works but ah well
Yep you can basically prove this inequality entirely by induction
nocturne shard
I mean you use the inequality (its very long but required for squeezing)
xlnx - x + 1 < ln(x!) < (x+1)lnx - x + 1
Sorry for letting you suffer
nocturne shard
heck its not even over after that, because you have to evaluate 2 limits to evaluate 1 limit
delicate chasm
XD
Target no problem
i will manage tomorrow to do the test
If i have luck
I i remember the leasons of koro sensei
All will be good
torn jolt
could anyone help me with this
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real barn
torn jolt
i have the cords 6,1 | 3,4 just cant seem to get it right when placing it on the grid
hot lily
could anyone help me with this
The function is in vertex form: $y = a(x - h)^2 + k$
glossy valveBOT
King Leo
hot lily
This means that the vertex is at (h, k)
hot lily
From there, you can test pretty much any other x value to find another coordinate of the parabola
restive geyser
(whispers x = 0)
slow sleet
am i right with D here?
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am i right with D here?
random oriole
am i right with D here?
Show us your working
slow sleet
Show us your working
man i would but its all on paper
random oriole
man i would but its all on paper
Just tell me your approach
What did you try?
This would be helpful for me to help you better
Slash my earlier approach. It's better to use the cosine rule here. That's my hint, come back with what you got
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ashen grove
Hello, I'm having some trouble figuring out the limit for this problem
ashen grove
here is what I have so far
It looks like the limit is 7 but I'm unsure
I'm wanting to say it doesn't even exist because one side is - and the other is +
<@&286206848099549185>
This is what it's asking for
#3
pine yew
well yeah it doesnt exist
sudden condor
It looks like the limit is 7 but I'm unsure
They both approach different values from left and right
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spring vigil
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spring vigil
do i attempt to graph this first?
viral jasper
do i attempt to graph this first?
Do you know what "epsilon-delta" limit is? If no, then yeah graphing is a good first step
spring vigil
Do you know what "epsilon-delta" limit is? If no, then yeah graphing is a good ...
not atm
we just had an introduction to limits
viral jasper
then yeah. Graph it
viral jasper
yes
spring vigil
ok let me attempt to graph it rq
for the values on the right its these are holes in my understanding
slate apex
do i attempt to graph this first?
you don't really have to graph it for the 0- you can substitute in the -4 and for the 0+ you can substitute in the x-4 and if both values are equal then the limit exists and is equal to this value and if they're not then it doesn't exist and do the same for the -2 but substitute in the 1st and 2nd definitions since the -2 is where the function definition changes and same goes for the 0
steel solar
for the values on the right its these are holes in my understanding
Yes, it defines where exactly the function is defined on the piecewise intervals.
steel solar
Looks good.
spring vigil
ok so how do i use this to evaluate a, b , c starting with a
steel solar
ok so how do i use this to evaluate a, b , c starting with a
Look at where the graph is approaching x=0 from the left and right.
spring vigil
im trying to understand the step by step process of how i should think about it
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glass lantern
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hot lily
Use $y = \qty(1 + e^x)^{-1}$
glossy valveBOT
King Leo
hot lily
,w d/dx (1 + e^x)^(-1)
glossy valveBOT
torn jolt
split it into partial fractions
glass lantern
split it into partial fractions
How?
torn jolt
$\frac{1}{e^x(1+e^x)} = \frac{a}{e^x} + \frac{b}{1+e^x}$
glossy valveBOT
torn jolt
solve for a and b by equating the coefficients
slate violet
it's pretty obvious actually
torn jolt
you could make it simpler by taking a different substitution
slate violet
solve for a and b by equating the coefficients
but yes if you don't know try this
I don't think there's a simpler way though
torn jolt
i thought e^-x sub would help
glass lantern
i thought e^-x sub would help
Ok I will try
torn jolt
what have i done
glass lantern
what have i done
Is this correct?
glass lantern
try this step again
Now?
torn jolt
👌
glass lantern
What were you telling me to do here?
torn jolt
maybe writing the answer will help you understand it
$\frac{1}{e^x(1+e^x)} = \frac{1}{e^x} - \frac{1}{1+e^x}$
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lethal shell
-4(2x^2)^3
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-4(2x^2)^3
lethal shell
Wie mache es
hot lily
-4(2x^2)^3
Was versuchen Sie mit diesem mathematischen Ausdruck zu tun?
What are you trying to do with this expression?
steel solar
-4(2x^2)^3
Hm?
hot lily
Wie mache es
-# "how do it"
steel solar
Yeah, I get the gist.
Just randomly putting an expression and leaving isn't the best though, lol.
hot lily
Versuchen Sie, dies zu vereinfachen? @lethal shell
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merry topaz
I know how to find the DNF but am not sure how to find the CNF
Could anyone please assist?
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merry topaz
So to find the CNF we first take the negation of the formula and then find the DNF of that and then whatever that DNF is, we flip the literals and the connectives to get the CNF?
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steel matrix
idk how to do this i tried using sine rule and got it wrong 😭
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quiet meadow
HI guysss
just asking. i can change this function to another one right and i can still do this same problem?
A hospital is tracking the number of blood donors each year using the function F(x) = 4x²-2x+3. Where 𝑥 represents the number of years since the hospital initially started its blood donation program. To certify that there will be a steady supply of blood for patients in need (especially for those undergoing surgery, trauma patients, cancer patients, and those with blood disorders), the hospital needs to estimate how many people will donate blood in 5 years.
Basically im js asking if its okay in the concept of limits to write a completely new function to make a word problem
narrow ermine
Yes, although taking any function whatsoever could also yield results that aren't really in line with the situation.
At the end of the day it'll still help you practice the same skills the initial problem helped you practice, minus maybe the whole comprehension part which will already be over.
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austere cove
<@&268886789983436800>
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strong phoenix
Can anyone explain this real quick?
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Can anyone explain this real quick?
void nova
Factor out x from the first two terms, and n from the other two
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vestal moat
Are you familiar with the relationship between the roots of a quadratic and its coefficients ?
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narrow shadow
anyone know why when I put cotx in my calculator as 1/tan(x) it shows all x values right, but the y values are all errors?
hot lily
anyone know why when I put cotx in my calculator as 1/tan(x) it shows all x valu...
- radians/degrees mode?
- if its
...E7or...E-5then you can likely "round" to -infinity/0/infinity
narrow shadow
- radians/degrees mode?
- if its `...E7` or `...E-5` then you can likely "round"...
it's in radians, idk y it did that
no E's
hot lily
it's in radians, idk y it did that
!done ?
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it's in radians, idk y it did that
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narrow shadow
wait
the problem is still there tho
it shows only errors
in the y value area
I put the step as pi/2
hot lily
,w tan(pi/2)
glossy valveBOT
narrow shadow
like is there an asymptote at y = 0
hot lily
like is there an asymptote at y = 0
$\tan(\theta)$ has an asymptote at $\theta = \frac \pi 2 \mathrm{rad}$.
glossy valveBOT
King Leo
narrow shadow
oh alr
narrow shadow
$\tan(\theta)$ has an asymptote at $\theta = \frac \pi 2 \mathrm{rad}$.
wait but this graph
shows the contrary
hot lily
$\cot = \frac 1{\tan}$
glossy valveBOT
King Leo
hot lily
$\cot(\frac \pi 2) = 0$
glossy valveBOT
King Leo
narrow shadow
yea
hot lily
$\frac 1{\tan(\frac \pi 2)} = \frac 1\infty = 0$
glossy valveBOT
King Leo
hot lily
But as soon as your calculator gets that infinity, it starts to bug out
narrow shadow
oh
should I be using cosx/sinx instead
or maybe that'd be too complicated to enter ig
hot lily
should I be using cosx/sinx instead
That works
solemn garden
Really dumb question but is there anyway to convert 1 millimeter^2 to meters?
wild sleet
no
solemn garden
Ok thanks
hot lily
Really dumb question but is there anyway to convert 1 millimeter^2 to meters?
There are 1,000,000 square millimeters in a single square meter.
umbral dome
to convert squared units you square the conversion factor
1 m = 1000 mm
(1 m)² = (1000 mm)²
1² m² = 1000² mm²
1 m² = 1 000 000 mm²
narrow shadow
is this elementary school math?
torn jolt
bro think if you have 7 out of 8 pizza slices is it close to a full pizza or no pizza
narrow shadow
what grade r u in?
cmon
this is easy
7/8 + 1/8 is what?
5/11 plus how much is 1?
which has a larger difference?
thus, which is closer?
oh ok
makes sense
actly wait not rlly
3rd graders should know this i believe
alr
just look at what is aid
and think
use the process of elimination - search up if you don't know
if u get stuck
but 5/11 is closest to 1/2
it's better in fact
no
0.5
from left to right
1, 0.5, 0.5
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spiral vigil
5th graders are 10-11 years old, right?
ok i'm sorry but we can't have you here until you're 13
spiral vigil
spice knot
discord terms of service
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torn jolt
really stupid question, why does the maclaurin/taylor series for ln(x+1) start at n=1, when any of the other dont?
torn jolt
the reason I ask this is cause I was integrating the series of 1/1+x, finding the genral term, and mine would be right if n was at 0, but since it's at one everything was shifted so
umbral dome
it starts at 1 because the constant term is 0
you can reindex your series to make the formula match the usual one
torn jolt
it starts at 1 because the constant term is 0
what's the constant term again? my brain is fried rn
umbral dome
the x^0 term, since x^0 = 1
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glad jasper
So I got to this, I guess the next step is supposed to be to distribute? But not sure how to do that here if I have to at all
glad jasper
Could be my parenthesis are off
grim skiff
Could be my parenthesis are off
No
You messed up with this term here
Try and see what you did wrong
ancient folio
I suggest u use assign function so everything looks cleaner
glad jasper
You messed up with this term here
Oh alright lemme see
glad jasper
I suggest u use assign function so everything looks cleaner
Assign function?
ancient folio
Yeah like calling (4x+7)^3 = g(x); do the same thing with the right part. Its just a way to begineer to not mess thing up
glad jasper
You messed up with this term here
Ohhhh wait is it cause I put u' instead of u for the first?
Oh wait nvm
glad jasper
Yeah like calling (4x+7)^3 = g(x); do the same thing with the right part. Its ju...
Oh ok
grim skiff
So it looks like you know product rule
glad jasper
Wait did I have to apply power rule somewhere here
grim skiff
Where it's F'(x) = f'(x)g(x) + f(x)g'(x)
glad jasper
Yes
grim skiff
Wait did I have to apply power rule somewhere here
Sorry product
What's the derivative of f(x)?
glad jasper
You mean like f'(x)?
glad jasper
Well I mean for your problem
Just a second looking back
ancient folio
U only need to subs the final g(x) and h(x) in then u're done
glad jasper
Ahhh
grim skiff
!nosols
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ancient folio
Its much cleaner
glad jasper
Yeah I can tell
Alright im gonna get back here in a second just gotta fix a couple of things
ancient folio
!nosols
By the look at his answer, he knows his work, he just need a way to not mess up
grim skiff
You messed up with this term here
My hint here was telling you that you messed up finding f'(x) @glad jasper
glad jasper
My hint here was telling you that you messed up finding f'(x) <@7178006791792887...
f'(x) for (4x+7)^3 right
grim skiff
Well f(x) = (4x + 7)^3
glad jasper
Yeah
glad jasper
Which we use chain rule right?
grim skiff
Yes
grim skiff
Yes that's why I pointed out that specific term
glad jasper
Omg bro im so dumb thanks a lot for that
Lemme retype everything now and see if it comes out right
YES thanks @ancient folio and @grim skiff
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silk ore
Anyone can help me check my answer?
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thorny shuttle
silk ore
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true sparrow
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@true sparrow Has your question been resolved?
leaden mica
@true sparrow you have there quite a lot of weird stuff that you are doing, but usually to find a max/min you use derivatives maybe try that
true sparrow
i need to check before replying
Er 1.13
true sparrow
<@1019501335768473600> you have there quite a lot of weird stuff that you are d...
Hmm why tho I don't understand why I Ned to differentatite the area
The max amt of water it can hold is volume right
If I differenate area I get perimeter right or am I understanding smth wrong
leaden mica
one of the main usages of a derivative is to see how a function changes, you have a function of an area if you will differentiate this function you will be able to find the maximum point of this function/area
I don't think you can get a perimeter using a derivative (of the function of the area) but maybe you can with some extra calculations
fallow thunder
Hmm why tho I don't understand why I Ned to differentatite the area
yeah like this guy said u need to diff A wrt theta
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marsh wedge
How do I know from my graph which is the interval
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How do I know from my graph which is the interval
leaden ermine
How do I know from my graph which is the interval
Ich würde einfach |x-3| und 2|x-1| zeichnen
sacred sparrow
How do I know from my graph which is the interval
Welcher Graph?
achso wenn man's zeichnen würde k
sacred sparrow
How do I know from my graph which is the interval
du hast hier btw vergessen die Conditions miteinzubeziehen
e.g. im ersten Case hast du als Voraussetzung x-3 >= 0 und x-1 >= 0
und löst die Ungleichung zu -1 <= x
die Voraussetzungen musst du aber miteinbeziehen, x-3 >= 0 ist dasselbe wie x >= 3
und x-1 >= 0 dasselbe wie x >= 1
also hast du im ersten Fall eigentlich x >= 3 UND x >= 1 UND x >= -1
nocturne shard
How do I know from my graph which is the interval
ouch, that's a lot of cases
sacred sparrow
was dasselbe ist wie x >= 3
auf die gleiche Weise bekommst du die richtigen Intervalle für die drei weiteren Fälle
Also du kannst es auch einmal graphisch bestimmen indem du beide Seiten zeichnest und schaust wann die rechte größer ist
aber es macht auf jeden Fall Sinn die Intervalle auch auszurechnen weil du es nicht immer graphisch testen kannst
@marsh wedge
marsh wedge
Lese es mir mal durch
So hats dieser daniel auf yt gemacht, aber halt nicht weitergerechnet der meinte dann ja nächstes video, hab aber kein gefunden
marsh wedge
also hast du im ersten Fall eigentlich x >= 3 UND x >= 1 UND x >= -1
Okay das verstehe ich nur nicht wieso auch x >= -1
sacred sparrow
Okay das verstehe ich nur nicht wieso auch x >= -1
das x >= -1 ist das was du am Ende rausbekamst
marsh wedge
😭
sacred sparrow
wenn du (x-3) <= 2(x-1) löst
heißt in allen 4 Spalten hast du erst jeweils 2 Conditions und dann hast du jeweils eine Ungleichung berechnet
marsh wedge
Yess, gibts für sowas auch ein schnelleren weg? Da rechnet man sich ja ☠️
marsh wedge
heißt in allen 4 Spalten hast du erst jeweils 2 Conditions und dann hast du jewe...
Rechne ich jz noch für alles aus und zeichne nochmal neu auf
Vllt ergibts dqnn mehr sinn
sacred sparrow
Yess, gibts für sowas auch ein schnelleren weg? Da rechnet man sich ja ☠️
je nach Ungleichung nein :[
weil hier die Terme linear sind könnte man's sich leichter machen aber ich denke es ist nicht schlecht zum üben
ich schreib die zweite Spalte hier auch nochmal hin dann kannst du gleich vergleichen
Conditions sind x-3 < 0, also x < 3 und x-1 >= 0, also x >= 1
und die Ungleichung ergibt x >= 5/3
also haben wir x < 3 UND x >= 1 UND x >= 5/3
also 5/3 <= x < 3
marsh wedge
also haben wir x < 3 UND x >= 1 UND x >= 5/3
Gut hab ich so 🤠
sacred sparrow
Dritte Spalte
x < 1
x >= 3
muss man gar nicht weiter machen
weil x < 1 und x >= 3 nicht gleichzeitig erfüllt sein kann
- Spalte
marsh wedge
also zusammen x <= -1
Habs geändert ups
sacred sparrow
1.Spalte: x >= 3
2.Spalte: 5/3 <= x < 3
3.Spalte: Geht nicht
4.Spalte: x <= -1
das müsstest du jz raus haben
so hast du direkt alle Intervalle
x >= 3 und 5/3 <= x < 3 kann man noch vereinen zu x >= 5/3
marsh wedge
- spalte zum Beispiel x>= 3 weil das am eindeutigsten von allen 3 werten oder?
sacred sparrow
1. spalte zum Beispiel x>= 3 weil das am eindeutigsten von allen 3 werten oder?
was meinst du
marsh wedge
Warte ich zeichne
sacred sparrow
die erste Spalte hatte als Conditions x >= 3 und x >= 1, die Ungleichung ergab x >= -1
wenn man die drei vereint bekommt man x >= 3
sacred sparrow
achso ja
marsh wedge
Okay check
sacred sparrow
(x >= 3) UND (x >= 1) UND (x >= -1) = (x >= 3)
marsh wedge
Ich mache mal kurz weiter ohne auf deine intervale zu gucken
sacred sparrow
kk
ich markier den Rest hier als Spoiler
||die Intervalle wo die ursprüngliche Ungleichung gilt sind also x<=-1 und x>=5/3||
marsh wedge
Tote hose
Das ist zwar eine andere aufgabe, aber ist es so zu rechnen einfacher?
Achso ne ist die gleiche
Jz bin ich verwirrt warte
Achso ja das war die wo ich dachte ich sei schon fertig
Ich glaube ich mach jz erstmal mit was anderem weiter bevor dass weiter meinen kopf fickt 
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weary vector
$9^{12}* (-3)^8 / [(-9^3)^2 -81]^2 / [(-5^3 + 2^2)^5]^0$
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$9^{12}* (-3)^8 / [(-9^3)^2 -81]^2 / [(-5^3 + 2^2)^5]^0$
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Simon James B
honest hill
loud dawn
!original
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loud dawn
It's fr above- and also pinned
You’re just trying to simplify?
weary vector
You’re just trying to simplify?
Nothing special just simplify calculate whatever it's called
the problem asks us to solve the problem
I got the correct answer at the end but not the right sign. I need to get a -1 not a +1 as i got
somwhere i got it wrong
honest hill
(3^2)^12 * 3^8 / [9^6 - 9^2]^2 / 1
why did you rewrite 9 as 3^2 but not the other 9?
loud dawn
You can just drop the /1 that doesn’t mean anything
weary vector
just noticed a tpyo imma show the problema gain
$9^{12}* (-3)^8 / [(-9^3)^2 * 81]^2 / [(-5^3 + 2^2)^5]^0$
glossy valveBOT
Simon James B
weary vector
now it should be right
weary vector
why did you rewrite 9 as 3^2 but not the other 9?
because i am about to re-write 81 as 9^2 so we have 9^6 * 9^2
loud dawn
because i am about to re-write 81 as 9^2 so we have 9^6 * 9^2
This can be rewritten to 9^8
What do you have now
honest hill
**Simon James B**
btw is this $\frac{a}{\left(\frac{b}{c}\right)}$ or $\frac{\left(\frac{a}{b}\right)}{c}$
glossy valveBOT
Bonk
weary vector
(3^2)^12 * 3^8 / [9^6 * 9^2]^2
3^24 * 3^8 / (9^8)^2
3^32 / 9 ^16
3^32 / (3^2)^16
3^32/ 3^32 = 1
loud dawn
It’s (-3)^8
weary vector
It’s (-3)^8
raised to 8 so we can say 3^8
i need to get a -1 not +1 this is my issue
but how is it getting negative if all we have is positive?
loud dawn
but how is it getting negative if all we have is positive?
I put the whole base equation into a calculator and I’m getting positive 1
So either there’s another typo or the grading program is wrong
weary vector
So either there’s another typo or the grading program is wrong
I see
let me check the problem again
yep no typo
maiden wadi
I don't know how to use latex, so bare with me. I'll attach images where possible.
Doing part (ii) of this question. (1st image)
By solving (i) I found that when dy/dx = 0, x = tan^-1(8)/4 to give us T1. (2nd image)
So to solve (ii) my thinking is that Tn = tan^-1(8)+nπ/4 (3rd image)
So all I have to do is equate tan^-1(8)nπ/4 = 25 and solve for n.
I got n = 31.3705
so logically the smallest value of Tn where the X coordinate is greater than 25 should be n = 32 (because 'n' is denoting the number of turning points since the first turning point and that should be a positive integer)
I check the answer sheet of the question I got this from and its given n = 33 so I'm utterly confused though. I also plugged the values into Desmos and when n = 32, the x coordinate is 25.5 while n = 32 gives x = 26.3
so am I wrong or is the answer sheet wrong
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gritty rose
I don't know how to use latex, so bare with me. I'll attach images where possibl...
Show your dy/dx
maiden wadi
i know i differentiated it correctly but ye 1 sec
gritty rose
And show how you solve for x when setting dy/dx=0
gritty rose
How does that become x = (1/4)*(arctan(8) +npi)
maiden wadi
nvm i got my answer
it should be (n-1)pi to account for the first turning point lol
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torn plinth
prove both are the same
x+y>0
-(x+y)<x+y
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prove both are the same
x+y>0
-(x+y)<x+y
grave elm
same in the sense of being equivalent?
grave elm
have you already tried anything?
torn plinth
i think i got it thanks
hot lily
Lol
hot lily
i think i got it thanks
!done ?
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i think i got it thanks
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torn plinth
.close
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rocky wraith
Hey all - I am having trouble understanding what it is I can solve for in the attached question. The first part is simple, as $a_{n}$ is a simple general term, but I cannot understand how to solve for the linear recursive relation that satisfies ${a_{n}}_{n=0}^{\infty}$. I have learned how to find solutions and find a basis with said solutions of the form $a = cr^{n}$, where $c$ is a constant, and we assume the geometric sequence, but we have normally done this from a recursive sequence to our solutions. Do I need to do the reverse? My work for 1(a) is attached along with the questions
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tokyofastfood
rocky wraith
Please don’t give me the answer, I just need help understanding why it’s “second-order” and how I could try to find said linear recursive sequence. I understand I might not have a very clear understanding at the moment, that’s why I’m asking and why I want to build it
Thank you in advance
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velvet sedge
well, have you solved linear recurrence relations of higher orders before?
what do you usually do in those circumstances? what do the solutions look like?
presumably you know how to solve a linear recurrence relation with a generating function
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rocky wraith
presumably you know how to solve a linear recurrence relation _with_ a generatin...
Yeah absolutely, but normally that generating function includes $a_{i}$ terms, where we could isolate for $a_{n}$ in terms of $a_{i}$, like for example
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tokyofastfood
rocky wraith
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