#help-13
cedar kilnBOT
balmy chasm
thats undefined for obvious reasons but i dont understand whats wrong with the radii
balmy chasm
oh sorry i wrote it wrong, i meant the larger radius to be (4/y)-1 and the smaller radius to be 1
crimson sedge
yes but you need to split into two integrals
at y=1 its bounded by x=3 now
drawing a graph makes these 10x easier
crimson sedge
yes
balmy chasm
i set it up this way and im getting an answer but its off
balmy chasm
ohh so its another washer?
crimson sedge
yes
balmy chasm
yes
thank you that makes a lot more sense
in general when do u know to split it into multiple integrals?
honest bobcat
cedar kilnBOT
honest bobcat
not really sure where to start with this tbh
crimson sedge
ok
crimson sedge
I think its false
so whats an example of that?
honest bobcat
but b im struggling with
crimson sedge
o alr
honest bobcat
so whats an example of that?
one sec ill send an image
@crimson sedge
i found a counter example so its fase
but b i have no idea
i cant intuit if its true or false
actually
with a bit of a shit venn diagram i kind of do see why
wait no i dont
lmao
modern compass
element chase.
If x is in A and C, then x is in A n C then x is in B n C, so x is in B
Can you do something similar if x is in A-C using the union statement to get that x is in B?
honest bobcat
element chase.
If x is in A and C, then x is in A n C then x is in B n C, so x ...
not really following
If x is in A and C, then x is in A n C
isnt this the same thing
modern compass
yes
modern compass
yep
dull oxide
I don't think the indefinite integral can be solved analytically by simple means
Is this for complex analysis?
Are you supposed to just be approximating this with series?
More context please
I don't remember series stuff, so I can't help you further. 
runic prawn
cedar kilnBOT
runic prawn
soo ik the formula for a circle, A = pi(r^2)
what would the radius be? im confused from that point on
<@&286206848099549185>
torpid blade
<@&286206848099549185>
Look for the formula for solid of revolution
runic prawn
could i do semicircle cross section and then multiply it by 2 since the graph is symmetrical
torpid blade
I guess u could. But not a good practice.
Because as I remember it did not work every time
runic prawn
oh
runic prawn
Because as I remember it did not work every time
if i did the area of a circle, could A = pi(b/2)^2
then pi/2 (integral 0 to 4) with an integrand of (2(sqrt x))^2
cedar kilnBOT
Available help channel!
crimson sedge
I need help with 1ii
cedar kilnBOT
I need help with 1ii
half forge
merry tinsel
cedar kilnBOT
crimson sedge
hm
crimson sedge
u=root(x)?
merry tinsel
yea
merry tinsel
merry tinsel
is it like a trig integral
improperfrac
crimson sedge
yeah i see it now
merry tinsel
,rotate
wraith daggerBOT
merry tinsel
ok so i got this
crimson sedge
yes i know
merry tinsel
crimson sedge
and at 0 too but idk if u rly care
crimson sedge
for ur final answer?
crimson sedge
,w integral from 0 to inf of 10/(root(x)(1+x))
wraith daggerBOT
crimson sedge
yea looks right
slow thicket
dct or lct no?
merry tinsel
comparison test
what do i compare to?
slow thicket
i guess 1/root(1+x^6)
you cant
unless you prove that converges too
with another test
crimson sedge
yea ic that
crimson sedge
show its smaller than like some f(x) that converges honestly my brain is dying lol
crimson sedge
yea that works
merry tinsel
is this correct?
crimson sedge
mhm maybe you could have done like < 5x/root(x^6) which is just like 5/x^2
wait i dont think thats correct
isnt 1/x^6 smaller?
,w 5/(root(1+2^6))
wraith daggerBOT
crimson sedge
,w 5/(1+2^6)
wraith daggerBOT
crimson sedge
yeah i dont think that works
merry tinsel
ok
crimson sedge
mhm maybe you could have done like < 5x/root(x^6) which is just like 5/x^2
this seems fine tho
cedar kilnBOT
@merry tinsel Has your question been resolved?
lime harbor
cedar kilnBOT
lime harbor
got an answer but its wrong
clear berry
what are you supposed to do?
crimson sedge
got an answer but its wrong
Show your workings
lime harbor
Show your workings
gimme a sec ill take a picture
i sorta got stuck here
i just expanded all three brackets with every possible combination
crimson sedge
Geez don't tell me you actually tried developping the equations
lime harbor
but when i got to line 3 i couldnt factorise
crimson sedge
Poor soul there was a shortcut
crimson sedge
Also clearly you did something very wrong because without even expanding it I can tell you the first term should be y^3
heavy sorrel
three roots of a equation it should cubic
crimson sedge
Yeah
lusty grotto
If the product of 3 numbers shud be 0 at least one of them numbers must be 0
buoyant latch
Those aren’t even quadratics
crimson sedge
(y-1)(y+5)(y+2)=0 implies that either y-1, y+5, or y+2 is 0
Becuase multiplying 3 non-zero numbers together just gives you another number that isn't 0
So it must be that one of them is 0
And, vice versa, multiplying 0 by any numbers is gonna give you 0
buoyant latch
Hey that’s called the null factor law
lime harbor
yup i got it now thanks for the help everyone
crimson sedge
Hey that’s called the null factor law
Why do mathematicians feel the need to name everything?
cedar kilnBOT
buoyant latch
Why do mathematicians feel the need to name everything?
Same reason everything gets named, easy to refer to
clear berry
Hey that’s called the null factor law
.reopen
cedar kilnBOT
✅
clear berry
Hey that’s called the null factor law
Never heard that name
crimson sedge
Same reason everything gets named, easy to refer to
When realistically do you need to refer to it though?
buoyant latch
Right now
crimson sedge
Right now I did not need to refer to its name to explain it
buoyant latch
https://en.m.wikipedia.org/wiki/Zero-product_property
It has a Wikipedia page so it must exist
clear berry
buoyant latch
Right now I did not need to refer to its name to explain it
Well you call a line a line without having to define a line
It’s the same with any names concept
lusty grotto
I mean they even have a name for the fact that you can add the same number to both sides of an equation
buoyant latch
I think it’s pretty ridiculous to argue that things should have names
lusty grotto
Is that necessary
crimson sedge
Well you call a line a line without having to define a line
Yeah you can
But I regularily talk about lines
buoyant latch
But I regularily talk about lines
Now you’re on the how regular is regular enough to have a name spectrum
clear berry
I think it's faster to explain ab = 0 => a=0 or b=0 then tell null factor law
cause you'll need to anyway explain what "null factor law" is
crimson sedge
Now you’re on the how regular is regular enough to have a name spectrum
Ah no don't hit me with the "How many grains of sands is a beach?" argument
buoyant latch
I think it's faster to explain ab = 0 => a=0 or b=0 then tell null factor law
Which is why I said “hey that’s called the null factor law” so hopefully they could remember it’s a thing, I didn’t start off the explanation with “null factor law, google it.”
crimson sedge
I employ it all the time
lusty grotto
Lol
clear berry
Which is why I said “hey that’s called the null factor law” so hopefully they co...
fair enough
crimson sedge
But for real though every f'ing time I find out some basic shting had a name the whole time
buoyant latch
I mean it’s easy to put as a topic too
crimson sedge
Like "Oh yeah that rule you've been using for years has a name actually it's called Goober's law" or something
buoyant latch
In a content sheet or something
It’s just easier to refer it as the null factor law compared to “the one where if ab = 0 then either a or b or both = 0”
That also doesn’t fully describe null factor law
Mhmm it looks like being able to refer to this with a name helps with talking about abstract algebra too
So it is indeed useful
.close
cedar kilnBOT
cedar kilnBOT
@solemn dune Has your question been resolved?
royal loom
No problem
cedar kilnBOT
cedar kilnBOT
Available help channel!
ornate dagger
Could someonme help me with this question? Work out the percentage change when a price of £20 is decreased to £3.
devout sinew
.reopen
shrewd tinsel
How do i do this?
cedar kilnBOT
How do i do this?
opaque hollow
how would i make a back and forth movement with linear interpolation? (i only know basic math but i need to know to implement smooth walking animations in my game)
shrewd tinsel
<@846900369514954792>
I put a picture
shrewd tinsel
How do i do this?
Here
shrewd tinsel
No i hav to go to school in less than 10 minutes
shrewd tinsel
9
shrewd tinsel
How do i do this?
know how to do this
silk osprey
How do i do this?
I believe you have to isolate either the Y or X
shrewd tinsel
I believe you have to isolate either the Y or X
I don’t know how
silk osprey
wait are they connected to each other or just are they just separate questions
for example 3
are they connected or separate
shrewd tinsel
I have to find x and y with both of the equations
silk osprey
are you stuck at like somewhere or do you just completely not understand what to do
@shrewd tinsel
shrewd tinsel
i completely dont know what to do
silk osprey
do you know the elimination method?
silk osprey
i would recommend watching a video on the elimination method first and then try to solve it yourself
if you still don't understand come back
shrewd tinsel
i don’t have time
silk osprey
alright ok ill try to explain
ok so basically in the elimination method you either add or substract the equations so you get an equation in one variable. When the coefficients of a variable is the opposite you add the equation so you can eliminate a variable but if they are equal you can just subtract the equations to eliminate a variable
shrewd tinsel
How do i do this?
so do u know what i would do for the first one here
silk osprey
so lets take question 1.
5x - 2y = -48
2x + 3y = -23
for them to eliminate x or y
they have to be equal yes
so its equal to 0
wait let me word it better
to eliminate x or y
they have to be equal to each other so that when you subtract or add each other it becomes 0
and you successfully eliminate x or y
shrewd tinsel
what would i subtract and add on 1
silk osprey
you can choose from x or y
lets try y
so -2y and 3y
if you add them to each other it isnt 0
so we have to make them equal
shrewd tinsel
Do i subtract 2x from -23
silk osprey
no
you want to isolate
x or y
from both equations
and there's a variable in 2x so you cant substract it from -23
shrewd tinsel
so i move it to the right side then not subtract
shrewd tinsel
yes
silk osprey
to eliminate both
they need to add to each other
so it becomes 0
because there is a negative number
-2y + 3y doesnt equal to 0 right?
shrewd tinsel
No
silk osprey
so what can you do to make them equal to 0
silk osprey
no because there's a variable
so you cant do that
so your only option is to multiply
you have to multiply -2y by 3 and 3y by 2
so that it becomes equal to -6y and 6y
-6y + 6y = 0
but
since you multiplied
the others in the equation also has to be multiplied
so in 5x - 2y = -48
5x has to be multiply by 3
because -2 got multiplied by 3
and same goes for -48
and it becomes 15x - 6y = -144
and 2x + 3y = -23
has to be multiplied by 2 because you multiplied 3y by 2
so 4x + 6y = -46
shrewd tinsel
be back soon gotta finish this class
silk osprey
alright ill finish this and you can read it all after you're done
and then try solve the rest
and you get
15x - 6y = -144
4x + 6y = -46
and now you add them all to each other
19x = -190
and now you've isolated the x but not completely
because of the 19
19x is the same as 19 * x
so to remove the 19
you divide it by 19 to get 1
because 1x is the same as x
and since you divided
the other side also has to be divided
so x = -10
and now that you have x
you just put it in one of the original equations
and you can solve y
cedar kilnBOT
@shrewd tinsel Has your question been resolved?
shrewd tinsel
so that it becomes equal to -6y and 6y
Are u here
shrewd tinsel
thanks @silk osprey
cedar kilnBOT
Available help channel!
tribal plank
height of a picture is (x+4)cm and the perimeter is (6x+14)cm. the width of the picture is 15cm. find the area of the picture
tribal plank
im doing work due in like 30 mins
so it would be helpful if people could get some questions done with me
tribal plank
yeah
eager sparrow
This is a picture, which is just a rectangle
tribal plank
yep
eager sparrow
so there are (x+4) + (x+4) = 2(x+4)
mellow loom
Um, isn't 2×(h+w) = p?
eager sparrow
Um, isn't 2×(h+w) = p?
there
eager sparrow
h is (x+4), w is 15 and the perimeter is (6x+14)
this is the values u gotta sub
eager sparrow
equate it to perimeter
U forgot the right side
U have the equation for perimeter
eager sparrow
height of a picture is (x+4)cm and the perimeter is (6x+14)cm. the width of the ...
here
eager sparrow
2( 15 + 6x +14)
here
at the first step
what u did is 2(width + THE PERIMETER)
The formula for permieter is this
eager sparrow
Um, isn't 2×(h+w) = p?
this one
tribal plank
2(15+ x+ 4
eager sparrow
yeah
tribal plank
30+2x+8
tribal plank
aight thanks
i know now
imma copy this down
and then close this
and ill open another
when i need help again
eager sparrow
yea yeah
tribal plank
i got 2 more pages to get through
eager sparrow
gl
mellow loom
Do you know which is the surface?
The idea is to combine shape
Noice
But let me note more for you
A hemisphere has 2 side (let's call it that way)
- the curve
- the flat (a cricle)
A cylinder has 3 as you said
- top (a circle)
- bottom (a circle)
- middle ( a rectangle)
latent bloom
Middle is not a square
mellow loom
Oh mybad
latent bloom
mellow loom
Now if we combine these shape the same as the picture
The surface is
Top: Hemisphere
- the curve
Middle: cylinder
- middle (a rectangle)
Bottom: hemisphere
- the curve
When you know what is the combination of it then you can work on it
The surface is
Surface of curve of upper hemisphere
- Surface of middle part of cylinder
- Surface of curve of lower hemisphere
And that's it
You can browse on internet for formula
cedar kilnBOT
@crimson sedge Has your question been resolved?
whole chasm
while finding the mean of 18 observations is 10 if each observation is increased by 4
ancient lodge
What's the question...
whole chasm
while finding the mean of 18 observations is 10 if each observation is increased by 4
whole chasm
What's the question...
Thank u for respoding sir
ancient lodge
That's a wonderful statement with no directive.
whole chasm
what do u mean ?
it an mcq
while finding the mean of 18 observations is 10 if each observation is increased by 4 the mean is ?
ancient lodge
Yeah 'the mean is ?' is kinda important tbh
Recall mean = (total)/(number of observations)
whole chasm
fx / f
ancient lodge
You can find the total of the observations before the increase, the total afterward follows nicely
Then divide by the number of observations again
Done.
whole chasm
Sorry but not able to understand on how can i do it
ancient lodge
What part don't you get?
whole chasm
as i know that total addition of f divided by total addtion of f + mid point of ci
fx/f
ancient lodge
That doesn't answer my question, but ok.
ancient lodge
Ig if you're not gonna read anything I say, someone else can help you.
whole chasm
can u tell me waht i am doing wrong or whom should i contact
<@&286206848099549185> who ca help me ?
vocal plank
So 18 different observations right?
whole chasm
while finding the mean of 18 observations is 10 if each observation is increased by 4 then mean is ?
whole chasm
So 18 different observations right?
yes
vocal plank
So to formulate this problem let’s just do it like this (O_18+O_17…O_1)/18=10
vocal plank
That’s the basis of the question if I am understanding correctly right?
whole chasm
idk tahts y i am asking for hel;p
vocal plank
Well assuming it’s correct
whole chasm
an MCQ with options
whole chasm
hmm i not understabding it are u using the addtion of f and x and multiplying it ?
vocal plank
Using the basic formula for finding the average
And then it says observations increased by 4
Gimmie a bit to work it out
vocal plank
average same thing as mean
whole chasm
oh ok
vocal plank
Yeah the answer is as I thought I was just double checking
Thing of averages in terms of percentages
whole chasm
Yeah the answer is as I thought I was just double checking
No problem
vocal plank
If every number was 1 the mean would be 1
Same for 2 the mean would be 2
So with that in mind if you increase every number by x the mean also increases by x
Makes sense?
vocal plank
Where are you getting 18 from
vocal plank
No your fine just gimmie a sec
whole chasm
ok
vocal plank
So to formulate this problem let’s just do it like this (O_18+O_17…O_1)/18=10
Let’s go back to this formula
And do some basic algebra
whole chasm
hm hmm
vocal plank
We want to isolate O so we can add 4 to each
whole chasm
bro to be honest , i am not good at maths so if possible can u tell me by easy wordings ?
vocal plank
Let me write this out to make it easier this may take a bit if this closes I’ll dm you if it’s not already solved
whole chasm
ok np
weak void
what does it mean when i write something like this 10^^^10
cedar kilnBOT
weak void
what does it mean when i write something like this 10^^^10??
solid juniper
nothing?
quartz frost
looks like the next step after tetration maybe
though that also has different notation
weak void
so like instead of writing 10^10^10^10 just like 10^^^10?
quartz frost
no
weak void
?
wraith daggerBOT
~Martin
quartz frost
or
weak void
**\~Martin**
what does that mean?
quartz frost
$10\uparrow\uparrow 4$
wraith daggerBOT
~Martin
quartz frost
that is the notation used for tetration
and we could continue this further to achieve something like 10^^^10
vagrant elbow
Stack 4 10s in a mad exponent tower
quartz frost
but it would not really be useful in most cases
vagrant elbow
I haven't seen tetration being used tbh
weak void
**\~Martin**
so this is 10^10^10^10?
quartz frost
well, to be more precise it is 10^(10^(10^(10)))
which is probably what you mean
at least that is what i think it is
tetration is pretty useless normally
weak void
i dont get it + thats not what i wanna know i wanna know what 10^(any amount of ^^^)10 means
vagrant elbow
Tetrate the tetration 
quartz frost
repeated summation for example 10+10+10 is multiplication (here 3*10)
where 3 is the number of tens used
repeated multiplication is exponentiation
example: 10 * 10 * 10=10^3
again where 3 is the number of tens used
repeated exponentiation is tetration
example: 10^10^10=10^^3
again where 3 is the number of tens used
repeated tetration is likely what you are after
so we would have:
x^^x^^x=x^^^3
marsh pond
.close
solemn bronze
guys I'm not getting 21(b)
cedar kilnBOT
guys I'm not getting 21(b)
lusty grotto
Also find the distance between two other points
solemn bronze
but using the distance formula on points $(0, p) and (x_0, y_0)$ I'm getting $d = \sqrt{x_0^2 + (y_0 - p)^2}$
wraith daggerBOT
math
solemn bronze
and idk how to simplify that to show equality
lusty grotto
using the distance formula on points (0, p) and (0, - y_0) I got d = -y_0 - p
Well |-y_0 - p|
solemn bronze
Well |-y_0 - p|
right right
solemn bronze
🤦♂️
how long until I start seeing stuff like that on my own 😭
I've read this question like 5 times
lusty grotto
🥲
solemn bronze
ngl, it's even worse
my algebra is awful, I still don't see how $
$\sqrt{4py_0 + (y_0 - p)^2} = what I need$
wraith daggerBOT
math
lone oxide
who can help me with those
solemn bronze
who can help me with those
🤨
solemn bronze
I’m stuck on this one bro and ixl sucks
you're hijacking my channel bud
lone oxide
Oh LO i thought that it’s a channel related to math
marble ermine
Hello, if $v(v(t))=t^{8n^2 + 8n}$, what might be v(t)?
cedar kilnBOT
Hello, if $v(v(t))=t^{8n^2 + 8n}$, what might be v(t)?
wraith daggerBOT
lilisworld
latent hamlet
Ohh I wanna know this too🥲
marble ermine
Fr 😭
wraith daggerBOT
박재현
clear berry
use \sqrt
latent hamlet
I think $v(t)=t^{\sqrt(8n^2+8n)}$
wraith daggerBOT
박재현
clear berry
$v(t)=t^{\sqrt{8n^2+8n}}$
wraith daggerBOT
numbpy
clear berry
I think this should work
marble ermine
Yes thank you both😂 idk why I was hoping for something simpler
glad kestrel
I think $v(t)=t^{\sqrt(8n^2+8n)}$
don't just give answers
clear berry
cause if you let v(t) = t^(f(x)), v(v(t)) = t^{v(t)^2}
cedar kilnBOT
latent hamlet
Hmm
cedar kilnBOT
Available help channel!
supple fiber
any one know how to do hamming code matrix?
cedar kilnBOT
any one know how to do hamming code matrix?
crimson delta
well we dont know how they are given in your lecture notes
supple fiber
lecture is useless does explain anything how to a (7,4) only but not (15,11)
the thing is idk but the chosen positions chosen
lethal jackal
well a (15, 11) Hamming code can be represented as a linear transformation in many ways
there's a linear transformation T: R^11 -> R^16 which represents the entire encoding process
one T: R^11 -> R^5 which actually produces the code
all of these include an extra parity bit over everything
cedar kilnBOT
@supple fiber Has your question been resolved?
heady salmon
Something something something F prime is velocity...
What do the first and second prime mean
all i know is that the first prime means the Slope and curvature....
crimson sedge
by f prime they mean the derivative of f
f(x) is probably a position function
f’(x) is ur velocity function
etc
heady salmon
whats f''(x)
crimson sedge
acceleration function
heady salmon
and f'''(x) means nothing since its goes to zero, right?
crimson sedge
depends on the function
heady salmon
lets say the Leading term of the polynomials has 9 as its exponent... what would f'''(x) mean? and every other prime after that
heady salmon
in respect to?
crimson sedge
fr?
lethal jackal
and it's usually written f(t), f'(t), f''(t), so on
heady salmon
idk if your joking or if that actually true lol
lethal jackal
I'm not joking lol
crimson sedge
then it's snap, crackle, pop
i cant tell if this is a joke or not
heady salmon
wtff
crimson sedge
o
heady salmon
well what do these terms mean then?
Is it just another way to describe a certain prime without saying acceleration 2 and 3?
lethal jackal
it's literally just like position, velocity, acceleration
just names for different derivatives of position
heady salmon
oh i see it, thanks
young gazelle
I know that a11 must be positive as if it were 0 the decomposition would break down because of the divisions and if it were negative then there would be complex alpha values and chokesky factorizations can’t have those but I feel like I am missing some way to prove it must be positive. The inductive step I can show that the resulting cholesky decomposition from K-ww^T/a11 is still positive definite but I feel like I am missing something on part 1
crimson delta
what do you know about the matrix A
ah wait it says it in the first sentence
A is pos def
young gazelle
It’s positive definite and symmetric Ye
crimson delta
what does that mean
young gazelle
By definition the entire diag must be positive
crimson delta
no that's not the def of positive definite
young gazelle
Is that not true? If any value is negative couldn’t there be a non positive eigenvalue?
crimson delta
but I mean if you know that one then you are done
do you mean the diag of the diagonalization?
or of A itself
young gazelle
Of A itself
crimson delta
well yes that is true but if you know that then clearly a_11 is positive
but again, that's not the usual definition of positive definite
also not sure right now if its even equivalent or just follows from positive definite
young gazelle
Well it’s symmetric and x^TAx is >0 for all non zero x that are elements of the reals
young gazelle
And I see how to use that for 2. To show the inductive step
young gazelle
But I’m confused what they want from me for part 1
I can set x to be x,y where x is not 0 and y is the bottom right term of A
crimson delta
think simpler
young gazelle
Like to prove it by contradiction?
crimson delta
no
we want to find some vector x so that a_11 = x^T A x
and then we immediately get a_11 > 0
by pos def
young gazelle
So just any vector like 1,1?
young gazelle
I
crimson delta
?
young gazelle
Identity
young gazelle
Sorry I haven’t slept for 24 hours .-.
young gazelle
Standard unit vectors like (0,1) and (1,0) with n length and rest of elements 0 yeah?
crimson delta
yes. (0,...,0,1,0,...,0)
young gazelle
I forgot how to do all math
I get a11 alone
With just 1,0,0…
So it must be positive
Cuz it has to be >0 because of positive definite definition
young gazelle
Thanks for the help, I feel like I need to re learn all of linear… I’ve done well in my last 2 classes and this one is just building on content I did well on and I can’t even figure this stuff out 😦
5th year of cpsc in a 400 level computational optimization course and it took me like 5 minutes to figure out how to multiply a vector by a matrix
Is there somewhere I can give you rep or a nice review or soemthing on here
crimson delta
dw about it
young gazelle
Have a good day 🙂
crimson delta
and you have a good night
young gazelle
.close
crimson sedge
cedar kilnBOT
crimson sedge
Do you guys have any idea about my mistake?
Maybe wrong way?
I mean if we say that lnn~n we obtain only e....but i am not sure
That we can say lnn~n
carmine bronze
You didn't apply e^lim(f(x) for one.
infinity^0 is one of the indeterminant conditions in which L'hopital applies.
crimson sedge
You didn't apply e^lim(f(x) for one.
Sorry i dont understand
carmine bronze
Seems like you may have skipped some reading.
crimson sedge
I mean, i am not apply hopital
I am applying the First formula
But maybe i am wrong and i have to apply hopital
carmine bronze
One moment, I need to find a reference for it.
crimson sedge
One moment, I need to find a reference for it.
Of course
carmine bronze
L'Hopital's Rule and the Forms $1^\infty$, $0^0$, and $\infty^0$.\\
$\text{If } \lim_{x\to a} \ln{f(x)} = L\\
\text{then } \lim_{x\to a} f(x) = \lim_{x\to a} e^{\ln{f(x)}} = e^L$
wraith daggerBOT
Kookiemon
crimson sedge
Ok but i dont understand how this Is useful to my case
wraith daggerBOT
Mehdi_Moulati
crimson sedge
Ok let me see
carmine bronze
As I said earlier, it seems you may have skipped some reading.
crimson sedge
For heavens sake
crimson sedge
**Mehdi\_Moulati**
And when i reached this point what i have to do
crimson sedge
M triyng
crimson sedge
ln(a/b) = ln(a) - ln(b)
crimson sedge
ln(a/b) = ln(a) - ln(b)
But i am stucked againg here
crimson sedge
try to simplify ln(n²/n+1)
Is this ok?
carmine bronze
ln(n+1)/ln(n) goes to 1 which results in e^(2-1) = e^1.
carmine bronze
It technically requires another application of L'hopital but yes.
turbid charm
need help with question 4.3 and 4.6
cedar kilnBOT
need help with question 4.3 and 4.6
@turbid charm Has your question been resolved?
Available help channel!
spare turtle
cedar kilnBOT
cedar kilnBOT
@spare turtle Has your question been resolved?
cedar kilnBOT
@spare turtle Has your question been resolved?
muted lantern
hi, can anyone help me with this?
cedar kilnBOT
hi, can anyone help me with this?
@muted lantern Has your question been resolved?
Available help channel!
ashen kite
Hello! I'm trying to learn how to graph cosine & sine functions (Precalculus). I have been able to find all the transformations, but I don't fully understand how they affect the graph. The question wants me to use two points to define my graph.
ashen kite
I am pretty sure I put the correct transformations, but the graph is incorrect
<@&286206848099549185>
azure horizon
Hello! I'm trying to learn how to graph cosine & sine functions (Precalculus). I...
i don't think it's centred correctly
i think that top orange dot should be at like -pi/4 on the x, but it's at -pi/8
ashen kite
I didn't attempt the graph yet, thats the randomized thing from the question
azure horizon
oh
ashen kite
I don't really know how to use the transformations to plot the graph
azure horizon
i mean ok you just sorta start from something and then go outwards
so start from cos(x)
then cos(2x) is that but like squished right
then cos(2x + pi/2), you move it left by pi/2
ashen kite
so start from cos(x)
wdym
azure horizon
then multiply by 4 and you just gotta make it bigger
ashen kite
this?
ashen kite
azure horizon
sure
azure horizon
yes
ashen kite
idk how to do the amplitude
ashen kite
azure horizon
no
ashen kite
lol
azure horizon
how is that 4
azure horizon
now it goes up and down 4, but you haven't got the +3 right
at x = 0, 4cos(x) + 3 should be 7
azure horizon
yes
ashen kite
shifted it down by accident
ok now for the other stuff
phase shift
because it was -pi?
azure horizon
was it?
ashen kite
azure horizon
ok i mean, how about this
let's do the cos(x) -> cos(2x) thing first
that'll be simpler
azure horizon
so basically
cos(0) = cos(2 * (0))
cos(pi) = cos(2 * (pi/2))
cos(2pi) = cos(2 * pi)
so when you're comparing cos(x) to cos(2x)
the cos(2x) goes twice as fast, sorta
it changes twice as fast
like, cos(x) goes from 1 to -1 between 0 and pi
but cos(2x) does it twice as fast
it goes from 1 to -1 between 0 and pi/2
ashen kite
azure horizon
yeah
ashen kite
ok
ashen kite
now vertical and phase?
azure horizon
so take this
this is like 4cos(x) + 3
turn it into 4cos(2x) + 3
in the same way
ashen kite
ashen kite
ok
azure horizon
yes
ashen kite
phase shift would = -pi/4?
ashen kite
howcome?
azure horizon
ok so
ashen kite
I was taught its h/b, and h is pi/2 and b is 2 in this equation i believe
ashen kite
oh good
azure horizon
because you can just turn it into 2(x-pi/4)
ashen kite
azure horizon
that's what matters here
yeah that looks good
so you can test it out by looking at the actual function and putting some stuff in
so at x = 0, the function should be equal to 3, and it is
ashen kite
you dont have to do anything for period right?
azure horizon
so cos(x) has period 2pi
so you made it into cos(2x) which goes twice as fast
so it has period pi
azure horizon
so you already did that
ashen kite
good
it gives me two attempts so ill see if this is right and ill try another
ay nice it was correct 🙂
azure horizon
coolio
azure horizon
sounds good
ashen kite
they gave a lot more points for this one lol
ill give it my best shot
I think I have it? Think I'm missing something though
azure horizon
i mean you can always just try stuff
compare what the result for x = 0 should be from the function with what the value for x = 0 is on your graph
and then do a few more
ashen kite
so at x=0 it should be -pi/4?