Have you tried examining sided limits?
#help-27
scarlet sequoia
polar chasm
limit from left and limit from right
wet haven
Well I looked at it I kinda get it
Idk how I missed that in class or how to determine which side it’s coming from
Yeah what do i do with this knowledge of sided limits
Granted it’s from the left it’s gonna be a very small number and if it’s from the right it’s a bit bigger
scarlet sequoia
Idk how I missed that in class or how to determine which side it’s coming from
Check both, we usually do it when we doubt that the limit exist or we suspect it
wet haven
If it’s for example 8.9 then the fraction becomes 1/0.1 which gives ten otherwise it’s gonna be -10 so the limit exists?
I am not getting this
scarlet sequoia
e.g. when x approaches 3 from the left abs(3-x) = abs(x-3) = -(x-3) and in the second case we have abs(3-x) = abs(x-3) = (x-3), so the result depends on the direction
same with 3^(1/(9-x^2))
scarlet sequoia
If it’s for example 8.9 then the fraction becomes 1/0.1 which gives ten otherwis...
Good intuition, now you can observe that if x tends to 3 from the left you'll be getting 3 to the power of bigger and bigger number, so it grows very fast
i.e. 3^(some really huge number) ---> +inf
on the other hand if x tends to 3 from the right you'll be getting 3 to the power of smaller and smaller number (large numbers with minus sign)
i.e. 3^(some really huge negative number) ---> 0
because it's (1/3)^(some really huge number)
and if you divide 1 by a really huge numbers result is close to zero
That's the logic behind it
wet haven
Hard to grasp honestly but it’s either positive or negative infinity right?
We get two possible outcomes then?
scarlet sequoia
We get two possible outcomes then?
Yes, two different outcomes
wet haven
Either one or infinity?
scarlet sequoia
Simply put, it's +inf (if x approaches from the left) and 0 for the other case
wet haven
Wait from the left is infinity?
So tough my head hurts I mean I get it but it’s very unusual
Alright looking at the graph it makes a bit more sense but still overall pretty tough concept
scarlet sequoia
You can understand it starting from some easier examples, like lim x -> 0 of 1/x
wet haven
From the right to infinity from the left minus infinity
I can’t understand it in number I need to visualise it still
But thanks I appreciate the help it still gives me more headaches than I thought
scarlet sequoia
From the right to infinity from the left minus infinity
Yes, and this is why the limit is DNE
wet haven
Only in cases with infinity on both sides?
scarlet sequoia
Because for a limit to exist, the sided limits must be equal to each other
wet haven
I mean we have two different outcomes 1 and inf in the original question so it’s DNE?
or should I leave it like this
scarlet sequoia
I mean we have two different outcomes 1 and inf in the original question so it’s...
Yes, it's DNE
Because the sided limits aren't equal
at x = 3
wet haven
Ooh that’s better
Ok yeah thats enough for today I will do some more tomorrow
Thanks Modus your pretty good at teaching this kind of stuff
Have a great time of the day
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viral rapids
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viral rapids
is question 5 ∫Fd
F=ma=mg=rho V g= rho πr² Δx g
and d=L-x
do you do $\int_0^h(L-x)\rho\pi r²g\dd{x}$
woven radishBOT
Jash
brittle prairie
Ok so I was using an ai tutor to help me learn limits. 2 different ai's gave me different answers so now im confused again.
I know B is no limit existing but i dont know exactly why.
The answer that came to mind for A: was 0 or 1 (ai gave me 1 but I thought it was 0)
devout snowBOT
Ok so I was using an ai tutor to help me learn limits. 2 different ai's gave me ...
winter torrent
it's 0
i just tried an AI and it gave me complete bunk
B has no limit because the limit from the right (1) is not equal to the limit from the left (-2)
brittle prairie
thank you but for B what does the limit mean exactly? idk my brain is saying the 2nd line sectiong thing isnt continuing and starts with an open circle
idk if im just confusing myself or not
winter torrent
the limit is the value that f approaches near the given point
winter torrent
thank you but for B what does the limit mean exactly? idk my brain is saying the...
yea but if you look at x = 2.01, x = 2.0001, x = 2.000000001, etc
then f(x) gets closer and closer to 1
so the limit from the right is 1
similarly the limit from the left is -2
the actual value of f(-2) doesn't matter at all
we only care about what's nearby
brittle prairie
ok i kinda have to let that sink it but thank you. Yeah ig ill have to stop using ai cause its not really reliable anymore. just confuses me more
thank you
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eternal crypt
heya,
so for this im unsure on how do i solve it or show it
i get that the equation has to be something that goes to 3 <= given <= something goes to 3
but how?
wraith anchor
hi
supple knot
heya,
so for this im unsure on how do i solve it or show it
i get that the equa...
try using 0 <= 2^n and then add 3^n to both sides
and same thing to 2^n < 3^n
eternal crypt
try using 0 <= 2^n and then add 3^n to both sides
wdym?
supple knot
what part of that is confusing
eternal crypt
why are we using 0 and why add 3^n?
wraith anchor
that is how you squeeze the thing!
eternal crypt
not getting it
supple knot
try using 0 <= 2^n and then add 3^n to both sides
did you do this yet
eternal crypt
did you do this yet
i dont get what to do, to do it
supple knot
what do you get after you add 3^n to both sides?
eternal crypt
what do you get after you add 3^n to both sides?
on the original equation or the 0 <= 2^n?
supple knot
0 <= 2^n
eternal crypt
well... 3^n <= 2^n + 3^n
supple knot
(3^n)^(1/n) = 3
then this is your next hint
wraith anchor
i myself am confused about the right side of the squeezing process
not that my understanding matters much in this interaction
eternal crypt
well... 3^n <= 2^n + 3^n
so...
(3^n)^1/n <= (2^n)^1/n + (3^n)^1/n
we get, 3 <= 2^n)^1/n + 3?
no thats not right
wraith anchor
dont worry about simplifying the middle
hollow ice
so...
(3^n)^1/n <= (2^n)^1/n + (3^n)^1/n
we get, 3 <= 2^n)^1/n + 3?
that doesnt follow from the previous step tho
you cant take nth root of individual terms
you have to (2^n + 3^n)^(1/n)
eternal crypt
so (3^n)^1/n <= (2^n + 3^n)^1/n
then (3^n)^1/n becomes 3?
3 <= (2^n + 3^n)^1/n
supple knot
and same thing to 2^n < 3^n
now add 3^n to both sides of this inequality
your next hint is $\lim_{n \to \y} \sqrt[n]{a} = 1, \forall a > 0$
woven radishBOT
riemann
supple knot
maybe a should be > 1 instead of a > 0
eternal crypt
im lost
wraith anchor
start with 2^n <= 3^n
eternal crypt
why can't you add 3^n to 2^n <= 3^n
i.. so
2^n + 3^n <= 3^n + 2^n?
eternal crypt
oh my bad read wrong:
i.. so
2^n + 3^n <= 3^n + 3^n?
eternal crypt
3(1^n + 1^n)
wraith anchor
id write it without the 1/n first and then take 1/n of each expression
and then you get to deliver the punchline !!!!
eternal crypt
im lost i dont get the why
like i get the lower bond
(2^n + 3^n)
(3^n)
and since everything was 1/n we get 3
hence the lower bond, it HAS to be greator than 3
but the upper is still confusing me
supple knot
3 <= (2^n + 3^n)^1/n <= 3^n(2)
you didn't take the nth root of the right side yet
you did a <= b then a^(1/n) <= b
,tex .exp rules
woven radishBOT
riemann
supple knot
you need to be really familiar with these in calculus
eternal crypt
you didn't take the nth root of the right side yet
dam it
eternal crypt
you need to be really familiar with these in calculus
nono yeah i know them ive been forgetting stuff a lot lately
(3)^1/n <= (2^n + 3^n)^1/n <= 3^n(2)
supple knot
(3)^1/n <= (2^n + 3^n)^1/n <= 3^n(2)
Still wrong. Now you took the nth root of the left side twice
supple knot
you didn't take the nth root of the right side yet
Right side, not left side.
eternal crypt
give me a moment i have to bang my head on the wall
devout snowBOT
@eternal crypt Has your question been resolved?
eternal crypt
Right side, not left side.
okay so after banging my head on the wall:
lower bond = (0 + 3^n)^1/n = 3
uppwer bond = (3^n + 3^n)^1/n = 3(2)^1/n
i still dont get the why for the upper bond, but yeah
supple knot
and same thing to 2^n < 3^n
Did you not understand this
gray timber
supple knot
oh my bad read wrong:
i.. so
2^n + 3^n <= 3^n + 3^n?
Or this
eternal crypt
Did you not understand this
i dont get the why
for lower i get what we did and why we did
supple knot
Because you want to get 3
supple knot
okay so after banging my head on the wall:
lower bond = (0 + 3^n)^1/n = 3
uppwe...
You're not done yet
eternal crypt
You're not done yet
really?
i mean after this isnt it just saying lim n-> infinity for lowe and upper
and just adidng a therefore statement blah blah blah
eternal crypt
Because you want to get 3
okay so... we need 3 as upper bond so we say
2^n + 3^n < 3?
supple knot
okay so after banging my head on the wall:
lower bond = (0 + 3^n)^1/n = 3
uppwe...
You need to take the limit as n goes to infinity still
supple knot
okay so... we need 3 as upper bond so we say
2^n + 3^n < 3?
This is very much wrong
devout snowBOT
@eternal crypt Has your question been resolved?
eternal crypt
You need to take the limit as n goes to infinity still
`yeah that happens afterwards
devout snowBOT
`yeah that happens afterwards
eternal crypt
like the basic was that, then afterwards the limit to infinity tells the actual limit
eternal crypt
This is very much wrong
i give up
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@eternal crypt Has your question been resolved?
wicked rover
okay so after banging my head on the wall:
lower bond = (0 + 3^n)^1/n = 3
uppwe...
what are the limits of these bounds?
rapid kayak
Hello, can someone give me a hint on how to solve this with trigonometry. I tried to do it but i got nothing
devout snowBOT
Hello, can someone give me a hint on how to solve this with trigonometry. I trie...
gloomy fog
Apply the Law of Sines iteratively
Then Use the Ceva's theorem trigonometric form
a=30° isn't it?
wicked turtle
you can also just give names to some of the other missing angles, and come up with N equations and N unknowns that you can solve for
(i just did it with N = 4, for example)
rapid kayak
a is 30 degrees
wicked turtle
how did you determine that?
wicked turtle
well what is the total angle at vertex D?
rapid kayak
how do you use ceva theorem in trigonometric form in this question?
rapid kayak
well what is the total angle at vertex D?
yes
wicked turtle
that was a question asking for a number, not a yes/no
the angles at A and C are 60, so what are the angles at B and D?
rapid kayak
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teal stirrup
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polar chasm
Are u trying to prove this?
teal stirrup
yeah
polar chasm
Not entirely wrong, but you made some wrong steps
polar chasm
$\frac{2\left(\cos^{2}\left(x\right)-\sin^{2}\left(x\right)\right)}{2\sin\left(x\right)\cos\left(x\right)}$
woven radishBOT
MathIsAlwaysRight
polar chasm
it should be written like this
the 2 was multiplying the whole cot(2x)
so you have to put that in parenthesis
polar chasm
and when you do that, it'll cancel nicely
$\frac{\cos\left(x\right)}{\sin\left(x\right)}-\frac{\cos^{2}\left(x\right)-\sin^{2}\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}$
woven radishBOT
MathIsAlwaysRight
polar chasm
so you'll be here
Now you need to convert them to a common denominator
A good candidate would be sin(x)cos(x) (So you'd just multiply the first fraction by cos(x) cos(x))
polar chasm
Somehow, you got sin^3(x) cos(x) here, which I dont understand how
teal stirrup
yep that's absolutely wrong
polar chasm
A good candidate would be sin(x)cos(x) (So you'd just multiply the first fractio...
Alright, try doing this then
and then remember that when you are subtracting fractions, you need to put the numerator in parenthesis again
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restive geyser
i need help with descriptive geometry exam can someone help mi with this task.
task text: On the shown roof drawing, mark the projections of the edges between roof planes with the same slope.
devout snowBOT
i need help with descriptive geometry exam can someone help mi with this task.
t...
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bitter garnet
Mine
pseudo basin
send your question
bitter garnet
Suppose
𝑈 = {(𝑥, 𝑦, 𝑥 + 𝑦, 𝑥 − 𝑦, 2𝑥) ∈ 𝐅5 ∶ 𝑥, 𝑦 ∈ 𝐅}.
Find a subspace 𝑊 of 𝐅5 such that 𝐅5 = 𝑈 ⊕ 𝑊.
I might be missing out on something, because I do know what a direct sum is
I maybe don't understand it?
pseudo basin
find a basis for U first
bitter garnet
find a basis for U first
I don't know what spans and basis are
pseudo basin
well damn.
bitter garnet
That is on chapter 2 of linear algebra done right
pseudo basin
btw what is F
bitter garnet
I think it wants something else
bitter garnet
btw what is F
It is implied to be a field
pseudo basin
is F assumed to be one of R or C
bitter garnet
it denotes either R or C
bitter garnet
I think so, yeah
pseudo basin
idk how to say it without giving the answer away but maybe here is a way you can reason about it intuitively:
for a vector in U, the first two coordinates can sort of "vary" "independently"
for the entire F^5, the same would be true of all five coordinates
try to think about what we could "add" to U to make all five coordinates "freely variable" like that
wicked turtle
ah found it
bitter garnet
try to think about what we could "add" to U to make all five coordinates "freely...
Okay
There should be a way to remove the chains that x + y give to each other
That way, it can truly move around all the field
x - y and 2x also need that
right?
pseudo basin
There should be a way to remove the chains that x + y give to each other
what
what chains 
bitter garnet
what chains <:thonk:406575732563902485>
x + y can't move freely if they are adding each other
you want each one to be indepent
let w = x + y. Maybe w - y = x could help solve this
it also works in the other direction
w - x = y
is this right?
pseudo basin
no i think you are overthinking it
the thing is that x and y appear alone in the first two coords
wicked turtle
isnt there an example in the text of axler finding a complement?
surprisingly, only a couple of trivial ones (e.g. the xy plane and the z axis in R^3) and a nonexample
bitter garnet
the thing is that x and y appear _alone_ in the first two coords
Yes
So we only need to think about the other components
$W = { (0, 0, w_3, w_4, ?) \in \mathbb{F}^5 }$
Would that work?
I don't know about 2x yet
bitter garnet
Would that work?
just for x + y and x - y
bitter garnet
do you even know about dimension yet in chapter 1?
No, but I have a rough idea of what it is conceptually
very poor conception of it
wicked turtle
ok loosely speaking, how many degrees of freedom are there in U (how many of the coordinates can be specified independently)
bitter garnet
W only needs to have 3 dimensions
wicked turtle
and then how many will you need in W
wicked turtle
W only needs to have 3 dimensions
right
bitter garnet
3
wicked turtle
so if you set the first two to zero (which is good), the other three need to be independently controllable
bitter garnet
ok loosely speaking, how many degrees of freedom are there in U (how many of the...
2
wicked turtle
so you're gonna need 3 variables
bitter garnet
so if you set the first two to zero (which is good), the other three need to be ...
Which means that using w twice isn't the right idea?
I should have separate variables?
wicked turtle
try it and see!
woven radishBOT
andre
wicked turtle
what might go in the ? slot
wicked turtle
what's your thinking there, why do you want a constant?
bitter garnet
what's your thinking there, why do you want a constant?
I got my algebra wrong
I just want to remove that 2x
and just work with a variable outside of U
wicked turtle
consider theorem 1.46
you just need W to be any subspace with dimension 3 that has trivial intersection with U
you've already set the first two coordinates to zero
what vectors in U have the first coordinates equal to zero?
bitter garnet
Only one where x, y = 0
wicked turtle
and what does that imply about the rest of the vector if x=y=0
wicked turtle
copying for reference 𝑈 = {(𝑥, 𝑦, 𝑥 + 𝑦, 𝑥 − 𝑦, 2𝑥) ∈ 𝐅5 ∶ 𝑥, 𝑦 ∈ 𝐅}.
if x = y= 0 then what is 2x?
wicked turtle
what numerical value is 2x
mystic scarab
Much simpler
bitter garnet
what numerical value is 2x
2x = 2 (0) = 0
mystic scarab
There you go
wicked turtle
well are there any other vectors in U that have the first two coordinates equal to zero?
bitter garnet
no
mystic scarab
So we know the zero vector exists
Well, this is taken for granted, since U is a subspace
wicked turtle
good
bitter garnet
Well, this is taken for granted, since U is a subspace
Yeah
wicked turtle
so you have started defining W by saying that the first two coordinates will be zero
so already you know W and U will only have the zero vector as intersection
now all you need to do is specify the other 3 coordinates so they're independent
(to get 3 dimensions)
wicked turtle
how many variables are there
bitter garnet
2
wicked turtle
how many do you need to get 3 dimensions
bitter garnet
3
wicked turtle
so that can't work
bitter garnet
what about now
wicked turtle
yea that will work
but you don't even need the -2
because if c varies over all of F, then so does -2c, and vice versa
wicked turtle
yea as soon as you set the first two coords to zero you know you're going to intersect trivially with U, so the rest of the definition of U doesn't really matter
you don't have to "cancel out" the other three coordinates when defining W, or anything like that
bitter garnet
mmmkay
wicked turtle
btw the solution is far from unique, there are infinitely many possibilities for W that will work
bitter garnet
Yes
Yes
I got very tripped over by that fact
I am more satisfied now
just had to wrap my ideas up
Thanks!
wicked turtle
yw
bitter garnet
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steep dust
Is this correct
devout snowBOT
Is this correct
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@steep dust Has your question been resolved?
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obsidian plank
Is this the most simplified it can be ?'
devout snowBOT
Is this the most simplified it can be ?'
obsidian plank
so the t is positive ?
lunar harbor
what
sand pumice
what is f(-x) if f is an odd function?
obsidian plank
idk what an odd function is supposed to entail what does that mean to me
is this what it means ?
sand pumice
yea
sand pumice
btw not a good idea to trust ai in general
it's right this time but often is wrong but sounds right
sand pumice
wait its -sin(t)
yes
obsidian plank
btw not a good idea to trust ai in general
it's right this time but often is wr...
I searched this up on google
sand pumice
yeah the result seems like their generative ai
obsidian plank
can I turn it off ?
sand pumice
idk but if you type -ai in the search bar it doesn't show up in the results
anyway you have -sint-sint
you can simplify this
obsidian plank
you can simplify this
-sint-a
sand pumice
what about the first one
obsidian plank
would it be -a-a ?
sand pumice
yes
obsidian plank
woah that's weird
alr
thanks for letting me know about the -ai thing I fucking hate ai It took my mom away
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obsidian plank
thanks for letting me know about the -ai thing I fucking hate ai It took my mom ...
BROOOO THE ANSWER WAS 2A
-2A
FUCK
.REOPEN NOW
I hate you @sand pumice maybe its not a good idea to trust you
next time I join this discord ill put -green in my question
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lost laurel
Kind of silly
devout snowBOT
Kind of silly
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glossy dew
im not even sure how the counting goes here
devout snowBOT
im not even sure how the counting goes here
glossy dew
i know there are 11 sets of points which can have either -1 or 1 as the y value but struggling to split cases
uncut crow
wdym 11 sets of points?
glossy dew
like {0}, {1}, {2}, {3}, {4}, {5}, (0, 1), (1, 2), (2, 3), (3, 4), (4, 5)
uncut crow
what if you just start with putting f(x) = 1 for all integers x in [0,5]. can you count how many functions there are?
glossy dew
one
glossy dew
because setting any in between interval to 1 would join adjacent integers having the same value?
uncut crow
well not quite
uncut crow
ok yea that’s good enough i guess
my next question will be
f(0) = -1
f(x) = 1 for integers > 0
how many functions?
glossy dew
three..
uncut crow
can you give one
glossy dew
f(x) = 1 at x = 1, 2, 3, 4, 5 and intervals (0, 1) and (2, 3)
f(x) = -1 at x = 0 and intervals (1, 2) and (3, 4) and (4, 5)
alpine python
im not even sure how the counting goes here
putting quantifiers after the statement they quantify is cursed
uncut crow
writing \forall in the first place is cured
alpine python
sorry to interrupt, carry on
uncut crow
ok well on each interval, all values must be -1 or 1
so we could think about each possible way to assign the intervals, and then how many ways we can assign points there
i think that’s easier
like we assign -1 or 1 to each interval. whenever there is a change, we can assign either -1 or 1 to that point between the intervals. if there is no change between the intervals, only one choice
do you see what i mean?
glossy dew
yeah but how do i divide the cases
since the choices can be either 2 or 1 for a point depending on the placement
alpine python
wait is f^2 iteration?
glossy dew
oh do i just split it like
- 4 points with 1 case
- 3 points with 1 case
and so on
uncut crow
well we just need to know how many strings of five -1s and 1s have 0 ‘changing points’, how many have 1, how many have 2, etc
glossy dew
ok yeah
uncut crow
the ones with 0 changing points are the ones that are all -1 or all 1
the ones with 1 changing point will be the ones that are 4 of a kind, with the first or last one different
glossy dew
wait is f^2 iteration?
no i think squared
since there was another simpler problem with this premise
uncut crow
f^2 is the function defined by f^2(x) = (f(x))^2
uncut crow
tis ok
the ones with 2 changing points will look like xyyyx or xyxxx (with the y anywhere in the interior)
alpine python
must f be discontinuous at each integer?
uncut crow
yea
well i would hope so. i guess ‘only’ is not 100% clear on that
that would be quite a bit easier if it just meant must be continuous at non integer points
alpine python
i'm guessing they included the word "all" to indicate that it must be discontinuous at every integer
glossy dew
yeah
uncut crow
that would be quite a bit easier if it just meant must be continuous at non inte...
that is what ‘discontinuous only at non integer points’ means but it just feels evil to write that
glossy dew
it IS an evil question
okay i somehow got the correct answer using that case splitting
this is plain torture bruh
uncut crow
gr8
devout snowBOT
glossy dew
that rhymed
alpine python
|| 2*3^4 ||
glossy dew
hmm..
alpine python
there are 2 choices at x=0 and 3 choices at x=1,2,3,4
violet wind
Does discontinuous "only" at integers mean it's discontinuous precisely at the set of integers?
alpine python
we're guessing yes
uncut crow
Does discontinuous "only" at integers mean it's discontinuous precisely at the s...
based on the answer, yes
uncut crow
should have written ‘at and only at’ smh
uncut crow
there are 2 choices at x=0 and 3 choices at x=1,2,3,4
i guess my way was overcomplicated then
glossy dew
there are 2 choices at x=0 and 3 choices at x=1,2,3,4
oh my LORD :facepalm
i might be a dumbass
uncut crow
that’s a lot better
glossy dew
instasolve 😭
violet wind
oh yeah I see
uncut crow
you can put the value to match the left interval and then you have to move the right interval away. or you can put the value away from the left interval
and then choose either value for the right interval
alpine python
ye
violet wind
let f(x) be a function from [0,5] to C, discontinuous at and only at integers. Let f(x)^7=3
might as well make it like [0,10]
alpine python
violet wind
||42×48×...×48×6|| I think the same way
uncut crow
i love ‘at and only at’ sm
violet wind
Imagine how messed up it would be if it meant f(f(x)) by f²
glossy dew
heh..
alpine python
yeah i thought they meant f(f(x)) at first
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austere nimbus
3rd questions?
loud monolith
Ya
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green crypt
try checking if this is an exact differential equation perhaps
sleek estuary
try checking if this is an exact differential equation perhaps
its a practice problem in the section for separable equations though
sleek estuary
number 19
green crypt
try putting y = kx?
sleek estuary
try putting y = kx?
what do you mean, I dont think ive seen that before
modern lance
factor denominator and numerator, it's quite trivial
green crypt
oh true
sleek estuary
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remote copper
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remote copper
I did not understand the phi definition of that set
diagonal matrix which has 1 and rest elements are 0
scarlet swallow
Hi guys, yes this is a physic problem, yes I'm praying for someone smart to enlighten me. I'm trying to calculate the electric potential of a very thin rod at a specific position away from the rod as shown above. The problem with what I have done so far is that the integral seems to produce an extra meters^(-1) which is the units for electric field 💀 if anyone could point out any problems here pls do, and if any additional info is needed I can give 🙏
devout snowBOT
Hi guys, yes this is a physic problem, yes I'm praying for someone smart to enli...
sand quarry
Hi guys, yes this is a physic problem, yes I'm praying for someone smart to enli...
Youre forgetting the dx inside the integral
dx = metres
m^-1 * m = 1
scarlet swallow
Youre forgetting the dx inside the integral
Doesn't the dx integral result in a arcsinh which is unitless? That's the main problem I'm facing actually
sand quarry
Doesn't the dx integral result in a arcsinh which is unitless? That's the main p...
no it results in a ln(something)
scarlet swallow
Oh yea that's the other form
Let me check that one real quick
Ooh yes the extra length appears there
Thanks for the help 🙏
.close
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covert shale
want to sanitycheck my reasoning here, i'm not too mature with complex numbers ^^;
devout snowBOT
want to sanitycheck my reasoning here, i'm not too mature with complex numbers ^...
rain summit
-# oh im cooked
covert shale
claim that \rho is abelian subgrp of C^\times has been proven previously, mainly want to know if my homomorphism checks are okay (*and if my reason for welldefn of \phi^-1 holds up)
hi infinity
rain summit
hi infinity
-# hi, im too scared of this
covert shale
lol
sand pumice
want to sanitycheck my reasoning here, i'm not too mature with complex numbers ^...
i think it's alright 👍
alpine python
look at the last step of the demonstration of the homomorphism property
Q/Z is an additive group
covert shale
group op should be preserved no?
alpine python
you should write $\phi((\mathbb{Z}+p/q)+(\mathbb{Z}+r/s))$
woven radishBOT
Axe
sand pumice
you have coset addition instead of mult
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fickle moon
what would the answer be for this one?
devout snowBOT
what would the answer be for this one?
rare kernel
check the signs properly
cos x is negative in 2nd and 3rd quadrants
is tan x positive in both these quadrants
sand dove
the question is ill posed
"what is/are the possible values of tan x" would make the answer c)
rare kernel
is it -12/5
no
sand dove
but "tan x = ..." is impossible to answer
rare kernel
im so lost
in 2nd quadrant is tan x positive or negative
fickle moon
negative
rare kernel
but "tan x = ..." is impossible to answer
we can infer the meaning of the question even though its ill posed
fickle moon
positive
sand dove
we can infer the meaning of the question even though its ill posed
ill posed questions are still bad questions
rare kernel
so it can be both negative and positive
fickle moon
so all of the above
sand dove
I suggest to kisei to report it for bad wording
fickle moon
that makes sense
fickle moon
I suggest to kisei to report it for bad wording
LMAOO
uncut crow
I suggest to kisei to report it for bad wording
amen
rare kernel
so all of the above
yes 👍
fickle moon
thank you so much
sand dove
LMAOO
not bad wording as in cursing xdddd just a question not written properly
tan(x) can't be equal to both -12/5 and 12/5
willow helm
what is going on with the font
fickle moon
what is going on with the font
bro one of them was so chopped
1 sec
lemem show u
nvm i cant find itr
restive river
E) one of the above
willow helm
They should have switched c and d
That would make it interesting
Nevermind it'd still be c
restive river
paradox
willow helm
Nevermind it'd still be c
yeah 🙁
restive river
seems like they wanted to make more of logic question
devout snowBOT
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vernal jay
Im sure this is obvious im just tired and haven't covered algebra in ages, but why is one 2x and one just x?
devout snowBOT
Im sure this is obvious im just tired and haven't covered algebra in ages, but w...
uncut forge
Im sure this is obvious im just tired and haven't covered algebra in ages, but w...
Wym 2x?
drifting sierra
It's 2(x-2)(x-5/2)
restive river
i wonder where does 3/2 come from
uncut forge
i wonder where does 3/2 come from
Ye same 😭
vernal jay
vernal jay
i wonder where does 3/2 come from
Yeea idk
drifting sierra
Probably from the other half of the screen
vernal jay
Im dead i might just look through the proper marking sceme
vernal jay
Probably from the other half of the screen
restive river
indeed it does
uncut forge
Huh
drifting sierra
What's the context?
vernal jay
I need to find the three solutions for x
vernal jay
vernal jay
Indeed
The final answers I understand
Its just in general when solving quadratics why was only one 2x
restive river
Shouldn't x never be -3/2
wdym
uncut forge
Til I saw this
restive river
Nvm I thought it was a division 💔
drifting sierra
Its just in general when solving quadratics why was only one 2x
Either you can guess the factorization from experience, or you use one of various techniques, like completing the square or using the quadratic formula
For 2x^2 - 9x + 10, you could guess that it's in the form (x + a)(2x + b) since it's 2x^2 + ...
Then to make 10 you could guess a = 2 and b = 5, or their opposites, or the other way around
vernal jay
Ah, thank you
drifting sierra
Since you need -9x as well, -5 - 2*2 works
vernal jay
Grand
drifting sierra
Otherwise just bring the 2 out, so 2(x^2 - 9/2x + 5) and try factoring that
vernal jay
Ok, thank you
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vernal jay
Oopsies
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lusty tapir
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torpid holly
So what's the question
lusty tapir
So what's the question
Is the thing i drew correct?
torpid holly
Should be
lusty tapir
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cerulean ruin
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cerulean ruin
im lowkey kind of confused what linear actually means
is it just a qualifer on the partial order that makes X a chain?
so like if X is a chain, then any two elements of it are comparable (which means some partial ordered must be used here)
and this partial order is considered linear
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@cerulean ruin Has your question been resolved?
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@cerulean ruin Has your question been resolved?
void fox
is it just a qualifer on the partial order that makes X a chain?
it is a qualifier on both the partial order and the set X
alpine python
and this partial order is considered linear
i think only if you restrict the definition of the partial order to X
or if X is the set that it's defined on
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undone egret
Graphing linear inequalities
I don't really understand this. The coordinate that satisfies the inequality is (8,2), and the equation is -8x-4y=-24. How do I tell what side is the right side to shade ?
devout snowBOT
**Graphing linear inequalities**
I don't really understand this. The coordinate ...
undone egret
I'll ping helpers <t:1769764020:R>
winter patrol
Shade the side the point that satisfies the inequality is on
alpine scaffold
hewo
undone egret
I didn't really attend any inequality lessons
alpine scaffold
oh
undone egret
so I don't really understand it fundamentally ngl
alpine scaffold
like me!!!
undone egret
like me!!!
twins!!
alpine scaffold
ok iguess uhhh
ok
so the inequality basic
<
the bigger mouth
which is the right side is usually where the bigger number is
undone egret
yeah I understand that
alpine scaffold
alr
undone egret
I forgot what the working out was for it to be 8,2 hold on
I wrote it down on the slide there
undone egret
so that inequality is true
but what relevance is the inequality to the graph?
-76 isn't exactly a coordinate
undone egret
It's substituted the coordinates into the provided equation
undone egret
2 LT looking thing
2 lt ?? what's LT?
alpine scaffold
oh
alpine scaffold
hold on my brain not braining
undone egret
hold on my brain not braining
What grade are you in if you don't mind me asking or are you post-grad ?
alpine scaffold
ts supposed to be easy for me, i always scored full marks
im sec 4
this is sec 1 work
undone egret
or is it just one of those things where you've crammed other stuff into your brain so more basic stuff gets pushed out lol
alpine scaffold
so the last time i did this was like 3 yrs ago
undone egret
ahh ok
alpine scaffold
or is it just one of those things where you've crammed other stuff into your bra...
yea something like that
but i'll try
undone egret
I'm in year 11 (Australian) but this is yr10 since i missed a lot of year10 work
undone egret
Hold on it has a tutorial video
alpine scaffold
you want to put it in y>mx+c form
undone egret
but I'm trying to understand the concept more than the answer
undone egret
you want to put it in y>mx+c form
Well the line is there
but the thing is I don't really understand the uhh where to shade
alpine scaffold
but I'm trying to understand the concept more than the answer
thats better than 50% of people i meet here
i think what you want to do is assume that y = 0 to get the
hold on
undone egret
i think what you want to do is assume that y = 0 to get the
no I don't think that's it
alpine scaffold
my brain is fahhked up
alpine scaffold
ye
alpine scaffold
im studying trigo rn so everything is out of my head
undone egret
(also I'm australian so I have absolutely no idea what sec 4 is)
alpine scaffold
i think its better to watch the video than
alpine scaffold
(also I'm australian so I have absolutely no idea what sec 4 is)
16 yrs old
undone egret
16 yrs old
me too lol
alpine scaffold
10th grade
alpine scaffold
me too lol
what i did this when i was 13
undone egret
man idk
frozen aurora
(also I'm australian so I have absolutely no idea what sec 4 is)
what time is it for you
undone egret
what time is it for you
QLD / AEST (7:03 pm)
frozen aurora
oh did i 😭 hello!
undone egret
I recognise the shrimp pfp lol
frozen aurora
it's a cuttlefish!!!
undone egret
Ohhhh
frozen aurora
so cool
undone egret
Man I've only ever seen dried out cuttlefish (used to feed them to our pet birds)
alpine scaffold
hewo
undone egret
The reason I'm not following the video is cause it's for a positive number
alpine scaffold
pls help my friend
undone egret
& it's a greaterthan rather than a smaller than
alpine scaffold
i forgotten how to do it
frozen aurora
omg i thought this was discussion LMAO
undone egret
i forgotten how to do it
it's ok lol
undone egret
omg i thought this was discussion LMAO
No lol it just turned into one lowkey
frozen aurora
what's the question
alpine scaffold
please i need this my brain kinda not braining
undone egret
**Graphing linear inequalities**
I don't really understand this. The coordinate ...
^^^
undone egret
im sorry for wasting your time
Nah it's all good
undone egret
I have the memory of a goldfish bru it's fine (metaphorically. i know goldfish have decent memories)
frozen aurora
^^^
well the right side to shade is the one that contains a point that satisfies your inequality
undone egret
well the right side to shade is the one that contains a point that satisfies you...
so -76 ?
But this shades -76, no?
Would that be on the X or Y axis?
frozen aurora
what's "-76"
undone egret
oh wait no i get what you mean
because we substituted the values into the equation
that means it's supposed to shade said coordinates?
is that it ??
frozen aurora
yup
undone egret
I was really overcomplicating it LOL
Ok I get it now tysm!!
I might reopen this channel in a sec tho since im still working on the module
frozen aurora
ofc! you can just keep it open
undone egret
Ohh alright
frozen aurora
check out desmos, it can plot these inequalities easily
https://www.desmos.com/calculator/9k1me9977c
undone egret
check out desmos, it can plot these inequalities easily
https://www.desmos.com/c...
Yeah but it's not necessarily about plotting, it's about understanding the reasoning behind it for me
frozen aurora
ye but it can really help with intuition if you play around with it yourself
undone egret
I'll keep working thru the modules for now but I've fiddled with it a little bit in class
new question !!
Is this supposed to be a simultaneous equation?
I forgot how they're formatted
Do you just substitute x or y with 0 ?
because there's no values provided this time
frozen aurora
no simultaneous equation here. just plot the line y=3x-3
if it asks you to plot y >= 3x-3, pick a random point above or below the line and test for the inequality: if it works, then shade that area, if it doesn't then shade the other one
undone egret
if it asks you to plot y >= 3x-3, pick a random point above or below the line an...
random point?
frozen aurora
the easiest point to test here is (0,0) for example
frozen aurora
Do you just substitute x or y with 0 ?
wdym by this btw
undone egret
oh wait isn't this literally just a linear thing
frozen aurora
yes
frozen aurora
well you do remember how to plot a line right?
undone egret
Yeah
Just did lol
how does the inequality relate to it tho?
that confused me a little bit
ahh wait nvm it's multi parts
frozen aurora
yes
undone egret
So is it just
u just sub the y value in?
wait isn't the x also important because it's not a parallel line
frozen aurora
both x and y yes
undone egret
i mean 90 degree line*
undone egret
again (1, -3) means the same thing as x=1 and y=-3
Yep
Oh wait
I forgot there was an x
in the equation
LOL
im forgetting the most basic things today i swear 💀
frozen aurora
if there wasn't x it would be a horizontal line
frozen aurora
ok well what did you get after the substitutions here
undone egret
oh wait
ohh
substituting
i forgot it gave coordinates again
wait
so like
if it's -1 > -6
doesn't that mean there's just two integers
not coordinates
there's two points but only one set of coordinates ?
OH
oh wait it's an equation
oHHhhHH
ok back to basics im just gonna put my working here since idk if it's right just yet
undone egret
dude a baby lizard just crawled onto my arm
I thought it was a bug and I shook it off 💀
frozen aurora
dude a baby lizard just crawled onto my arm
average australia things
frozen aurora
why are you doing x=0?
undone egret
oh wait
so is it that one point goes at 0, c (y-intercept)
and the other one goes at the given coordinates?
frozen aurora
oh ok but you have m and c now
undone egret
It was always there
does M get used?
Doesn't that mean it's just 3 up 1 right?
I did that but it's wrong
wait no i think i didnt flip it or something
is the line correct ?
frozen aurora
yes
undone egret
wait what on earth is the other set of coordinates fo
oh wait
is the other set of coordinates for like
where to shade ?
wait but
where do the coordinates get inserted into the equation
frozen aurora
yes, what did you get when you subsituted the points above?
undone egret
is it on the right side or left side of the equation ?
undone egret
yes, what did you get when you subsituted the points above?
lemme check
frozen aurora
it shouldn't be a single number, it should be some inequality between numbers that is either true or false
undone egret
-6 i think i erased it
frozen aurora
let's go through this again step by step
undone egret
undone egret
uhh it's true
frozen aurora
you sure?
undone egret
oh wait
frozen aurora
is -3 bigger than -6
undone egret
😭
frozen aurora
💀
frozen aurora
and you got a true statement by plugging in (-1, -3)
so (-1, -3) must be inside the solution set
frozen aurora
I did that but it's wrong
can you plot where (-1, -3) is on this graph
undone egret
undone egret
So how do I tell what side it should be with with the > again ?
so we got this but how do I tell with the > thingy
frozen aurora
so the shaded region must cover it
so you need to shade the other part
undone egret
so the shaded region must cover it
but how do I tell whether it should cover or not cover ?
like how does the > thing work in this context
frozen aurora
because when you plug in (1, -3), you get -3 >= 0, which is false, so that point should not be covered
and if you plug in (-1, -3), you get -3 >= -6, which is true, so that point should be covered
undone egret
no I mean how does the > function work
frozen aurora
wdym
undone egret
how do you use that to tell what regions should be covered/ujncovered
just in the context of fundamentals, ignoring the question altogether
frozen aurora
you do it by testing different points
undone egret
you do it by testing different points
Isn't it possible to determine just from the equation / information provided alone ??
frozen aurora
it is possible, i personally find it easier to just test. to go off of the infomation you need to rearrange it to be in the form y >= mx+c or y <= mx+c
which you already have
i am just not sure if this is what the question/teacher wants you to do
undone egret
mmgmgasgdkjgj
Uhhhh
I mean like
how do you tell if it should or should not be shaded just based on the > thing ??? I'm still so confused by that
like based on the satisfied inequality
frozen aurora
it is possible, i personally find it easier to just test. to go off of the infom...
you can determine the region of y >= 3x-3 if you plot the line y = 3x-3 and see that y >= 3x-3 means you shade everything above the line 3x-3
undone egret
you can determine the region of y >= 3x-3 if you plot the line y = 3x-3 and see ...
but sometimes I won't have the graph to work with, right?
I don't want to rely on visualisations if that means I don't understand it without
frozen aurora
there's nothing wrong with working with visualizations
frozen aurora
but sometimes I won't have the graph to work with, right?
but yes which is when you test points
rain summit
so we got this but how do I tell with the __>__ thingy
$y \geq 3x - 3$ so the trend should be on the top because as you go top, the $y$ increases
woven radishBOT
1 divided by 0 equals Infinity
rain summit
that's how i usually do
frozen aurora
how do you tell if it should or should not be shaded just based on the __>__ thi...
ok winding back, do you understand what the shade represents?
undone egret
$y \geq 3x - 3$ so the trend should be on the top because as you go top, the $y$...
What ??????
frozen aurora
ok winding back, do you understand what the shade represents?
like what is it
undone egret
I have absolutely NO idea what that is
(the 1 divided by 0 equals infinity thing)
undone egret
like what is it
I honestly can't tell you 💀
frozen aurora
ok well there we go that's the issue lol
rain summit
so this is the graph of $y \geq 3x - 3$
undone egret
$y \geq 3x - 3$ so the trend should be on the top because as you go top, the $y$...
I'm so confused what is this and how is this relevant
woven radishBOT
1 divided by 0 equals Infinity
rain summit
these are just points that satisfy the condition above
which happens to be the shaded area
frozen aurora
I'm so confused what is this and how is this relevant
the $ stuff is for writing math with the TeXit bot, you can ignore the text and look at the images it sends
undone egret
the $ stuff is for writing math with the TeXit bot, you can ignore the text and ...
OHhhh
rain summit
**1 divided by 0 equals Infinity**
and as you go up, the $y$ increases
woven radishBOT
1 divided by 0 equals Infinity
rain summit
so that's why the shaded part is above the $y = 3x - 3$ graph
woven radishBOT
1 divided by 0 equals Infinity
undone egret
I'm still not understanding this icl 😭
rain summit
I'm still not understanding this icl 😭
tell us what do you not understand about?
what are you confused about?
undone egret
tell us what do you not understand about?
Shading in inequalities
You explained it fine probably it's just that I'm not getting the way you explained it